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Is it possible?

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Is it possible?

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mathman

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Actually, this is something I wonder about. Technically, what string theory requires is that the central charge be zero. Right?

Is it the case that space must be 11 dimensions in order for the central charge to be zero? Or is it just that 11 dimensions is the

What is the central charge in infinite-dimensional Hilbert space?

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Haelfix

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And string theory and later Mtheory are only anomaly free in exactly D =10 and D = 11 respectively from a straightforward calculation found in most textbooks.

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Haelfix, thanks much for the explanation.

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But if your question applies universally, then parallel universes, the multiverse, considerations make it appear rather likely more dimensions exist. In fact parallel universes might just be partitions of an infinite number of dimensions with different boundary conditions....whatever the case, if there are an infinite number of universes (hard to imagine, I know) then it's not impossible to imagine some of them possibly having infinite dimensions....

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I think that question may be linked to the other question as to whether there is an infinite regression into smaller and smaller particles. As I recall there is a theorem which states that there is a limit to discreteness of particles. I think it has something to do with entropy, event horizons, and number of microstates. Maybe someone here can give more info on that. But anyway, if there were an infinite number of dimensions, then wouldn't that mean there were an infinite number of degrees of freedom, and you'd have the same issues as with an infinite number of infinitesimal particles. Right?Is it possible?

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apeiron

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But the most salient point here is that "particles" would be as much like zero-D entities as possible - discrete points. An infinity of dimensions would be at the other end of the spectrum - infinite-D.

We think of dimensions as spatial - flat euclidean space in fact - but that is a special case. So again, the question would be rather different depending on whether you meant infinite flat space-like dimensions or just the more abstract thing of an infiinty of degrees of freedom.

There are many people who have tried to argue that "only three extended and flat dimensions" are physically possible. So if we could prove that - and I feel it is likely to be the case - then an infinity of dimensions could not crisply exist. It would be a imaginary thing.

On the somewhat broader question of what would be the story for an infinity of degrees of freedom, this is also enlightening to consider. I would argue that an infinity would actually be continuous - unbroken. So it would be total freedom with, in effect, no orderly directions. A perfect symmetry that in certain logics would be called a vagueness.

I have started a thread on vagueness at...

https://www.physicsforums.com/showthread.php?t=301514

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Chronos

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Dimensionality is only useful to the extent it is required to explain reality. Thus far particle phyisics has not proven more than three spatial dimensions are necessary to explain the universe. More may exist, but, the ball is in the experimental camp at this point. Mathematics is rife with solutions that are unphysical. Just because a solution is mathematically valid does not mean it has a real life application. The simplest solution that works is always preferred in science [occam's razor]. This does not mean higher order mathematical solutions are irrelevant, merely the need to demonstrate they offer a better explanation.

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