Inquire about purchasing the book | Table of Contents | Annotated Bibliography | Class on Nature of Mind

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

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 ("On the Unification Problem of Physics", published only
in 1921) 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.
Note that Einstein’s Relativity does not say anything about the number of
dimensions of our world: it works in any dimensions, unlike Newton’s theory that yields the correct
(inverse square) formula for the force of gravity only in the case of three
spatial dimensions. 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 ("Quantum theory and five-dimensional
theory of relativity", 1926) 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 US physicist Bryce DeWitt (“Quantum Theory of Gravity”, 1967) 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 1970s led the US physicist John Schwarz to formulate Superstring Theory. His early
studies had been triggered by a formula discovered by the Italian physicist Gabriel Veneziano
(“Construction Of A Crossing-Symmetric, Reggeon Behaved Amplitude For Linearly
Rising Trajectories”, 1968) and its interpretation as a vibrating string by the
Japanese physicist Yoichiro Nambu (“Quark Model And The Factorization Of The
Veneziano Amplitude”, 1970). Schwarz realized that both the standard model for
elementary particles and General Relativity’s theory of gravitation were
implied by Superstring Theory (“Dual Models For Nonhadrons”, 1974). 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 to matter
are 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 an “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 US physicist David Gross (“Heterotic String“, 1985) and others, 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). Some believed that Einstein's General Theory of Relativity
is implied by Superstring Theory, to the point that another US physicist,
Edward Witten, wrote that
Relativity Theory was discovered first by mere accident. Incidentally, the same
Witten, provided the most complete "field string theory" yet
("Noncommutative Geometry and String Field Theory", 1986). In the meantime
Superstring Theory progressed towards a peculiar form of duality. A Finnish and
a British physicist, Claus Montonen and David Olive (“Magnetic monopoles as gauge particles?“, 1977), 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 could be built on top of a theory of quarks, or a theory of quarks
could be built on top of a theory of solitons. The US physicist
Andrew Strominger (“Microscopic origin of the Bekenstein-Hawking entropy “, 1996)
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
the Romanian-born Peter Freund (“Higher Dimensions, Supersymmetry, Strings”, 1985) and Michio
Kaku 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? 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. Back to the beginning of the chapter "The New Physics" | Back to the index of all chapters |