From Eternity to Here (65 page)

It’s interesting to approach this scenario like real scientists, and ask whether there could be any testable consequences of a low-entropy future condition. Even if such a condition existed, it would be easy enough to avoid any prospective consequences, just by putting the Big Crunch very far in the future. But if it were relatively near in time (a trillion years from now, say, rather than a googol years), we might be able to
see
the effects of the future decrease in entropy.
²⁸¹

Imagine, for example, that there was a bright source of light (which we’ll call a “star” for convenience) that lived in the future collapsing phase. How might we detect it? The way we detect an ordinary star is that it emits photons, which travel on light cones radially outward from the star; we absorb the photon in the future of the emitting event, and declare that we see the star. Now let’s run this backward in time.
²⁸²
We find photons moving radially
toward
the star in the future; instead of shining, the star sucks light out of the universe.

So you might think that we could “see” the future star by looking in the opposite direction from where the star actually is, and detecting one of the photons that was headed its way. But that’s not right—if we absorb the photon, it never makes it to the star. There is a future boundary condition, which requires that photons be absorbed by the star—not merely that they are headed its way. What we would actually see is our telescopes
emitting
light out into space, in the direction of the future star.
²⁸³
If the telescope is pointed in the direction of a future star, it emits light; if it’s not, it remains dark. That’s the time-reverse of the more conventional idea: “If the telescope is pointed in the direction of a past star, it sees light; if it’s not, it doesn’t see anything.”

All this seems crazy; but that’s only because we’re not used to thinking about a world with a future boundary condition. “How does the telescope know to emit light when it’s pointed in the direction of a star that won’t even exist for another trillion years?” That’s what future boundary conditions are all about—they pick out the fantastically tiny fraction of microstates within our current macrostate in which such a seemingly unlikely event happens.
²⁸⁴
Deep down, there is nothing stranger about this than there is about the past boundary condition in our actual universe, other than we’re used to one but not the other. (By the way, so far nobody has found any experimental evidence for future stars, or any other evidence of a future low-entropy boundary condition. If they had, you probably would have heard about it.)

Meanwhile, the example of the Gold universe serves more as a cautionary tale than as a serious candidate to account for the arrow of time. If you think you have some natural explanation for why the early universe had such a low entropy, but you claim not to invoke any explicit violations of time-reversal symmetry, why shouldn’t the late universe look the same way? This thought experiment drives home just how puzzling the low-entropy configuration of the Big Bang really is.

The smart money these days is that the universe won’t actually re-collapse. The universe is accelerating; if the dark energy is an absolutely constant vacuum energy (which is the most straightforward possibility), the acceleration will continue forever. We don’t know enough to say for sure, but it’s most likely that our future is absolutely unlike our past. Which, again, places the unusual circumstances surrounding the Big Bang front and center as a puzzle we would like to solve.

BEFORE THE BIG BANG

We almost seem to have run out of options. If we don’t put in time asymmetry by hand (either in the dynamical laws or in a boundary condition), and the Big Bang has a low entropy, but we don’t insist on a low-entropy future condition—what is left? We seem to be caught in a viselike grip of logic, with no remaining avenues to reconcile the evolution of entropy in our observable universe with the reversibility of the fundamental laws of physics.

There is a way out: We can accept that the Big Bang had a low entropy, but deny that the Big Bang was the beginning of the universe.

This sounds a bit heretical to anyone who has read about the success of the Big Bang model, or who knows that the existence of an initial singularity is a firm prediction of general relativity. We are often told that there is no such thing as “before the Big Bang”—that time itself (as well as space) doesn’t exist prior to the initial singularity. That is, the concept of “prior to the singularity” just doesn’t make any sense.

But as I mentioned briefly in Chapter Three, the idea that the Big Bang is truly the beginning of the universe is simply a plausible hypothesis, not a result established beyond reasonable doubt. General relativity doesn’t predict that space and time didn’t exist before the Big Bang; it predicts that the curvature of spacetime in the very early universe became so large that general relativity itself ceases to be reliable. Quantum gravity, which we can happily ignore when we’re talking about the curvature of spacetime in the relatively placid context of the contemporary universe, absolutely must be taken into account. And, sadly, we don’t understand quantum gravity well enough to say for sure what actually happens at very early times. It might very well be true that space and time “come into existence” in that era—or not. Perhaps there is a transition from a phase of an irredeemably quantum wave function to the classical spacetime we know and love. But it is equally conceivable that space and time extend beyond the moment that we identify as “the Big Bang.” Right now, we simply don’t know; researchers are investigating different possibilities, with an open mind about which will eventually turn out to be right.

Some evidence that time doesn’t need to have a beginning comes from quantum gravity, and in particular from the holographic principle we talked about in Chapter Twelve.
²⁸⁵
Maldacena showed that a particular theory of gravity in five-dimensional anti-de Sitter space is exactly equivalent to a “dual” four-dimensional theory that doesn’t include gravity. There are plenty of questions that are hard to answer in the five-dimensional gravity theory, just like any other model of quantum gravity. But some of these issues become very straightforward from the dual four-dimensional perspective. For example: Does time have a beginning? Answer: no. The four-dimensional theory doesn’t involve gravity at all; it’s just a field theory that lives in some fixed spacetime, and that spacetime extends infinitely far into the past and the future. That’s true even if there are singularities in the five-dimensional gravity theory; somehow, the theory finds a way to continue on beyond them. So we have an explicit example of a complete theory of quantum gravity, where there exists at least one formulation of the theory in which time never begins or ends, but stretches for all eternity. Admittedly, our own universe does not look much like five-dimensional anti-de Sitter space—it has four macroscopic dimensions, and the cosmological constant is positive, not negative. But Maldacena’s example demonstrates that it’s certainly not necessary that spacetime have a beginning, once quantum gravity is taken into account.

We can also take a less abstract approach to what might have come before the Big Bang. The most obvious strategy is to replace the Bang by some sort of bounce. We imagine that the universe before what we call the Big Bang was actually collapsing and growing denser. But instead of simply continuing to a singular Big Crunch, the universe—somehow—bounced into a phase of expansion, which we experience as the Big Bang.

The question is, what causes this bounce? It wouldn’t happen under the usual assumptions made by cosmologists—classical general relativity, plus some reasonable restrictions on the kind of matter and energy in the universe. So we have to somehow change those rules. We could simply wave our hands and say “quantum gravity does it,” but that’s a little unsatisfying.

Figure 83:
A bouncing-universe cosmology replaces the singularity of the standard Big Bang by a (more or less) smooth crossover between a contracting phase and an expanding phase.

Quite a bit of effort in recent years has gone into developing models that smooth out the Big Bang singularity into a relatively gentle bounce.
²⁸⁶
Each of these proposals offers the possibility of extending the history of the universe beyond the Big Bang, but in every case it’s still hard to tell whether the model in question really hangs together. That’s life when you’re trying to understand the birth of the universe in the absence of a full theory of quantum gravity.

But the crucial point is worth keeping in mind: Even if we don’t have one complete and consistent story to tell about how to extend the universe before the Big Bang, cosmologists are hard at work on the problem, and it’s very plausible that they will eventually succeed. And the possibility that the Big Bang wasn’t really the beginning of the universe has serious consequences for the arrow of time.

AN ARROW FOR ALL TIME

If the Big Bang was the beginning of time, we have a very clear puzzle: why was the entropy so small at that beginning? If the Big Bang was
not
the beginning, we still have a puzzle, but a very different one: why was the entropy small at the bounce, which wasn’t even the beginning of the universe? It was just some moment in an eternal history.

For the most part, modern discussions of bouncing cosmologies don’t address the question of entropy directly.
²⁸⁷
But it’s pretty clear that the addition of a contracting phase before the bounce leaves us with two choices: Either the entropy is increasing as the universe approaches the bounce, or it’s decreasing.

At first glance, we might expect that the entropy should increase as the universe approaches the bouncing phase from the past. After all, if we started with an initial condition in the ultra-far past, we expect entropy to increase as time goes on, even if space is contracting; that’s just the Second Law as it is ordinarily understood, and it would make the arrow of time consistent through the whole history of the universe. This possibility is illustrated in the bottom left plot of Figure 84. Implicitly or explicitly, that’s what many people have in mind when they discuss bouncing cosmologies.

Figure 84:
At the top, the size of a bouncing universe through time; at bottom, two possible scenarios for the evolution of entropy. The entropy could simply rise forever, as shown at bottom left, giving rise to a consistent arrow of time through all eternity. Or it could decrease during the contracting phase before beginning to increase in the expanding phase, as shown at bottom right.

But a scenario in which the entropy of our comoving patch increases consistently through a universal bounce faces an incredible problem. In conventional Big Bang cosmology, we have the problem that the entropy is relatively small in the current observable universe, and was substantially smaller in the past. This implies a great deal of hidden fine-tuning in the
present
microstate of the universe, so that entropy would decrease if we used the laws of physics to run it backward in time. But in the bouncing scenario, where we have pushed the “beginning of the universe” infinitely far away, the amount of fine-tuning needed to make this happen becomes infinitely bad. If we believe in reversible laws of physics, we need to imagine a state of the universe today with the property that it could be evolved backward in time forever, with the entropy continually decreasing all the way. That’s a lot to ask.
²⁸⁸

We should also mention a closely related problem. We know that the entropy of our comoving patch immediately after the bounce has to be small—that is, much smaller than it might have been. (From the estimates we made in Chapter Thirteen, it had to be 10
⁸⁸
or smaller, while it might have been as large as 10
¹²⁰
.) Which implies that the entropy was as small, or smaller, just before the bounce. If the entropy were large, you wouldn’t get a bounce; you would get a chaotic mess that would have no hope of coming out the other side as the nice smooth universe from which we emerged. So what we have to imagine is that this comoving patch of space had been contracting for an infinitely long time (from the far past to the moment of the bounce), and in that time the entropy was increasing all along, but managed to increase only a tiny bit. That’s not impossible to imagine, but it strikes us as unusual, to say the least.
²⁸⁹