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FUTURE AND PAST VS. UP AND DOWN
The arrow of time, therefore, is not a feature of the underlying laws of physics, at least as far as we know. Rather, like the up/down orientation space picked out by the Earth, the preferred direction of time is also a consequence of features of our environment. In the case of time, it’s not that we live in the spatial vicinity of an influential object; it’s that we live in the temporal vicinity of an influential event: the birth of the universe. The beginning of our observable universe, the hot dense state known as the Big Bang, had a very low entropy. The influence of that event orients us
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NATURE’S MOST RELIABLE LAW
The entropy of an isolated system either remains constant or increases with time.
What Carnot realized was that even the most efficient engine possible is not perfect; some energy is lost along the way. In other words, the operation of a steam engine is an irreversible process. So Carnot appreciated that engines did something that could not be undone. It was Clausius, in 1850, who understood that this reflected a law of nature. He formulated his law as “heat does not spontaneously flow from cold bodies to warm ones.”
An equilibrium configuration is simply one in which the entropy has reached its maximum value, and has nowhere else to go; all the objects in contact are at the same temperature.
THE RISE OF ATOMS
ENTROPY AND DISORDER
Entropy is a measure of the number of particular microscopic arrangements of atoms that appear indistinguishable from a macroscopic perspective.
In an isolated system entropy tends to increase, because there are more ways to be high entropy than to be low entropy.
Before Boltzmann, the Second Law was absolute—an ironclad law of nature. But the definition of entropy in terms of atoms comes with a stark implication: entropy doesn’t necessarily increase, even in a closed system; it is simply likely to increase.
Some people didn’t like that. They wanted the Second Law of Thermodynamics, of all things, to be utterly inviolate, not just something that holds true most of the time. Boltzmann’s suggestion met with a great deal of controversy, but these days it is universally accepted.
ENTROPY AND LIFE
It is because the Sun is a hot spot in a mostly cold sky that the Earth doesn’t just heat up, but rather can absorb the Sun’s energy, process it, and radiate it into space. Along the way, of course, entropy increases; a fixed amount of energy in the form of solar radiation has a much lower entropy than the same amount of energy in the form of the Earth’s radiation into space.
To this day, scientists haven’t yet determined to anyone’s satisfaction whether the universe will continue to evolve forever, or whether it will eventually settle into a placid state of equilibrium.
WHY CAN’T WE REMEMBER THE FUTURE?
THE ART OF THE POSSIBLE
It’s a bit embarrassing, frankly, that with all of the progress made by modern physics and cosmology, we still don’t have a final answer for why the universe exhibits such a profound asymmetry in time. I’m embarrassed, at any rate, but every crisis is an opportunity, and by thinking about entropy we might learn something important about the universe.
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THE BEGINNING AND END OF TIME
Conventional statistical mechanics can account for why it’s easy to turn an egg into an omelet but hard to turn an omelet into an egg. What it can’t account for is why, when we open our refrigerator, we are able to find an egg in the first place. Why are we surrounded by exquisitely ordered objects such as eggs and pianos and science books, rather than by featureless chaos?
The truth is, we don’t know much about why the early universe was in the configuration it was; that’s one of the questions motivating us in this book. The ultimate explanation for the arrow of time as it manifests itself in our kitchens and laboratories and memories relies crucially on the very low entropy of the early universe.
THE VISIBLE UNIVERSE
In every direction we look, and at every different distance from us, the number of galaxies is roughly equal. The observable universe looks pretty much the same everywhere.
BIG AND GETTING BIGGER
All of the galaxies are moving away from all of the other galaxies, and each of them sees the same kind of behavior. It’s almost as if the galaxies aren’t moving at all, but rather that the galaxies are staying put and space itself is expanding in between them.
When we say space is expanding, we mean that more space is coming into existence in between galaxies. Galaxies themselves are not expanding, nor are you, nor are individual atoms; anything that is held together by some local forces will maintain its size, even in an expanding universe.
What we see is a relatively homogeneous collection of galaxies, about 100 billion of them all told, steadily expanding away from one another. But outside our observable patch, things could be very different.
THE BIG BANG
The future of our universe is dilute, cold, and lonely.
So what happened before the Big Bang?
The truth is, we just don’t know.
Most physicists suspect that a quantum theory of gravity, reconciling the framework of quantum mechanics with Einstein’s ideas about curved spacetime, will ultimately be required to make sense of what happens at the very earliest times.
HOT, SMOOTH BEGINNINGS
It was the discovery of the microwave background that converted most of the remaining holdouts for the Steady State theory of cosmology (in which the temperature of the universe would be constant through time, and new matter is continually created) over to the Big Bang point of view.
TURNING UP THE CONTRAST KNOB ON THE UNIVERSE
Every direction we look in the sky, we see microwave background radiation that looks exactly like that from an object glowing serenely at some fixed temperature—what physicists call “blackbody” radiation. However, the temperature is ever so slightly different from point to point on the sky; typically, the temperature in one direction differs from that in some other direction by about 1 part in 100,000. These fluctuations are called anisotropies—tiny departures from the otherwise perfectly smooth temperature of the background radiation in every direction.
These variations in temperature reflect slight differences in the density of matter from place to place in the early universe.
The answer lies in gravity, which acts to turn up the contrast knob on the universe.
So the relative smoothness of the early universe, illustrated in the image of the cosmic microwave background, reflects the very low entropy of those early times.
THE UNIVERSE IS NOT STEADY
We still don’t know why the early universe had a low entropy, but at least we know when the early universe was: It was 14 billion years ago, and its entropy was small but not strictly zero.
BUT IT IS ACCELERATING
Like most such predictions of general relativity, there are hidden assumptions: in this case, that the primary source of energy in the universe consists of matter.
For our present purposes, the crucial aspect of matter is that it dilutes away as the universe expands.
What general relativity actually predicts is that the expansion should be decelerating, as long as the energy is diluting away. If it’s not—if the density of energy, the amount of energy in each cubic centimeter or cubic light-year of space, is approximately constant—then that energy provides a perpetual impulse to the expansion of space, and the universe will actually be accelerating.
We don’t know much about dark energy, but we do know two very crucial things: It’s nearly constant throughout space (the same amount of energy from place to place), and also nearly constant in density through time (the same amount of energy per cubic centimeter at different times). So the simplest possible model for dark energy would be one featuring an absolutely constant density of energy through all space and time. And in fact, that’s an old idea, dating back to Einstein: He called it “the cosmological constant,” and these days we often call it “vacuum energy.” (Some people may try to
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You can’t feel it, you can’t see it, you can’t do anything with it, but it is there. And we know it is there because it exerts a crucial influence on the universe, imparting a gentle push that causes distant galaxies to accelerate away from us.
THE MYSTERY OF VACUUM ENERGY
So instead of appealing to the correct theory of quantum gravity, which we still don’t have, we can simply examine the contributions to the vacuum energy of virtual particles at energies below where quantum gravity becomes important. That’s the Planck energy, named after German physicist Max Planck, one of the pioneers of quantum theory, and it turns out to be about 2 billion joules (a conventional unit of energy).
