Q: I was wondering if you could explain what duality is and what it means with respect to the origin of the universe.
A: Duality means that a theory (and hopefully the world it describes) has two aspects,
or two sets of properties, that seem quite different but are in fact related in a deep way.
If we understand one set of properties rather well, we can use this understanding to discuss,
or calculate, the "dual" set of properties, which may be very hard to calculate directly.
Duality has found important applications in string theory, and is relevant to the origin of
the universe because the very early universe must be described by quantum gravity, and "strings"
seem to occur naturally in quantum gravity. Actuallly, the latest trend is to go beyond string
theory, to M-theory.
For details on duality in string theory, and web links, click here.
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Q: Are there an infinite number of dimensions?
A: The short answer is no. Prevailing theories indicate that the number of dimensions
is 9+1 (nine spacelike dimensions plus time), or perhaps 10+1. However,
in quantum gravity the number of dimensions is fluctuating, and could be arbitrarily
large in some parts of the universe. In our corner
(in the visible universe) there are probably 9 space-like dimensions
(3 extended and 6 compacted), but somewhere else there could be any number (for instance, 5
extended and 9 compacted).
For details on fluctuating dimensions and spaces with an infinite number of
dimensions, click here.
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Q: Why are physicists so sure that there is a Theory of Everything (TOE)? Do they seriously believe that, as Einstein put it, we can understand the mind of God?
A: It is very reasonable to search for a theory that describes everything we know about the universe today, in the same sense that today’s theories are capable of describing everything known to science a century ago. General Relativity describes very precisely all the motions of the planets, and the quantum theory of electrons and nuclei is more than adequate to describe all chemistry and the behavior of matter, as it was known in 1895. In an "1895-TOE" we need not worry about the internal structure of nuclei, because radioactivity was discovered (by Becquerel) in 1896; but, as a matter of fact, we also have now a pretty good theory of radioactivity and many other things that nobody had dreamed of in 1895. Today’s physics cannot describe what happens when the energy concentration is so high that space-time is violently distorted. The mass-energy of an elementary particle is concentrated in such a small volume that its description eludes us, just as the internal structure of atoms eluded our ancestors in 1895. Remember that the existence of electrons was established in 1897 (by J.J. Thomson). When the behavior of electrons was accurately described by quantum theory, we did not just get a good theory of chemistry, we also had to change our ideas about determinism in science and about reality itself, in ways that no philosopher or theologian had ever dreamed of. It is not farfetched to say that we got a better understanding of the mind of God, if we assume with Einstein that the laws of nature reflect the mind of God. With quantum electromagnetic theory, we can describe more than isolated atoms and molecules; we can also understand fire and lightning and complex structures such as a cell. Most things are so complicated that they outstrip our ability to apply the theory, but we are pushing farther every day with clever math and better computers. Similarly, with quantum gravity we can hope to understand not only the constitution of electrons and quarks, but also what goes on inside a black hole, and how the Big Bang came about. At the center of a black hole, electrons and quarks are pushed close together and dissolve, somewhat like atoms fuse into a solid or become ionized in a fire. It is almost certain that radically new notions will emerge from quantum gravity, like the notions of quantization and spacetime emerged a century ago. We will master a deeper level of reality, but of course the question is: will it be the ultimate level of reality? Or will we just have a theory of everything we know now, a 1998-TOE? My personal opinion is that superstring theories are already breaking into a deeper level of reality. I have no idea how far we are from the ultimate level, if it exists.
Vittorio Celli