« October 3, 2011 | Main | October 23, 2011 »
Monday, October 10, 2011
Reading List: Cycles of Time
- Penrose, Roger. Cycles of Time. New York: Alfred A. Knopf, 2010. ISBN 978-0-307-26590-6.
-
One of the greatest and least appreciated mysteries of
contemporary cosmology is the extraordinarily special state
of the universe immediately after the big bang. While at
first glance an extremely hot and dense mass of elementary
particles and radiation near thermal equilibrium might seem
to have near-maximum entropy, when gravitation is taken into
account, its homogeneity (the absence of all but the most
tiny fluctuations in density) actually caused it to have
a very small entropy. Only a universe which began in such a
state could have a well-defined arrow of time which permits
entropy to steadily increase over billions of years as
dark matter and gas clump together, stars and galaxies form, and black
holes appear and swallow up matter and radiation. If
the process of the big bang had excited gravitational
degrees of freedom, the overwhelmingly most probable outcome
would be a mess of black holes with a broad spectrum of
masses, which would evolve into a universe which looks
nothing like the one we inhabit. As the author has
indefatigably pointed out for many years, for some reason
the big bang produced a universe in what appears to be
an extremely improbable state. Why is this? (The
preceding sketch may be a bit telegraphic because I discussed
these issues at much greater length in my review of
Sean Carroll's
From Eternity to Here [February 2010]
and didn't want to repeat it all here. So, if you aren't
sure what I just said, you may wish to read that review
before going further.)
In this book, Penrose proposes “conformal cyclic cosmology”
as the solution to this enigma. Let's pick this apart, word by
word.
A conformal
transformation is a mathematical mapping which
preserves angles in infinitesimal figures. It is possible to
define a conformal transformation (for example, the
hyperbolic transformation
illustrated by M. C. Escher's Circle Limit III)
which maps an infinite space onto a finite one. The author's own
Penrose diagrams
map all of (dimension reduced) space-time onto a finite plot
via a conformal transformation. Penrose proposes a conformal transformation
which maps the distant future of a dead universe undergoing runaway expansion
to infinity with the big bang of a successor universe, resulting in
a cyclic history consisting of an infinite number of
“æons”, each beginning with its own big bang and
ending in expansion to infinity. The resulting cosmology is
that of a single universe evolving from cycle to cycle, with the
end of each cycle producing the seemingly improbable conditions required
at the start of the next. There is no need for an inflationary epoch
after the big bang, a multitude of unobservable universes in a
“multiverse”, or invoking the anthropic principle to
explain the apparent fine-tuning of the big bang—in Penrose's
cosmology, the physics makes those conditions inevitable.
Now, the conformal rescaling Penrose invokes only works if the universe
contains no massive particles, as only massless particles which always
travel at the speed of light are invariant under the conformal transformation.
Hence for the scheme to work, there must be only massless particles in the universe
at the end of the previous æon and immediately after the big bang—the
moment dubbed the “crossover”. Penrose argues that at the
enormous energies immediately after the big bang, all particles were
effectively massless anyway, with mass emerging only through symmetry
breaking as the universe expanded and cooled. On the other side of the
crossover, he contends that in the distant future of the previous æon
almost all mass will have been accreted by black holes which then
will evaporate through the
Hawking process
into particles
which will annihilate, yielding a universe containing only massless
photons and gravitons. He does acknowledge that some matter may
escape the black holes, but then proposes (rather dubiously in my
opinion) that all stable massive particles are ultimately
unstable on this vast time scale (a hundred orders of magnitude
longer than the time since the big bang), or that mass may just
“fade away” as the universe ages: kind of like the
Higgs particle
getting tired (but then most of the mass of stable
hadrons doesn't come from the Higgs process, but rather the
internal motion of their component quarks and gluons).
Further, Penrose believes that information is lost when it falls
to the singularity within a black hole, and is not preserved in
some correlation at the event horizon or in the particles
emitted as the black hole evaporates. (In this view he is now
in a distinct minority of theoretical physicists.) This makes
black holes into entropy destroying machines. They devour all of
the degrees of freedom of the particles that fall into them and
then, when they evaporate with a “pop”, it's all
lost and gone away. This allows Penrose to avoid what would otherwise
be a gross violation of the second law of thermodynamics. In his
scheme the big bang has very low entropy because all of the entropy
created in the prior æon has been destroyed by falling into
black holes which subsequently evaporate.
All of this is very original, clever, and the mathematics is quite
beautiful, but it's nothing more than philosophical speculation
unless it makes predictions which can be tested by observation
or experiment. Penrose believes that gravitational radiation emitted
from the violent merger of galactic-mass black holes in the previous
æon may come through the crossover and imprint itself
as concentric circles of low temperature variation in the cosmic background
radiation we observe today. Further, with a colleague, he argues that
precisely such structures
have been observed in two separate surveys of the background
radiation. Other researchers
dispute
this
claim,
and the
debate continues.
For the life of me, I cannot figure out to which audience this book
is addressed. It starts out discussing the second law of thermodynamics
and entropy in language you'd expect in a popularisation aimed at
the general public, but before long we're into territory like:
Ahhhh…now I understand! Seriously, much of this book is tough going, as technical in some sections as scholarly publications in the field of general relativity, and readers expecting a popular account of Penrose's proposal may not make it to the payoff at the end. For those who thirst for even more rigour there are two breathtakingly forbidding appendices. The Kindle edition is excellent, with the table of contents, notes, cross-references, and index linked just as they should be.We now ask for the analogues of F and J in the case of the gravitational field, as described by Einstein's general theory of relativity. In this theory there is a curvature to space-time (which can be calculated once knows how the metric g varies throughout the space-time), described by a [ 04]-tensor R, called the Riemann(-Christoffel) tensor, with somewhat complicated symmetries resulting in R having 20 independent components per point. These components can be separated into two parts, constituting a [ 04]-tensor C, with 10 independent components, called the Weyl conformal tensor, and a symmetric [ 02]-tensor E, also with 10 independent components, called the Einstein tensor (this being equivalent to a slightly different [ 02]-tensor referred to as the Ricci tensor[2.57]). According to Einstein's field equations, it is E that provides the source to the gravitational field. (p. 129)
Posted at
21:09
