Piero Scaruffi(Copyright © 2013 Piero Scaruffi | Legal restrictions )
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.
It is puzzling that there can be so many string theories. First, Andrew Strominger discovered that string theory comes in a wild variety of possible variations ("Superstrings with Torsion", 1986). Then Shamit Kachru discovered that a very large number of string theories with small positive values of the cosmological constant are possible ("De Sitter vacua in string theory", 2003) and Washington Taylor discovered that an infinite number of string theories with small negative values of the cosmological constant are possible ("Type IIA Moduli Stabilization", 2005).
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