The Fabric of the Cosmos: Space, Time, and the Texture of Reality

by Brian Greene

Chance and the Arrow

DOES TIME HAVE A DIRECTION?

Perhaps the most pointed example of all is that our minds seem to have access to a collection of events that we call the past—our memories—but none of us seems able to remember the collection of events we call the future. So it seems obvious that there is a big difference between the past and the future. There seems to be a manifest orientation to how an enormous variety of things unfold in time. There seems to be a manifest distinction between the things we can remember (the past) and the things we cannot (the future). This is what we mean by time’s having an orientation, a direction, or an arrow.1

The laws treat what we call past and future on a completely equal footing. Even though experience reveals over and over again that there is an arrow of how events unfold in time, this arrow seems not to be found in the fundamental laws of physics.

First, entropy is a measure of the amount of disorder in a physical system.

Second, in physical systems with many constituents (for instance, books with many pages being tossed in the air) there is a natural evolution toward greater disorder, since disorder can be achieved in so many more ways than order. In the language of entropy, this is the statement that physical systems tend to evolve toward states of higher entropy.

Entropy, the Second Law, and the Arrow of Time

The tendency of physical systems to evolve toward states of higher entropy is known as the second law of thermodynamics.

Since Newton’s laws of physics have no built-in temporal orientation, all of the reasoning we have used to argue that systems will evolve from lower to higher entropy toward the future works equally well when applied toward the past.

Thus, not only is there an overwhelming probability that the entropy of a physical system will be higher in what we call the future, but there is the same overwhelming probability that it was higher in what we call the past.

The second law actually says that if at any given moment of interest, a physical system happens not to possess the maximum possible entropy, it is extraordinarily likely that the physical system will subsequently have and previously had more entropy.

It tells us that the entropic arrow of time is double-headed. From any specified moment, the arrow of entropy increase points toward the future and toward the past. And that makes it decidedly awkward to propose entropy as the explanation of the one-way arrow of experiential time.

The ultimate source of order, of low entropy, must be the big bang itself.

A splattering egg tells us something deep about the big bang. It tells us that the big bang gave rise to an extraordinarily ordered nascent cosmos.

A huge puzzle remains. How is it that the universe began in such a highly ordered configuration, setting things up so that for billions of years to follow everything could slowly evolve through steadily less ordered configurations toward higher and higher entropy?

Time and the Quantum

INSIGHTS INTO TIME’S NATURE FROM THE QUANTUM REALM

In principle, if we knew precisely how things were now—knew the positions and velocities of every single particle making up the universe—classical physics says we could use that information to predict how things would be at any given moment in the future or how they were at any given moment in the past.

Even though we measure an electron’s position as right here right now, a moment ago all it had were probabilities of being here, or there, or way over there.

Surprisingly, this strange and wonderful idea—the brainchild of the Nobel laureate Richard Feynman, one of the twentieth century’s most creative physicists—provides a perfectly viable way of thinking about quantum mechanics. According to Feynman, if there are alternative ways in which a given outcome can be achieved—for instance, an electron hits a point on the detector screen by traveling through the left slit, or hits the same point on the screen but by traveling through the right slit—then there is a sense in which the alternative histories all happen, and happen simultaneously. Feynman showed that each such history would contribute to the probability that their common outcome would be realized, and if these contributions were correctly added together, the result would agree with the total probability predicted by quantum mechanics. Feynman called this the sum over histories approach to quantum mechanics; it shows that a probability wave embodies all possible pasts that could have preceded a given observation, and illustrates well that to succeed where classical physics failed, quantum mechanics had to substantially broaden the framework of history.

Does an electron that strikes the detector screen really get there by traveling along all possible routes, or is Feynman’s prescription merely a clever mathematical contrivance that gets the right answer?

As far as the theory’s verification and predictive utility are concerned, the story we tell of how the electron got to that point on the screen is of little relevance.

Feynman’s coalescing histories are nothing but a particular way of thinking about probability waves, they, too, must evade direct observation. And they do.

So, if you change the setup to observe the electrons in flight, you will see each electron pass by your additional detector in one location or another; you will never see any fuzzy multiple histories.

Quantum mechanics is starkly efficient: it explains what you see but prevents you from seeing the explanation.

For large objects, it turns out that classical paths are, by an enormous amount, the dominant contribution to the averaging process and so they are the ones we are familiar with. But when objects are small, like electrons, quarks, and photons, many different histories contribute at roughly the same level and hence all play important parts in the averaging process.

Pruning History

Niels Bohr liked to summarize such things using his principle of complementarity. Every electron, every photon, everything, in fact, has both wavelike and particlelike aspects. They are complementary features.

Nature does weird things. It lives on the edge. But it is careful to bob and weave from the fatal punch of logical paradox.

Reality and the Quantum Measurement Problem

If a wavefunction says that an electron can be here, there, and way over there, then in one universe a version of you will find it here; in another universe, another copy of you will find it there; and in a third universe, yet another you will find the electron way over there. The sequence of observations that we each make from one second to the next thus reflects the reality taking place in but one part of this gargantuan, infinite network of universes, each one populated by copies of you and me and everyone else who is still alive in a universe in which certain observations have yielded certain outcomes.

In the Many Worlds approach, then, no potential outcome remains merely a potential. Wavefunctions don’t collapse. Every potential outcome comes out in one of the parallel universes.

The alternate paths an electron can follow from the two slits to the detector are not separate, isolated histories. The possible histories commingle to produce the observed outcome. Some paths reinforce each other, while others cancel each other out. Such quantum interference between the various possible histories is responsible for the pattern of light and dark bands on the detector screen. Thus, the telltale difference between the quantum and the classical notions of probability is that the former is subject to interference and the latter is not.

Does decoherence resolve the quantum measurement problem? Is decoherence responsible for wavefunctions’ closing the door on all but one of the potential outcomes to which they can lead?

Decoherence allows quantum probabilities to be interpreted much like classical ones, but does not provide any finer details that select one of the many possible outcomes to actually happen.

Quantum Mechanics and the Arrow of Time

Thus, even though a time-asymmetric law would provide a partial explanation for why things unfold in one temporal order but never in the reverse order, it could very well call for the same key supplement required by time-symmetric laws: an explanation for why entropy was low in the distant past.

III

SPACETIME AND COSMOLOGY

SYMMETRY AND THE EVOLUTION OF THE COSMOS

As will become clear, the practical connotation of time as a measure of change, as well as the very existence of a kind of cosmic time that allows us to speak sensibly of things like “the age and evolution of the universe as a whole,” rely sensitively on aspects of symmetry.

Symmetry and the Laws of Physics

This symmetry is known as translational symmetry or translational invariance. It applies not only to Newton’s laws but also to Maxwell’s laws of electromagnetism, to Einstein’s special and general relativities, to quantum mechanics, and to just about any proposal in modern physics that anyone has taken seriously.

The laws of physics didn’t have to operate this way.

In fact, we don’t know with absolute certainty that the laws that work here are the same ones that work in far-flung corners of the cosmos. But we do know that should the laws somehow change way out there, it must be way out there, because ever more precise astronomical observations have provided ever more convincing evidence that the laws are uniform throughout space, at least the space we can see.

rotational invariance is a close cousin of translational invariance. It is based on the idea that every spatial direction is on an equal footing with every other.

Every measurement ever done fully confirms this expectation. Thus, we believe that the laws that govern the experiments you carry out and explain the results you find are insensitive both to where you are—this is translational symmetry—and to how you happen to be oriented in space—this is rotational symmetry.

Thus, according to Einstein’s more refined perspective, the laws of physics do not change when you accelerate, as long as you include an appropriate gravitational field in your description of the environment.

So the symmetries of nature are not merely consequences of nature’s laws. From our modern perspective, symmetries are the foundation from which laws spring.

To paraphrase John Wheeler, time is nature’s way of keeping everything—all change, that is—from happening all at once.