- Carroll, Sean.
From Eternity to Here.
New York: Dutton, 2010.
ISBN 978-0-525-95133-9.
-
The nature of time has perplexed philosophers
and scientists from the ancient Greeks (and
probably before) to the present day. Despite two and half
millennia of reflexion upon the problem and spectacular
success in understanding many other aspects of the universe
we inhabit, not only has little progress been made on
the question of time, but to a large extent we are still
puzzling over the same problems which vexed thinkers in the
time of Socrates: Why does there seem to be an inexorable
arrow of time which can be perceived in physical processes
(you can scramble an egg, but just try to unscramble one)?
Why do we remember the past, but not the future? Does time
flow by us, living in an eternal present, or do we move
through time? Do we have free will, or is that an illusion and
is the future actually predestined? Can
we travel to the past or to the future? If we are typical
observers in an eternal or very long-persisting universe, why
do we find ourselves so near its beginning (the big bang)?
Indeed, what we have learnt about time makes these puzzles
even more enigmatic. For it appears, based both on theory
and all experimental evidence to date, that the microscopic
laws of physics are completely reversible in time: any physical
process can (and does) go in both the forward and reverse
time directions equally well. (Actually, it's a little more
complicated than that: just reversing the direction of time
does not yield identical results, but simultaneously reversing
the direction of time [T], interchanging left and right [parity: P],
and swapping particles for antiparticles [charge: C] yields
identical results under the so-called “CPT” symmetry
which, as far is known, is absolute. The tiny violation of
time reversal symmetry by itself in weak interactions seems,
to most physicists, inadequate to explain the perceived
unidirectional arrow of time, although
some disagree.)
In this book, the author argues that the way in which we
perceive time here and now (whatever “now” means)
is a direct consequence of the initial conditions which
obtained at the big bang—the beginning of time, and
the future state into which the universe is evolving—eternity.
Whether or not you agree with the author's conclusions, this
book is a tour de force
popular exposition of thermodynamics and statistical mechanics,
which provides the best intuitive grasp of these concepts of
any non-technical book I have yet encountered. The science
and ideas which influenced thermodynamics and its
practical and philosophical consequences
are presented in a historical context, showing how in many
cases phenomenological models were successful in grasping the
essentials of a physical process well before the actual underlying
mechanisms were understood (which is heartening to those trying
to model the very early universe absent a
theory of quantum gravity).
Carroll argues that the
Second
Law of Thermodynamics entirely
defines the arrow of time. Closed systems
(and for the purpose of the argument here we can consider the
observable universe as such a system, although it is not precisely
closed: particles enter and leave our horizon as the universe
expands and that expansion accelerates) always evolve from a state
of lower probability to one of higher probability: the “entropy”
of a system is (sloppily stated) a measure of the probability of finding
the system in a given macroscopically observable state, and over
time the entropy always stays the same or increases; except for
minor fluctuations, the entropy increases until the system reaches
equilibrium, after which it simply fluctuates around the equilibrium
state with essentially no change in its coarse-grained observable
state. What we perceive as the arrow of time is simply systems
evolving from less probable to more probable states, and since
they (in isolation) never go the other way, we naturally observe
the arrow of time to be universal.
Look at it this way—there are vastly fewer configurations of the
atoms which make up an egg as produced by a chicken: shell
outside, yolk in the middle, and white in between, as there are
for the same egg scrambled in the pan with the fragments of
shell discarded in the poubelle. There are an almost inconceivable
number of ways in which the atoms of the yolk and white can mix
to make the scrambled egg, but far fewer ways they can end up
neatly separated inside the shell. Consequently, if we see a movie
of somebody unscrambling an egg, the white and yolk popping up from
the pan to be surrounded by fragments which fuse into an unbroken
shell, we know some trickster is running the film backward: it
illustrates a process where the entropy dramatically decreases, and
that never happens in the real world. (Or, more precisely, its
probability of happening anywhere in the universe in
the time since the big bang is “beyond vanishingly small”.)
Now, once you understand these matters, as you will after reading the
pellucid elucidation here, it all seems pretty straightforward:
our universe is evolving, like all systems, from lower entropy
to higher entropy, and consequently it's only natural that we
perceive that evolution as the passage of time. We remember
the past because the process of storing those memories increases
the entropy of the universe; we cannot remember the future
because we cannot predict the precise state of the coarse-grained
future from that of the present, simply because there are far
more possible states in the future than at the present. Seems
reasonable, right?
Well,
up to a point, Lord Copper.
The real mystery, to which Roger
Penrose and others have been calling attention for some
years, is not that entropy is increasing in our universe, but
rather why it is presently so low compared to what
it might be expected to be in a universe in a randomly chosen
configuration, and further, why it was so absurdly low in the
aftermath of the big bang. Given the initial conditions after
the big bang, it is perfectly reasonable to expect the
universe to have evolved to something like its present state.
But this says nothing at all about why the big bang
should have produced such an incomprehensibly improbable set of
initial conditions.
If you think about entropy in the usual thermodynamic sense
of gas in a box, the evolution of the universe seems distinctly
odd. After the big bang, the region which represents today's observable
universe appears to have been a thermalised system of particles and
radiation very near equilibrium, and yet today we see nothing
of the sort. Instead, we see complex structure at scales from
molecules to superclusters of galaxies, with vast voids in between,
and stars profligately radiating energy into space with a temperature
less than three degrees above absolute zero. That sure doesn't look
like entropy going down: it's more like your leaving a pot of tepid water
on the counter top overnight and, the next morning, finding
a village of igloos surrounding a hot spring. I mean, it
could happen, but how probable is that?
It's gravity that makes the difference. Unlike all of the other
forces of nature, gravity
always attracts.
This means that when
gravity is significant (which it isn't in a steam engine or
pan of water), a gas at thermal equilibrium is actually in a state
of very low entropy. Any small compression or rarefaction in a
region will cause particles to be gravitationally attracted to volumes with
greater density, which will in turn reinforce the inhomogeneity,
which will amplify the gravitational attraction. The gas at thermal
equilibrium will, then, unless it is perfectly homogeneous (which
quantum and thermal fluctuations render impossible) collapse into
compact structures separated by voids, with the entropy increasing
all the time. Voilà galaxies, stars, and planets.
As sources of energy are exhausted, gravity wins in the end, and
as structures compact ever more, entropy increasing apace, eventually
the universe is filled only with black holes (with vastly more
entropy than the matter and energy that fell into them) and cold
dark objects. But wait, there's more! The expansion of the universe
is accelerating, so any structures which are not gravitationally
bound will eventually disappear over the horizon and the remnants
(which may ultimately decay into a gas of unbound particles,
although the physics of this remains speculative) will occupy
a nearly empty expanding universe (absurd as this may sound, this
de Sitter space
is an exact solution to Einstein's equations of General
Relativity). This, the author argues, is the highest entropy
state of matter and energy in the presence of gravitation, and it
appears from current observational evidence that that's indeed
where we're headed.
So, it's plausible the entire evolution of the universe from
the big bang into the distant future increases entropy all the
way, and hence there's no mystery why we perceive an arrow of
time pointing from the hot dense past to cold dark eternity.
But doggone it, we still don't have a clue why the
big bang produced such low entropy! The author surveys a number
of proposed explanations, some of which invoke fine-tuning with
no apparent physical explanations, summon an enormous
(or infinite) “multiverse” of all possibilities and
argue that among such an ensemble, we find ourselves in one of
the vanishingly small fraction of universes like our own because
observers like ourselves couldn't exist in all the others (the
anthropic argument), or that the big bang was not actually the
beginning and that some dynamical process which preceded the
big bang (which might then be considered a “big bounce”)
forced the initial conditions into a low entropy state. There
are many excellent arguments against these proposals, which are
clearly presented. The author's own favourite, which he concedes
is as speculative as all the others, is that de Sitter space
is unstable against a quantum fluctuation which nucleates
a disconnected bubble universe in which entropy is initially low.
The process of nucleation increases entropy in the multiverse,
and hence there is no upper bound at all on entropy,
with the multiverse eternal in past and future, and entropy
increasing forever without bound in the future and decreasing
without bound in the past.
(If you're a regular visitor here, you know what's coming, don't you?)
Paging friar
Ockham! We start out having discovered yet another piece of
evidence for what appears to be a fantastically improbable fine-tuning
of the initial conditions of our universe. The deeper we investigate
this, the more mysterious it appears, as we discover no reason in the
dynamical laws of physics for the initial conditions to be have been
so unlikely among the ensemble of possible initial conditions.
We are then faced with the “trichotomy” I discussed
regarding the
origin of life on Earth: chance (it just happened
to be that way, or it was every possible way, and we, tautologically,
live in one of the universes in which we can exist), necessity (some
dynamical law which we haven't yet figured out caused the initial
conditions to be the way we observe them to have been), or
(and here's where all the scientists turn their backs upon me,
snuff the candles, and walk away) design. Yes, design. Suppose
(and yes, I know, I've used this analogy before and will certainly
do so again) you were a character in a video game who somehow became
sentient and began to investigate the universe you inhabited. As
you did, you'd discover there were distinct regularities which governed
the behaviour of objects and their interactions. As you probed
deeper, you might be able to access the machine code of the
underlying simulation (or at least get a glimpse into its operation
by running precision experiments). You would discover that
compared to a random collection of bits of the same length, it
was in a fantastically improbable configuration, and you could
find no plausible way that a random initial configuration could
evolve into what you observe today, especially since you'd found
evidence that your universe was not eternally old but rather came
into being at some time in the past (when, say, the game cartridge
was inserted).
What would you conclude? Well, if you exclude the design hypothesis,
you're stuck with supposing that there may be an infinity of
universes like yours in all random configurations, and you
observe the one you do because you couldn't exist in all but a very
few improbable configurations of that ensemble. Or you might argue that
some process you haven't yet figured out caused the underlying substrate
of your universe to assemble itself, complete with the copyright
statement and the Microsoft security holes, from a generic configuration
beyond your ability to observe in the past. And being clever, you'd
come up with persuasive arguments as to how these most implausible
circumstances might have happened, even at the expense of invoking
an infinity of other universes, unobservable in principle, and an
eternity of time, past and present, in which events could play out.
Or, you might conclude from the quantity of initial information you
observed (which is identical to low initial entropy) and the
improbability of that configuration having been arrived at by
random processes on any imaginable time scale, that it was
put in from the outside by an intelligent designer:
you might call Him or Her the
Programmer,
and some might even
come to worship this being, outside the observable universe,
which is nonetheless responsible for its creation and the wildly
improbable initial conditions which permit its inhabitants to exist
and puzzle out their origins.
Suppose you were running a simulation of a universe,
and to win the science fair you knew you'd have to show the
evolution of complexity all the way from the get-go to the point
where creatures within the simulation started to do precision
experiments, discover
curious
fine-tunings and discrepancies,
and begin to wonder…? Would you start your simulation at
a near-equilibrium condition? Only if you were a complete
idiot—nothing would ever happen—and whatever you might
say about
post-singularity
super-kids, they aren't idiots (well, let's not talk about the music
they listen to, if you can call that music). No, you'd start the
simulation with extremely low entropy, with just enough inhomogeneity
that gravity would get into the act and drive the emergence of
hierarchical structure. (Actually, if you set up quantum mechanics the
way we observe it, you wouldn't have to put in the inhomogeneity; it will
emerge from quantum fluctuations all by itself.) And of course you'd
fine tune the parameters of the standard model of particle physics so
your universe wouldn't immediately turn entirely into neutrons,
diprotons, or some other dead end. Then you'd sit back, turn up the
volume on the MultIversePod, and watch it run. Sure 'nuff, after a
while there'd be critters trying to figure it all out, scratching
their balding heads, and wondering how it came to be that way. You
would be most amused as they excluded your existence as a hypothesis,
publishing theories ever more baroque to exclude the possibility of
design. You might be tempted to….
Fortunately, this chronicle does not publish comments. If you're
sending them from the future, please use the
antitelephone.
(The author
discusses this “simulation argument”
in endnote 191. He leaves it to the reader to judge its plausibility,
as do I. I remain on the record as saying, “more likely
than not”.)
Whatever you may think about the Big Issues raised here,
if you've never experienced the beauty of thermodynamics
and statistical mechanics at a visceral level, this is the book
to read. I'll bet many engineers who have been completely
comfortable with computations in “thermogoddamics”
for decades finally discover they “get it” after
reading this equation-free treatment aimed at a popular audience.
February 2010 