There are two avenues of research that i find particularly intriguing in 2007. One has introduced a new paradigm to explain why Nature created Life and why Life needed a brain. The other one may have just proven that spacetime must have an atomic structure (just like matter has an atomic structure), a notion whose impact could be momentous.
Last but not least, i am still trying to prove that Quantum Theory can be
interpreted as the "ripples" that an observer causes as it moves in spacetime.
Bio-energeticsThe 1990s have brought a wealth of experimental data on the structure and the processes of the brain. We now know that you do X or feel Y because some messages traveled from this part of the brain to that part of the brain. But it is like knowing that the car moves because the engine burns fuel, without knowing what caused the engine and the rest of the car to be built in the first place.
Bioenergetics is almost an alternative to Darwin in explaining where it all came from. There were several pioneers who emphasized that Life is about Energy. Eventually, a lot of Biologists started agreeing and started applying Thermodynamics (the discipline of Energy) to Biology. They soon realized that
The thermodynamics of Life is not traditional thermodynamics: it is non-equilibrium thermodynamics, because anything that is alive is not in equilibrium (you will reach a state of equilibrium only when you die). Thus Physicists and Mathematicians developed non-equilibrium thermodynamics, that happens to be based on non-linear equations (unlike classical Physics that is based on linear equations). The study of non-linear equations led to all the speculation on chaos, complexity, self-organization, etc. The result of all these speculations, calculations and simulations is that, to some extent, we don't need that much of Darwin's theory anymore: once life happened, it was bound to "evolve". Darwinian evolution (which, strictly speaking, is about natural selection applied to variation and yielding fitter and fitter individuals, certainly helped. But bioenergetics alone proves that, given life, it has to evolve.
That happened in the 1990s. More and more sophisticated thoeries of bioenergetics are beginning to approach the very form of life that we observe on Earth, and in particular the human brain.
Ronald Fox, for example, makes an important point. Biologists are agreed for a long time (see my chapter on Ecological Realism) that a living organism can survive only if it can make predictions. Fox shows that non-linear systems can only be predicted by simulating them faster than they move. There is no simple mathematical solution to the problem of predicting what is going to happen next in a natural environment. There are just too many interacting factors. You need to simulate the environment and carry out the simulation very quickly.
Thus it is not a coincidence that Life evolved the nervous system, and in particular the brain: the brain can be viewed as a rapid simulator of non-linear systems. Your brain is capable of simulating what will happen next in the environment. For example, it can simulate the consequence of a movement, which in turn helps refine the movement as it happens. Bioenergetics can explain very fundamental facts of our cognitive life based only on physical, chemical and mathematical laws.
Quantum GravityThere have many attempts at unifying Relativity Theory and Quantum Theory. One of the most promising is an approach based purely on geometry.
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)
A theorem by Jakob Bekensteinís 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 Bekensteinís and Unruhís 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.
Ripples in SpacetimeSee On the relationship between Quantum Theory and Relativity Theory