Piero Scaruffi(Copyright © 2006 Piero Scaruffi | Legal restrictions - Termini d'uso )
The New Physics: The Ubiquitous Asymmetry
Physics and the Mind
20th century science, in particular Relativity and Quantum theories, presents us with a world that is hardly the one we intuitively know. The reason is simple: Quantum and Relativity theories deal with the problems of the immensely large or the immensely small. Our brains were built to solve a different class of problems. They were built to deal with midsize, colored objects that move slowly in a three-dimensional space over a span of less than a century.
The vast majority of theories of mind still assume that the world is a Newtonian world of objects, of continuous time, of absolute reality and of force-mediated causality. What that means is very simple: most theories of mind are based on a Physics that has been proven wrong. Newton's Physics does work in many cases, but today we know that it does not work in other cases. We don't know whether mind belongs to the set of cases for which Newton's Physics is a valid approximation of reality, or whether mind belongs to the set of cases for which Newton's Physics yields wrong predictions. Any theory of mind that is based on Newton's Physics is a gamble.
For example, psychologists often like to separate the senses and feelings based on the intuitive fact that the senses gives us a photograph of the world, whereas pleasure and pain are the outcome of an interpretation of the world. When I see an object, I am transferring a piece of reality as it is inside my mind. When I feel pleasure, I am interpreting something and generating a feeling. This separation makes sense only if one assumes that objects do exist. Unfortunately, modern Physics has changed our perception of reality. What exists is a chaos of elementary particles, that our eyes "interpret" as object. A chair is no more real than a feeling of pain. They are both created by my mind. Actually, what exists is truly waves of probabilities, that somehow our brain reduces to objects.
Modern Physics is not necessarily right (although Newton is necessarily wrong on several issues, otherwise Hiroshima would still be standing). But many theories of mind rely on a Physics that, de facto, is either Newton's or is a Physics that has not been invented yet.
The Classical World: Utopia
Since we started with the assumption that our Physics is inadequate to explain at least one natural phenomenon, consciousness, and therefore cannot be "right" (or, at least, complete), it is worth taking a quick look at what Physics has to say about the universe that our consciousness inhabits.
Our view of the world we live in has undergone a dramatic change over the course of this century. Quantum Theory and Relativity Theory have changed the very essence of Physics, painting in front of us a completely different picture of how things happen and why they happen.
Let’s first recapitulate the key concepts of classical Physics. Galileo laid them down in the Sixteenth century. First of all, a body in free motion does not need any force to continue moving. Second, if a force is applied, then what will change is the acceleration, not the velocity (velocity will change as a consequence of acceleration changing). Third, all bodies fall with the same acceleration. A century later, Newton expressed these findings in the elegant form of differential calculus and immersed them in the elegant setting of Euclid's geometry. Three fundamental laws explain all of nature (at least, all that was known of nature at the time). The first one states that the acceleration of a body due to a force is inversely proportional to the body’s "inertial" mass. The second one states that the gravitational attraction that a body is subject to is proportional to its "gravitational" mass. The third one indirectly states the conservation of energy: to every action there is always an equal reaction.
They are mostly rehashing of Galileo’s ideas, but they state the exact mathematical relationships and assign numerical values to constants. They lent themselves to formal calculations because they were based on calculus and on geometry, both formal systems that allowed for exact deduction. By applying Newton’s laws, one can derive the dynamic equation that mathematically describes the motion of a system: given the position and velocity at one time, the equations can determine the position and velocity at any later time. Newton’s world was a deterministic machine, whose state at any time was a direct consequence of its state at a previous time. Two conservation laws were particularly effective in constraining the motion of systems: the conservation of momentum (momentum being velocity times mass) and the conservation of energy. No physical event can alter the overall value of, say, the energy: energy can change form, but ultimately it will always be there in the same amount.
In 1833 the Irish mathematician William Hamilton, building on the 1788 work of the Italian mathematician Luigi Lagrange (the trajectory of an object can be derived by finding the path which minimizes the "action", such action being basically the difference between the kinetic energy and the potential energy), realized something that Newton had only implied: that velocity, as well as position, determines the state of a system. He also realized that the key quantity is the overall energy of the system. By combining these intuitions, Hamilton redefined Newton’s dynamic equation with two equations that derived from just one quantity (the Hamiltonian function, a measure of the total energy of the system), that replaced acceleration (a second-order derivative) with the first-order derivative of velocity, and that were symmetrical (once velocity was replaced by momentum). The bottom line was that position and velocity played the same role and therefore the state of the system could be viewed as described by six coordinates, the three coordinates of position plus the three coordinates of momentum. At every point in time one could compute the set of six coordinates and the sequence of such sets would be the history of the system in the world. One could then visualize the evolution of the system in a six-dimensional space, the "phase" space.
In the 19th century two phenomena posed increasing problems for the Newtonian picture: gases and electromagnetism. Gases had been studied as collections of particles, but, a gas being made of many minuscule particles in very fast motion and in continuous interaction, this model soon revealed to be a gross approximation. The classical approach was quickly abandoned in favor of a stochastic approach, whereby what matters is the average behavior of a particle and all quantities that matter (from temperature to heat) are statistical quantities.
In the meantime, evidence was accumulating that electric bodies radiated invisible waves of energy through space, thereby creating electromagnetic fields that could interact with each other, and that light itself was but a particular case of an electromagnetic field. In the 1860s the British physicist James Maxwell expressed the properties of electromagnetic fields in a set of equations. These equations resemble the Hamiltonian equations in that they deal with first-order derivatives of the electric and magnetic intensities. Given the distribution of electric and magnetic charges at a time, Maxwell’s equation can determine the distribution at any later time. The difference is that electric and magnetic intensities refer to waves, whereas position and momentum refer to particles. The number of coordinates needed to determine a wave is infinite, not six...
By then, it was already clear that Science was faced with a dilemma, one which was bound to become the theme of the rest of the century: there are electromagnetic forces that hold together particles in objects and there are gravitational forces that hold together objects in the universe, and these two forces are both inverse square forces (the intensity of the force is inversely proportional to the square of the distance), but the two quantities they act upon (electric charge and mass) behave in a completely different way, thereby leading to two completely different descriptions of the universe.
Another catch hidden in all of these equations was that the beautiful and imposing architecture of Physics could not distinguish the past from the future, something that is obvious to all of us. All of Physics' equations were symmetrical in time. There is nothing in Newton's laws, in Hamilton's laws, in Maxwell's laws or even in Einstein's laws that can discriminate past from future. Physics was reversible in time, something that goes against our perception of the absolute and (alas) irrevocable flow of time.
The Removal of Consciousness
In the process, something else had also happened, something of momentous importance, even though its consequences would not be appreciated for a few centuries. Rene` Descartes had introduced the "experimental method": science has to be based on experiments and proofs. Descartes started out by defining the domain of science. He distinguished between matter and mind, and decided that science had to occupy itself with matter. Therefore the schism was born that would influence the development of human knowledge for the next three centuries: science is the study of nature, and our consciousness does not belong to nature. Galileo improved Descartes' method by fostering the mathematical study of nature. Newton built on Galileo's foundations. Physics, in other words, had been forced to renounce consciousness and developed a sophisticated system of knowledge construction and verification that did not care about, and therefore did not apply to, consciousness. Scientists spoke of "nature" as if it included only inanimate, unconscious objects. No wonder that they ended up building a science that explains all known inanimate, unconscious phenomena, but not consciousness.
The Austrian physicist Erwin Schroedinger, one of the founders of Quantum Physics, identified two fundamental tenets of classical science: object and subject can be separated (i.e., the subject can look at the object as if it were a completely disconnected entity); and the subject is capable of knowing the object (i.e., the subject can look at the object in a way that creates a connection, one leading to knowledge). There is a subtle inconsistency in these two tenets: one denies any connection between subject and object, while the other one states an obvious connection between them.
Entropy: The Curse of Irreversibility
The single biggest change in scientific thinking may have nothing to do with Relativity and Quantum theories: it may well be the discovery that some processes are not symmetric in time. Before the discovery of the second law of Thermodynamics, all laws were symmetric in time, and change could always be bi-directional. Any formula had an equal sign that meant one can switch the two sides at will. We could always replay the history of the universe backwards. Entropy changed all that.
Entropy was "discovered" around 1850 by the German physicist Rudolf Clausius in the process of revising the laws proposed by the French engineer Sadi Carnot, that would become the foundations of Thermodynamics. The first law of Thermodynamics is basically the law of conservation of energy: energy can never be created or destroyed, it can only be transformed. The second law states that any transformation has an energetic cost: this "cost" of transforming energy Clausius called "entropy" (which is numerically obtained by dividing heat by temperature). Natural processes generate entropy. Entropy explains why heat flows spontaneously from hot to cold bodies, but the opposite never occurs: "useful" energy can be lost in entropy, not viceversa. There can never be an isolated process that results in a transfer of energy from a cold body to a hotter body: it is just a feature of our universe.
The first law talks about the quantity of energy, while the second law talks about the quality of such energy. Energy is always conserved, but something happens to it that causes it to "deteriorate". Entropy measures the amount of energy that has deteriorated (is not available anymore for further work).
Clausius summarized the situation like this: the energy of the universe is constant, the entropy of the universe is increasing.
In the 1870s, the German physicist Ludwig von Boltzmann tried to deduce entropy from the motion of gas particles, i.e. from dynamic laws that are reversible in nature. Basically, Boltzmann tried to prove that entropy (and therefore irreversibility) is an illusion, that matter at microscopic level is fundamentally reversible. Convinced that bodies are made of a large number of elementary particles, Boltzmann used statistics and probability theory to summarize their behavior, since it would be impossible to describe each particle’s motion and their innumerable interactions. He noticed that many different configurations (microstates) of those particles could lead to the same external appearance (macrostate) of the system as a whole.
Boltzmann ended up with a statistical definition of entropy to characterize the fact that many different microscopic states of a system result in the same macroscopic state: the entropy of a macrostate is the logarithm of the number of its microstates. It is not very intuitive how this definition of entropy relates to the original one, but it does.
Boltzmann’s definition emphasized that entropy turns out to be also a measure of "disorder" in a system: an ordered system has fewer microstates corresponding to a given macrostate.
The second law of Thermodynamics is an inequality: it states that entropy can never decrease. Indirectly, this law states that transformation processes cannot be run backward, cannot be "undone". Young people can age, but old people cannot rejuvenate. Buildings do not improve over the years: they decay. Scrambled eggs cannot be unscrambled and dissolved sugar cubes cannot be recomposed. The universe must evolve in the direction of higher and higher entropy. Some things are irreversible.
The universe as a whole is proceeding towards its unavoidable fate: the "heat death", i.e. the state of maximum entropy, in which no heat flow is possible, which means that temperature is constant everywhere, which means that there is no energy available to produce more heat, which means that all energy in the universe is in the form of heat. (An escape from the heat death would be if the energy in the universe were infinite).
Scientists were (and still are) puzzled by the fact that irreversibility (the law of entropy) had been deduced from reversibility (basically, Newton's laws). Mechanical phenomena tend to be reversible in time, whereas thermodynamic phenomena tend to be irreversible in time. Since a thermodynamic phenomenon is made of many mechanical phenomena, the paradox is how can an irreversible process arise from many reversible processes? It is weird that irreversibility should arise from the behavior of molecules which, if taken individually, obey physical laws that are reversible. We can keep track of the motion of each single particle in a gas, and then undo it. But we cannot undo the macroscopic consequence of the motion of thousands of such particles in a gas.
If one filmed the behavior of each particle of a gas as the gas moves from non-equilibrium to equilibrium, and then played back the film backwards, the film would be perfectly consistent with the laws of Mechanics. In practice, though, systems never spontaneously move from equilibrium to non-equilibrium: the film is perfectly feasible, but in practice it is never made.
The only reason one could find was probabilistic, not mechanical: the probability of low-entropy macrostates is smaller, by definition, than the probability of high-entropy macrostates, so the universe tends to proceed towards higher entropy. Thus the second law seems to express the tendency of systems to transition from less probable states (states that can be realized by few microstates) to more probable states (states that can be realized by many microstates). Basically, there are more ways to be disorderly than to be orderly.
And one can rephrase the same idea in terms of equilibrium: since equilibrium states are states that correspond to the maximum number of microstates, it is unlikely that a system moves to a state of non-equilibrium, likely that it moves to a state of equilibrium.
The trick is that Boltzmann assumed that a gas (a discrete set of interacting molecules) can be considered as a continuum of points and, on top of that, that the particles can be considered independent of each other: if these arbitrary assumptions are dropped, no rigorous proof for the irreversibility of natural processes exists. The French mathematician Jules Henri Poincare', for example, proved just about the opposite: that every closed system must eventually revert in time to its initial state (the "recurrence theorem"). Thus everything that can happen "will" happen, and will happen infinite times. Poincare' proved eternal recurrence where Thermodynamics had just proved eternal doom.
Entropy is a measure of disorder, and information is found in disorder (the more microstates the more information, ergo the more disorder the more information), so ultimately entropy is also a measure of information.
Later, several scientists interpreted entropy as a measure of ignorance about the microscopic state of a system, for example as a measure of the amount of information needed to specify it. Murray Gell-mann summarized these arguments when he gave his explanation for the drift of the universe towards disorder. The reason that nature prefers disorder over order is that there are many more states of disorder than of order, therefore it is more probable that the system ends up in a state of disorder. In other words, the probability of disorder is much higher than the probability of spontaneous order, and that's why disorder happens more often than disorder.
It took the Belgian (but Russian-born) physicist and Nobel-prize winner Ilya Prigogine, in the 1970s, to provide a more credible explanation for the origin of irreversibility. He observed some inherent time asymmetry in chaotic processes at the microscopic level, which would cause entropy at the macroscopic level. He reached the intriguing conclusion that irreversibility originates from randomness which is inherent in nature.
Equilibrium states are also states of minimum information (a few parameters are enough to identify the state, e.g. one temperature value for the whole gas at a uniform temperature). Information is negative entropy and this equivalence would play a key role in applying entropy beyond Physics.
Note that Boltzmann’s reformulation of the second law was probabilistic: it explained the entropy of the system as a property about a population of particles, not just one particle. The second law does not claim that every single particle is subject to it, but that closed systems (made of many particles) are subject to it. An individual particle may well be violating the second law for a few microseconds, but the millions of particles that make up a system will obey it (just like one person might win at the roulette once, but that episode does not change the statistical law that people lose money at the roulette). In 2002 Australian researchers, in fact, showed that microscopic systems may spontaneously become more orderly for short periods of time.
An Accelerated World
Science has been long obsessed with acceleration. Galileo and Newton went down into history for managing to express that simple concept of acceleration. After them Physics assumed that an object is defined by its position, its velocity (i.e., the rate at which its position changes) and its acceleration (i.e., the rate at which its velocity changes). The question is: why stop there? Why don't we need the "rate an object changes its acceleration" and so forth? Position is a space coordinate. Velocity is the first derivative with respect to time of a space coordinate. Acceleration is the second derivative with respect to time of a space coordinate. Why do we only need two orders of derivative to identify an object, and not three or four or twenty-one?
Because the main force we have to deal with is gravity, and it only causes acceleration. We don't know any force that causes a change in acceleration, therefore we are not interested in higher orders of derivatives. To be precise, forces are defined as things that cause acceleration, and only acceleration (as in Newton's famous equation "F=ma"). We don't even have a word for things that would cause a third derivative with respect to time of a space coordinate.
As a matter of fact, Newton explained acceleration by introducing gravity. In a sense Newton found more than just a law of Physics, he explained a millenary obsession: the reason mankind had been so interested in acceleration is that there is a force called gravity that drives the whole world. If gravity did not exist, we would probably never have bothered to study acceleration. Car manufacturers would just tell customers how long it takes for their car to reach such and such a speed. Acceleration would not even have a name.
Relativity: The Primacy of Light
The Special Theory of Relativity was born (in 1905) out of Albert Einstein’s belief that the laws of nature must be uniform, whether they describe the motion of bodies or the motion of electrons. Therefore, Newton’s equations for the dynamics of bodies and Maxwell’s equations for the dynamics of electromagnetic waves had to be unified in one set of equations. In addition, they must be the same in all frames of reference that are "inertial", i.e. whose relative speed is constant. Galileo had shown this to be true for Newton's mechanics, and Einstein wanted it to be true for Maxwell's electromagnetism as well. In order to do that, one must modify Newton’s equations, as the Dutch physicist Hendrik Lorentz had already pointed out in 1892. The implications of this unification are momentous.
Relativity conceives all motions as "relative" to something. Newton's absolute motion, as the Moravian physicist Ernst Mach had pointed out over and over, is an oxymoron. Motion is always measured relative to something. Best case, one can single out a privileged frame of reference by using the stars as a meta-frame of reference. But even this privileged frame of reference (the "inertial" one) is still measured relative to something, i.e. to the stars. There is no frame of reference that is at rest, there is no "absolute" frame of reference. While this is what gave Relativity its name, much more "relativity" was hidden in the theory.
In Relativity, space and time are simply different dimensions of the same space-time continuum (as stated in 1908 by the Russian mathematician Hermann Minkowski). Einstein had shown that the length of an object and the duration of an event are relative to the observer. This is equivalent to calculating a trajectory in a four-dimensional spacetime that is absolute. The spacetime is the same for all reference frames and what changes is the component of time and space that is visible from your perspective.
All quantities are redefined in space-time and must have four dimensions. For example, energy is no longer a simple (mono-dimensional) value, and momentum is no longer a three-dimensional quantity: energy and momentum are one space-time quantity which has four dimensions. Which part of this quantity is energy and which part is momentum depends on the observer: different observers see different things depending on their state of motion, because, based on their state of motion, a four-dimensional quantity gets divided in different ways into an energy component and a momentum component. All quantities are decomposed into a time component and a space component, but how that occurs depends on the observer’s state of motion.
This phenomenon is similar to looking at a building from one perspective or another: what we perceive as depth, width or height, depends on where we are looking from. An observer situated somewhere else will have a different perspective and measure different depth, width and height. The same idea holds in space-time, except that now time is also one of the quantities that change with "perspective" and the motion of the observer (rather than her position) determines what the "perspective" is. This accounts for bizarre distortions of space and time: as speed increases, lengths contract and time slows down (the first to propose that lengths must contract was, in 1889, the Irish physicist George Fitzgerald, but he was thinking of a physical contraction of the object, and Lorentz endorsed it because it gave Maxwell's equations a particularly elegant form, whether the observer was at rest or in motion). This phenomenon is negligible at slow speeds, but becomes very visible at speeds close to the speed of light.
A further implication is that "now" becomes a meaningless concept: one observer's "now" is not another observer's "now". Two events may be simultaneous for one observer, while they may occur at different times for another observer: again, their perspective in space-time determines what they see.
Even the very concept of the flow of time is questionable. There appears to be a fixed space-time, and the past determines the future. Actually, there seems to be no difference between past and future: again, it is just a matter of perspective.
Mass and energy are not exempted from "relativity". The mass and the energy of an object increase as the object speeds up. This principle violates the traditional principle of conservation, which held that nothing can be destroyed or created, but Einstein proved that mass and energy can transform into each other according to his famous formula (a particle at rest has an energy equal to its mass times the speed of light squared), and a very tiny piece of matter can release huge amounts of energy. Scientists were already familiar with a phenomenon in which mass seemed to disappear and correspondingly energy seemed to appear: radioactivity, discovered in 1896. But Einstein's conclusion that all matter is energy was far more reaching.
Light has a privileged status in Relativity Theory. The reason is that the speed of light is always the same, no matter what. If one runs at the same speed of a train, one sees the train as standing still. On the contrary, if one could run at the speed of light, one would still see light moving at the speed of light. Most of Relativity's bizarre properties are actually consequences of this postulate. Einstein had to adopt the Lorentz transformations of coordinates, which leave the speed of light constant in all frames of reference, regardless of the speed it is moving at, but in order to achieve this result must postulate that moving bodies contract and moving clocks slow down by an amount that depends on their speed.
If all this sounds unrealistic, remember that according to traditional Physics the bomb dropped on Hiroshima should have simply bounced, whereas according to Einstein’s Relativity it had to explode and generate a lot of energy. That bomb remains the most remarkable proof of Einstein’s Relativity. Nothing in Quantum Theory can match this kind of proof.
Life On A World Line
The speed of light is finite and one of Relativity’s fundamental principles is that nothing can travel faster than light. As a consequence, an object located in a specific point at a specific time will never be able to reach space-time areas of the universe that would require traveling faster than the light.
The "light cone" of a space-time point is the set of all points that can be reached by all possible light rays passing through that point. Because the speed of light is finite, that four-dimensional region has the shape of a cone (if the axis for time is perpendicular to the axes for the three spatial dimensions). The light cone represents the potential future of the point: these are all the points that can be reached in the future traveling at the speed of light or slower. By projecting the cone backwards, one gets the light cone for the past. The actual past of the point is contained in the past light cone and the actual future of the point is contained in the future light cone. What is outside the two cones is unreachable to that point. And, viceversa, no event located outside the light cone can influence the future of that point. The "event horizon" of an observer is a space-time surface that divides space-time into regions which can communicate with the observer and regions which cannot.
The "world line" is the spatiotemporal path that an object is actually traveling through space-time. That line is always contained inside the light cone.
Besides the traditional quantity of time, Relativity Theory introduces another type of time. "Proper" time is the space-time distance between two points on a world line, because that distance turns out to be the time experienced by an observer traveling along that world line.
Relativity erased the concept of an absolute Time, but in doing so it established an even stronger type of determinism. It feels like our lives are rigidly determined and our task in this universe is simply to cruise on our world line. There is no provision in Relativity for free will.
General Relativity: Gravity Talks
Newton explained how gravity works, but not what it is.
Einstein’s Relativity Theory is ultimately about the nature of gravitation, which is the force holding together the universe. Relativity explains gravitation in terms of curved space-time, i.e. in terms of geometry.
The fundamental principle of this theory (the "principle of equivalence") is actually quite simple: any referential frame in free fall is equivalent to an inertial reference frame. That is because if you are in a free fall, you cannot perceive your own weight, i.e. gravity (gravity is canceled in a frame of reference which is free falling, just like the speed of an object is canceled in a frame of reference which is moving at the same speed). The laws of Special Relativity still apply.
Einstein's principle of equivalence simply expresses the fact that gravitation and acceleration are equivalent. If you can't see what is going on, and all you can measure is the 9.8 m/sec2 acceleration of an object that you let fall, you can't decide whether you are standing still, and subject to Earth’s gravity, or you are accelerating in empty space. All you observe is an acceleration of 9.8. If you are still, that's the acceleration you expect for any falling object. If you are in a rocket that is accelerating upwards at 9.8, that's the acceleration you expect for any falling object. Unless you can see, you cannot know which one it is. The effect is the same. Therefore, Einstein concluded, you can treat them as one: gravity and acceleration are equivalent.
Since gravitation is natural motion, Einstein’s idea was to regard free falls as natural motions, i.e. as straight lines in spacetime. The only way to achieve this was to assume that the effect of a gravitational field is to produce a curvature of space-time: the straight line becomes a "geodesic", the shortest route between two points on a warped surface (if the surface is flat, then the geodesic is a straight line). Bodies not subject to forces other than a gravitational field move along geodesics of space-time.
The curvature of space-time is measured by a "curvature tensor" originally introduced in 1854 by the German mathematician Bernhardt Riemann. The Riemann geometry comprises the classical Euclidean geometry as a special case, but it is much more general.
Minkowsky's four-dimensional spacetime is characterized by a "metrics". A metrics is a 4x4 matrix, each row and column representing one of the dimensions. The metrics for Newton's spacetime has zeros everywhere except in the diagonal of the matrix. The diagonal has values 1,1,1 and -1. This means that Pitagora's theorem still works, and time is an added dimension. The zeros in the other positions of the matrix specify that the space is flat. When the ones and the zeros change, their values specify a curvature for spacetime. Euclidean geometry works only with the flat-space metrics. Riemann's geometry works with any combination of values, i.e. with any degree and type of curvature.
A specific consequence of Riemann's geometry is that "force" becomes an effect of the geometry of space. A "force" is simply the manifestation of a distortion in the geometry of space. Wherever there is a distortion, a moving object feels a "force" affecting its motion. Riemann's geometry is based on the notion of a "metric (or curvature) tensor", that expresses the curvature of space. On a two-dimensional surface each point is described by three numbers. In a four-dimensional world, it takes ten numbers at each point. This is the metric tensor. Euclid's geometry corresponds to one of the infinite possible metric tensors (the one that represents zero curvature).
Not only space and time are relative, but space-time is warped.
With his 1915 field equations, Einstein made the connection with the physical world: he related the curvature of space-time caused by an object to the energy and momentum of the object (precisely, the curvature tensor to the "energy-momentum tensor"). Einstein therefore introduced two innovative ideas: the first is that we should consider space and time together (three spatial dimensions and one time dimension), not as separate; the second is that what causes the warps in this space-time (i.e., what alters the metric from Euclid's geometry) is mass. A mass does not voluntarily cause gravitational effects: a mass first deforms space-time and that warping will affect the motion of other objects that will therefore be indirectly feeling the "gravitational force" of that mass.
The mass also has an effect on the "time" part of space-time: clocks in stronger gravitational fields (bigger warp) slow down compared with clocks in weaker gravitational fields (smaller warp).
Summarizing: the dynamics of matter is determined by the geometry of space-time, and that geometry is in turn determined by the distribution of matter. Space-time acts like an intermediary device that relays the existence of matter to other matter.
General Relativity can in fact be understood as a theory of dynamically evolving relationships (as Julian Barbour did).
Incidentally, this implies that mass-less things are also affected by gravitation. This includes light itself: a light beam is bent by a gravitational field. Light beams follow geodesics, which may be bent by a space-time warp.
Special Relativity asked the laws of nature be the same in all inertial frames; which implied that they had to be invariant with respect to the Lorentz transformations. As a consequence, Einstein had to accept that clocks slow down and bodies contract. With General Relativity he wanted laws of nature to be the same in all frames, inertial or not (his field equations basically removed the need for inertial frames). This implies that the laws of nature must be "covariant" (basically must have the same form) with respect to a generic transformation of coordinates. That turned out to imply a further erosion of the concept of Time: it turned out that clocks slow down just for being near a gravitational field.
While apparent paradoxes (such as the twins paradox) have been widely publicized, Relativity Theory has been amazingly accurate in its predictions and so far no serious blow has been dealt to its foundations. While ordinary people may be reluctant to think of curved spaces and time dilatations, all these phenomena have been corroborated over and over by countless experiments.
The paradox of the twins (devised by Einstein in person) is due to the fact that... everything is relative. If a twin leaves the Earth, travels to another planet with a speed close to the speed of light, and comes back to the Earth, this twin will be younger than the one that stayed on Earth. The reason is that clocks slow down as speed increases (time dilation).
However, according to Relativity, one can also run the experiment the other way around: from the point of view of the twin that departs the Earth, it is the Earth that travels away and then comes back. In this case, the twin to travel at high speed, and therefore who is younger, is the twin who stayed on the Earth. Thus the second twin is younger if measured from the first twin, but the first twin is younger if measured from the second twin: these measurements cannot be both true at the same time. Depending on which reference frame you use, you get two contradictory results.
Einstein solved the paradox by pointing out that the two situations are not symmetric. The twin who leaves the Earth has to apply an acceleration to get out of the Earth; then decelerate, turn and accelerate again to return to the Earth. All of this violates the principle of Relativity: the twin that departed the Earth has done something absolute.
Even if one assumes that the twin does not accelerate and decelerate, the fact remains that it changes direction. In a sense, there are three (not just two) inertial frames: the twin that stays on Earth, the twin that travels away from the Earth, and the twin that travels towards the Earth. Thus the elapsed time for the first twin is calculated by adding up two motions referred to the same frame (the Earth), whereas the elapsed time for the second twin must be calculated by adding up two motions referred to two different frames (the one moving away from the Earth and the one moving towards the Earth). Thus there is an absolute difference between the first twin measuring the second twin and the second twin measuring the first twin. The twin to be younger is the one leaving the Earth.
That said, it is important to remember that this "being younger" has nothing to do with bodily aging: it is only referred to time measured by clocks.
You can in fact dream up several "paradoxes" based on the same idea of going back and forth. Imagine, for example, that I cut a 1 cm circular hole from a sheet of paper. Now I move the sheet of paper far away, and move the circular piece high up in the air. Then I move the sheet of paper at very high speed towards the point where it will meet the circular piece that I am letting fall at some instant to perfectly hit the hole. From the point of view of the circular piece, the sheet of paper is traveling at a very high speed, therefore it is shrinking, and, in particular, the hole in the middle is shrinking: therefore the circular piece will no longer be able to go through the hole. From the point of view of the sheet of paper, it is the circular piece that is traveling at very high speed, and thus shrinking: therefore the circular piece will easily pass through the hole. Imagine if instead of paper, you used spaceships: depending on which reference frame you use, the spaceships collide or they smoothly pass each other. This is not just a detail.
The solution of this second paradox is similar to the first one: we have done something at the very beginning, i.e. moving the sheet of paper far away. No matter how slowly we did that, we caused a change in its size relative to the circular hole (and viceversa). Thus, when we start moving the sheet of paper in the opposite direction, we cannot use its original size to compute the shrinking. When the sheet of paper and the circular piece meet, they are again the exact same size that they were at the beginning of the experiment.
Einstein’s equations described more than just the interaction between two bodies (like Newton’s gravitational equations did): they described the very story of the universe. One could play that film backwards or forward, and derive how the universe used to be or what it will be like.
Einstein briefly toyed with the idea of a "cosmological constant". He was not happy to discover that his equations predicted a universe in continuous turmoil (and most likely doomed to collapse under the effect of gravitation), so he introduced a constant in his equations to counterbalance gravitation (basically, a sort of "anti-gravity")and make the universe static. When Edwin Hubble showed that the universe was expanding, Einstein realized that the turmoil was real and decided that there was no need for his cosmological constant.
Density of mass plays a crucial role in Einstein’s equations: the denser the mass, the bigger the warp it causes to space-time, the stronger the gravitational effect felt by nearby matter. Thus collapsing stars are particularly relevant objects in Einstein’s universe. In 1967, the first "pulsar" was observed: a rapidly-spinning collapsed star.
Shortly after Einstein published his gravitational field equation, in 1916 the German physicist Karl Schwarzschild found a solution that determines the gravitational field for any object, given its mass and its size. That solution goes to infinity for a specific ratio between mass and size: basically, if the object is dense enough (lots of mass in a tiny size), the gravitational attraction it generates is infinite. Nothing, not even light, can escape this object, which was therefore named "black hole" (by John Wheeler). And everything that gets near it is doomed to fall into it, and be trapped in it forever.
Quantum Theory: The Wave
Quantum Theory was the logical consequence of two discoveries. In 1900 the German physicist Max Planck solved the mystery of radiation emitted by heated objects (that Newton’s physics failed to explain): he realized that atoms can emit energy only in discrete amounts. Nature seemed to forbid exchanges of energy in between those discrete values.
In 1913 the Danish physicist Niels Bohr solved another mystery, the structure of the atom: electrons turn around the nucleus and are permitted to occupy only some orbits. (or, better, the angular momentum of an electron occurs only in integer multiples of a constant, which happens to be proportional to Planck’s constant). Again, Nature seemed to forbid existence in between orbits. The electron "jumps" from one orbit to another orbit without ever being in the space in between the two orbits (as if it stopped existing in the old orbit and was suddenly created again in the next orbit).
In 1925 George Uhlenbeck and Samuel Goudsmit discovered that each electron "spins" with an angular momentum of one half Planck constant. The "spin" does not vary: the electron always rotates with the same "spin". It would turn out that every particle has its own spin, and the spin for any kind of particle is always the same.
The fundamental assumption of Quantum Theory is that any field of force manifests itself in the form of discrete particles (or "quanta"). Forces are manifestations of exchanges of discrete amounts of energy. For example, electromagnetic waves carry an energy which is an integer multiple of a fundamental constant, the "Planck constant".
A way to solve the apparent paradox of Bohr’s electrons was discovered by the French physicist Louis DeBroglie in 1923 (after Einstein had made the same assumption regarding light): if an electron is viewed as a wave spreading over many orbits, the electron does not need to "jump" from one orbit to another. The electron "is" in all orbits at the same time, to some degree. DeBroglie proved that the equation for a standing wave matched the behavior of the electron. That equation expressed a relationship between quantities of matter (e.g., speed) and quantities of waves (e.g., wavelength). Thus he concluded that waves and particles are dual aspects of the same phenomena: every particle behaves like a wave. One can talk of energy and mass (quantities previously associated only to matter), or one can talk of frequency and wavelength (quantities previously associated only to waves). The two descriptions are equivalent, or, better, one complements the other. It didn’t take long to observe "interference patterns" (typical of waves) among streams of electrons, and therefore confirm DeBroglie’s theory. Einstein’s Relativity had shown that energy and matter were dual aspects of the same substance. DeBroglie showed that particles and waves were dual aspects of the same phenomenon.
The character of this relationship was defined in 1925 by Werner Heisenberg in Germany and Erwin Schroedinger in Austria. Both devised equations that replaced the equations of Newton's physics, but both equations had unpleasant consequences: Heisenberg's equations implied that the result of a physical experiment depends on the order in which the calculations were performed, and Schroedinger's equations implied that each particle could only really be considered a wave. In 1926 Max Born realized the implications of the wave-particle duality: the wave associated to a particle turns out to be a "wave of probabilities", that accounts for the alternative possibilities that open up for the future of a particle. In other words, the wave summarizes the possible values for the electron’s attributes (e.g., position, energy, spin) and how those values may evolve over time (the square of the wave’s amplitude represents the probability of finding a given value for an attribute when measuring that attribute).
The state of a particle is described by a "wave function" which summarizes (and superposes) all the alternatives and their probabilities. The wave function contains all the information there is about the particle (or, in general, about a system). It contains the answers to all the questions that can be asked about the particle.
The reason this is a "wave" of probabilities and not just a set of probabilities is that Schroedinger’s equation that describes it is the equation of an electromagnetic wave.
Schroedinger's equation describes how this wave function evolves in time, and is therefore the quantum equivalent of Hamilton's equations. The Schroedinger equation fixes, deterministically, the temporal development of the state of the universe. But at every point in time the wave function describes a set of possibilities, not just one actuality. The particle’s current state is actually to be thought of as a "superposition" of all those alternatives that are made possible by its wavelike behavior. A particle's current state is, therefore, a number of states: one can view the particle as being in all of those states at the same time. This is a direct consequence of a particle not being just a particle but being also a wave.
As Born phrased it, the motion of particles follows the law of probabilities, but the probability itself follows the law of causality.
In 1927 Bohr stated the ultimate paradox of the wave-particle duality: everything is both particle and wave, but one must choose whether to measure one or the other aspect of nature, and then stick to it. If you try to mix the two, you run into contradictions.
The Planck Constant
Of course, one explanation begs for another one: introducing the Planck constant helps explain phenomena that Newton could not explain, but the mystery now is the Planck constant itself: what is it, what does it represent? Newton’s physics (as well as Einstein’s physics) assumed that the most fundamental units of the universe were the point and the instant. Quantum Theory introduces a fundamental unit that is bigger than a point and an instant, and seems to be as arbitrarily finite as Newton’s points were infinitesimally small. Unlike Newton’s points and instants, that have no size, the Planck constant has a size: a length, height and width of 10-33 centimeters and a time interval of 10-43 seconds.
Einstein had warped space and time, but Quantum Theory did worse: it turned them into grids. (One could even argue that the very notion of measuring a distance such as "10-33 centimeters" depends on Newton’s concept of space, and thus we don’t quite know what we mean when we say that Planck’s length is "10-33 centimeters").
In classical Physics, a quantity (such as the position or the mass) is both an attribute of the state of the system and an observable (a quantity that can be measured by an observer). Quantum Theory makes a sharp distinction between states and observables. If the system is in a given state, an observable can assume a range of values (so called "eigenvalues"), each one with a given probability. The evolution over time of a system can be viewed as due (according to Heisenberg) to time evolution of the observables or (according to Schroedinger) to time evolution of the states.
An observer can measure at the same time only observables that are compatible. If the observables are not compatible, they stand in a relation of mutual indeterminacy: the more accurate a measurement of the one, the less accurate the measurement of the other. Position and momentum are, for example, incompatible. This is a direct consequence of the wave-particle dualism: only one of the two natures is "visible" at each time. One can choose which one to observe (whether the particle, that has a position, or the wave, that has a momentum), but cannot observe both aspects at the same time.
Precisely, Heisenberg’s famous "uncertainty principle" states that there is a limit to the precision with which we can measure, at the same time, the momentum and the position of a particle. If one measures the momentum, then it cannot measure the position, and viceversa. This is actually a direct consequence of Einstein's equation that related the wavelength and the momentum (or the frequency and the energy) of a light wave: if coordinates (wavelength) and momentum are related, they are no longer independent quantities. Einstein never believed in this principle, but he was indirectly the one who discovered it.
The wave function contains the answers to all the questions that can be asked about a system, but not all those questions can be asked simultaneously. If they are asked simultaneously, the replies will not be precise.
The degree of uncertainty is proportional to the Planck constant. This implies that there is a limit to how small a physical system can be, because, below a quantity proportional to the Planck constant and called "Planck length", the physical laws of Quantum Theory stop working altogether. The Planck scale (10–33 cm, i.e. the shortest possible length, and 10–43 sec, i.e. the time it takes for a light beam to cross the Planck length, i.e. the shortest possible time tick) is the scale at which space-time is no longer a continuum but becomes a grid of events separated by the Planck distance. What happens within a single cell of the grid, is beyond the comprehension of Physics. As the USA physicist John Wheeler suggested in the 1950s, even the very notions of space and time stop making sense in this "quantum foam".
Note that Heisenberg does not forbid precise measurements of "compatible observables", for example of position, charge and spin. It only applies to "incompatible observables", which are couples: position/momentum, energy/time, electric field/magnetic field, angle/angular momentum, etc.
One cannot measure exactly both the position and the momentum (speed) of a particle at the same time. A consequence of Heisenberg's principle is that no particle can be completely at rest. If a particle were at rest, then both its position and its speed would be measured exactly (both being zero), a fact that would contradict Heisenberg. Even if the particle has absolutely no energy, there would still be some random form of motion (the "zero-point motion").
By the same token, one cannot measure the electrical and the magnetic field simultaneously with absolute precision. The more accurate one measurement is, the less accurate the other one is. Even if one removed all the energy from the vacuum, there would still be some random fluctuations of the electrical and/or magnetic fields, the "quantum vacuum fluctuations".
The uncertainty predicted by Quantum Theory (and verified by countless experiments in countless laboratories) has been sometimes interpreted as a consequence of the fact that, at the microscopic level, one cannot pretend that a measurement is "objective" at all: a measurement is an interaction between two systems, which, like all interactions, affects both. But that is not quite where Heisenberg’s calculations came from. They originate, as everything else, from Planck’s constant.
As a consequence of quantum uncertainty, Planck and Heisenberg proved that at that scale, the vacuum of empty space is actually "full" of all sorts of subtle events.
In 1948 the Dutch physicist Hendrick Casimir even showed how this all-pervading zero-point energy could be measured (thus it is now known as "Casimir force").
This was the culmination of the eccentricities of Quantum Theory: that the vacuum was not empty.
(The first experimental confirmation of zero-point energy had to wait until the 1990s).
Thus Quantum Theory predicts that the universe exists on a grid of spacetime values, and that there is something within the elements of this grid, something that does not quite belong to the universe (or, at least, does not belong to Quantum Physics) but has nonetheless an energy that can interact with the universe (be measured by people living on the grid of our universe).
Galileo "discovered" inertia: bodies that are at rest tend to remain at rest, and bodies that are moving tend to continue moving at the same speed in the same direction, unless a force is applied. Newton turned Galileo’s inertia into a quantitative property of matter: mass. Newton showed that mass was the object of forces, and the effect of forces on mass was to accelerate it. Forces and accelerations were visible entities. Mass was an invisible property of matter.
Newton’s mass was three things in one: it was resistance to acceleration, it was the ability of attracting other masses, and it was the propensity to be attracted by other masses. Einstein introduced "rest" mass, an aspect of energy, expressed by the equation E=mc2. Einstein also showed that things that possess "mass" cannot travel faster than the speed of light, a speed that is reserved for things that do not possess mass (such as the photon).
Quantum Mechanics showed that "mass" is indeed a property of every elementary particle, but introduced another oddity: while there is an anti-particle for every particle (electrical charge can be positive or negative), both a particle and its anti-particle have the same (positive) mass. Mass is only positive, never negative. (In 1957 British physicist Hermann Bondi showed that the encounter between a mass and its anti-mass would result in infinite acceleration, with no need for a source of energy: the negative mass would be attracted to the positive mass, while the positive mass would be repelled by the negative mass. Thus the two masses would experience equal accelerations in the same direction, in violation of Newton's third law, and continue to accelerate forever, the negative mass chasing the positive mass and the positive mass fleeing from the negative mass with constant acceleration).
Neither Relativity nor Quantum Theory explained what "mass" is (where it comes from) and what causes its odd properties. They both took it for granted that Nature is that way. It was the odd behavior of "mass" that allowed physicists to create an elegant world. But the elegance was mostly based on an abstract, arbitrary, "catch all" definition.
The World And The Mind
Relativity Theory and Quantum Theory said something important about the mind. They were as much about mind as they were about matter, only in a more subtle way.
Relativity Theory was not only about reality being "relative" to something. It was (first and foremost) about reality being beyond the reach of our senses.
Einstein's underlying principle is that we don't always see the universe as it is. Newton's underlying principle was that we see the universe as it is. Newton's Physics is a description of how our mind perceives the universe. There are bodies, there is absolute time, etc.
Einstein's Physics is a "guess" about what the universe really is, even if our mind cannot perceive it. Einstein's Physics implied that there may be aspects of the universe that our mind cannot perceive, and that we can guess only by analyzing the aspects that we can perceive.
Quantum Theory was not only about reality being "quantized". It was also about reality being beyond the reach of our mind. The single most distressing finding of Quantum Theory is that reality as we know it only occurs when somebody observes it. The electron is in a certain place only when somebody actually looks at it, otherwise the electron is, simultaneously, in several different places.
We can analyze this finding with either of two stances. According to the first one, our mind has no limitations. It can perfectly perceive nature as it is. It observes only one value because that is what nature does: the multiple choices for a quantity's value collapse to just one value when that quantity is observed by an observer.
According to the second one, our mind has limitations. The quantum collapse from many values to just one value is due to a limitation of our mind. Our mind cannot perceive nature as it is. It can only perceive one value for each quantity.
The electron is in many places, but our mind cannot perceive a thing being in many places at the same time, so it "collapses" the electron into only one specific place at a time. This is just an effect due to the limitation of our mind. We are forced to "sample" reality because we can't handle all of it. After all, that's what all our senses do. They are bombarded all the time with data from the environment, and they only pick up some of those data. We don't perceive every single detail of what is going on around us, we are forced to be selective. The mind turns out to be a sense that also has limited capacity, although the limitation is of a different kind. Each item of reality (a position, a speed, etc) "has" many values. The reason we observe only one value is that our mind can't handle a universe in which quantities have more than one value.
The conceptual revolution caused by Quantum Theory was somewhat deeper than the one caused by Relativity Theory. Reconciling Newton and Einstein is relatively easy: Newton's theory was not false, it was just a special case of Einstein's theory, the one in which the spacetime is Euclidean. Reconciling Newton and Quantum Theory is, on the other hand, impossible: Newton's theory is just false. It seems to work because insist to assume that such things as big objects truly exist.
A theory of mind that does not take into account Relativity is a legitimate approximation, just like a theory of the Earth that does not take into account Relativity is a legitimate approximation. But no theory of mind can ignore Quantum Theory.
The Power of Constants
At this point we can note that all the revolutionary and controversial results of these new theories arose from the values of two constants. Quantum Mechanics was a direct consequence of Planck's constant: were that constant zero, there would be no uncertainty. Relativity Theory was a direct consequence of the speed of light being constant in all frames of reference: were the speed of light infinite, there would be no time dilatation and contraction of length.
These two constants were determined, indirectly, by studying two minor phenomena that were still unsolved at the end of the century: the ether and the black body radiation.
The presence of the ether could not be detected by measuring the speed of light through it; so Einstein assumed that the speed of light is always the same.
The black body does not radiate light with all possible values of energy but only with some values of energy, those that are integer multiples of a certain unit of energy; so Planck assumed that energy exchanges must only occur in discrete packets.
These two universal constants alone revealed a whole new picture of our universe.
Quantum Reality: Fuzzy or Incomplete?
Many conflicting interpretations of Quantum Theory were offered from the beginning.
Niels Bohr claimed that only phenomena (what appears to our senses, whether an object or the measurement of an instrument) are real, in the human sense of the word: particles that cannot be seen belong to a different kind of reality, which, circularly, cannot be perceived by humans; and the wave function is therefore not a real thing. Reality is unknowable because it is inherently indeterminate, and we humans do not live in a world of indeterminate things, we live in a world of phenomena (where "phenomena" presumably includes also houses and trees, the effect of those elementary processes).
Werner Heisenberg, the man who discovered in 1925 the first complete theory of the quantum, believed that the world "is" made of possibility waves and not particles: particles are not real, they are merely "potentialities", something in between ideas and actualities. Our world, what we call "reality", is a sequence of collapses of wave of possibilities. The quantum world and our world are bridged by the "measurement". Reality arises from quantum discontinuities (or "quantum jumps"): classical evolution of the Schroedinger equation builds up "propensities", then quantum discontinuities (the collapse of the wave function) select one of those propensities. Every time this happens, reality changes. Therefore reality "is" the sequence of such quantum discontinuities. What turns the unknowable world of particles into human-perceivable "phenomena" is the observation: the moment we observe something, we create a phenomenon. As John Wheeler put it, "no phenomenon is a real phenomenon until it is an observed phenomenon". The universe had to wait for a conscious observer before it started existing for real. Furthermore, Heisenberg interpreted this reality as "knowledge": the quantum state is a mathematical description of the state of the observer's knowledge rather than a description of the objective state of the physical system observed.
The British physicist Paul Dirac, the man who in 1928 merged Quantum Physics and Special Relativity in Quantum Field Theory, pointed out that Quantum Physics is about our knowledge of a system. It does not describe reality but our knowledge of reality. A wave function represents our knowledge of a system before an experiment and the reduced wave function our more precise knowledge after the measurement.
The Indivisible Universe
Albert Einstein was so unhappy with the uncertainty principle that he accepted Quantum Mechanics only as an incomplete description of the universe. He thought that Quantum Mechanics had neglected some "hidden variables". Once those hidden variables were found, we would have a complete theory without Quantum Theory’s oddities but with all of Quantum Theory’s results.
Quantum Theory is a practical tool to calculate probabilities for sets of particles, but no prescription is provided for calculating quantities of individual particles. Einstein thought that there is an underlying reality where determinism rules and the behavior of the individual particle can be predicted. It is just that Quantum Mechanics is incomplete and has not found out that underlying reality yet.
Einstein was particularly unhappy about the "nonlocality" of Quantum Physics, which he thought constituted a paradox. "Nonlocality" means "action at a distance". In Quantum Physics one can prove that, if they were once part of the same state, two particles will be always connected: once we measure the position of the first one, we instantaneously determine the position of the other one, even if, in the meantime, it has traveled to the other end of the universe. Since no information can travel faster than light, it is impossible for the second particle to react instantaneously to a measurement that occurs so far from it. The only possible explanation for this "paradox" was, to Einstein, that the second particle must have properties which are not described by Quantum Mechanics.
Einstein thought that Quantum Physics provides a fuzzy picture of a sharp reality, whereas for Bohr it provides a compete picture of a fuzzy reality.
Einstein was proven wrong in 1964 by the Irish physicist John Bell, whose theorem basically ruled out "local hidden variables", precisely the type that Einstein invoked. Bell's conclusion is that, on the contrary, there are objective, non-local connections in the universe. In other words, two particles, once they have interacted, will keep interacting forever (their wave functions get entangled forever). Einstein believed in the law of locality, i.e. that two objects can interact only if they touch each other or if their interaction is mediated by some other object; but Bell proved that the "wave" is enough to provide interaction. Two measurements can be related instantaneously even if they are located in regions too far apart for a light signal to travel between them. Non-locality, or inseparability, is a fact of nature. Objects are not only affected by forces. They are also affected by what happens to other objects.
(More precisely, Bell showed how to test whether a world of properties that are not due to observation and of separated objects is possible. In 1972 John Clauser carried out an actual experiment to perform the test, and its result proved Einstein wrong: either properties are due to observation, or objects are forever connected, or both. Our world cannot possibly have both an observer-independent reality and entanglement-free objects).
This shattered another belief of classical Physics. Newton believed that objects interact through forces that somehow have to travel from one to the other. A cannonball has to travel from the cannon to the walls before the walls explode; and nothing else in the universe is affected. The sun attracts the earth into an orbit, but it doesn't have any effect on the other stars. These are "local" interactions. Einstein added that forces can only travel as fast as light. Therefore, the impact of a force o an object is delayed by the time it takes for the force to reach that object at a speed which cannot exceed the speed of light. "Locality" became a distance: there is only so much in the universe that can exert a force on me, because only so much of the universe can send its force to me during my lifetime. If I live 80 years, an event that occurs more than 80 light-years away from here will never cause any disturbance on my life. Bell proved that this is not the case, because Quantum Theory prescribes the existence of a non-local "force": once two waves have interacted, they are forever entangled.
Note that Heisenberg's "knowledge interpretation" never had a problem with non-locality: obviously, a change in the observer's knowledge does change the observer's knowledge about the entire system, regardless of how "extended" in space the system is. For example, if I observed the two particles at the beginning, when they were in the same place, and noticed that one is black and the other one is white, and later I observe the white one, I will "know" that the other one is black even if the other one is light-years away from me.
The USA physicist David Bohm believed in an "undivided whole" even before Bell's experiment. His idea was that the whole universe is entangled in one gigantic wave.
One of Quantum Theory's most direct consequences is indeterminism: one cannot know at the same time the value of both the position and the momentum of a particle. One only knows a probability for each of the possible values, and the whole set of probabilities constitute the "wave" associated with the particle. Only when one does observe the particle, does one particular value occur; only then does the wave of probabilities "collapse" to one specific value.
Bohm’s "ontological" interpretation of Quantum Theory ("A Suggested Interpretation of the Quantum Theory in Terms of Hidden Variables", 1952) almost resurrected determinism at the quantum level. Bohm’s bold assumption was that the quantum "wave" is a real wave, due to a real potential.
Bohm assumed that the wave function does not represent just a set of probabilities: it represents an actual field. A particle is always accompanied by such a field. This field is a real field and acts upon particles the same way a classical potential does. (Bohm resurrected an interpretation of Quantum Theory that DeBroglie had abandoned, the theory of an ordinary wave guiding an ordinary particle).
The beauty of this assumption is that, with the introduction of this additional potential, something momentous happens to the equations of Quantum Mechanics: position and momentum of a particle are no longer incompatible, they can be measured precisely at the same time, and Heisenberg’s principle is defeated.
The behavior of the particle in Bohm’s theory is determined by the particle's position and momentum, by whatever force is acting on it, and by the quantum potential.
For Bohm, particles do exist and are always accompanied by a field. An electron is neither a particle nor a wave (field), it is a particle plus a wave (that cannot be separated). But Bohm's wave is not Born's wave: Born's wave is only a function of probabilities that helps compute the particle's position, whereas Bohm's wave is a real wave that guides the particle (therefore also referred to as the "pilot-wave").
Everything is both a particle and a wave, and is acted upon by both a classical potential and a quantum potential (the "pilot wave"). Basically, the wave-function provides an additional potential that, once inserted in the traditional Hamiltonian of classical Physics, yields a well-determined trajectory for each particle (but since the initial position cannot be known, we still can't predict the path of a particle, only notice that there exists a well-determined path prescribed by nature).
Bohm had found an interpretation of Quantum Theory in terms of particles with well-defined position and momentum. What Bohm had done with his assumption was, basically, to add some "hidden variables" (the quantum potential) to the equations, precisely what Einstein had suggested to restore determinism in Physics.
To explain the function of the quantum potential, Bohm introduced the notion of "active in-formation" ("information" as in "give form", for example to a particle's movement). A particle is moved by whatever energy it has (for example, because a force is acting on it) but its movement is guided by the "in-formation" in the quantum field (in the "pilot-wave").
In Physics, a potential describes a field in terms of how, at each point in space, the particle located at that point will be affected by that field. In Newton's physics the effect of the classical potential on a particle is proportional to the magnitude of the field.
Bohm thought that his quantum field, in particular, had to reflect whatever is going on in the environment, including the measuring apparatus. Therefore, the quantum potential depends only on the form, and not on the magnitude, of the quantum field. The "strength" of the quantum potential does not depend on the intensity of the wave but only on the form of the wave. Even a very weak quantum potential can affect the particle. Even a very distant event can affect the particle.
The previous interpretations of Quantum Theory were trying to reconcile the traditional, classical concept of "measurement" (somebody who watches a particle through a microscope) with a quantum concept of "system". Bohm dispensed with the classical notion of "measurement": one cannot separate the measuring instrument from the measured quantity, as they interact all the time. It is misleading to call this act "measurement". It is an interaction, just like any other interaction, and, as Heisenberg's principle states, the consequence of this interaction is not a measurement at all.
The field that Bohm introduced in the equations to fix Heisenberg’s indeterminism represents a "sub-quantum" reality.
Bohm's quantum potential does not act within the four-dimensional geometry of spacetime; it acts beyond it. In a sense, it defines a common pool of information, a way to connect everything together, just like dancers can use the music to move together in harmony.
Bohm thought that this field must be fluctuating rapidly and what Quantum Theory observes is merely an average over time (just like Newton's physics reads a value for quantities that are actually due to the Brownian motion of many particles). Quantum physics deals with mean values of an underlying reality just like Newton's physics deals with mean values of thermodynamic quantities.
At this "sub-quantum" level, quantum effects all but disappear: a particle’s position and momentum are well-determined. The mystery of the collapse of the wave function, of the discontinuity in the transition from the quantum world to the classical world, occurs only at the quantum level, whereas Bohm believes there is a deeper level at which the apparent discontinuity of the collapse disappears.
After all, the study of "elementary" particles has shown that even elementary particles can be destroyed and created, which means that they are not the ultimate components of the universe, that there must be an underlying reality, or, in Bohm's terms, an underlying "flux". Bohm thought that the basic problem lied in an obsolete notion of "order".
Thus, Bohm distinguished between the "explicate" order (the world of isolated spacetime thing-events that our senses experience) and the "implicate" order (all thing-events are part of a whole, the "holomovement"). The explicate order emerges from the holomovement. The holomovement contains all instances of explicate order as potentialities.
Cartesian order (the "grid" of space-time events) is appropriate for Newtonian physics in which the universe is divided in separate objects, but inadequate for Quantum and Relativity theories to reflect their idiosyncrasies and in particular the undivided wholeness of the universe that Bohm has been focusing on.
Bohm's solution was to contrast the "explicate order" that we perceive and that Physics describes (the Cartesian order of isolated space-time thing-events) with the "implicate order", which is an underlying, hidden layer of relationships. The explicate order is but a manifestation of the implicate order. Space and time, for example, are "forms" of the explicate order that are derived from the implicate order.
The implicate order is similar to the order within a hologram: the implicate order of a hologram gives rise to the explicate order of an image, but the implicate order is not simply a one-to-one representation of the image. In fact, each region of the hologram contains a representation of the entire image. The implicate order and the explicate order are fundamentally different. The main difference is that in the explicate order each point is separate from the others. In the intricate order, the whole universe is "enfolded" in everything, and everything is enfolded in the whole. In the explicate order "things" become (relatively) independent.
In the implicate order, all thing-events are part of a whole, the "holomovement". The explicate order emerges from the holomovement. The holomovement contains all instances of explicate order as potentialities.
Bohm suggested that the implicate order could be defined by the quantum potential, the field consisting of an infinite number of pilot waves. The overlapping of the waves generates the explicate order of particles and forces, and ultimately space and time.
Since Bohm’s quantum field is affected by all particles (the pilot-wave that guides all particles is affected by all particles), nonlocality is a feature of reality: a particle can depend strongly on distant features of the environment.
Bohm's universe is one indivisible whole.
Everything in the universe is entangled in everything else, and ultimately in the whole. It does not make sense to analyze particles of subsets of the world as independent and separate parts.
Einstein's objection did not die there and is still very much alive, if nothing else because, ultimately, it can be read as an objection to the role that the observer plays in Quantum Theory.
The USA physicist Alwyn Scott has recently resuscitated Einstein's hypothesis. Scott argues in favor of an interpretation of Quantum Theory as an approximation to a not yet discovered non-linear theory. The new theory must be non-linear because it is the only way to remove Heisenberg's uncertainty principle, which descends from the linearity of Schroedinger's equation.
Again inspired by Einstein, the Australian philosopher Huw Price thinks that backward causation (that future can influence the past), or advanced action, is a legitimate option. Price believes that our theories are time-asymmetric because we are conditioned by folk concepts of causality. Physical theories are built starting with the assumption that the future cannot influence the past, and therefore it is no surprise that they prescribe that the future cannot influence the past. If we remove our preconceptions about causality, then we can redraw Quantum Physics. Then it turns out that Einstein was right with his hypothesis of hidden variables, and that Quantum Physics provides an incomplete description of the universe. A complete Quantum Physics will not assign any critical role to the observer.
In the 1980s the USA physicist John Cramer has traveled the opposite route with his "transactional interpretation" of Quantum Theory, which aims at sending back the observer to the laboratory and removing her from the formalism. Cramer builds on "absorber theory" developed in the 1940s by John Wheeler and Richard Feynman. They described a radiation process as a "transaction" in which the emitter of the radiation and the absorber of the radiation exchange waves: the emitter sends a "retarded" wave to the absorber, and simultaneously the absorber sends an "advanced" wave to the emitter. Advanced waves are canceled and therefore cannot be detected. An observer perceives only that a retarded wave has traveled from the emitter to the absorber.
"Advanced" waves are solutions of a wave equation which contain only the second time derivative. Advanced waves have "eigenvalues" of negative energy and frequency, and they propagate in the negative time direction. Advanced waves are basically the time-reversed counterparts of normal (or retarded) waves. Both "advanced" and "retarded" waves are valid orthogonal solutions of the electromagnetic wave equation, but in conventional electrodynamics the advanced solutions are usually ignored as unnatural, because they violate the law of causality, and only "retarded" solutions are retained. Wheeler and Feynman proposed that the time symmetry in the wave equation reflects a property of nature, that both types of waves actually occur.
In the Wheeler-Feynman absorber theory, any emission process makes advanced waves on an equal basis with ordinary "retarded" waves.
Cramer has extended the idea and claims that any quantum event is a "handshake" executed through an exchange of advanced and retarded waves. The exchange of a quantum of energy between a present emitter and a future absorber occurs through a Wheeler-Feynman exchange of advanced and retarded waves. The emitter sends an "offer" wave to the absorber (forward in time). The absorber then returns a "confirmation" wave to the emitter (backwards in time). The transaction is then completed with an "handshake" across space-time, which leads to the transfer of energy from emitter to absorber.
The transaction is explicitly non-local because the future is affecting the past. Einstein's paradox is solved without resorting to a knowledge-based interpretation.
One of Newton's postulates was that "time flows equably".
The biggest problem with Quantum Theory is how the observed world (the world we know, made of well-defined objects) emerges from the quantum world (a world of mere possibilities and uncertainties, thanks to Heisenberg’s principle).
The Hungarian mathematician John Von Neumann (the same one who virtually invented the computer) distinguished between processes of the first and second kinds that occur when one is analyzing the evolution of a system with Quantum Theory. First-kind processes occur in isolated systems, on which no measurements can be carried out, and they closely resemble classical, deterministic evolution of a physical system. Second-kind processes occur when a measurement is carried out and they are non-deterministic (or at least probabilistic): when an observable is measured, the state of the system suddenly jumps to an unpredictable state (or "eigenstate") associated with the measured eigenvalue of the observable. Unlike classical Physics, in which the new state can be determined from the prior state of the system, Quantum Theory can only specify the probabilities of moving into any of the observable’s eigenstates. In quantum lingo, a measurement causes a "collapse of the wave function", after which the observable assumes a specific value. A continuous process of the first kind gives rise to a discontinuous process of the second kind.
Isolated systems obey to the Schroedinger equation, observed systems obey to Heisenberg's quantum jumps. Quantum Theory therefore implies that something turns a process of the first kind into a process of the second kind when it is observed.
The problem is that Quantum Theory does not prescribe or describe when and how this happens. The flow of time is mysteriously altered by measurements: a system evolves in a smooth and deterministic fashion until a measurement is performed, then it jumps more or less randomly into an eigenstate of the measured observable, from where it resumes its smooth evolution until the next measurement. Time seems to behave in an awkwardly capricious way.
As Bohr pointed out, a measurement also introduces irreversibility in nature: collapse cannot be undone. Once we measured a quantity, at that point in time a discontinuity is introduced in the evolution of the wave function. If, after a while, we proceeded backwards in time, we would reach the same point from the future with a wave function which could collapse in any of the legal ways, only one of which is the one that originated the future we are coming from. It is very unlikely that we would retrace the same past.
The Measurement Problem
According to Quantum Theory, our universe needs both kinds of processes. Von Neumann tried to figure out how they interact and realized that the answer lies in the "measurement" of the system.
Reality seems to proceed on two parallel tracks. The Schroedinger equation determines (in a deterministic manner) the evolution of the state of the system, but that state is a set of possible states each with its own probability of happening. So long as nobody observes the system, the Schroedinger equation predicts future probabilities of the system. Then Heisenberg's principle causes that wave function to "collapse" whenever the system is observed. The collapse causes the system to choose only one of the possible states. Once the observer has observed the system, only a part of the wave survives and evolves according to the Schroedinger equation. At this point the Schroedinger equation can calculate a new set of possible states. And so forth. The two views are both necessary to explain the evolution of the universe. They are not alternative views of the universe. One complements the other.
Note that the observer does more than just observe something: the observer also decides "what" to observe. That decision has an effect on the state of the system, because it forces the system to choose among all the possible states. Nature's role is really only to choose one of those possible states, and Quantum Theory can only presume that this is done randomly.
Von Neumann pointed out that measurement of a system consists in a process of interactions between the instrument and the system, whereby the states of the instrument become dependent on the states of the system. There is a chain of interactions that leads from the system to the observer’s consciousness. For example, a part of the instrument is linked to the system, another part of the instrument is linked to the previous part, and so forth until the interaction reaches the observer’s eye, then an interaction occurs between the eye and the brain and finally the chain arrives to the observer’s consciousness. Eventually, states of the observer’s consciousness are made dependent on states of the system, and the observer "knows" what the value of the observable is. Somewhere along this process the collapse has occurred, otherwise the end result of the chain would be that the observer’s consciousness would exhibit the same probabilistic behavior of the observable: if the observer reads one specific value on the instrument, it means that the wave of possibilities has collapsed (has chosen just that one specific value) somewhere between the system and the observer’s consciousness. At which point? What exactly causes the "collapse"? The instrument? The lense? The electrons inside the instrument? The observer's retina? The observer's nervous system? The observer's consciousness?
What constitutes a valid observer? Does it have to be big? Does it have to be in the brain? Does it have to be conscious? Does it have to be human?
Von Neumann showed mathematically that Quantum Theory is indifferent: it makes no difference to the statistical predictions of Quantum Theory where exactly this happens and what causes it. But humans are curious and would like to find out.
In a sense, Von Neumann was trying to reconcile "objective being" and "subjective knowing". In classical Physics they are one and the same, but in Quantum Physics they are different, and it is not completely clear how subjective knowing relates to objective being.
Later, the Hungarian physicist Eugene Wigner introduced another step in Von Neumann’s thought experiment: what if a friend is part of the chain that leads to the observation? If a friend measures the position of a particle and then relates to me the result, for me the wave "collapses" only when he tells me the result of her experiment. But the wave has already collapsed for her when he carried out the measurement. Did the wave collapse also for me at the same time? If not, do our waves collapse to the same value? Or does each of us live in an independent universe?
The Brain as a Measurement Device
Quantum Theory is really about waves of possibilities. A particle is described by a wave function as being in many possible places at the same time. When the particle is observed, its wave function "collapses" with definite attributes, including the location it occupies, but such attributes cannot be foreseen until they actually collapse. In other words, the observer can only observe a quantum system after having interfered with it.
Von Neumann highlighted an inconsistency in the standard interpretation of Quantum Theory: the objects to be observed are treated as quantum objects (or waves), while the objects that observe (the instruments) are classical objects, with a shape, a position and no wave. The "measurer" is a natural object as much as the "measured", but we grant it immunity from Quantum Theory. Von Neumann objected to dividing the world into two parts that behaved differently. Quantum Theory unequivocally states that everything is a quantum system, no matter how small or big it is. On the other hand, if everything is a quantum system regulated by a wave of possibilities, what makes it collapse? Von Neumann was led again to postulate that something "different" from a quantum system has the power to cause such a collapse, and that something had to be human consciousness. Nothing in the world is real unless perceived by a mind, as the British philosopher Berkeley had argued centuries before Von Neumann.
What if we built an instrument which is smaller than the system to be observed? What would be a quantum system: the smaller or the bigger, the measurer or the measured?
The range of uncertainty of a particle is measured by Max Planck's constant. Because Planck's constant is so small, big objects have a well-defined position and shape and everything. The features of small objects such as particles are instead highly uncertain. Therefore, large objects are granted an immunity from quantum laws that is based only on their size.
Consciousness Creates Reality
John Wheeler believes that the collapse can be caused by anything that (aware or unaware) makes a "record" of the observation. An observer is anything in Nature that causes the observation to become public and irreversible. An observer could be a crystal.
Recently, Roger Penrose, inspired by work done initiated by Frenkel Karolyhazy in the 1960s, has invoked gravity to justify that special immunity: in the case of large objects, the space-time curvature affects the system's wave function, causing it to collapse spontaneously into one of the possibilities. Precisely, Penrose believes that different space-time curvatures cannot overlap, because each curvature implies a metric and only one metric can be the metric of the universe at a certain point at a certain time. If two systems engage in some interaction, Nature must choose which metrics prevails. Therefore, he concludes, the coupling of a field with a gravitational field of some strength must cause the wave function of the system to collapse. This kind of self-collapse is called "objective" reduction to distinguish it from the traditional reduction of Quantum Theory which is caused by environmental interaction (such as a measurement). Self-collapse occurs to everything, but the mass of the system determines how quickly it occurs: large bodies self-collapse very quickly, elementary particles would not for millions or even billions of years. That is why the collapse of wave functions for elementary particles in practice occurs only when caused by environmental interaction.
In practice, the collapse of the wave, which is the fundamental way in which Quantum Theory can relate to our perceptions, is still a puzzle, a mathematical accident that still has no definite explanation.
It is not clear to anybody whether this "collapse" corresponds to an actual change in the state of the particle, or whether it just represents a change in the observer's amount of knowledge or what. It is not even clear if "observation" is the only operation that can cause the collapse. And whether it has to be "human" (as in "conscious") observation: does a cat collapse the wave of a particle? Does a rock?
What attributes must an object possess to collapse a wave? Is it something that only humans have? If not, what is the smallest object that can collapse a wave? Can another particle collapse the wave of a particle? (In which case the problem wouldn't exist because each particle's wave would be collapsed by the surrounding particles).
What is the measuring apparatus in Quantum Physics? Is it the platform that supports the experiment? Is it the pushing of a button? Is it a lens in the microscope? Is it the light beam that reaches the eye of the observer? Is it the eye of the observer? Is it the visual process in the mind?
It is also a mystery how Nature knows which of the two systems is the measurement system and which one is the measured system: the one that collapses is the measured one, but the two systems are just systems, and it is not clear how Nature can discriminate the measuring one from the measured one and let only the latter collapse.
If a wave collapses (i.e., a particle assumes well-defined attributes) only when observed by a conscious being, then Quantum Theory seems to specify a privileged role for the mind: the mind enters the world through the gap in Heisenberg's uncertainty principle. Indeed, the mind "must" exist for the universe to exist, otherwise nobody would be there to observe it and therefore the world would only be possibilities that never turn into actualities. Reality is just the content of consciousness, as the Hungarian physicist Eugene Wigner pointed out in 1961. Of course, mind must therefore be an entity that lies outside the realm of Quantum Theory and of Physics in general. The mind must be something special that does not truly belong to "this" world.
Wigner pointed out that to every action there is a reaction: why shouldn’t there be a reaction to a conscious observation of a physical phenomenon? If a phenomenon exerts an influence on my consciousness when I observe it, then my consciousness must exert an influence on the phenomenon. Otherwise the fundamental tenet that to every action there is a reaction is no longer true.
Wigner observed that Schroedinger’s equation is linear, but would stop being linear if its object were the very consciousness that collapses the wave. Therefore, Schroedinger’s equation (which is linear) would result in a non-linear algorithm that may justify the mind’s privileged status.
If the collapse occurs only when observed by a conscious being, if the collapse occurs at the border between mind and matter, as Wigner believes, then the evolution of the universe changed after the appearance of human beings (there was no collapse anywhere before mind appeared).
Undeterred by this objection, the USA physicist John Wheeler believes that ours is a "participatory" universe, one in which consciousness participates in creating reality. The observer and the phenomenon are engaged in a creative act that yields reality. Consciousness does not create reality. Consciousness' role is extremely limited: it can't even choose which of the possibilities contained in the wave function will become reality. It can only "precipitate" reality out of many possibilities. Which possibility becomes reality is up to nature. Nonetheless, Wigner and Wheeler believe that consciousness is crucial to creating reality: as limited as its contribution is, without it there would be no reality, only possibilities. Wheeler even speculated that the rise of consciousness retroactively determined the history of the universe because it collapsed the mother of all waves that had never been collapsed before, thereby fixing every single event in the previous life of the universe.
Quantum theoretical effects could be considered negligible if they only affected particles. Unfortunately, Erwin Schroedinger, with his famous cat experiment, established that Heisenberg's uncertainty affects big objects too. Basically, Schroedinger devised a situation in which a quantum phenomenon causes the cat to die or stay alive. Since any quantum phenomenon is uncertain, the cat's life is also uncertain: until we look at the cat, the cat is neither alive nor dead, but simply a wave of possibilities itself. (A popular objection to Schroedinger’s argument is that the cat can never be in a superimposed state because every big object, by definition, is never isolated, it is always entangled with the rest of its surroundings, and therefore it is "collapsed" all the time).
In the 1940s Richard Feynman offered another interpretation of Quantum Theory: he assumed that all possible states allowed by a wave function exist at any moment. In other words, he took Schroedinger’s equation to the letter. The state that is revealed by measurement is merely the state which represents the "path of least action" for the particle relative to the observer. But the particle is in every place allowed by its wave function. An observation does not reveal reality: an observation is an interaction between the observer and the observed system, and the observation simply reveals that: the interaction between the observer and the observed system. In a sense, the observer "invents" the particle. The particle per se does not exist (or, better, it is merely a field). What exist is a range of values, or, better, a set of ranges of values, which our observations translate into values for attributes of a particle.
The Multiverse: The Quest for Certainty
The traditional (or "Copenhagen") interpretation of Quantum Mechanics seems to be trapped in its unwavering faith in uncertainty. Others have looked for ways out of uncertainty.
One possibility is to deny that the wave function collapses at all. Instead of admitting a random choice of one of many possibilities for the future, one can subscribe to all of the possibilities at the same time. In other words, the probabilistic nature of Quantum Mechanics allows the universe to unfold in an infinite number of ways.
Hugh Everett's "many-universes" interpretation of Quantum Mechanics, originally put forward in 1957, states, basically, that if something physically can happen, it does: in some universe. Everett interpreted quantum "possibilities" as actualities. A particle "is" in many places at the same time: those places are in different universes. Physical reality consists of a collection of universes: the "multiverse". We exist in one copy for each universe and observe all possible outcomes of a situation. It is not only the universe that splits in many universes, it is also the observer that splits in many observers. For a particle there is no wave of possibilities: each possibility is an actuality in one universe. (Alternatively, one can say that there is one observer for each possible outcome of a measurement).
Each measurement splits the universe in many universes (or, as Michael Lockwood puts it, each measurement splits the observer). Biographies form a branching structure, and one which depends on how often they are observed.
No reduction/collapse occurs. The wave function evolves in a deterministic way, just like in Newton's physics.
Naturally, the observer perceives exactly what I am perceiving: a flow of smooth changes.
There is an alternative way to present Everett's ideas. Everett basically accepts that the Schroedinger equation is all there is. The world is described by that equation. We have to take it literally. The particle is in all the states that the equation prescribes. The trick is that the state of the observer is as superposed as that of the observed system. Therefore the observer sees all of the possible states of the observed system. This way the world does not split, but the mind of the observer does. Each mind observes only one state of the many that are possible according to the Schroedinger equation. Therefore each mind perceives a separate world, that is a subset of the world described by the Schroedinger equation. In a sense, each mind views the world from a subjective perspective. The objective state of the world is the one described by the equation, and it corresponds to the superposition of all the states observed by all the minds of the observer.
The British physicist Stephen Hawking is even trying to write down the wave function of the universe, which will actually describe an infinite set of possible universes. Basically, he looks at the universe as if it were one big particle. Just like the wave function of a particle describes an infinite set of possible particles, the wave function of the universe actually describes an infinite set of possible universes.
In Everett's multiverse, Quantum Theory is deterministic and the role of the observer is vastly reduced (we really don't need an observer anymore, since the wave collapses in every single universe, albeit in different ways). Quantum Theory looks more like classical theory, except for the multiplication of universes.
The Immanent Manyverse
Because of the apparent approximation of any quantum theory description of a phenomenon, the Israeli physicist David Deutsch also thinks that our universe cannot possibly constitute the whole of reality, it can only be part of a "multiverse" of parallel universes. But Deutsch's multiverse is not a mere collection of parallel universes, with a single flow of time. He highlights the contradiction of assuming an external, superior time in which all spacetimes flow. This would still be a classical view of the world. Deutsch's manyverse is instead a collection of moments. There is no such a thing as the "flow of time". Each "moment" is a universe of the manyverse. Each moment exists forever, it does not flow from a previous moment to a following one. Time does not flow because time is simply a collection of universes. We exist in multiple versions, in universes called "moments".
Each version of us is indirectly aware of the others because the various universes are linked together by the same physical laws, and causality provides a convenient ordering. But causality is not deterministic in the classical way: it is more like predicting than like causing. If we analyze the pieces of a jigsaw puzzle, we can predict where some of the missing pieces fall. But it would be misleading to say that our analysis of the puzzle "caused" those pieces to be where they are, although it is true that their position is "determined" by the other pieces being where they are.
Furthermore, Deutsch claims that Quantum Theory is not enough to understand reality. He does not adhere to the dominant philosophical stance, that to understand a system is to understand its parts and to have a theory of that system is to have a set of predictions of its future behavior. Deutsch thinks that the predictions are merely the tools to verify if the theory is correct, but what really matters is the "explanation" that the theory provides. Scientific knowledge consists of explanations, not of facts or of predictions of facts. And, contrary to the dominant "reductionist" approach, an explanation that reduces large-scale events to the movement of the smallest possible constituents of matter is not an explanation. As he puts it, why is a specific atom of copper on the nose of the statue of Churchill? Not because the dynamic equations of the universe predict this and that, and not because of the story of that particle, but because Churchill was a famous person, and famous people are rewarded with statues, and statues are built of bronze, and bronze is made of copper.
Scientists who adhere to the reductionist stance believe that the rules governing elementary particles (the base of the reductionist hierarchy) explain everything but they do not provide the kind of answer that we would call "explanation".
So we need four strands of science to understand reality: a theory of matter (quantum theory), a theory of evolution, a theory of knowledge (epistemology), and a theory of computation. The combined theory provides the "explanations" that Deutsch is interested in.
Einselection: Darwinian Collapse
One man who has been studying the problem of how classical Physics emerges from Quantum Physics (how objects that behave deterministically emerge from particles that behave probabilistically, how coherent states of Quantum Mechanics become classical ones) is the Polish-born Wojciech Zurek. He does not believe that consciousness has anything to do with it: it is rather the environment that determines the emergence of reality.
Since 1991, experiments have been performed to show the progressive evolution of a system from quantum to classical behavior. The goal is to observe the progressive collapse of the wave function, the progressive disappearance of quantum weirdness, and the progressive emergence of reality from probability.
Zurek ("Reduction of the Wave Packet", 1984) proposed a different twist to the debate on the "collapse of the wave". It doesn't necessarily take an observer. Zurek thinks that the environment destroys quantum "coherence" (superposition). The environment includes anything that may interact with the quantum system, from a single photon to a microscope. The environment causes "decoherence" (the choice of one or some of the possible outcomes) and decoherence causes selection (or "einselection") of which possibilities will become reality. The "best fit" states turn out to be the classical states. Systems collapse to classical states because classical states are the ones that best "fit" the environment.
The environment causes the collapse of the wave just like an observer. Decoherence occurs to any system that interacts with other systems. Large objects are classical and not quantum objects because they are inherently "decohered" by being a collection of interacting parts. Small objects are isolated to some extent and therefore exhibit quantum behavior.
In the USA, James Anglin, a close associate of Zurek, is studying the evolution of "open quantum systems" far from equilibrium, which resemble Prigogine's studies on open classical systems.
This line of research is, indirectly, establishing intriguing similarities between the emergence of classical systems from quantum systems and the emergence of living systems from non-living systems.
The "consistent histories formulation" of Quantum Theory originated with the USA physicist Robert Griffiths ("Consistent Histories and the Interpretation of Quantum Mechanics", 1984).
The history of a system is a sequence of quantum events (i.e., wave functions). Quantum Theory, according to this interpretation, is simply a tool to calculate the probability of a history.
This only applies to "consistent histories", later renamed "decoherent histories" by Murray Gell-Mann and James Hartle ("Alternative Decohering Histories in Quantum Mechanics", 1990), i.e. to sequences of "questions" about the system that are compatible.
In a sense, this is a theory of which sets of "classical" questions can be consistently asked of a quantum system. Questions that are fundamentally inconsistent are meaningless if asked at the same time.
Histories can be used to calculate the usual probabilities for quantum systems (e.g., a particle) to be measured by a measuring device, but they can also be used to assign probabilities in the absence of any measurement (e.g., to describe a system in outer space).
Another advantage of this approach is that, philosophically speaking, the "collapse" of the wave becomes merely a mathematical procedure for calculating probabilistic correlations rather than an actual physical phenomenon, thus eliminating the special role of the conscious observer.
At any point in time, there can be a whole set of consistent histories for a given system, each corresponding to a particular set of consistent questions.
Thus, quantum uncertainty is still there. In a sense, this is a mirror interpretation of Everett's multi-verse interpretation: many histories for one world, instead of one history of many worlds.
According to Lee Smolin, there is only one universe for everybody, but each observer only has a partial view of it, and therefore produces a different mathematical description of it, and therefore a different quantum theory. This is a relativistic view that recognizes the subjectivity of the observation: each observer sees a different world, or "context", and describes it with a different quantum theory. The catch is that they must all be consistent, i.e. different observers must get the same answer to the same question.
Fotini Markopoulou ("An Insider's Guide To Quantum Causal Histories", 2000) proposed that the "context" is nothing but the past of the observer. The past of an observer at a given time (a relativistic concept) determines the quantum history of the world for that observer (a quantum concept).
Thus Lee Smolin argued that "the universe is made of processes, not things".
In the 1990s another interpretation of quantum mechanics has been put forth by the Austrian physicist Anton Zeilinger.
He set out to find a fundamental principle that would explain the three odd features of the quantum world:
He proposed a very simple principle: each elementary system, called "qubit" (e.g., the spin of the electron), carries one and only one bit of information; two systems carry two and only two bits of information; and so forth.
After all, our physical description of the world is represented by propositions, and each proposition can be true or false, i.e. each elementary system carries one and only one bit of information.
The consequences of this principle are simple to derive:
Zeilinger's interpretation is therefore that only information truly exists and that quantum mechanics is simply a theory of how information behaves in this world.
In the 1990s the Dutch physicist Gerard’t Hooft proposed that Quantum Physics is Classical Physics after an information loss. This is yet another variation on Einstein’s "hidden variables" theory. Hooft noticed that classical variables can take any value, whereas quantum variables can take only some values. Thus, de facto, a classical system gives rise to a quantum system when it loses information. He thinks that this information loss can be due to some "dissipative forces". We know that different starting conditions can lead to the same results because of dissipative forces in the macro-world. For example, if you throw two coins from the top of a skyscraper at different speeds, air friction will cause them to reach the ground at the same speed. The observer will conclude that nature only allows some discrete values for the speed of the coins, when in fact it is air friction that caused them to land at the same speed. Nature is classical at its most fundamental level, but quantum at the level of the laboratory because of "dissipation".
Interpretations of Classical Physics
The fact that Quantum Physics lends itself to many contradicting interpretations has been widely publicized from the very beginning. Less publicized is the fact that Newton’s Physics is no less open to interpretations.
Newton’s greatest invention was the concept of "mass". Ask ten scientists what "mass" is and you will get ten different answers. Mass is at least three things in Newton’s Physics: a measure of resistance to acceleration, a measure of how much an object attracts other objects, and a measure of how much an object is attracted by other objects (laziness, allure and weakness). Whichever of the three you choose, where does it come from? Why do objects have this exoteric quantity of "mass"?
Another fundamental tenet of Newton’s Physics (that actually comes from Galileo) is the notion that objects tend to move in a straight line at constant speed. Aristotle thought that objects tend to stop if they are not pushed. Galileo realized that objects (such as arrows) keep moving even when no force is pushing them. Thus it made sense to assume that objects want to keep moving indefinitely. (Friction and gravity cause them to slow down or bend). This works. But: why do objects have a preference for traveling in a straight line at constant speed? Where does this property come from? Again, this is open to interpretation.
In concluding, it is not surprising at all there are several different interpretations of what Quantum Physics means: there are still, three centuries later, different interpretations of what Newton’s Physics means.
The Physics of Elementary Particles: Close Encounters with Matter
Quantum Theory redrew our picture of nature and started a race to discover the ultimate constituents of matter. This program culminated in formulation of the theories of Quantum Electrodynamics (virtually invented by the British physicist Paul Dirac in 1928 when he published his equation for the electron in an electromagnetic field, which combined Quantum Mechanics and Special Relativity) and Quantum Chromodynamics (virtually invented by the USA physicist Murray Gell-Mann in 1963 when he hypothesized the breakdown of the nucleus into quarks).
It follows from Dirac’s equation that for every particle there is a corresponding anti-particle which has the same mass and opposite electric charge, and, generally speaking, behaves like the particle moving backwards in space and time.
Forces are mediated by discrete packets of energy, commonly represented as virtual particles or "quanta". The quantum of the electromagnetic field (e.g., of light) is the photon: any electromagnetic phenomenon involves the exchange of a number of photons between the particles taking part in it. Photons exchange energy in units of the Planck constant, a very small value, but nonetheless a discrete value.
Other forces are defined by other quanta: the weak force by the W particle, gravitation by the graviton and the nuclear force by gluons.
Particles can, first of all, be divided according to a principle first formulated (in 1925) by the Austrian physicist Wolfgang Pauli: some particles (the "fermions", named after the Italian physicist Enrico Fermi) never occupy the same state at the same time, whereas other particles (the "bosons", named after the Indian physicist Satyendra Bose) do. The wave functions of two fermions can never completely overlap, whereas the wave functions of two bosons can completely overlap (the bosons basically lose their identity and become one).
(Technically, "boson" is the general name for any particle with an angular momentum, or spin, of an integer number, whereas "fermion" is the general name for any particle with a odd half quantum unit of spin).
It turns out (not too surprisingly) that fermions (such as electrons, protons, neutrons) make up the matter of the universe, while bosons (photons, gravitons, gluons) are the virtual particles that glue the fermions together. Bosons therefore represent the forces that act on fermions. They are the quanta of interaction. An interaction is always implemented via the exchange of bosons between fermions.
(There exist particles that are bosons but do not represent interactions, the so called "mesons". Mesons decay very rapidly. No stable meson is known).
Three forces that act on elementary particles have been identified: the electromagnetic, the "weak" and the "strong" forces. Correspondingly, there are bosons that are weak (W and Z particles), strong (the gluons) and electromagnetic (the photon).
Fermions can be classified in several ways. First of all, the neutron and the proton (the particles that made up the nuclei of atoms) are not elementary: they are made of 18 quarks (six quarks, each one coming in three "colors"). Then there are twelve leptons: the electron, the muon, the tau, their three neutrinos and their six anti-particles. A better way to organize Fermions is to divide them in six families, each led by two leptons: the electron goes with the electron's neutrino, the down quark and the up quark. This family makes up most of the matter we know. Another family of Fermions is led by the muon and contains its neutrino and contains two more quarks. The third family contains the tau particle, its neutrino and two more quarks (bottom and top).
Particles made of quarks are called "hadrons" and comprise "baryons" (made of three quarks, and therefore fermions, such as the proton and the neutron) and "mesons" (made of one quark and one antiquark, and therefore bosons).
The electromagnetic force between leptons is generated by the virtual exchange of mass-less particles called "photons". The weak force is due to the W and Z particles (there are two W particles). The "strong" force between quarks (the one that creates protons and neutrons) is generated by the virtual exchange of "gluons". Quarks come in "six" flavors and three "colors". Gluons are sensitive to color, not to flavor. The strong force between protons and neutrons is a direct consequence of the color force.
Leptons do not have color, but have flavor (for example, the electron and its neutrino have different flavors). The "weak" force is actually the flavor force between leptons. W+ and W- are the quanta of this flavor force.
In general, according to Quantum Field Theory, quantum fluctuations cause vibrations that we perceive as attributes of particles: mass, spin, charge, etc. Thus a particle (e.g., an electron) is a vibrational pattern (a pattern of vibrations in a quantum field). Vibrations interact among themselves. When we observe this interaction, we perceive it as particles interacting with each other by exchanging virtual particles (that we interpret as forces, e.g. electromagnetism).
This model explains what we know of matter. It does not explain why there are 4 forces (fields), 18 quarks, six leptons, etc. The numbers seem to be arbitrary.
In particular, it does not explain why particles have the masses they have (rather arbitrary numbers that span ten orders of magnitude, the top quark being about 100,000 times "heavier" than the electron, and more than one trillion times heavier than the electron-neutrino). A field (called the Higgs field, mediated by the Higgs boson, an idea of 1964 by Peter Higgs) is supposed to permeate the universe, and the mass of a particle is supposed to be a measure of the intensity of its interaction with the Higgs field.
Unification: In Search of Symmetry
Since the electric charge also varies with flavor, it can be considered a flavor force as well. Along these lines, in 1967 Steven Weinberg and Abdus Salam unified the weak and the electromagnetic forces into one flavor force (incidentally founding "Quantum Flavor Dynamics", analogous of "Quantum Chromodynamics"), and discovered a third flavor force, mediated by the Z quanta. The unified flavor force therefore admits four quanta: the photon, the W- boson, the W+ boson and the Z boson. These quanta behave like the duals of gluons: they are sensitive to flavor, not to color. All quanta are described by the so called "Yang-Mills field", which is a generalization of the Maxwell field (Maxwell's theory becomes a particular case of Quantum Flavor Dynamics: "Quantum Electrodynamics").
Therefore, the world is made of six leptons, six quarks, four bosons for leptons, and eight gluons for quarks.
Alternatively, leptons and quarks can also be combined in three families of fermions: one comprising the electron, its neutrino and two flavors of quarks ("up" and "down"); one comprising the muon, its neutrino and two flavors of quarks ("strange" and "charmed"); and one comprising the tau lepton ("tauon"), its neutrino and two flavors of quarks ("bottom" and "top"). Plus the three corresponding families of anti-particles. Eight particles per family (each flavor of quark counts as three particles). The grand total is 48 fermions. The bosons are twelve: eight gluons, the photon and the three bosons for the weak interaction. Sixty particles overall.
The profusion of particles is simply comic. Quantum Mechanics has always led to this consequence: in order to explain matter, a multitude of hitherto unknown entities is first postulated and then "observed" (actually, verified consistent with the theory). More and more entities are necessary to explain all phenomena that occur in the laboratory. When the theory becomes a self-parody, a new scheme is proposed whereby those entities can be decomposed in smaller units. So physicists are already, silently, seeking evidence that leptons and quarks are not really elementary, but made of a smaller number of particles. It is easy to predict that they will eventually break the quark and the electron, and start all over again.
Several other characteristics look bizarre. For example, the three families of fermions are very similar: what need did Nature have to create three almost identical families of particles?
The spins of these particles is totally arbitrary. Fermions have spin 1/2 and bosons have integral spin. Why?
The whole set of equations for these particles has 19 arbitrary constants. Why?
Gluons are fundamentally different from photons: photons are intermediaries of the electromagnetic force but do not themselves carry an electric charge, whereas gluons are intermediaries of the color force that do carry themselves a color (and therefore interact among themselves). Why?
Also, because color comes in three varieties, there are many gluons, while there is only one photon. As a result, the color force behaves in a fundamentally different way from the electromagnetic force. In particular, it extends to infinite. The electromagnetic force gets weaker as the distance increases, while the color force rises to a constant value that does not change as the quarks are pulled apart. That confines quarks inside protons and neutrons. Why?
Also, the symmetry of the electroweak force (whereby the photon and the bosons get transformed among themselves) is not exact as in the case of Relativity (where time and space coordinates transform among themselves): the photon is mass-less, whereas bosons have masses. Only at extremely high temperatures the symmetry is exact. At lower temperatures a spontaneous breakdown of symmetry occurs.
This seems to be a general caprice of nature. At different temperatures symmetry breaks down: ferromagnetism, isotropic liquids, the electroweak force... A change in temperature can create new properties for matter: it creates magnetism for metals, it creates orientation for a crystal, it creates masses for bosons.
The fundamental forces exhibit striking similarities when their bosons are mass-less. The three families of particles, in particular, acquire identical properties. This leads scientists to believe that the "natural" way of being for bosons in a remote past was mass-less. How did they acquire the mass we observe today in our world? And why do they all have different masses? The Higgs mechanism gives fermions and bosons a mass. Naturally it requires bosons of its own, the Higgs bosons (particles of spin 0).
Each interaction exhibits a form of symmetry, but unfortunately they are all different, as exemplified by the fact that quarks cannot turn into leptons. In the case of the weak force, particles (e.g., the electron and its neutrino) can be interchanged, while leaving the overall equations unchanged, according to a transformation called SU(2), meaning that one particle can be exchanged for another one. For the strong force (i.e., the quarks) the symmetrical transformation is SU(3), meaning that three particles can be shuffled around. For the electromagnetic force, it is U(1), meaning that only the electrical and magnetic component of the field can be exchanged for each other. Any attempt to find a symmetry of a higher order results into the creation of new particles. SU(5), for example, entails the existence of 24 bosons... but it does allow quarks and leptons to mutate into each other (five at the time), albeit at terribly high temperatures.
Finally, Quantum Theory does not incorporate gravity. Since gravity is an interaction (albeit only visible among large bodies), it does require its own quantum of interaction, the so called "graviton" (a boson of spin 2). Once gravity is quantized, one can compute the probability of a particle interacting with the gravitational field: the result is... infinite.
The difficulty of quantizing gravity is due to its self-referential (i.e., non-linear) nature: gravity alters the geometry of space and time, and that alteration in turns affects the behavior of gravity.
The fundamental differences between Quantum Theory and General Relativity can also be seen topologically: the universe of Relativity is curved and continuous; the universe of Quantum Theory is flat and granular. Relativity prescribes that matter warps the continuum of spacetime, which in turns affects the motion of matter. Quantum Theory prescribes that matter interacts via quanta of energy in a flat spacetime. (Even finding a common vocabulary is difficult!) The bridge between the two views would be to "quantize" spacetime, the relativistic intermediary between matter and matter: then the two formulations would be identical. If spacetime warping could be expressed in terms of quanta of energy, then the two prescriptions would be the same.
The truth is that Quantum Theory had reached an impasse. There seems to be no way that (General) Relativity can be modified to fit Quantum Mechanics.
Superstring Theory: Higher Dimensions
Countless approaches have been proposed to integrate the quantum and the (general) relativistic views of the world.
The two theories are obviously very different and the excuse that they operate at different "granularity" levels of nature (Quantum Theory being for the very small and Relativity Theory being for the very big) is not very credible.
Physicists have been looking for a theory that explains both, a theory of which both would be special cases. Unfortunately, applying Quantum Theory to Relativity Theory has proved unrealistic.
The problem is that they are founded on different "metaphors" of the world. Relativity Theory binds together space-time and matter. Quantum Theory binds together matter and the observer (an observer who is supposed to verify the consequences of binding together matter and the observer who is supposed to...).
Relativity focuses on how the gravity of massive bodies bends the structure of time and space and are in turn influenced in their motion by the curvature of space-time. Quantum Theory focuses on the fuzziness in the life of elementary particles.
If one simply feeds Schroedinger's equation (how the world evolves according to Quantum Theory) into Einstein's equation (how the world evolves according to Relativity Theory) the resulting equation appears to be meaningless.
Basically, we don’t have a Physics that holds in places where both gravity and quantum effects are crucial, like at the centers of black holes or during the first moments of the Big Bang.
General Relativity explains motion. Einstein’s equations are precise. Quantum Theory explains that motion is undefined. Heisenberg’s principle is fuzzy.
General Relativity shows that time is relative. Quantum Theory assumes a universal watch setting the pace for the universe. "Time" looks completely different in one theory and in the other, almost as if the two theories used the term "time" to refer to two different things.
Ditto for the "observer": Einstein’s observer is part of the universe and in fact is affected by the universe, whereas Quantum Theory’s observer has a special status that exempts her from quantum laws (the quantum universe is divided into particles that are measured and "observers" who make measurements).
A route to merging Quantum Theory and Relativity Theory is to start with Relativity and see if Quantum Theory can be found as a special case of Einstein's equations.
In 1919, the German physicist Theodor Kaluza discovered that electromagnetism arises if a fifth dimension is added to Einstein's four-dimensional spacetime continuum: by re-writing Einstein's field equations in five dimensions, Kaluza obtained a theory that contained both Einstein's General Relativity (i.e., the theory of gravitation) and Maxwell's theory of electromagnetism. Kaluza thought that light's privileged status came from the fact that light is a curling of the fourth spatial dimension.
Basically, it was an extension of Einstein’s fundamental intuition: gravitation is due to the geometry of a four-dimensional space-time. Kaluza realized that one only has to add a fifth dimension in order to obtain the same statement for electromagnetism: electromagnetism is due to the geometry of a five-dimensional space-time. A theory of gravitation in five dimensions yields both a theory of gravitation and a theory of electromagnetism in four dimensions.
The price to pay is that the fifth dimension behaves in a weird way. The Swedish mathematician Oskar Klein explained how the fifth dimension might be curled up in a loop the size of the "Planck length" (the shortest length that Quantum Physics can deal with). The universe may have five dimensions, except that one is not infinite but closed in on itself. In the 1960s, the USA physicist Bryce DeWitt and others proved that a Kaluza theory in higher dimensions is even more intriguing: when the fifth and higher dimensions are curled up, the theory yields the Yang-Mills fields required by Quantum Mechanics.
The Kaluza-Klein theory made a fundamental assumption: the physical world as we know it, and in particular its fundamental forces, originate from the geometry of hidden dimensions. The fundamental forces appear to be "forces" only in a four-dimensional subset of the universe. They are actually just geometry.
It was this approach that in 1974 led the USA physicist John Schwarz to formulate Superstring Theory. His early studies had been triggered by a formula discovered in 1968 by the Italian physicist Gabriel Veneziano and its interpretation as a vibrating string by the Japanese physicist Yoichiro Nambu. Schwarz quickly realized that both the standard model for elementary particles and General Relativity’s theory of gravitation were implied by Superstring Theory.
Superstring Theory views particles as one-dimensional entities (or "strings") rather than points: tiny loops of the magnitude of the Planck length. Particles are simply "resonances" (or modes of vibrations) of tiny strings. In other words, all there is vibrating strings and each particle is due to a particular mode of vibration of the string. Each vibrational mode has a fixed energy, which means a mass, charge and so forth. Thus the illusion of a particle. All matter consists of these tiny vibrating strings. The key point is that one of these vibrational modes is the "graviton", the particle that accounts for gravitation: Superstring theory is a Quantum Theory that predicts the existence of General Relativity’s gravitation.
The behavior of our universe is largely defined by three universal constants: the speed of light, the Planck constant and the gravitational constant. The "Planck mass" is a combination of those three magic numbers and is the mass (or energy) at which the superstring effects would be visible. Unfortunately, this is much higher than the mass of any of the known particles. Such energies were available only in the early stages of the universe and for a fraction of a second. The particles that have been observed in the laboratory are only those that require small energies. A full appreciation of Superstring Theory would require enormous energies. Basically, Superstring Theory is the first scientific theory that states the practical impossibility of being verified experimentally (at least during the lifetime of its inventors).
Furthermore, the superstring equations yield many approximate solutions, each one providing a list of mass-less particles. This can be interpreted as allowing a number of different universes: ours is one particular solution, and that solution will yield the particles we are accustomed with. Even the number of dimensions would be an effect of that particular solution.
There is, potentially, an infinite number of particles. Before the symmetry breaks down, each fermion has its own boson, which has exactly the same mass. So a "photino" is postulated for a "photon" and a "s-electron" for the electron.
Space-time must have ten dimensions. Six of them are curved in minuscule tubes that are negligible for most uses. Matter originated when those six dimensions of space collapsed into superstrings. Ultimately, elementary particles are "compactified" hyper-dimensional space.
Einstein's dream was to explain matter-energy the same way he explained gravity: as fluctuations in the geometry of space-time. The "heterotic" variation of Superstring Theory, advanced by the USA physicist David Gross and others in the 1980s, does just that: particles emerge from geometry, just like gravity and the other forces of nature. The heterotic string is a closed string that vibrates (at the same time) clockwise in a ten-dimensional space and counterclockwise in a 26-dimensional space (16 dimensions of which are compactified).
Einstein's General Theory of Relativity is implied by Superstring Theory, to the point that another USA physicist, Edward Witten, has written that Relativity Theory was discovered first by mere accident. Incidentally, the same Witten, in 1985, has provided the most complete "field string theory".
In the meantime Superstring Theory has progressed towards a peculiar form of duality. In 1977 a Finnish and a British physicists, Claus Montonen and David Olive, proposed that there may exist a dual Physics which deals with "solitons" instead of "particles". In that Physics, magnetic monopoles are the elementary units, and particles emerge as solitons, knots in fields that cannot be smoothed out (in our conventional Physics, magnetic monopoles are solitons of particles). Each particle corresponds to a soliton, and viceversa. They proved that it would not matter which Physics one chooses to follow: all results would automatically apply to the dual one.
In particular, one could think of solitons are aggregates of quarks (as originally done in 1974 by the Dutch physicist Gerard't Hooft). Then a theory of solitons can be built on top of a theory of quarks, or a theory of quarks can be built on top of a theory of solitons.
In 1996 the USA physicist Andrew Strominger has even found a connection between black holes and strings: if the original mass of the black hole was made of strings, the Hawking radiation (see later) would ultimately drain the black hole and leave a "thing" of zero size, i.e. a particle. Since a particle is ultimately a string, the cycle could theoretically resume: black holes decaying into strings and strings decaying into black holes.
Superstring Theory is the only scientific theory of all times that requires the universe to have a specific number of dimensions: but why ten?
Physicists like Peter Freund, a Romanian native, and Michio Kaku have observed that the laws of nature become simpler in higher dimensions. The perceptual system of humans can only grasp three dimensions, but at that level the world looks terribly complicated. The moment we move to a fourth dimension, we can unify phenomena that looked very different. As we keep moving up to higher and higher dimensions, we can unify more and more theories. This is precisely how Einstein unified Mechanics and Electromagnetism (by introducing a fourth dimension), how quantum scientists unified electromagnetism with the weak and strong nuclear forces and how particle physicists are now trying to unify these forces with gravity.
Still: why ten?
Are there more phenomena around that we still have to discover and that, once unified with the existing scientific theories, will yield even more dimensions? Are these dimensions just artifices of the Mathematics that has been employed in the calculations, or are they real dimensions that may have been accessible in older times?
And why mono-dimensional strings, and not multidimensional objects? Paul Dirac, way back in 1962, had thought that the electron could be a bubble, which is a membrane closed in on itself.
One important implication of superstring theory is that the "constants" of nature are fields, and can therefore change in time and in space. The "dilaton" is the field of all fields, that determines the strength of all interactions.
Another important implication is that our universe might not be all that there is. The electron uses only three of the available dimensions (the so called "Dirichlet membrane" or "D-brane"), and our universe may simply be confined to those three dimensions, but the other dimensions might be "filled" with something else.
The problem with superstring theory is that, quite simply, there are too many superstring theories (at least five), each of them perfectly valid. M-theory (originating from an idea of Edward Witten in 1995) is the theory of all possible superstring theories. M-theory can also be viewed as an eleven-dimensional theory of ten-dimensional theories.
M-theory does not constrain the universe to be the one we observe: a staggering to the 500th power different kinds of universe are technically possible, each with its own laws of nature. The USA physicist Leonard Susskind actually thinks that all those universes do exist: anything that can exist, does exist. Our universe is merely one item in the "megaverse."
Penrose also agrees that the right approach to the integration of Quantum Theory and Relativity Theory is not to be concerned about the effects of the former on the latter but viceversa.
Penrose (like everyone else) is puzzled by the two different, and incompatible, quantum interpretations of the world. One is due to Schroedinger's equation, which describes how a wave function evolves in time. This interpretation is deterministic and provides a continuous history of the world. The other is due to the collapse of the wave function in the face of a measurement, which entails determining probabilities of possible outcomes from the squared moduli of amplitudes in the wave function ("state-vector reduction"). This interpretation is probabilistic and provides a discontinuous history of the world, because the system suddenly jumps into a new state. We can use Schroedinger's equation to determine what is happening at any point in time; but, the moment we try to actually measure a quantity, we must resort to state-vector reduction in order to know what has happened.
Penrose postulates that these two incompatible views must be reconciled at a higher level if abstraction by a new theory, and such a theory must be based on Relativity Theory. Such a theory, which he calls "quantum gravity", would also rid Physics of the numerous infinites that plague it today. It should also be time-asymmetrical, predicting a privileged direction in time, just like the second law of Thermodynamics does. Finally, in order to preserve free will, it would contain a non-algorithmic element, which means that the future would not be computable from the present. Penrose even believes that Quantum Gravity will explain consciousness.
The Trail of Asymmetry
Somehow asymmetry seems to play a protagonist role in the history of our universe and our life. Current cosmological models speculate that the four fundamental forces of nature arose when symmetry broke down after the very high temperatures of the early universe began to cool down. Today, we live in a universe that is the child of that momentous split. Without that "broken symmetry" there would be no electrical force and no nuclear force, and our universe would be vastly impoverished in natural phenomena.
Scientists have also speculated at length about the asymmetry between matter and antimatter: if one is the mirror image of the other and no known physical process shows a preference for either, why is it that in our universe protons and electrons (matter) overwhelmingly prevails over positrons and antiprotons (antimatter)?
Most physical laws can be reversed in time, at least on paper. But most will not. Time presents another asymmetry, the "arrow of time" which points always in the same direction, no matter what is allowed by Mathematics. The universe, history and life all proceed forward and never backwards.
Possibly related to it is the other great asymmetry: entropy. One can't unscramble an egg. A lump of sugar which is dissolved in a cup of coffee cannot become a lump of sugar again. Left to themselves, buildings collapse, they do not improve. Most artifacts require periodic maintenance, otherwise they would decay. Disorder is continuously accumulated. Some processes are irreversible.
It turns out that entropy is a key factor in enabling life (and, of course, in ending it). Living organisms maintain themselves far from equilibrium and entropy plays a role in it.
Moreover, in 1848 the French biologist Louis Pasteur discovered that aminoacids (which make up proteins which make up living organisms) exhibit another singular asymmetry: for every aminoacid there exist in nature its mirror image, but life on Earth uses only one form of the aminoacids (left-handed ones). Pasteur’s mystery is still unexplained (Pasteur thought that somehow that "was" the definition of life). Later, biologists would discover that bodies only use right-handed sugars, thereby confirming that homochirality (the property of being single-handed) is an essential property of life.
Finally, an asymmetry presents itself even in the site of thinking itself, in the human brain. The two cerebral hemispheres are rather symmetric in all species except ours. Other mammals do not show preferences for grasping food with one or the other paw. We do. Most of us are right-handed and those who are not are left-handed. Asymmetry seems to be a fundamental feature of our brain. The left hemisphere is primarily used for language and the interplay between the two hemispheres seems to be important for consciousness.
It may turn out to be a mere coincidence, but the most conscious creatures of our planet have also the most asymmetric brains.
Was there also a unified brain at the origin of thinking, whose symmetry broke down later on in the evolutionary path?
A Fuzzy World
Modern physics relies heavily on Quantum Mechanics. Quantum Mechanics relies heavily on the theory of probabilities. At the time, probabilities just happened to fit well in the model.
Quantum Mechanics was built on probabilities because the theory of probabilities is what was available in those times. Quantum Mechanics was built that way not because Nature is that way, but because the mathematical tools available at the time were that way; just like Newton used Euclid's' geometry because that is what Geometry could provide at the time.
Boltzmann's stochastic theories had showed that the behavior of gases (which are large aggregates of molecules) could be predicted by a dynamics which ignored the precise behavior of individuals, and took into account only the average behavior. In retrospect Boltzmann's influence was enormous on Quantum Mechanics. His simplification was tempting: forget about the individual, focus on the population.
Quantum Mechanics therefore prescribed a "population" approach to Nature: take so many electrons, and some will do something and some will do something else. No prescription is possible about a single electron. Quantum phenomena specify not what a single particle does, but what a set of particles do. Out of so many particles that hit a target, a few will pass through, a few will bounce back. And this can be expressed probabilistically.
Today, alternatives to probabilities do exist. In particular, Fuzzy Logic can represent uncertainty in a more natural way (things are not black or white, but both black and white, to some extent). Fuzzy Logic is largely equivalent to Probability Theory, but it differs in that it describes single individuals, not populations.
On paper, Quantum Mechanics could thus be rewritten with Fuzzy Logic (instead of probabilities) without altering any of its conclusions. What would change is the interpretation: instead of a theory about "set of individuals" (or populations) it would become a theory about "fuzzy individuals". In a Fuzzy Logic scenario, a specific particle hitting a potential barrier would both go through and bounce back. To some extent. It is not that out of a population some individuals do this and some individuals do that; a specific individual is both doing this and doing that. The world would still behave in a rather bizarre way, but somehow we would be able to make statements about individuals. However, this approach would allow Physics to return to a science of individual objects, not of populations of objects.
The uncertainty principle could change quite dramatically: instead of stating that we can never observe all the parameters of a particle with absolute certainty, it could state that we can observe all the parameters of a particle with absolute certainty, but certainty not being exact. When I say that mine is a good book, I am being very certain. I am not being exact (what does "good" mean? How good is good? Etc).
The fact that a single particle can be in different, mutually exclusive states at the same time has broad implications on the way our mind categorizes "mutually exclusive" states; not on what Nature actually does. Nature never constrained things to be either small or big. Our mind did. Any scientific theory we develop is first and foremost a "discourse" on Nature; i.e., a representation in our mind of what Nature is and does.
Some of the limits we see in Nature (i.e., the fact that something is either big or small) are limits of our mind; and conversely some of the perfection that we see in Nature is the perfection of our mind (i.e., the fact that there is a color white or something is cold or a stone is round, while in Nature no object is fully white, cold or round). Fuzzy Logic is probably a better compromise between our mind and Nature, because it allows us to express the fact that things are not just zero or one, white or black, cold or warm, round or square; they are "in between", both white and black, both cold and warm, both...
On closer inspection, the main subject of Thermodynamics, Relativity and Quantum theories may well be Time. Most of the bizarre implications of those theories are things that either happen "in time" or are caused by Time.
Boltzmann interpreted the second law of Thermodynamics (that entropy can never decrease) as basically a definition of time, and, de facto, an unmasking of "time" as an illusion of being alive in a particular time and place. Boltzmann reasoned that the illusion of time is due to the processes of change that we observe. Those processes (especially the most visible ones, such as decay) are driven by the second law of Thermodynamics, which he had proved to be a statistical law of transition from less probable states to more probable states. Thus a living being "feels" the flow of time only because it lives in a world that is transitioning from a less probable state to a more probable state. If life is possible in states of absolute equilibrium, then those living beings would not perceive any flow of time.
Relativity turned Time into one of several dimensions, mildly different from the others but basically very similar to the others. This clearly contrasts with our perception of Time as being utterly distinct from space. Hawking, for example, thinks that originally Time was just a fourth spatial dimension, then gradually turned into a different type of dimension and, at the Big Bang, it became Time as we know it today.
The mathematician Hermann Bondi has argued that the roles of Time are utterly different in a deterministic and in a non-deterministic universe. Whereas in a deterministic universe, Time is a mere coordinate, in a universe characterized by indeterminacy, such as one governed by Quantum Theory, the passage of time transforms probabilities into actualities, possibility into reality. If Time did not flow, nothing would ever be. Things would be trapped in the limbo of wave functions.
The Australian physicist Paul Davies claims exactly the opposite: Time is rather meaningless in the context of a quantum model of the universe, because a general quantum state of the universe has no well-defined time. With Hawking, Time may not have existed before the Big Bang, and may have originated afterwards by mere accident.
The subject of Time has puzzled and fascinated philosophers since the dawn of consciousness. What is Time made of? What is the matter of Time? Is Time a human invention?
There is no doubt that physical Time does not reflect psychological Time. Time, as we know it, is subjective and relative. There is a feeling to the flow of time that no equation of Physics can reproduce. Somehow, the riddle of Time reminds us of the riddle of consciousness: we know what it is, we can feel it very clearly, but we cannot express it, and we don't know where it comes from.
If you think that there is absolute time, think again. Yes, all clocks display the same time. But what makes you think that what they display is Time? As an example, let's go back to the age when clocks had not been invented yet: time was defined by the motion of the sun. People knew that a day is a day because the sun takes a day to turn around the Earth (that's what they thought). And a day was a day everywhere on the Earth, even among people who had never communicated to each other. Is that absolute Time?
What would happen if the Sun all of a sudden slowed down? People all over the planet would still think that a day is a day. Their unit of measurement would be different. They would be measuring something else, without knowing it. What would happen today if a galactic wave made all clocks slow down? We would still think that ten seconds are ten seconds. But the "new" ten seconds would not be what ten seconds used to be. So clocks do not measure Time, they just measure themselves. We take a motion that is the same all over the planet and use that to define something that we never really found in nature: Time.
At the least, we can say that measurement of Time is not innate: we need a clock to tell "how long it took".
Unfortunately, human civilization is founded on Time. Science, the Arts and technology are based on the concept of Time. What we have is two flavors of Time: psychological time, which is a concrete quantity that the brain creates and associates to each memory; and physical time, an abstract quantity that is used in scientific formulas for the purpose of describing properties of matter.
The latter was largely an invention of Isaac Newton, who built his laws of nature on the assumption of an absolute, universal, linear, continuous Time. Past is past for everybody, and future is future for everybody.
Einstein explained that somebody's past may be somebody else's present or even future, and thereby proved that time is not absolute and not universal. Any partitioning of space-time into space and time is perfectly legal. The only requirement on the time component is that events can be ordered in time. Time is pretty much reduced to a convention to order events, and one way of ordering is as good as any other way.
In the meantime, the second law of Thermodynamics had for the first time established formally the arrow of time that we are very familiar with, the flowing from past to future and not viceversa.
Once the very essence of Time had been doubted, scientists began to doubt even its existence.
The British physicists Arthur Milne and Paul Dirac are two of the scientists who have wondered if the shaky character of modern Physics may be due to the fact that there are two different types of time and that we tend to confuse them. Both maintained that atomic time and astronomical time may be out of sync. In other words, the speeds of planets slowly change all the time in terms of atomic time, although they remain the same in terms of astronomical time. A day on Earth is a day regardless of the speed of the Earth, but it may be lasting less and less according to an atomic clock. In particular, the age of the universe may have been vastly exaggerated because it is measured in astronomical time and astronomical processes were greatly speeded up in the early stages of the universe.
Not to leave anything untried, the USA physicist Richard Feynman even argued in favor of matter traveling backwards in time: an electron that turns into a positron (its anti-particle) is simply an electron that turns back in time. His teacher John Wheeler even argued that maybe all electrons are just one electron, bouncing back and forth in time; and so all other particles. There is only one instance of each particle. That would also explain why all electrons are identical: they are all the same particle.
Einstein proved that Time is not absolute and said something about how we experience time in different ways depending on how we are moving. But he hardly explained what Time is. And nobody else ever has.
The British physicist Julian Barbour believes that Time does not exist, and that most of Physics' troubles arise from assuming that it does exist. We have no evidence of the past other than our memory of it. We have no evidence of the future other than our belief in it. Barbour believes that it is all an illusion: there is no motion and no change. Instants and periods do not exist. What exists is only "time capsules", which are static containers of "records". Those records fool us into believing that things change and events happen. There exists a "configuration space" that contains all possible instants, all possible "nows". This is "Platonia." We experience a set of these instants, i.e. a subset of Platonia. Barbour is inspired by Leibniz' theory that the universe is not a container of objects, but a collection of entities that are both space and matter. The universe does not contain things, it "is" things.
Barbour does not answer the best part of the puzzle: who is deciding which "path" we follow in Platonia? Who is ordering the instants of Platonia? Barbour simply points to quantum mechanics, that prescribes we should always be in the "instant" that is most likely. We experience an ordered flow of events because that is what we were designed for: to interpret the sequence of most likely instants as an ordered flow of events.
Barbour also offers a solution to integrating relativity and quantum mechanics: remove time from a quantum description of gravity. Remove time from the equations. In his opinion, time is precisely the reason why it has proved so difficult to integrate relativity and quantum theories.
In classical and quantum Physics, equations are invariant with respect to time inversion. Future and past are equivalent. Time is only slightly different from space. Time is therefore a mere geometrical parameter. Because of this, Physics offers a static view of the universe. The second law of Thermodynamics made official what was already obvious: that many phenomena are not reversible, that time is not merely a coordinate in space-time.
In the 1970's Prigogine showed, using Boltzmann's theorem and thermodynamic concepts, that irreversibility is the manifestation at macroscopic level of randomness at microscopic level.
Prigogine then attempted a microscopic formulation of the irreversibility of laws of nature. He associates macroscopic entropy with a microscopic entropy operator. Time too becomes an operator, no longer a mere parameter. Once both time and entropy have become operators, Physics has been turned upside down: instead of having a basic theory expressed in terms of wave functions (i.e., of individual trajectories), he obtains a basic theory in terms of distribution functions (i.e., bundles of trajectories). Time itself depends on the distribution and therefore becomes itself a stochastic quantity, just like entropy, an average over individual times. As a consequence, just like entropy cannot be reversed, time cannot: the future cannot be predicted from the past anymore.
Traditionally, physical space is geometrical, biological space (the space in which biological form develops) is functional (for example, physical time is invariant with respect to rotations and translations, biological space is not). Prigogine's Time aims at unifying physical and biological phenomena.
Black Holes and Wormholes: Gateways to Other Universes and Time Travel
By definition, all information about the matter that fell into a black hole is lost forever: a black hole may have been generated by any initial configuration of matter, but there is no record of which one it was. In 1974 the British physicist Stephen Hawking proved that black holes evaporate, therefore information is not only trapped inside the black hole: it truly disappears forever. (The time it will take for a black hole to evaporate is proportional to the cube of its mass).
Hawking’s study was particularly relevant because it was the first major attempt to integrate Relativity, Quantum Theory and Thermodynamics.
The disappearance of matter, energy and information in a black hole has puzzled physicists since the beginning, as it obviously violates the strongest principle of conservation that our Physics is built upon. It also highlights the contradictions between Quantum Theory and Relativity Theory: the former guarantees that information is never lost, the latter predicts that it will be lost in a black hole.
Einstein himself realized that black holes implied the existence of a "bridge" between our universe and a mirror universe which is hidden inside the black hole, and in which Time runs backwards. It was the Austrian mathematician Kurt Goedel, the same individual who had just single-handedly shattered the edifice of Mathematics, who, in 1949, pointed out how Einstein's equations applied to a rotating universe implied that space-time can curve to the point that a particle will return to a previous point in time; in other words, "wormholes" exist connecting two different points in time of the same universe. In the 1950s, John Wheeler speculated that two points in space can be connected through several different routes, because of the existence of spatial wormholes. Such wormholes could act like shortcuts, so that travel between the two points can occur even faster than the speed of light.
The New Zealand mathematician Roy Kerr in 1963 and the USA physicist Frank Tipler in 1974 found other situations in which wormholes were admissible. In the U.S., Kip Thorne even designed a time machine capable of exploiting such time wormholes. In the U.K., Stephen Hawking came up with the idea of wormholes connecting different universes altogether. Hawking's wave function allows the existence of an infinite set of universes, some more likely than others, and wormholes the size of the Planck length connect all these parallel universes with each other.
The History of the Universe
One of the consequences of General Relativity is that it prescribes the evolution of the universe. A few possible futures are possible, depending on how some parameters are chosen. These cosmological models regard the universe as one system with macroscopic quantities. Since the discovery that the universe is expanding in all directions (by the British physicist Edwin Hubble in 1929), the most popular models have been the ones that predict expansion of space-time from an initial singularity, the "Big Bang" (first speculated by the Belgian physicist Georges Lemaitre in 1927). Since a singularity is infinitely small, any cosmological model that wants to start from the very beginning must combine Relativity and Quantum Physics.
The story usually starts with an infinitely small universe (Roger Penrose and Stephen Hawking have proved that Relativity implies this), in which quantum fluctuations of the type predicted by Heisenberg's principle are not negligible, especially when the universe was a size smaller than the Planck length.
The fluctuations actually "created" the universe (space, time and matter) in a "Big Bang". Time slowly turned into space-time, giving rise to spatial dimensions. Space-time started expanding, the expansion that we still observe today. In a sense, there was no beginning of the universe: the "birth" of the universe is an illusion. There is no need to create the universe, because its creation is part of the universe itself. There is no real origin. The universe is self-contained, it does not require anything external to start it.
Then the universe expanded. If the mass of the universe is big enough (and this is still being debated, but most cosmologists seem to believe so), then at some point the expansion will peak and it will reverse: the universe will contract all the way back into another singularity (the "Big Crunch"). At that point the same initial argument holds, which is likely to start another universe. For example, John Wheeler claims that the universe oscillates back and forth between a Big Bang and a Big Crunch. Each time the universe re-starts with randomly assigned values of the physical constants and laws.
Both the beginning and the end are singularities, which means that the laws of Physics break down. The new universe can have no memory of the old universe, except for a higher entropy (assuming that at least that law is conserved through all these singularities), which implies a longer cycle of expansion and contraction (according to Richard Tolman's calculations).
Some scientists believe that they can remove the singularities. In particular, Hawking has proposed a model in which Time is unbounded but finite, and therefore it is not created in the Big Bang even if the universe today has a finite age. (According to Einstein, space is also finite yet unbounded). In his model, Time emerges gradually from space and there is no first moment.
The real conundrum for cosmologists, however, is to find the missing matter: most of the matter required for the universe to be the way it is (to account for the gravity that holds together the galaxies the way they are held together) has never been observed. Physicists are searching for "dark matter" (perhaps 25% of the mass-energy of the universe) that does not interact with ordinary matter, does not emit and does not reflect light (but whose gravitational effect has been inferred by observing the motion of galaxies), as well as for "dark energy" (energy that is not associated with particles), that could account for 71% of the mass-energy of the universe (the mass-energy needed to account for the acceleration of the expansion of the universe that was discovered in 1998 by Adam Riess). Whatever the reason, more than 90% of the mass-energy of the universe has not been found. Today’s Physics is really a scientific theory about the mere 5% of mass-energy that we can account for.
Note that Einstein’s cosmological constant would play the same "repulsive" role as the "dark energy".
The Creation Of Information
The universe before the Big Bang was in a state of equilibrium. That means minimal information and minimal order. That means maximum entropy. Today it is in a state of non-equilibrium, which implies that entropy declined, which contradicts the second law of Thermodynamics. The solution of the apparent paradox is gravitation: gravitation causes the creation of order (and therefore information).
Gravitation also solves the other puzzle: where did the initial energy come from? It turns out that gravitation behaves like negative energy that equals the positive energy that has created all matter: the two together yield zero energy. There is no need for an initial source of energy to start the Big Bang.
One oddity still remains: the effect of creating the universe does have a visible effect, and that is the many ordered structures that we see in the sky. In other words, the creation of the universe has created an entropy gap. Information has been created that was not there. Where did it come from?
The End of Entropy
Very few people are willing to take the second law of Thermodynamics as a primitive law of the universe. Explicitly or implicitly, we don't seem happy with this law that states an inequality. Somehow it must be a side effect of some other phenomenon.
Thomas Gold (among others) believes that the second law follows the direction of the universe: entropy increases when the universe expands, it decreases when the universe contracts (or, equivalently, when Time flows backwards). The second law would simply be an effect of the expansion or contraction. In that case the universe might be cyclic.
Roger Penrose has also investigated the mystery of entropy. A gravitational effect results in two dual phenomena: a change in shape and a change in volume of space-time. Consequently, Penrose separates the curvature tensor in two components: the Ricci tensor (named after the Italian mathematician Gregorio Ricci who founded the theory of tensors) and the Weyl tensor (named after the German mathematician Hermann Weyl, a close associate of Einstein's). The Weyl tensor measures the change in shape, and, in a sense, the gravitational field, whereas the Ricci tensor measures the change in volume, and, in a sense, the density of matter. The Weyl tensor measures a "tidal" effect and the Ricci tensor measures an effect of volume reduction. The Ricci tensor is zero in empty space, it is infinite in a singularity. The Weyl tensor is zero in the initial singularity of the Big Bang, but infinite at the final singularity of the Big Crunch. Penrose has showed that entropy follows the Weyl tensor and the Weyl tensor may hide the puzzling origin of the second law of Thermodynamics.
The Resurrection of Information
The curvature in proximity of a black hole is infinite: all objects are doomed. There is a distance from the black hole which is the last point where an object can still escape the fall: the set of those points defines the horizon of the black hole.
In 1974 Stephen Hawking discovered that black holes may evaporate and eventually vanish. The "Hawking radiation" that remains has lost all information about the black hole. This violates the assumption of determinism in the evolution of the universe, i.e. that, if we know the present, we can always derive the past, because the present universe contains all information about how the past universe was.
Only two options have been found to allow for the conservation of information. The first one is to allow for information to travel faster than light. That would allow it to escape the black hole. But it would violate the law of causality (that nothing can travel faster than light).
The second option is that a vanishing black hole may leave behind a remnant the size of the Planck length. Andrew Strominger has argued for the latter option. This option calls for an infinite number of new particles, as each black hole is different and would decay into a different particle. Strominger believes that such particles are extreme warps of space-time, "cornucopions", that can store huge amount of information even if they appear very small to an outside observer and their information would not be accessible.
After all, in 1972 the Israeli physicist Jacob Bekenstein proved that the entropy of a black hole is proportional to its surface (or, better, the surface area of its event horizon), which means that entropy should decrease constantly during the collapse of the black hole, which means that information must somehow increase, and not disappear.
Note that a consequence of Bekenstein’s theorem is that a black hole can hold only a finite amount of information, because its horizon is finite, and therefore its entropy is finite, and its entropy is a measure of the missing information. In fact Bekenstein proved that there is also a maximum amount of information that can possibly be hidden into a black hole, the "Bekenstein bound".
Inflation: Before Time
What was there before the Big Bang created our universe? A widely held "cosmological principle" requires that the universe has no center, no special place. That means that the Big Bang did not occur in a specific point of the universe: it occurred everywhere in the universe, it was the universe. The universe was a point and the Big Bang is merely the moment when it began to expand. By cosmological standards, the Big Bang is still occurring now, in every single point of the universe. Space is being created as the universe expands. There was "nothing" before the Big Bang and there is "nothing" beyond the universe. The Big Bang creates the universe which is everything that exists.
This "inflationary" model (proposed by Alan Guth in 1981 and expanding on the 1948 theory of cosmogenesis by the Ukrainian physicist George Gamow who, in turn, developed a 1927 idea by the Belgian physicist Georges Lemaitre) assumes that the universe began its life in a vacuum-like state containing some homogeneous classical fields but no particles (no matter as we know it). Then it expanded exponentially (that’s the "inflation") and the vacuum-like state decayed into particles.
Guth's model is based on the existence of scalar fields. A scalar field is one caused by a quantity which is purely numerical, such as temperature or household income. Gravitational and electromagnetic fields, in contrast, also point in a specific direction, and are therefore "vector" fields. Vector fields are perceived because they exert some force on the things they touch, but scalar fields are virtually invisible. Nonetheless, scalar fields play, for example, a fundamental role in unified theories of the weak, strong and electromagnetic interactions. Like all fields, scalar fields carry energy. Guth assumed that in the early stage of the universe a scalar field provided a lot of energy to empty space. This energy produced the expansion, which for a while occurred at a constant rate, thereby causing an exponential growth.
Guth's model solves a few historical problems of cosmology: the "primordial monopole" problem (grand unified theories predict the existence of magnetic monopoles); the "flatness" problem (why the universe is so flat, i.e. why the curvature of space is so small); and the "horizon" problem (how causally disconnected regions of the universe can have started their expansion simultaneously). It does not account for dark matter and energy.
While everybody agrees that the universe is expanding, not everybody agrees on what that means. In the quest for an explanation of dark matter and dark energy, the British physicist Geoffrey Burbidge, the British physicist Fred Hoyle and the Indian physicist Jayant Narlikar have developed the "Quasi Steady State Cosmology" (reprised in the "Cyclic Universe Theory" by the USA physicist Paul Steinhardt and the British physicist Neil Turok), according to which there is no "Big Bang" to begin with, and there will be no "Big Crunh" to end with. Space and time existed ever since and will exist forever. There is no beginning nor end. The evolution of the universe is due to a series of "bangs" (explosive expansions) and "crunches" (contractions). The Big Bang that we observe today with the most powerful detectors of microwave radiations (first detected in 1964) is simply one of the many expansions following one of the many contractions. Each phase may last a trillion years, and therefore be undetected by human instruments. Burbidge doubts black holes, quasars and the cosmic radiation.
Natural Selection for Universes
Refining Guth’s vision, in the 1980s the Russian physicist Andrei Linde came up with a "chaotic inflationary" model. Linde realized that Guth's inflation must litter the universe with bubbles, each one expanding like an independent universe, with its own Big Bang and its own Big Crunch.
Linde's model is "chaotic" because it assumes a chaotic initial distribution of the scalar field: instead of being uniform, the original scalar field was fluctuating wildly from point to point. Inflation therefore began in different points at different times and at different rates.
Regions of the universe that are isolated by a length greater than the inverse of the Hubble constant cannot be in any relation with the rest of the universe. They expand independently. Any such region is a separate mini-universe. In any such region the scalar field can give rise to new mini-universes.
One mini-universe produces many others. It is no longer necessary to assume that there is a "first" universe.
Each mini-universe is very homogeneous, but on a much larger scale the universe is extremely inhomogeneous. It is not necessary to assume that the universe was initially homogeneous or that all its causally disconnected parts started their expansion simultaneously.
One region of the inflationary universe gives rise to a multitude of new inflationary regions. In different regions, the properties of space-time and elementary particles may be utterly different. Natural laws may be different in each mini-universe.
The evolution of the universe as a whole has no end, and may have no beginning.
The "evolution" of mini-universes resembles that of any animal species. Each mini-universe leads to a number of mini-universes that are mutated versions of it, as their scalar fields is not necessarily the same. Each mini-universe is different, and mini-universes could be classified in a strict hierarchy based on a parent-child relationship.
This mechanism sort of "reproduces" mini-universes in a fashion similar to how life reproduces itself through a selection process. The combinatorial explosion of mini-universes can be viewed as meant to create mini-universes that are ever better at "surviving".
Each mini-universe "inherits" the laws of its parent mini-universe to an extent, just like living beings inherit behavior to an extent through genetic code. A "genome" is passed from parent universe to child universe, and that "genome" contains instructions about which laws should apply. Each genome only prescribes a piece of the set of laws governing the behavior of a universe. Some are random. Some are generated by "adaptation" to the environment of many coexisting universes.
At the same time, expansion means that information is being propagated like in a neural network through the hierarchy of expanding universes.
It may also be that a universe is not born just out of a parent universe, but of many parent universes. A region of the universe expands because of the effect of many other regions. This is similar to what happens with neural networks.
With a little imagination, the view of the chaotic inflationary theory can be interpreted in this way:
Obviously, this scenario bears strong similarities with biological scenarios.
Another theory that presupposes evolving universes is the one advanced in 1992 by the USA astrophysicist Lee Smolin. He thinks that black holes are the birthplaces of offspring universes. The constants and laws of Physics are randomly changed in the new universes, just like the genome of offspring is randomly mutated. Black holes guarantee reproduction and inheritance. Universes that do not give rise to black holes cannot reproduce: there is therefore also a kind of "natural selection" among Smolin's universes. In this scenario, our universe's delicate balance of constants and forces is the result of evolution.
Loop Quantum Gravity
The ultimate goal of Loop Quantum Gravity (LQG) is still the "quantization" of general relativity, but the way it approaches the problem is very different: it is purely geometric.
In 1971 Roger Penrose introduced the notion of a "spin network" (derived from Louis Kauffman's "knot theory") in an attempt to explain the structure of three-dimensional space. A spin network is a graph whose edges are labeled by integers, corresponding to the possible values of the angular momentum. Penrose sensed that these could be the simplest geometric structures to describe space.
In 1976 the Canadian physicist Bill Unruh ("Notes on black-hole evaporation", 1976) discovered that an accelerating observer must measure a temperature (a black-body radiation) where an inertial observer observes none, the temperature being proportional to the acceleration. This means that the very concept of "vacuum" depends on the state of motion of the observer: an accelerating observer will never observe any vacuum. (This also proved that Einstein's principle of equivalence was slightly incorrect: a constantly-accelerating observer and an observer at rest in a gravitational field are not equivalent, as the former would observe a temperature and the latter would not). Every accelerating observer has a hidden region (all the photons that cannot reach her because she keeps accelerating, getting closer and closer to the speed of light) and a horizon (the boundary of her hidden region)
Jakob Bekenstein’s theorem implies that every horizon separating an observer from her hidden region has an entropy. That entropy turns out to be proportional to the information that is hidden or trapped in the hidden region (the missing information). According to Bekenstein's theorem, the entropy of the radiation that the accelerated observer experiences is proportional to the area of her horizon.
Lee Smolin put Unruh and Bekenstein together and realized something that is built into any theory of "quantum gravity" (into any quantization of relativity): the volumes of regions in space must come in discrete units, just like energy comes in discrete units. If energy comes in discrete units, then space must come in discrete units. Just like matter is made of discrete particles, space itself must be made of discrete units. A volume cannot be divided forever: there is an elementary unit of volume.
Smolin used Bekenstein’s and Unruh’s theorems to prove that spacetime must be discrete. If spacetime were continuous, then a volume of spacetime (no matter how small) would contain an infinite amount of information. But for any volume of spacetime an accelerating observer would observe a finite entropy (finite because it is proportional to the surface of the volume) and therefore a finite amount of missing information. The amount of information is finite because the surface of the horizon is finite and therefore entropy is finite. The amount of information within a volume of spacetime must be finite, therefore spacetime cannot be continuous. Spacetime must have an "atomic" structure just like matter has an atomic structure. (This conclusion had been reached independently by Jacob Bekenstein in his studies on the thermodynamics of black holes).
Kenneth Wilson had first hypothesized in the 1970s that space was a discrete lattice. What Smolin did was to make Wilson's discrete lattice also change dynamically, able to evolve in time, as General Relativity requires. In his formulations the inter-relationships among Wilson's structures (the "loops") define space itself. Smolin used the work of two Indian scientists. Abhay Ashtekar came up with the "loop-space model", based on the 1985 theory of Amitaba Sen, that splits time and space into two distinct entities subject to quantum uncertainty (analogous to momentum and position). The solutions of Einstein's equations would then be quantum states that resemble loops. Smolin's theory was simply a theory of loops and how they interact and combine. (The Uruguayan physicist Rodolfo Gambini had independently reached similar conclusions).
Loop states turned out to be best represented by Penrose's spin networks. The lines of a spin network carry units of area. The structure of spin networks generates space.
The space that we experience is continuous. Spin networks, instead, are discrete. They are graphs with edges labeled by spins (that come in multiples of 0.5) and with three edges meeting at each vertex. As these spin networks become larger and more complex, they "yield" our ordinary, continuous, smooth 3-dimensional space. A spin network, therefore, "creates" geometry. It is not that a spin network yields a metrics (the metrics being what defines the geometry of a region of space) but that each vertex of a spin network creates the volume of a region of space.
An evolving spin network (a "spin foam") is basically a discrete version of Einstein's spacetime. Spin-foams are four-dimensional graphs that describe the quantum states of spacetime, just like spin networks describe the quantum states of space. Spin foams describe the quantum geometry of spacetime (not just space). A spin foam may be viewed as a quantum history. Spacetime emerges as a quantum superposition of spin foams (topologically speaking, it is a two-dimensional "complex").
The way spin networks combine to form space is not clear, as there seems to be no "natural law" (no equivalent of gravitation or of electromagnetism) at work. Spin networks "spontaneously" combine to form space. The formation of space resembles the Darwinian process that creates order via natural selection of self-organizing systems. Space appears to be the result of spontaneous processes of self-organization a` la Stuart Kauffman.
The hypothesis that space is discrete also helps remove some undesired "infinites" from Quantum Theory. For example, charged particles interact with one another via electromagnetic fields. The electromagnetic field gets stronger as one gets closer to the particle. But a particle has no size, so one can get infinitely closer to it, which means that the field will get infinitely strong. If space is discrete instead of continuous, the paradox is solved: there is a finite limit to how close to a particle one can get.
Spin networks thus solve "quantum gravity" in three dimensions. Spin networks describe the quantum geometry of space. In order to introduce the (fourth) temporal dimension, a concept of "history" has been added by some researchers.
In 2001 the Greek physicist Fotini Markopoulou showed that spin networks evolve in time in discrete steps: at every step, the change of each vertex of the spin network only depends on its immediate neighbors. This is reminiscent of Von Neumann's cellular automata and of algorithm-based thinking, as opposed to the traditional formula-oriented thinking of Physics.
Fotini Markopoulou introduced causality in Loop Quantum Gravity. In her view, time is not an illusion, just an approximation. She compares it to the river that seems to flow in a smooth way even though the motion of its water molecules is chaotic. Causality does exist at a very fundamental level, although it may not be the one that we perceive in our daily life.
The idea of Loop Quantum Gravity was further expanded by Causal Dynamical Triangulation, a theory introduced in the 1990s by Renate Loll (Dutch), Jan Ambjorn (Danish) and Jerzy Jurkiewicz (Polish) that constructs spacetime from elementary structures called "four-simplexes". A four-simplex is the four-dimensional equivalent of a tetrahedron.
Yet another approach to quantum gravity is purely mathematical. For example, Fotini Markopoulou ("The Internal Description of a Causal Set - What the Universe Looks Like from the Inside", 1999) noticed similarities between the "categories" used by General Relativity and those used by Quantum Theory. These have little in common with the traditional category of Physics whose objects are sets and whose morphisms are functions. In her view Quantum Theory is better understood as a theory of spacetime.
The Holographic Principle
Inspired by the fact that the entropy of a black hole is proportional to its surface and believing that the Planck length is one side of an area that can hold only one bit of information, in 1993 Gerard't Hooft generalized those ideas and proposed that the informational content of a region of space can always be equivalently expressed by a theory that lives on the boundary of that region (the so called "holographic principle").
In 1997 Argentine physicist Juan Maldacena realized that one could represent a universe described by superstring theory functioning in an anti-DeSitter spacetime (a negatively curved spacetime) with a quantum field theory operating on the boundary of that spacetime. And viceversa.
In other words, one could imagine a two-dimensional universe with no gravity that exists on the boundary of a three-dimensional universe with gravity. The two universes are equivalent. The three-dimensional universe which we perceive might instead be encoded on a two-dimensional surface, like a hologram.
USA physicist Lisa Randall believes that particles and gravity live in different "membranes" (regions of multi-dimensional spaces): particles live in one three-dimensional membrane, while gravity lives in a different membrane. Both membranes are part of a five-dimensional spacetime whose geometry is an anti-DeSitter one. Gravity can travel to our membrane, but it arrives considerably weakened, and that is why it is much weaker than the other forces.
Gravity As The Vacuum
The striking difference between the gravitational force and the other three forces is that the gravitational force is much weaker. Gravitational force operates among "bodies" (e.g., complex aggregates of interacting particles), but does not seem to have any effect on interactions between elementary particles.
The effects of the gravitational force are not considered in the Standard Model because they are assumed to be negligible among subatomic particles, but, of course, the other rational explanation would be that... there are no such effects on subatomic particles: based on empirical evidence, one could assume that gravitation does not operate at all among elementary particles but only among bodies made of many interacting particles.
Physicists had known for a long time that there is a superficial similarity between Einstein's equation of how the momentum-energy tensor affects the curvature of space-time and Maxwell's equation of the electromagnetic field, but the connection between gravitation and electromagnetism was made only in 1948, and it had to do with the vacuum.
In 1930, Paul Dirac speculated that, as a consequence of Heisenberg's uncertainty principle, the all-pervading vacuum must actually be filled with particles that continuously appear and disappear in a random way. They live very short lives (limited by Heisenberg's principle), but the total effect of their brief existence is a fluctuation of energy in the vacuum. Thus the "vacuum" is not empty at all, and it actually generates some energy. In 1948, Hendrik Casimir speculated that the activity of the vacuum must translate into energy and thus a force, the "Casimir effect", that is due solely to the vacuum itself. The Casimir effect turns out to be inversely proportional to the fourth power of the distance. The way to create the vacuum is to lower the temperature to the absolute zero: this gets rid of any radiation. The energy produced by the vacuum is thus called the "zero-point energy". For example, helium near the absolute zero does not freeze, because the vacuum "warms it up" with its zero-point energy.
In 1968, Russian physicist Andrei Sakharov proposed a simple explanation to these "oddities": that gravitation might be not a fundamental interaction but a by-product of the electromagnetic interaction, precisely an electromagnetic phenomenon induced by the presence of matter in the quantum vacuum (the quantum field that is present even in "empty" space). Thus, according to Sakharov, matter is not just "there" but is "in" the quantum vacuum, and therefore interacts with it, causing some kind of quantum-fluctuation energy. That fluctuation is gravitation. In a sense, Sakharov moved to Quantum Theory the same objection that Mach had moved to Newton's Physics: you can't assume that a body is isolated, because a body is always "interacting" with something. Except that Sakharov updated this idea to the terminology of Quantum Theory. A body, any body, is immersed in quantum fields, and thus interacts with them. One such field is the quantum vacuum. Sakharov thought that this was not negligible at all, in fact that it was the origin of the gravitational interaction itself.
In 1989, the USA physicist Harold Puthoff proposed that a body's inertia (as expressed by Newton's equation "F=ma") is due, as Mach speculated, to the distribution of matter in the universe, and, more precisely, to the electromagnetic interaction that arises from quantum fluctuations of the zero-point field in accelerated frames. Basically, a particle's inertia is a function of the particle's interaction with the zero-point field. Inertia is resistance to acceleration: Puthoff showed that the resistance which defines the inertia of a particle is, ultimately, electromagnetic resistance caused by the zero-point field on the particle. Matter (made of leptons and quarks) continuously interacts with the zero-point field, and this interaction yields a force (the "resistance" to motion) whenever acceleration takes place. Inertia is due to the distortion of the zero-point field under acceleration. Newton's equation "F=ma" is merely an effect of zero-point fluctuations in an accelerated reference frame.
Puthoff has, de facto, offered the first rational explanation of why force and acceleration are related; and has also given a definition of what "mass" is (Newton introduced it as a primitive property of matter). Technically, inertia is due to the high frequencies of the distortion of the zero-point spectrum, whereas gravity is due to its low frequencies. Newton and Mach measured inertia against a reference frame. Puthoff is using the zero-point field as the reference frame, and is claiming that inertia originates from the reference frame itself.
The "gravitational field" is the set of all electromagnetic fields generated by all particles (leptons and quarks) as they interact with the zero-point field.
The Standard Model has been able to predict correctly all sorts of complicated experiments. However, a skeptic would object that the Standard Model does not quite explain everything that we see in nature (falling rocks, flying birds or suspended bridges). It only explains phenomena that quantum physicists perform in laboratories and that cosmologists presume are happening billions of light-years away. Newton's Physics does explain the phenomena of the human world (the world of objects). It had been relatively easy to reduce Relativity Theory to Newton's Physics, but it had been very difficult to reduce Quantum Theory to Newton's Physics. If he is right, Puthoff did just that.
Ripples in Spacetime
In 2005 the Italian mathematician Piero Scaruffi proposed just the opposite approach to reconciling Quantum Theory and Relativity Theory. If both are correct representations of nature, how can they be so different and even contradictory? Relativity prescribes a spacetime continuum, whereas Quantum Theory prescribes a discrete world. Relativity is deterministic, Quantum Theory is, at best, stochastic. How can one be derived from the other?
So far, the most popular approach to unification has been "bottom-up: from Quantum Theory to Relativity. A more appropriate approach could be top-down: deriving Quantum Theory as a special case of Relativity Theory.
Quantum Theory has not explained why nature only likes some discrete values. (The next breakthrough will be the observation of values that are forbidden by Quantum Theory. That will shed light on what Quantum Theory actually is).
Relativity Theory appears as stating some grander and somewhat more absolute about the universe; basically, about the dimensions of existence. Quantum Theory appears as telling us something about the human world of objects and measurements; basically, about the world of "sizes".
The best way to visualize these ideas is to think of relativistic spacetime as an ocean, and of quantum values as the ripples caused by an object moving through spacetime. The ocean is a continuum, but the ripples are discrete. Both the ocean and the ripples are real, and one can construct a theory to describe the ocean and a different theory to describe the ripples. Then Relativity is the theory about the ocean, and Quantum Theory is the theory about the ripples.
If this is correct, then Quantum Theory describes the ripples caused in spacetime by energy-matter in motion. Einstein's equations describe how spacetime warps because of matter. Schroedinger's equations describe the ripples caused by such matter.
If this is correct, Relativity's space and time are different from Quantum Theory's space and time. We use the same name for two different things: Relativity's space is a dimension, an underlying framework, whereas Quantum Theory's space is about the "size" of an object. Spacetime is the continuum that energy-matter interacts with. Quantum values are the results of measuring the ripples caused by that interaction. The reason that the ripples are discrete and not continuum is exactly the same that ripples form on a surface. Any attribute of an object over the ripples admits only some values, because it exists and it is measured only over the ripples.
Scaruffi believes that the probabilistic nature of Quantum Theory emerges because of the translation from "ocean" to "ripples". Ditto for the attributes (charge, spin, etc). They are all manifestations of the ripples.
General relativity is about the dynamics of the universe: it describes an eternal dance between the distribution of masses and the geometry of spacetime, the former determining the latter and the latter determining the motion of the former. Indirectly, Einstein's equations can be interpreted as the relationship (or the connection" of everything to everything else. As connections change, other connections change. Each connection gets adjusted to as to preserve some global feature of the universe. Basically, the universe behaves like a giant brain.
The quantization of spacetime is a superficial consequence of the "connection of everything to everything else", as this is equivalent to constructing a landscape of attractors.
Brains, Lives, Universes
Let's take a closer look at Life. We have organisms. Each organism is defined by its genome. An organism's genome does not vary during its lifetime. The genome of its offspring varies. The variation is the result of random processes. Each organism interacts with the environment and may or may not survive such interactions. Indirectly, interactions with the environment determine how genomes evolve over many generations.
Then we have neural networks. The behavior of each thinking organism is controlled by a neural network. The principle of a neural network is that of interacting with the environment, propagating the information received from the environment through its neurons and thereby generating behavior. Each neuron has influence over many neurons and what determines the behavior is the connections between neurons. A neural network changes continuously during the life of an organism, especially at the very beginning.
Within neural networks a selection process also applies. Connections survive or die depending on how useful they are. Connections are stronger or weaker depending on how useful they are. Usefulness is defined by interaction with the environment.
Genomes and neural networks are systems that have in common the principle of propagating information about the environment within itself through a process of a) interaction with the environment, b) feedback from the environment, c) selection.
Neural networks, genetic algorithms and chaotic inflationary universes seem to obey very similar principles. They "expand" in order to
The Nature of the Laws of Nature
Even with the sophistication of Relativity Theory, our universe presents us with an uncomfortable degree of arbitrariness.
What is still not clear is why laws (e.g. Einstein's field equations) and constants (e.g., the Planck distance) are the way they are. Why is the universe the way it is?
In 1916 the German physicist Arnold Sommerfeld introduced a quantity that he called "fine-structure constant" that combined all the main constants of Physics: the speed of light, the electric charge of the electron, Planck’s constant and the vacuum permittivity. The universe behaves the way it behaves because the value of the fine-structure constant is 1/137. Why 137? (Physicists such as John Barrow and John Webb actually believe that this constant changed over the course of our universe’s life, and our universe is but one of many universes, each with a different value for the fine-structure constant).
Furthermore: why do properties of matter such as electrical charge and mass exert forces on other matter? Why do things interact at all?
The most popular cosmological models presume that the physical laws we know today were already in effect at the very beginning, i.e. were born with the universe, and actually pre-existed it. The laws of Physics are simply regularities that we observe in nature. They allow us to explain what happened, and why it happened the way it happened. They also allow us to make predictions. Science is all about predictions. If we couldn't make predictions, any study of Nature would be pretty much useless. We can build bridges and radios because we can make predictions on how things will work.
Three aspects of the fundamental laws are especially puzzling.
The first has to do with the nature of the laws of Nature. How absolute are they? Some laws can be reduced to other laws. Newton's law of gravitation is but a special case of Einstein's. It was not properly a law of Nature, it was an effect of a law of nature that Newton did not know. These days, we are witnessing a quest for a unification theory, a theory that will explain all four known forces (weak, nuclear, electric and gravitational) in one "megaforce": if the program succeeds, we will have proved that those four forces were effects, not causes. Is the second law of Thermodynamics a law indeed, or just the effect of something else?
After all, the laws as we study them today in textbooks are the product of a historical process of scientific discovery. Had history been different (had progress followed a different route) we may have come up with a description of the universe based on different laws, that would equally well fit (individually) all the phenomena we are aware of.
The second question is why are they mathematical formulas. Mathematics is a human invention, but it is amazing how well it describes the universe. True, Mathematics is more a discovery process than an invention process. But, even so, it is a discovery of facts that occur in the realm of mathematical ideas (theorems and the likes). It is amazing that facts occurring in that abstract realm reflect so well facts that occur in the physical realm.
Most Mathematics that is employed today so effectively for describing physical phenomena was worked out decades and even centuries before by mathematicians interested only in abstract mathematical problems. The rule almost never fails: sooner or later a physical phenomenon will be discovered that perfectly matches a mathematical theory. It feels like the universe is a foreign movie, subtitled in mathematical language.
Even more intriguing is the fact that the world of Mathematics is accessible by the human mind. Our bodies have privileged access to physical space, our minds have privileged access to the notes that describe it. We get both treats. The body perceives physical reality through the senses, the mind perceives mathematical reality through reasoning.
The third question is whether they are truly eternal. Were they always the same? Will they always be the same?
Naturally, if the answer is negative, then we don't know anything.
It would seem more likely that they are part of the universe and therefore came to be precisely when the universe came to be. In that case it would therefore be impossible to compute a model of how the universe was born, because we don't know which laws (if any) were in place before the universe was born!
(We don't even know for sure whether the laws of Nature are the same in the whole universe. We don't even know if they have been the same all the time or if they have been changing over time).
Similar arguments hold for the "constants" of Physics, for the dimensionless parameters that shape the laws of nature, in particular for the speed of light, the Planck constant, and the charge of the electron. Why do they have the value they have? Einstein asked: did God have a choice when he created the universe? Could those numbers be different, or are they the only combination that yields a stable universe? A famous formula has been puzzling scientists: the square of the charge of the electron divided by the speed of light and by the Planck constant is almost exactly 1/137. Why?
We don't have a science of natural laws which studies where laws come from. Laws are assumed to transcend the universe, to exist besides and despite the existence of a universe. But that's a rather arbitrary conclusion (or, better, premise).
The Nature of Spacetime
According to Relativity, everything sits in spacetime. According to Relativity, spacetime is not a substance. Sound waves require a medium to travel (and their speed depends on the medium), but light waves do not require any medium (and it is always the same). According to Einstein, light travels in vacuum. There is no need for an "ether".
In 1981 the Canadian physicist William Unruh proved the stunning similarity between sound waves propagating in moving fluid and light waves propagating in curved spacetime. In 1999 the USA physicist Ted Jacobson speculated that spacetime might indeed be a "substance", a kind of fluid (and be discrete at the microscopic scale).
The Prodigy of Stability
Chaos is a matter of life in this universe. What is surprising is that we do not live in chaos. We live in almost absolute stability. The computer I am writing on right now is made of a few billion particles of all kinds that interact according to mechanic, gravitational, electric, magnetic, weak and strong forces.
The equations to describe just a tiny portion of this computer would take up all my life. Nonetheless, every morning I know exactly how to turn on my computer and every day I know exactly how to operate on it. And the "stability" of my computer will last for a long time, until it completely breaks down. My body exhibits the same kind of stability (for a few decades, at least), so much so that friends recognize me when they see me and every year the IRS can claim my tax returns (no quantum uncertainty there).
Stability is what we are built to care for. We care very little about the inner processes that lead to the formation of a tomato plant: we care for the tomatoes. We care very little for the microscopic processes that led a face to be what it is: we care for what "it looks like". At these levels stability is enormous. Shape, size, position are stable for a number of days, weeks, months, maybe years. Variations are minimal and slow. The more we get into the detail of what we were not built to deal with and the more confused (complex and chaotic) matter looks to us, with zillions and zillions of minuscule particles in permanent motion.
Science was originally built to explain the world at the "natural" level. Somehow scientists started digging into the structure of matter and reached for lower and lower levels. The laws of Physics got more and more complicated, less and less useful for the everyman.
Even more surprising, each level of granularity (and therefore complexity) seems largely independent of the lower and higher levels. Sociology doesn't really need Anatomy and Anatomy doesn't really need Chemistry and Chemistry doesn't really need Quantum Theory.
The smaller we get the more the universe becomes messy, incomprehensible, continuously changing, very unstable. We have grown used to thinking that this is the real universe, because the ultimate reduction is the ultimate truth.
The surprising thing is that at higher levels we only see stability. How does chaos turn into stability? We witness systems that can create stability, order, symmetry out of immense chaos.
One answer is that maybe it is only a matter of perception. Our body was built to perceive things at this level, and at that level things appear to be stable just because our senses have been built to perceive them stable. If our senses weren't able to make order out of chaos, we wouldn't be able to operate in our environment.
Another answer, of course, could be that all other levels are inherently false...
A Self-organizing Universe
The main property of neural networks is feedback: they learn by doing things. Memory and learning seem to go hand in hand. Neural networks are "self-organizing" objects: response to a stimulus affects, among other things, the internal state of the object. To understand the behavior of a neural network one does not need to analyze the constituents of a neural network; one only needs to analyze the "organization" of a neural network.
Physics assumes that matter has no memory and that the laws of Nature entail no feedback. Physics assumes that all objects in the universe are passive and response to a stimulus does not affect the internal state of the object: objects are non-organizing, the opposite of self-organizing objects. To understand the behavior of a physical object, one needs analyze its constituents: the object is made of molecules, which are made of atoms, which are made of leptons and quarks, which are made of...
There is no end to this type of investigation, as history has proved. The behavior of matter still eludes physicists even if they have reached a level of detail that is millions of times finer-grained than the level at which we operate. There is no end to this type of investigation, because everything has constituents: there is no such thing as a fundamental constituent. Just like there is no such thing as a fundamental instant of time or point of space. We will always be able to split things apart with more powerful equipment. The equipment itself might be what creates constituents: atoms were "seen" with equipment that was not available before atoms were conceived.
In any case it is the essence itself of a "reductionist" (constituent-oriented) science that requires scientists to keep going down in levels of detail. No single particle, no matter how small, will ever explain its own behavior. One needs to look at its constituents to understand why it behaves the way it behaves. But then it will need to do the same thing for each new constituent. And so on forever. Over the last century, Physics has gotten trapped into this endless loop.
Could matter in general be analyzed in the same that we analyze neural networks? Could matter be explained in terms of self-organizing systems? Neural networks remember and learn. There is evidence that other objects do so too: a piece of paper, if folded many times, will "remember" that it was folded and will learn to stay folded. Could we represent a piece of paper as a self-organizing system?
Nature exhibits a "hierarchy" of sort of self-organizing systems, from the atomic level to the biological level, from the cognitive level to the astronomical level. The "output" of one self-organizing system (e.g. the genome) seems to be a new self-organizing system (e.g. the mind). Can all self-organizing systems be deduced from one such system, the "mother" of all self-organizing systems?
We are witnessing a shift in relative dominant roles between Physics and Biology. At first, ideas from physical sciences were applied to Biology, in order to make Biology more "scientific". This led to quantifying and formalizing biological phenomena by introducing discussions on energy, entropy and so forth. Slowly, the debate shifted towards unification of Physics and Biology, rather then unidirectional import of ideas from Physics. Biological phenomena just don't fit in the rigid deterministic model of Physics. Then it became progressively clear that biological phenomena cannot be reduced to Physics the way we know it. And now we are moving steadily towards the idea that Physics has to be changed to cope with biological phenomena, it has to absorb concepts that come from Biology.
In order to accommodate biological concepts, such as selection and feedback, in order to be able to encompass neural and living systems, which evolve in a Darwinian fashion and whose behavior is described by non-linear equations, Physics will need to adopt non-linear equations and possibly an algorithm-oriented (rather than equation-oriented) approach.
Almost all of Physics is built on the idea that the solution to a problem is the shortest proof from the known premises. The use and abuse of logic has determined a way of thinking about nature that tends to draw the simplest conclusions given what is known (and what is not known) about the situation. For example, it was "intuitive" for scientists to think that the immune system creates anti-bodies based on the attacking virus. This is the simplest explanation, and the one that stems from logical thinking: a virus attacks the body, a virus is killed by the body; therefore the body must be able to build a "killer" for that virus. The disciplines of life constantly remind us of a different approach to scientific explanation: instead of solving a mathematical theorem through logic, nature always chooses to let things solve themselves. In a sense, solutions are found by natural systems not via the shortest proof but thanks to redundancy. The immune systems creates all sorts of antibodies. An invading virus will be tricked into "selecting" the one that kills it. There is no processor in the immune system that can analyze the invading virus, determine its chemical structure and build a counter-virus, as a mathematician would "intuitively" guess. The immune system has no ability to "reason" about the attacking virus. It doesn't even know whether some virus is attacking or not. It simply keeps producing antibodies all the time. If a virus attacks the body, the redundancy of antibodies will take care of it.
This represents a fundamental shift of paradigm in thinking about Nature. For many centuries, humans have implicitly assumed that the universe must be behaving like a machine: actions follow logically from situations, the history of the universe is but one gigantic mathematical proof. It is possible that the larger-scale laws of nature resemble very little a mathematical proof. They might have more to do with randomness than with determinism.
The distinction between instruction and selection is fundamental. Physics has evolved around the concept of instruction: mathematical laws instruct matter how to behave. Selection entails a different set of mind: things happen, more or less by accident, and some are "selected" to survive. The universe as it is may be the product of such selection, not of a logical chain of instructions.
Physics is meandering after the unified theory that would explain all forces. What seems more interesting is a unification of physical and biological laws. We are now looking for the ultimate theory of nature from whose principles the behavior of all (animate and inanimate) systems can be explained. Particles, waves and forces seem less and less interesting objects to study. Physics has been built on recurring "themes": planets revolve around the sun, electrons revolve around the nucleus; masses attract each other, charged particles attract each other. Still, Physics has not explained these recurring patterns of Nature. Biology is explaining its recurring patterns of evolution.
A new scenario may be emerging, one in which the world is mostly non-linear. And somehow that implies that the world self-organizes. Self-organizing systems are ones in which very complex structures emerge from very simple rules. Self-organizing systems are about where regularity comes from. And self-organizing systems cannot be explained by simply analyzing their constituents, because the organization prevails: the whole is more than its parts.
The Universe as the Messenger
One pervasive property of the universe and everything that exists is communication. Things communicate all the time.
The Austrian physicist and philosopher Ernst Mach had a vision of the universe that proved influential on all Twentieth century Physics. Newton defined inertial systems as systems that are not subject to any force. They move at constant or null speed. Systems that are accelerated are not inertial and, by magic, strange forces ("inertial forces") appear in them. Mach realized that all systems are subject to interactions with the rest of the universe and redefined inertial systems as systems which are not accelerated in the frame of fixed stars (basically, in the frame of the rest of the universe). The inertia of a body is due to its interaction with the rest of the matter in the universe.
Mach's principle implies that all things communicate with all other things all the time. This universe appears to be built on messages.
The dynamics of the universe is determined to a large extent by the messages that are exchanged between its parts (whether you look at the level of RNA, synapses or gravitation).
Things communicate. It is just their nature to communicate. More: their interactions determine what happens next. Things communicate in order to happen. Life happens because of communication. We think because of communications.
If all is due to messages, a theory of the universe should de-couple the message from the messenger.
Messages can be studied by defining their "languages". Maybe, just maybe, instead of sciences like Physics and Biology we should focus on the "language" of the universe.
Not in Our Name
If one takes the Copenhagen interpretation of Quantum Mechanics to the letter, in the beginning there were only probabilities.
There was no observer to "collapse" the wave functions of whatever existed, therefore there were only evolving wave functions: probabilities.
There was, technically speaking, no reality to talk about, because there was no observer to cause it to collapse to the state of reality.
Human reality depends on humans to exist and to observe it.
Then at some point, out of this giant network of probabilities a conscious observer was created.
That conscious observer was not a probability: it was a reality.
That conscious observer (the human race) is making the entire universe metamorphose from probabilities into reality.
In this story there seems to be something missing: how do probabilities create a conscious observer?
How does a state of probabilities evolve into a state of conscious observers?
Was the conscious observer merely a probability from the beginning, that turned out to exist out of sheer luck, or was it meant to exist from the beginning?
Is everything that can possibly exist eventually going to exist, given enough time, given enough trials and errors?
Is today's conscious observer still only a probability herself, and not an actual "reality"?
Relativity tells a different story, a story of pure determinism: our future is determined by the past.
If Relativity and Quantum Mechanics are both true (despite the fact that we are not capable of explaining one with the other), then the emergence of the observer must have been written in the original conditions, in the original set of probabilities.
The story of the universe may be the story of an entity that is slowly transforming itself from one kind of substance to another kind of substance, and consciousness might be just the tool that it is employing in order to achieve that transition.
The Science of Impossibility: The End of Utopia
It is intriguing that the three scientific revolutions of the last century all involved introducing limits to classical Physics. Newton thought that signals could travel at infinite velocities, that position and momentum could be measured simultaneously and that energy could be manipulated at will. Relativity told us that nothing can travel faster than the speed of light. Quantum Mechanics told us that we cannot measure position and momentum simultaneously. Thermodynamics told us that every manipulation of energy implies a loss of order. There are limits in our universe that did not exist in Newton's ideal universe.
These limits are as arbitrary as laws and constants. Why these and not others? May they be just clues to a more general limit that constrains our universe? May they be simply illusions, due to the way our universe is evolving?
Then Newton's world has been shaken to its foundations by Darwin's revolution. Natural systems look different now. Not monolithic artifacts of logic, but flexible and pragmatic side effects of randomness. By coincidence, while Physics kept introducing limits, Biology has been telling us the opposite. Biological systems can do pretty much anything, at random. Then the environment makes the selection. We have been evangelized to believe that nothing is forbidden in Nature, although a lot will be suppressed.
Once all these views are reconciled, Newton's Utopia may be replaced by a new Utopia, with simple laws and no constraints. But it's likely to look quite different from Newton's.
Where to, Albert?
Ashtekar Abbay: CONCEPTUAL PROBLEMS OF QUANTUM GRAVITY (Birkhauser, 1991)
Barbour Julian: THE END OF TIME (Oxford Univ Press, 2000)
Bohm David: THE UNDIVIDED UNIVERSE (Routledge, 1993)
Bohm David: QUANTUM THEORY (Constable, 1951)
Bohm David: WHOLENESS AND THE IMPLICATE ORDER (Routledge, 1980)
Bondi, Hermann: "Negative Mass in General Relativity" (1957)
Bohr Niels: ATOMIC THEORY AND THE DESCRIPTION OF NATURE (Cambridge University Press, 1934)
Bunge Mario: QUANTUM THEORY AND REALITY (Springer, 1967)
Davies Paul: ABOUT TIME (Touchstone, 1995)
Deutsch David: THE FABRIC OF REALITY (Penguin, 1997)
Ferris Timothy: THE WHOLE SHEBANG (Simon And Schuster, 1997)
Flood Raymond & Lockwood Michael: NATURE OF TIME (Basil Blackwell, 1986)
Gell-Mann Murray: THE QUARK AND THE JAGUAR (W.H.Freeman, 1994)
Greene Brian: THE ELEGANT UNIVERSE (WW Norton, 1999)
Griffiths, Robert: CONSISTENT QUANTUM THEORY (Cambridge University Press, 2001)
Guth Alan: THE INFLATIONARY UNIVERSE (Helix, 1997)
Hawking Stephen: A BRIEF HISTORY OF TIME (Bantam, 1988)
Heisenber Werner: THE REPRESENTATION OF NATURE IN CONTEMPORARY PHYSICS (Deadalus, 1958)
Hoyle Fred, Burbidge Geoffrey, and Narlikar Jayant: A DIFFERENT APPROACH TO COSMOLOGY (Cambridge Univ Press, 2000)
Kaku Michio: HYPERSPACE (Oxford University Press, 1994)
Linde Andrei: PARTICLE PHYSICS AND INFLATIONARY COSMOLOGY (Harwood, 1990)
Linde Andrei: INFLATION AND QUANTUM COSMOLOGY (Academic Press, 1990)
Omnes, Roland: QUANTUM PHILOSOPHY (Princeton University Press, 1999)
Penrose Roger: THE EMPEROR'S NEW MIND (Oxford Univ Press, 1989)
Price Huw: TIME'S ARROW AND ARCHIMEDE'S POINT (Oxford University Press, 1996)
Prigogine Ilya: FROM BEING TO BECOMING (W. H. Freeman, 1980)
Puthoff, Harold: Gravity as a Zero Point Fluctuation Force (1989)
Rees, Martin: BEFORE THE BEGINNING (Simon And Schuster, 1996)
Rosenblum, Bruce & Kuttner, Fred: QUANTUM ENIGMA (Oxford Univ Press, 2006)
Sakharov, Andrei: Vacuum Quantum Fluctuations in Curved Space and the Theory of Gravitation (1968)
Scott, Alwyn: STAIRWAY TO THE MIND (Copernicus, 1995)
Smolin, Lee: THREE ROADS TO QUANTUM GRAVITY (Weidenfeld and Nicolson, 2000)
Susskind, Leonard: THE COSMIC LANDSCAPE (Little & Brown, 2005)
Von Neumann, John: DIE MATHEMATISCHE GRUNDLAGEN DER QUANTENMECHANIK/ MATHEMATICAL FOUNDATIONS OF QUANTUM MECHANICS (Princeton University Press, 1932)
Webb, John: THE CONSTANTS OF NATURE (Pantheon, 2002)
Weinberg, Steven: DREAMS OF A FINAL THEORY (Pantheon, 1993)
Wigner, Eugene: SYMMETRIES AND REFLECTIONS (Indiana Univ Press, 1967)