Re: Photons in other dimensions

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

> I was asked about this today:
>
>         "photons from another dimension that still act as photons in ours?"
>
>
> Some links or sort answers would be appreciated.
>
>
> Josh Green

Herb wanted to know what is meant by "'another dimension.'" The question
might be turned around to ask which are "ours." When I was in school in
the 1940's, the fourth dimension of Einstein's relativity was "just a
theory" in the popular view. My sixth grade arithmetic teacher tried to
explain the fourth dimension to us. He held a book in front of us,
explaining that three dimensions of space were needed to locate its
position. Then he moved the book a few feet, saying that it was moving
in time, the fourth dimension -- at least as I recall his explanation.
Anyway, it was a start. Of course, physicists already knew that
relativity was valid, especially special relativity. In response to
Josh's question, I started reading from Michio Kaku's fascinating book,
_Hyperspace_(8). Before Einstein, there was much speculation about the
fourth dimension in England. However, it was generally regarded as a
spatial dimension rather than a time dimension. It might have been
possible to see projections of four dimensional space in the
three-dimensional space that we perceive, much
as we see two dimensional shadows of three dimensional objects. Some
held that the fourth dimension was the abode of ghosts. One
mathematician, Charles Hinton, was obsessed with the fourth dimension
and its visualization. He is known for his popularization of the four
dimensional hypercube and its projections on three dimensional space.
When asked why the fourth dimension wasn't visible -- at least to most
peoople -- he explained in detail that it was too small. (Charles Hinton
was a British mathematician. He found it necessary to come to the United
States, where he taught at Princeton until he was fired. While at
Princeton, he invented the baseball pitching machine. See Kaku's book
for further details.)

By now, most people who have studied physics accept four dimensions --
three of space and one of time. However, in 1919, Theodr Kaluza sent
Einstein a letter (Kaku, p. 99 ff.) in which he extended Einstein's 16
element (10 independent) to a 25 element (15 independent) metric tensor,
the idea of which Einstein got from Riemann. The fifth row and fifth
column of the new metric tensor contained field quantities from
Maxwell's theory, the common fifth element being a scalar term.
Kaluza's theory combined Maxwell's electromagnetic theory with
Einstein's general relativity theory of gravitation. It was a five
dimensional theory, the fifth dimension being interpreted as a spatial
dimension. Einstein took Kaluza's work very seriously. Why didn't one
observe the fifth dimension or its projections?  Kaluza explained that
it had collapsed down onto a circle. (Kaku, p.105)(1). In 1926, Oskar
Klein further developed the theory, tying it in with quantum theory.
(Kaku, p. 106. According to Klein, the size of the fifth dimension was
the Planck length (10^-33 cm).

The Kaluza-Klein theory was largely forgotten until the fairly recent
advent of string theory, of which it was a predecessor. Earlier versions
of string theory had something like 26 dimensions, but it was shown that
10 dimensions could do just as well. Four of these dimensions are the
familiar space and time dimensions, but the remaining six are
compactified just as the fifth dimension was in the Kaluza-Klein theory.
These dimensions would require incredibly high energies to probe
directly, but I think string theorists think consequences of the the
theory might be observable with the next generation of particle
accelerators.

Where are the photons in the 10 dimensions of string theory? Are all ten
dimensions "our" dimensions? I am not a string theorist, but according
to some accounts, the coordinates of a particle that we can observe
change in the six hidden dimensions, sometimes even when a particle is
at rest as observed in the four non-compactified dimensions (2).
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, and a 3-d brane
could be space as we know it. According to one version (3) of string
theory, photons can exist only in this 3-d brane, the remaining
compactified dimensions being "dark dimensions." I don't know how well
this interpretation is accepted among string theorists. I searched the
web for "photons in string theory," getting many hits. Some were
reponses in advanced forums. Others were popular presentations by
physicists well-known in string theory (4). Some of these mention that
particles including photons result from vibrations on strings, often in
the form of a closed loop, but they are usually not explicit about which
of the hidden dimensions are involved.

After I spent several hours reading from Kaku's _Hyperspace_, Bernard
Cleyet posted a message, suggesting that if Josh meant photons in
parallel universes, that he should ask Kaku, referring to the latter's
web site. That is a good idea. The Preface to _Hyperspace_ is on that
site along with much other information. I haven't gotten to the parallel
universes part of _Hyperspace_ except for a brief mention in connection
with the Kaluza- Klein theory. He explains a one-dimensional line
extended into two dimensions by a circular dimension, sort of like a
straw. If one imagines walking around a circular cross-section of the
straw, one might imagine crossing an infinite number of parallel lines
along the straw, each representing a parallel universe, eventually
returning to the original line.

(1)"Searching for Extra Dimensions," Stephen Abel and John
March-Russell, http://physicsweb.org/article/world/13/11/9/1  .
Article from Physics World, which appears to be the British counterpart
of Physics Today. There is a diagram of the Kaluza fifth dimension in
this article showing the straw-like cylinder.

(2)http://physicsweb.org/article/world/16/11/8. This article tells of
the motion of particles in hidden dimensions, but it is not explicit
about photons.

(3)http://tena4.vub.ac.be/beyondstringtheory/index.html . This is the
title page. Click to get to th introduction. From the menu, select "VII.
Branes." Then look down the page to "A World of Light." Reading the
earlier sections might be helpful.

(4)"A World of Strings" by John Schwarz and David Gross.
http://www.hyper-mind.com/hypermind//universe/content/gsst.htm . Schwarz
and Gross are among the leading string theorists.

There are many other good web sites on string theory, but it would take
a while to see if any of them located the photons among the 10
dimensions of current string theory. My introduction to string theory
was at the Dirac Symposium at FSU (where I obtained my M.S. degree).
There I met some of the leading string theorists, not knowing who some
of them were until I found them on the web later. One good introductory
web site is

(5) "Superstrings," http://www.sukidog.com/jpierre/strings/  .There is a
list of links to other string theory web sites including one to Brian
Greene's "Elegant Universe."

(6) "The Official String Theory Web Site," http://superstringtheory.com/ .
There are a very large number of interesting links here.

Still another resource about string theory is one of many lecture series
online at the Kavli Institute for Theeoretical Physics at UCSB. The
following conference, intended for high school teachers, has talks by
Joe Polchinski (who gave a talk at the Dirac Symposium), Hirosi Ooguri,
 and David Gross. It would take too long to search for photons, but
Polchinski's work on branes is certainly relevant. I can no longer find
the slides for these lectures that were once present on the web.

(7) http://online.itp.ucsb.edu/online/mt01teach/

(8) _Hyperspace, A Scientific Odyssey Through Parallel Universes, Time
Warps, and the 10th Dimension_," Michio Kaku, Oxford University Press, 1994.

I hope that string theory might have something to do with what Josh has
in mind. I am just learning a little about string theory, so I hope
someone more expert can better answer the question. I can't say much
about parallel universes.

Hugh Logan
Retired physics teacher


Herbert H Gottlieb wrote:
> > > Before answering this question, it would be helpful
> > > to know what is meant by "another dimension".  Does it
> > > refer to a dimension such as time, other worlds, or
> > > something in science fiction??
> > > Herb Gottlieb
> >
> > I don't really have an answer for that, but I'm taking it as a real
> > physics topic and not star trek.  If there is an answer that makes
>
> sense to
>
> > you, then I'd like to hear where it leads you.  I'm just fishing with
>
> no
>
> > real assumptions about an answer or even if there is an answer.
> >
> > Josh Green
>
>
> Your question, "Can photons exist in other dimensions" is a question
> in this dimension about another dimension. Therefore one would have
> to be fishing in the other dimension already to obtain meaningful
> insights.
> I'm afraid that your question is fishing far beyond the realm of any real
>
> extra galaxial physics topics.
>
> Herb Gottlieb from New York City
> (Where we have not yet been able to reach other dimensions by "fishing")