Re: Question about space, time and string theory

"Igor Khavkine" <igor.kh@xxxxxxxxx> wrote in message
news:slrnfsmn7f.v6s.igor.kh@xxxxxxxxxxxxxxxxxxxxxx
.. . .

There is a simple way to address this question. I fear, though, that
it
may not make you very happy, since it doesn't answer your question
directly.

Simply put, string theory neither demands nor offers any special
insights into the nature of space-time, beyond what is required by
special relativity.

I can try to describe the kind of space-time used in string theory. If
the description is clear enough, it may help you answer your original
question to your own satisfaction. If not, you can ask followup
questions to make the description more clear.

Imagine space-time as described in standard special relativity. String
theory's space-time has three key differences: (a) it is higher
dimensional, (b) it has non-trivial topology, (c) it is curved.

Concerning (a), whenever special relativity makes reference to 3 being
the number of spatial dimensions, replace that number by something
larger (usually 25 or 9, depending on the version of string theory).

Concerning (b), different topologies are easier to picture in lower
dimensions. Suppose there is only one spatial dimension and one
temporal. Then, the space-time of special relativity looks like a flat
*** of paper (infinitely extended). On the other hand, one could
imagine a piece of paper rolled into a cylinder (infinitely extended
along its length). The axial direction would be the temporal
dimension,
while the transverse direction would be the spatial one. The cylinder
cannot be deformed into a flat *** without being torn. Thus, the two
kinds of space-time are said to have different topologies. One special
feature of the cylindrical space-time is that the circumference of the
spatial dimension is finite. Now, translate this to the higher
dimensional case. String theory supposes that the space-time is, say,
10
dimensional. Of those, 4 are infinitely extended (one temporal and
three spatial), while the remaining 6 are similar to the spatial
dimension of the cylindrical space-time: their circumferences are
finite. These 6 are the so-called "hidden dimensions".

Concerning (c), curvature corresponds to the presence of gravity
(exactly as in general relativity). However, often, gravity can be
neglected if one is only concerned with very short distances and time
intervals, hence so can curvature.

Finally, about observability of the hidden dimensions. String theory
supposes them to be just as observable as the other 4. However, it
also
supposes that their circumferences are extremely tiny (possibly
smaller
than subnuclear scales). If that is true, they are unobservable due to
technological difficulties (there is no particle accelerator large
enough to probe them), but not in principle. If, on the other hand,
one
could ask what size should the hidden dimensions be to be detectable
with current technology. Supposing that they are in deed that large
leads to proposals generally called "large extra dimensions". There
have
been experiments designed to test for large extra dimensions. However,
they've only produced null results. So, from the point of view of
string
theory, the hidden dimensions are in principle observable, but so far
unobserved.

Hope this helps.

Igor

Igor,

Following your exposition above, I would like to know your educated
personal opinion -- which I have a great deal of respect for -- as to
whether you believe the compact dimensions in string theory will one day
turn out to be real physics, or science fiction.

I have myself gone from being highly skeptical of compact dimensions to
believing that they have some merit. I have also come to realize just
how heatedly some people feel about string theory and compact dimensions
on both sides.

Are you willing to share your views on this?

Also, you say that the hidden dimensions "are unobservable due to
technological difficulties (there is no particle accelerator large
enough to probe them), but not in principle." Might there be indirect
effects that can be observed, even if the dimensions themselves cannot
be? For example, presumably, field quanta such as electrons can have
some motion through these dimensions. How might motion of an electron
through a cylindrical dimension be manifest on a scale we can observe?

Thanks,

Jay.
____________________________
Jay R. Yablon
Email: jyablon@xxxxxxxxxxxx
co-moderator: sci.physics.foundations
Weblog: http://jayryablon.wordpress.com/
Web Site: http://home.nycap.rr.com/jry/FermionMass.htm

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