The laws of physics as we know them—putting aside the important question of wave function collapses in quantum mechanics—seem to be reversible. But we don’t know the final laws of physics; all we have are very good approximations. Is it conceivable that the real laws of physics are fundamentally irreversible, and that explains the arrow of time?
First let’s untangle a potential misconception about what that would really mean. To “explain” the arrow of time means to come up with a set of laws of physics, and an “initial” state of the universe, so that we naturally (without fine-tuning) witness a change in entropy over time of the sort we observe around us. In particular, if we simply assume that the initial conditions have low entropy, there is nothing to be explained—the entropy will tend to go up, in accordance with Boltzmann, and we’re done. In that case there’s simply no need to posit irreversible laws of physics; the reversible ones are up to the task. But the problem is that such a low-entropy boundary condition seems unnatural.
So if we wish to explain the arrow of time in a natural way by invoking irreversible fundamental laws, the idea would be to postulate a high-entropy condition—a “generic” state of the universe—and imagine that the laws of physics, when acting on that state, naturally work to decrease its entropy. That would count as a real explanation of the arrow. It might seem that this setup gets it backward—it predicts that entropy goes down, rather than up. But the essence of the arrow of time is simply that entropy changes in a consistent direction. As long as that is true, observers who lived in such a world would always “remember” the direction of time that had a lower entropy; likewise, relationships of cause and effect would always put the causes on the lower-entropy side of things, as that is the direction with fewer allowed choices. In other words, such observers would call the high-entropy end of time the “future,” and the low-entropy end “the past,” even though the fundamental laws of physics in this world would only precisely reconstruct the past from the future, and not vice versa.
Such a universe is certainly conceivable. The problem is, it seems like it would be dramatically different from our universe.
Think carefully about what would have to happen for this scenario to work. The universe, for whatever reason, finds itself in a randomly chosen high-entropy state, which looks like empty de Sitter space. Now our postulated irreversible laws of physics act on that state to decrease the entropy. The result—if all this is to have any chance of working out—should be the history of our actual universe, just reversed in time compared to how we traditionally think about it. In other words: Out of the initial emptiness, some photons miraculously focus on a point in space to create a white hole. That white hole gradually grows in mass through the accretion of additional photons (Hawking radiation in reverse). Gradually a collection of additional white holes come into view from far away, arrayed almost uniformly through space. All of these white holes start belching out gas into the universe, which implodes to make stars, which spiral gently away from the white holes to form galaxies. These stars absorb more radiation from the outside world, and use the energy to break down heavy elements into lighter ones. As the galaxies continue to move toward one another in an increasingly rapid contraction of space, the stars disperse into a uniform distribution of gas. Ultimately the universe collapses to a Big Crunch, as matter and radiation form an extremely smooth and uniform distribution near the end of time.
This is the real history of our observable universe, just played backward in time. It’s a perfectly good solution to the laws of physics as we currently understand them; all we have to do is start with the state near the Big Bang, evolve it forward in time to whatever high-entropy microstate it eventually becomes, and then time-reverse that state. But the hypothesis we’re currently considering is very different: It says that an evolution of this form would happen for almost any high-entropy state of empty de Sitter space. That’s a lot to ask of some laws of physics. It’s one thing to imagine entropy going down as a result of irreversible laws, but it’s another thing entirely to imagine it going down in precisely the right way to produce a time-reversed history of our universe.
We can be more specific about where our discomfort with this scenario comes from. We don’t need to think about the whole universe to experience the arrow of time: It’s right here in our kitchen. We drop an ice cube into a glass of warm water, and the ice melts as the water cools off, eventually reaching a uniform temperature. The fundamental-irreversibility hypothesis claims that this can be explained by the deep laws of physics, starting with the uniformly cool glass of liquid water. In other words, the laws of physics purportedly act on the water to separate out different molecules into the form of an ice cube sitting in a glass of warm water, in precisely the way we would expect had we started with the ice cube and water, only backward in time.
But that’s crazy. For one thing: How does it know? Some glasses of cool water were, five minutes ago, glasses of warm water with ice cubes; but others were just glasses of cool water even five minutes ago. Even though there are relatively few microstates corresponding to each low-entropy macrostate, there are a lot more individual low-entropy macrostates than there are high-entropy ones. (More formally, each low-entropy state contains more information than a high-entropy one.)
The problem is closely tied to the issue of complexity I talked about at the end of Chapter Nine. In the real world, as the universe evolves from a low-entropy Big Bang to a high-entropy future, it creates delicate complex structures along the way. The initially uniform gas doesn’t simply disperse as the universe expands; it first collapses into stars and planets, which increase the entropy locally, and sustain intricate ecosystems and information-processing subsystems along the way.
It’s extremely hard, bordering on impossible, to imagine all of that arising from an initially high-entropy state that gets evolved according to some irreversible laws of physics. This is not an airtight argument, but it seems likely that we will have to look somewhere else for an explanation of the arrow of time in the real world.
A SPECIAL BEGINNING
From here on, we’ll be operating under the hypothesis that the fundamental laws of physics are truly reversible: The space of allowed states remains fixed, and the dynamical rules of time evolution conserve the information contained in each state. So how can we possibly hope to account for the low-entropy condition in our observable universe?
For Boltzmann, thinking in the context of an absolute Newtonian space and time, this was quite a puzzle. But general relativity and the Big Bang model offer a new possibility, namely: There was a beginning to the universe, including to time itself, and that the beginning state was one with very low entropy. And you’re not allowed to ask why.
Sometimes, the condition “you’re not allowed to ask why” is rephrased as follows: “We posit a new law of nature, which holds that the initial state of the universe had a very low entropy.” It’s not clear why these two formulations are really any different. In our usual understanding of the laws of physics, two ingredients are required to completely specify the evolution of a physical system: a set of dynamical laws that can be used to evolve the system from one state to another through time, and a boundary condition that fixes which state the system is in at some particular moment. But, even though both the laws and the boundary condition are necessary, they seem like very different things; it’s not clear what is to be gained by thinking of the boundary condition as a “law.” A dynamical law demonstrates its validity over and over again; at every moment, the law takes the current state and evolves it into the next state. But the boundary condition is just imposed once and for all; its nature is more like an empirical fact about the universe than an additional law of physics. There isn’t any substantive distinction between the statements “the early universe had a low entropy” and “it is a law of physics that the early universe had a low entropy” (unless we imagine that there are many universes, all with the same boundary condition).275
Be that
as it may, it’s undoubtedly possible that this is the most we’ll ever be able to say: The low entropy of the early universe is not to be explained via a better understanding of the dynamical laws of physics, but is simply a brute fact, or (if you prefer) an independent law of nature. An example of this approach has been explicitly advocated by Roger Penrose, who has suggested what he calls the “Weyl curvature hypothesis”—a new law of nature that distinguishes explicitly between spacetime singularities that are in the past and those that are in the future. The basic idea is that past singularities have to be smooth and featureless, while future singularities can be arbitrarily messy and complicated.276 This is an explicit violation of time-reversal symmetry, which would ensure that the Big Bang had a low entropy.
The real problem with a proposal like this is its essentially ad hoc nature.277 Asserting that past singularities had to be very smooth doesn’t help you understand anything else about the universe. It “explains” time asymmetry by putting it in by hand. Nevertheless, one could think of it as a placeholder for a more fundamental understanding: If some deeper principles were uncovered that led to a fundamental distinction between initial and final singularities, such that the curvature of the former were constrained but not the latter, we would certainly have made substantial progress toward understanding the origin of the arrow of time. But even this formulation suggests that the real agenda is to keep looking for something deeper.
A SYMMETRIC UNIVERSE
If the fundamental laws of physics are reversible, and we don’t allow ourselves to simply impose time-asymmetric boundary conditions, the remaining possibility seems to be that the evolution of the universe actually is time-symmetric itself, despite appearances to the contrary. It’s not hard to imagine how that might happen, if we are open to the possibility that the universe will eventually stop expanding and re-collapse. Before the discovery of dark energy, many cosmologists found a re-collapsing universe philosophically attractive: Einstein and Wheeler, among others, were drawn to the notion of a universe that was finite in both space and time. A future Big Crunch would provide a pleasing symmetry to the history of a universe that began with a Big Bang.
In the conventional picture, however, any such symmetry would be dramatically marred by the Second Law. Everything we know about the evolution of the entropy of the universe is readily explained by assuming that the entropy was very low near the beginning; from there, it naturally increases with time. If the universe were to re-collapse, there is nothing in the known laws of physics that would prevent the entropy from continuing to increase. The Big Crunch would be a messy, high-entropy place, in stark contrast to the pristine smoothness of the Big Bang.
In an attempt to restore the overall symmetry of the history of the universe, people have occasionally contemplated the need for an additional law of physics: a boundary condition in the future (a “Future Hypothesis,” in addition to the Past Hypothesis), which would guarantee that entropy was low near the Crunch as well as the Bang. This idea, suggested by Thomas Gold (better known as a pioneer of the Steady State model) and others, would imply that the arrow of time would reverse at the moment the universe hit its maximum size, and it would always be true that entropy increased in the direction of time toward which the universe was expanding.278
The Gold universe never really caught on among cosmologists, for a simple reason: There’s no good reason for there to be a future boundary condition of any particular sort. Sure, it restores the overall symmetry of time, but nothing we have experienced in the universe demands such a condition, nor does it follow from any other underlying principles.
Figure 82: At the top, the size of a re-collapsing universe through time; at bottom, two possible scenarios for the evolution of entropy. By conventional lights, we would expect the entropy to increase even as the universe collapsed, as shown at bottom left. In the Gold universe, the entropy is constrained to decrease by a low-entropy future boundary condition.
On the other hand—there’s no good reason for there to be a past boundary condition, either, except for the stubborn fact that we need to invoke one to explain the universe we actually see.279 Huw Price has championed the Gold universe as something that cosmologists should take seriously—at least at the level of a thought experiment, if not as a model for the real world—for just this reason.280 We don’t know why entropy was low near the Big Bang, but it was; therefore, the fact that we don’t know why the entropy should be low near a Big Crunch is not a sufficient reason to discard the possibility. Indeed, without introducing time asymmetry by hand, it stands to reason that whatever unknown principle of physics enforces the low entropy at the Bang could also do so at the Crunch.
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 an
d 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.
From Eternity to Here: The Quest for the Ultimate Theory of Time Page 44
