From Eternity to Here (42 page)

Just to be careful, though—are you
really
sure you are not a Boltzmann brain? You might respond that you feel the rest of your body, you see other objects around you, and for that matter you have memories of a lower-entropy past: All things that would appear inconsistent with the idea that you are a disembodied brain recently fluctuated out of the surrounding molecules. The problem is, these purported statements about the outside world are actually just statements about your brain. Your feelings, visions, and memories are all contained within the state of your brain. We could certainly imagine that a brain with exactly these sensations fluctuated out of the surrounding chaos. And, as we have argued, it’s much more likely for that brain to fluctuate by itself than to be part of a giant universe. In the Boltzmann-Lucretius scenario, we don’t have recourse to the Past Hypothesis, so it is overwhelmingly likely that all of our memories are false.

Nevertheless, we are perfectly justified in dismissing this possibility, as long as we think carefully about what precisely we are claiming. It’s not right to say, “I know I am not a Boltzmann brain, so clearly the universe is not a random fluctuation.” The right thing to say is, “If I were a Boltzmann brain, there would be a strong prediction: Everything else about the universe should be in equilibrium. But it’s not. Therefore the universe is not a random fluctuation.” If we insist on being strongly skeptical, we might wonder whether not only our present mental states, but also all of the additional sensory data we are apparently accumulating, represent a random fluctuation rather than an accurate reconstruction of our surroundings. Strictly speaking, that certainly is possible, but it’s cognitively unstable in the same sense that we discussed in the last chapter. There is no sensible way to live and think and behave if that is the case, so there is no warrant for believing it. Better to accept the universe around us as it appears (for the most part) to be.

This point was put with characteristic clarity by Richard Feynman, in his famous
Lectures on Physics
:

[F]rom the hypothesis that the world is a fluctuation, all of the predictions are that if we look at a part of the world we have never seen before, we will find it mixed up, and not like the piece we just looked at. If our order were due to a fluctuation, we would not expect order anywhere but where we have just noticed it . . .

We therefore conclude that the universe is
not
a fluctuation, and that the order is a memory of conditions when things started. This is not to say that we understand the logic of it. For some reason, the universe at one time had a very low entropy for its energy content, and since then the entropy has increased. So that is the way toward the future. That is the origin of all irreversibility, that is what makes the processes of growth and decay, that makes us remember the past and not the future, remember the things which are closer to that moment in history of the universe when the order was higher than now, and why we are not able to remember things where the disorder is higher than now, which we call the future.
¹⁸⁹

WHO ARE WE IN THE MULTIVERSE?

There is one final loophole that must be closed before we completely shut the door on the Boltzmann-Lucretius scenario. Let’s accept the implications of conventional statistical mechanics, that small fluctuations in entropy happen much more frequently than large fluctuations, and that the overwhelming majority of intelligent observers in a universe fluctuating eternally around equilibrium will find themselves alone in an otherwise high-entropy environment, not evolving naturally from a prior configuration of enormously lower entropy.

One might ask: So what? Why should I be bothered that
most
observers (under any possible definition of “observers”) find themselves alone as freak fluctuations in a high-entropy background? All I care about is who I am, not what most observers are like. As long as there is one instance of the universe I see around me somewhere in the eternal lifetime of the larger world (which there will be), isn’t that all I need to proclaim that this picture is consistent with the data?

In other words, the Boltzmann-brain argument makes an implicit assumption: that we are somehow “typical observers” in the universe, and that therefore we should make predictions by asking what most observers would see.
¹⁹⁰
That sounds innocuous, even humble. But upon closer inspection, it leads to conclusions that seem stronger than we can really justify.

Imagine we have two theories of the universe that are identical in every way, except that one predicts that an Earth-like planet orbiting the star Tau Ceti is home to a race of 10 trillion intelligent lizard beings, while the other theory predicts there are no intelligent beings of any kind in the Tau Ceti system. Most of us would say that we don’t currently have enough information to decide between these two theories. But if we are truly typical observers in the universe, the first theory strongly predicts that we are more likely to be lizards on the planet orbiting Tau Ceti, not humans here on Earth, just because there are so many more lizards than humans. But that prediction is not right, so we have apparently ruled out the existence of that many observers without collecting any data at all about what’s actually going on in the Tau Ceti system.

Assuming we are typical might seem like a self-effacing move on our part, but it actually amounts to an extremely strong claim about what happens throughout the rest of the universe. Not only “we are typical observers,” but “typical observers are like us.” Put that way, it seems like a stronger assumption than we have any right to make. (In the literature this is known as the “Presumptuous Philosopher Problem.”) So perhaps we shouldn’t be comparing the numbers of different kinds of observers in the universe at all; we should only ask whether a given theory predicts that observers like us appear
somewhere
, and if they do we should think of the theory as being consistent with the data. If that were the right way to think about it, we wouldn’t have any reason to reject the Boltzmann-Lucretius scenario. Even though most observers would be alone in the universe, some would find themselves in regions like ours, so the theory would be judged to be in agreement with our experience.
¹⁹¹

The difficulty with this minimalist approach is that it offers us too little handle on what is likely to happen in the universe, instead of too much. Statistical mechanics relies on the Principle of Indifference—the assumption that all microstates consistent with our current macrostate are equally likely, at least when it comes to predicting the future. That’s essentially an assumption of typicality: Our microstate is likely to be a typical member of our macrostate. If we’re not allowed to assume that, all sorts of statistical reasoning suddenly become inaccessible. We can’t say that an ice cube is likely to melt in a glass of warm water, because in an eternal universe there will occasionally be times when the opposite happens. We seem to have taken our concerns about typicality too far.

Instead, we should aim for a judicious middle ground. It’s too much to ask that we are typical among all observers in the universe, because that’s making a strong claim about parts of the universe we’ve never observed. But we can at least say that we are typical among observers
exactly like us
—that is, observers with the basic physiology and the same set of memories that we have, the same coarse-grained experience of the universe.
¹⁹²
That assumption doesn’t allow us to draw any unwarranted conclusions about the possible existence of other kinds of intelligent beings elsewhere in the universe. But it is more than enough to rule out the Boltzmann-Lucretius scenario. If the universe fluctuates around thermal equilibrium for all eternity, not only will most observers appear all by themselves from the surrounding chaos, but the same is true for the subset of observers with precisely the features that you or I have—complete with our purported memories of the past. Those memories will generally be false, and fluctuating into them is very unlikely, but it’s still much more unlikely than fluctuating the entire universe. Even this minimal necessary condition for carrying out statistical reasoning—we should take ourselves to be chosen randomly from the set of observers exactly like us—is more than enough to put the Boltzmann-Lucretius scenario to rest.

The universe we observe is not a fluctuation—at least, to be more careful, a statistical fluctuation in an eternal universe that spends most of its time in equilibrium. So that’s what the universe is not; what it
is
, we still have to work out.

ENDINGS

On the evening of September 5, 1906, Ludwig Boltzmann took a piece of cord, tied it to a curtain rod in the hotel room where he was vacationing in Italy with his family, and hanged himself. His body was discovered by his daughter Emma when she returned to their room that evening. He was sixty-two years old.

The reasons for Boltzmann’s suicide remain unclear. Some have suggested that he was despondent over the failure of his ideas concerning atomic theory to gain wider acceptance. But, while many German-speaking scientists of the time remained skeptical about atoms, kinetic theory had become standard throughout much of the world, and Boltzmann’s status as a major scientist was unquestioned in Austria and Germany. Boltzmann had been suffering from health problems and was prone to fits of depression; it was not the first time he had attempted suicide.

But his depression was intermittent; only months before his death, he had written an engaging and high-spirited account of his previous year’s trip to America to lecture at the University of California at Berkeley, and circulated it among his friends. He referred to California as “Eldorado,” but found American water undrinkable, and would drink only beer and wine. This was problematic, as the Temperance movement was strong in America at the time, and Berkeley in particular was completely dry; a recurring theme in Boltzmann’s account is his attempts to smuggle wine into various forbidden places.
¹⁹³
We will probably never know what mixture of failing health, depression, and scientific controversy contributed to his ultimate act.

On the question of the existence of atoms and their utility in understanding the properties of macroscopic objects, any lingering doubts that Boltzmann was right were rapidly dissipating when he died. One of Albert Einstein’s papers in his “miraculous year” of 1905 was an explanation of Brownian motion (the seemingly random motion of small particles suspended in air) in terms of collisions with individual atoms; most remaining skepticism on the part of physicists was soon swept away.

Questions about the nature of entropy and the Second Law remain with us, of course. When it comes to explaining the low entropy of our early universe, we won’t ever be able to say, “Boltzmann was right,” because he suggested a number of different possibilities without ever settling on one in particular. But the terms of the debate were set by him, and we’re still arguing over the questions that puzzled him more than a century ago.

11

QUANTUM TIME

Sweet is by convention, bitter by convention, hot by convention, cold by convention, color by convention; in truth there are but atoms and the void.

—Democritus
¹⁹⁴

Many people who have sat through introductory physics courses in high school or college might disagree with the claim “Newtonian mechanics makes intuitive sense to us.” They may remember the subject as a bewildering merry-go-round of pulleys and vectors and inclined planes, and think that “intuitive sense” is the last thing that Newtonian mechanics should be accused of making.

But while the process of actually calculating something within the framework of Newtonian mechanics—doing a homework problem, or getting astronauts to the moon—can be ferociously complicated, the underlying concepts are pretty straightforward. The world is made of tangible things that we can observe and recognize: billiard balls, planets, pulleys. These things exert forces, or bump into one another, and their motions change in response to those influences. If Laplace’s Demon knew all of the positions and momenta of every particle in the universe, it could predict the future and the past with perfect fidelity; we know that this is outside of our capabilities, but we can imagine knowing the positions and momenta of a few billiard balls on a frictionless table, and at least in principle we can imagine doing the math. After that it’s just a matter of extrapolation and courage to encompass the entire universe.

Newtonian mechanics is usually referred to as “classical” mechanics by physicists, who want to emphasize that it’s not just a set of particular rules laid down by Newton. Classical mechanics is a way of thinking about the deep structure of the world. Different types of things—baseballs, gas molecules, electromagnetic waves—will follow different specific rules, but those rules will share the same pattern. The essence of that pattern is that everything has some kind of “position,” and some kind of “momentum,” and that information can be used to predict what will happen next.

This structure is repeated in a variety of contexts: Newton’s own theory of gravitation, Maxwell’s nineteenth-century theory of electricity and magnetism, and Einstein’s general relativity all fit into the classical framework. Classical mechanics isn’t a particular theory; it’s a paradigm, a way of conceptualizing what a physical theory is, and one that has demonstrated an astonishing range of empirical success. After Newton published his 1687 masterwork,
Philosophiæ Naturalis Principia Mathematica
, it became almost impossible to imagine doing physics any other way. The world is made of things, characterized by positions and momenta, pushed about by certain sets of forces; the job of physics was to classify the kinds of things and figure out what the forces were, and we’d be done.