Re: Photons in other dimensions

[Hugh Logan <HloganPHY@CFL.RR.COM>]

Larry Smith wrote:
> At 9:37 PM -0400 4/15/04, Hugh Logan wrote:
>
>
> > The Kaluza-Klein theory was largely forgotten until the fairly recent
> > advent of string theory, of which it was a predecessor.

Incidentally, the name "Kaluza-Klein particle" is now used as the name
of a possible candidate for at least one kind of WIMP
(Weakly-Interacting Massive Particles) that could make up cold dark
matter. There is a short article from Physical Review Focus, "Detecting
Dark Dimensions," at http://focus.aps.org/story/v10/st21 with a link to
the abstract of Kaluza-Klein Dark Matter
Hsin-Chia Cheng, Jonathan L. Feng, and Konstantin T. Matchev
Phys. Rev. Lett. 89, 211301 (issue of 18 November 2002). According to
the Phys. Rev. Focus article:

"Kaluza-Klein particles are named for the two theorists who first
proposed that extra dimensions could be "curled up" to a size too small
for us to notice them. In the simplest case, these particles would be
much like those of the standard model, but would move through four
spatial dimensions instead of three. Their momentum along the fourth
dimension would appear as additional mass in three dimensions, so we
would observe heavy photons or heavy electrons, for example. The smaller
the extra dimension, the greater the mass."

I first heard about WIMPS at the Dirac Symposium
( http://www.physics.fsu.edu/DiracSymposium/ . Click on "Program."),
probably in the talk by A. Linde -- unfortunately not among those for
which the slides are shown on the web site. The Dirac Symposium was a
great learning experience.

 Earlier versions
> > of string theory had something like 26 dimensions, but it was shown that
> > 10 dimensions could do just as well.
>
>
> My understanding (very limited) is that we need one more (total of 11) in
> order to make the 5 versions of string theory unify into one M-theory.
Yes. My copy of _Hyperspace_ by Kaku from 1994 has "10th dimension" on
the front cover, and the article I referred to below treats string
theory as a 10 dimensional theory until the very last section on
M-theory, where it is mentioned that the latter must be a 11-dimensional
theory. That does ring a bell with me from talks at the Dirac Symposium
I referred to and my subsequent web searches over a year ago.

But I just looked up the dimensions of the various flavors of string
theory. There are two charts at
http://www.superstringtheory.com/basics/basic5a.html, the first showing
four bosonic theories each with 26 spacetime dimensions. Five
superstring theories are listed, apparently called "superstring" because
supersymmetry was needed to include fermionic matter. All five
superstring theories listed involve 10 dimensions of spacetime. They do
more than just as well as the 26 dimensional theories if only because
they include fermionic matter as well as bosons. I recall reading that
Neveu, Schwarz, and Ramond were the ones that brought the number of
dimensions down from 26 to 10 in the RNS model, Pierre Ramond
introducimg fermions into the theory. I remember him from the Dirac
Symposium. There is an account of the RNS model at
http://www.superstringtheory.com/experm/exper4a1.html .

> > According to fairly recent developments in string theory, there are
> > subspaces within the nine spatial dimensions of string theory caled
> > branes, which can have dimensios 1, 2, ... up to 9. A one dimensional
> > brane would be a point, a 2-d brane would be a membrane,
>
>
> Wouldn't one dimensional be a line or string?

Certainly not a point, which would be 0-d. That was a slip. I don't know
if an infinitely extended line would qualify as a 1-brane. According to
my reference, "Beyond String Theory,"
http://tena4.vub.ac.be/beyondstringtheory/index.html  ,
"The branes that we find can have dimension 0 (points), 1 (stringlike
branes), 2 (membranes), 3 (volumes, like the space we live in), and even
higher dimensions, up to nine, since otherwise they wouldn't fit into
our nine-dimensional space anymore." A more physical explanation of
branes (p-branes) may be found at
http://www.superstringtheory.com/basics/basic7.html . They refer to a
1-d brane as a string. The branes have physical as well as geometrical
properties. D-branes are also discussed, as is M-theory. Regarding the
dimensionality of M-theory,
"Technically speaking, M theory is is the unknown eleven-dimensional
theory whose low energy limit is the supergravity theory in eleven
dimensions discussed above." But there are other ideas of what M theory
should be.

"The Official String Theory Web Site" at
http://www.superstringtheory.com/index.html, pages of which have been
cited above, is a wonderful source of information. It contains
practically a minicourse in string theory in which one can toggle back
and forth between basic and advanced versions of the explanations. There
is also a section on the possibility of experimental verification. And
there are two "theater" presentations -- one about the history of string
theory, "String Theory: A Multihistory," in which John Schwarz, Michael
Green, Pierre Ramond, and Lars Brink are interviewed (The voices are
sometimes a little difficult to understand.)and a colloquium, "The
Second Superstring Revolution" by John Schwarz. The sound is good on the
latter-- at least in what I have heard so far.

Hugh Logan
Retired physics teacher