Dear Colleagues,Science & Ultimate Reality
More than eighty years ago the German mathematician Theordor Kaluza spotted
a curious property about Einstein's general theory of relativity. The field
equations of this theory describe how spacetime is warped by matter, which
is generally accepted as the most satisfactory account of gravitation.
Kaluza noticed that if Einstein's equations are written down for a universe
in which space has four dimensions rather than three, then not only is
gravity correctly described, but electromagnetism too. In other words, if
the world were really five dimensional rather than four (adding in time as
well) then both electromagnetism and gravitation would have a common
geometrical basis. By all accounts Einstein wasn't very impressed with the
idea.
Clever though Kaluza's theory was, it had a major drawback. Where is the
fifth dimension? Why don't we see it? A possible answer was provided by
Oskar Klein. Imagine viewing a hosepipe from afar; it would look like a
wiggly line. On closer inspection, however, the line would be revealed as a
tube, and what was apparently a point on the line would turn out to be a
little circle going around the tube. In the same way, what we might take to
be a structureless point in three-dimensional space might in actuality be a
little circle going around a fourth space dimension. So the reason we don't
see the extra space dimension could be because it is rolled up to a tiny
size (a configuration known to physicists as 'compactigfication'). Klein
computed the circumference to be about twenty powers of ten smaller than an
atomic nucleus.
The idea can be generalized. Perhaps there are two, three, four. extra space
dimensions folded up out of sight in this manner? Maybe the nuclear forces
could be incorporated this way into a Kaluza-Klein theory, thus reducing all
the forces of nature to pure geometry? Such theories were developed in
earnest in the 1980s. By the time string theory came along, the assumption
of extra dimensions seemed natural. A popular string model, for example, has
26 dimensions in total.
But rolling dimensions up is only one way to hide them. Another is to
suppose that although real space might have four dimensions, we are trapped
in three of them, just as a two-dimensional being is trapped in a surface in
Edwin Abbott's famous (but outrageously sexist) Flatland fable. The
confining entity in the case of three-dimensional space embedded inside four
dimensions is called a 'brane' (after membrane). We could be trapped in a
three-brane if the forces that control normal matter, and the photons
whereby we see other matter, are confined by a sort of potential well. So in
normal circumstances we would not be able to see out into the enveloping
higher dimension. But it would be there alright, and might affect the
physical within our confining brane, for example, by modifying gravity on a
small scale. We can even imagine that collisions between neighboring branes
might occur, creating big bangs. Braney researchers have explored many such
speculative ideas
Lisa Randall is a high-energy physicist from Harvard who hopes we will be
able to detect the fifth dimension at work through subtle experiments. If
she is right, then in cosmology what you get might be much more than what
you see.
Paul Davies
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Title: The Shape of Gravity
Author: Lisa Randall
Summary:
When thinking about the outstanding issues in cosmology, it is a good idea
to separate the late-time from the early-time issues. It is fairly clear
that at late times standard FRW evolution applies because of the
observations of the CMBR, the abundance of the elements as predicted by
big-bang nucleosynthesis, and the Hubble expansion. However, these probe
only late-time/low-energy cosmology back to when the temperature of the
universe was of order an MeV. The evolution of the early universe is much
less definitive. Early universe cosmology could differ substantially from
the conventional picture. Many of the open questions in cosmology center
around the range of possibilities for this early universe evolution.
Some, such as inflation, are motivated by specific flaws in the conventional
picture (in themselves important questions in cosmology). Some, such as
extra dimensions, are interesting in that they permit substantially
different early universe evolution while nonetheless conforming at late
times to what has been observed. New insights into theories with extra
dimensions have the potential to address other outstanding issues.
Before discussing any specific theory, we list some of the major problems
that cosmologists face. There are the horizon, flatness, and homogeneity
problems that might be addressed by inflation, which itself raises questions
about its implementation. There are questions related to problems raised by
gravity as measured on long distance scales, namely the dark matter and dark
energy problems. There is the question of why the world appears to be
four-dimensional. There is the black hole information paradox, and questions
about the holographic nature of gravitational systems and possible evidence
for nonlocality. And of course there is the long-standing dilemna of the
cosmological constant. Having listed some problems, we now list possible
particle physics or gravity systems and which problems they might help
address.
As with the standard model of particle physics, which agrees with all
existing low-energy data but leaves many naturalness problems unresolved,
the standard theory of late-time cosmology leaves open several naturalness
problems of at least as big proportion. These are successfully addressed by
inflation. However, we have yet to find a fully satisfactory inflationary
model, that is one that does not require some unnatural assumption or
parameter choice. Moreover, the existence of theories of inflation, which
rely on a time period of large nonvanishing cosmological constant, cannot
necessarily be decoupled from the ultimate resolution of the cosmological
constant problem.
Many other intriguing questions have evolved around the issue of the
dimensionality of space. Ultimately, we would like to address the question
of why our universe appears to be four-dimensional. There is the associated
question of whether the ultimate theory is four-dimensional, or only appears
so in cosmology and particle physics that has been observed. Given that they
might exist, it is important to examine the role they might play in
addressing questions in particle physics or cosmology. Within this realm,
there exist many potential directions, including discovering interesting
aspects of gravity theories, exploring new and different time-dependent
solutions, and possibly gaining insight into the fundamental nature of
quantum gravity. By interesting aspects of gravity theories, I refer to the
many new things we have discovered about gravitational theories within only
the last few years. For example, the fact that compactification of
additional dimensions is not essential, that the graviton can have a mass in
AdS space, and the fact that four-dimensional gravity can be a local
phenomenon are all new developments. The last point means that local physics
can be independent of the space far away. Have we been assuming too much by
assuming all of the universe evolves four-dimensionally?
Another property of note is that the cosmological constant problem is
completely revamped in the context of brane-world physics. The problem is no
longer why there is no vacuum energy, but instead why there is a precise
relation between brane energy and that of the surrounding bulk spacetime. By
insight into the fundamental nature of gravity, I refer to the fact that
with explicit new solutions, we can explore questions about holography for
example, which have precise and specific implications in particular
theories. These allow tests of holographic conjectures in regulated versions
of the theories. By exploring features of known holographic examples, we
might also learn features that can be extrapolated to gravitational theories
in general.
It is likely there are many more unanticipated phenomenon yet to be
discovered, and that some major problems remaining in cosmology might
thereby be addressed.
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