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**These are excerpts and elaborations from my book "The Nature of Consciousness"**

Quantum Theory
was the logical consequence of three 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. According to
Planck, therefore, the
energy of light is proportional to the frequency: E=hv (where “h” is Plack’s
constant). In 1905 Einstein, to explain the photoelectric
effect, argued that light must be
physically made of packets (“photons”) whose energy is proportional to the
frequence. 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. (Particles actually
don’t spin, but interact as if they were spinning, hence the property that
defines how they interact is called “spin” and particles are said to be
“spinning”). 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 de Broglie (“Waves and Quanta”, 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. De Broglie proved that the equation for a standing wave
matched the behavior of the electron. Each particle is associated with a wave
whose wavelength is inversely proportional
the particle’s momentum. That equation expressed a relationship between
quantities of matter (e.g., speed, momentum, energy) and quantities of waves
(e.g., wavelength and frequency). 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 de
Broglie’s theory. Einstein’s Relativity had shown that energy and matter were
dual aspects of the same substance. De Broglie showed that particles and waves
were dual aspects of the same phenomenon. The character of
this relationship was defined by Werner Heisenberg in Germany ("Quantum-Theoretical Re-interpretation of
Kinematic and Mechanical Relations", 1925) and Erwin Schroedinger in Austria ("An
Undulatory Theory of the Mechanics of Atoms and Molecules", 1926). Both
devised equations that replaced the equations of Newton's physics, but both equations
had unpleasant consequences: Heisenberg's equation (based on matrix algebra)
implied that the result of a physical experiment depends on the order in which
the calculations were performed, and Schroedinger's equation (based on wave
mechanics) implied that each particle could only really be considered a wave.
Schroedinger wanted to remove the discrete jumps (that were inherent in
Heisenberg’s formulation) and restore the continuum of classical Physics. His
equation, after all, simply replaces Newton's (or, better, Hamilton's) equations and predicts the
state of the system at a later time given the current state; except that his
"system" is not a confined object but a wave. He thought of the wave
as describing the location of the object (i.e., the object being spread out in
space). However, experiments showed that the object (e.g., the electron) was a
very confined object (just like in classical Physics) while Schroedinger's
equation described it as a wave spread out in space. Max Born (“On the quantum mechanics of collisions”, 1926) 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). In particular, Schroedinger’s wave
is not a representation of where the
object is spread out but of all the places where the object could possibly be,
each to a certain degree of probability. This meant that the position of a
particle cannot be known for sure: we can only guess it from a distribution of
probability. We only know the probability of finding a particle in a given
position. The state of a
particle is described by this “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. John von Neumann
realized that, mathematically speaking, a classical system is represented in
Newton’s Physics by a
point in a six-dimensional phase space (three coordinates for the position and
three for the velocity), whereas quantum systems are represented by vectors in
a vector space. As Born put 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. A particle is
described by a function of probabilities. When it is observed by an instrument,
the function “collapses” to one specific value. The transition from the world
of the wave to the world of the particle is traumatic. The measurement that
collapses the wave function creates an irreversible arrow of time. The fact
that a measurement causes the collapse of the wave function (also called
“state-vector reduction”) is de facto a natural law that has to be added to the
classical ones. In
Thermodynamics the microscopic laws of Physics were still Newtonian and
therefore reversible. In Quantum Mechanics the microscopic laws of Physics are
already irreversible, because nothing can undo the measurement: once you
measure the position or the momentum of a particle, you have forever changed
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