I was driving through Ithaca, New York a while back, and came to a stoplight, and the car in front of me had a bumper sticker that said, "Time is that without which everything would happen at once."
I laughed, but I kept thinking about it, because in one sentence it highlights one of the most persistent mysteries of physics: why we perceive a flow of time. The problem is, just about all of the laws of physics, from quantum mechanics to the General Theory of Relativity, are time-reversible; they work equally well in forward as in reverse. Put another way, most physical processes look the same both ways. If I were to show you a short video clip of two billiard balls colliding on a pool table, then the same clip backwards, it would be hard to tell which was which. The Laws of Conservation of Momentum and Conservation of Energy that describe the results of the collision work in either direction.
There are exceptions, though. The Second Law of Thermodynamics is the most commonly-cited one: closed systems always increase in entropy. It's why when I put sugar in my coffee in the morning and stir it, the sugar spreads through the whole cup. If I were to give it one more stir and all the sugar molecules were to come back together as crystals and settle out on the bottom, I'd be mighty surprised. I might even wonder if someone had spiked the sugar bowl with something other than sugar.
In fact, that's why I had to specify a "short clip" in the billiard ball example. There is a time-irreversible aspect of such classical physics; as the balls roll across the table, they lose momentum, because a little of the kinetic energy of their motion leaks away as thermal energy due to friction with the surface. When they collide, a little more is lost because of the sound of the balls striking each other, the (slight) physical deformation they undergo, and so on. So if you had a sensitive enough camera, or a long enough clip, you could tell which was the forward and which the reverse clip, because the sum of the kinetic energies of the balls in the forward clip would be (slightly) greater before the collision than after it.
But I am hard-pressed to see why that creates a sense of the flow of time. It can't be solely from our awareness of a movement toward disorder. When there's an energy input, you can generate a decrease in entropy; it's what happens when a single-celled zygote develops into a complex embryo, for example. There's nothing in the Second Law that prevents increasing complexity in an open system. But we don't see those situations as somehow running in reverse; entropy increase by itself doesn't generate anything more than expected set of behaviors of certain systems. How that could affect how time is perceived by our brains is beyond me.
The problem of time's arrow is one of long standing. Einstein himself recognized the seeming paradox; he wrote, "The distinction between past, present, and future is only a stubbornly persistent illusion." "Persistent" is an apt word; more than sixty years after the great man's death, there was an entire conference on the nature of time, which resolved very little but giving dozens of physicists the chance to defend their own views, and in the end convinced no one.
It was, you might say, a waste of time. Whatever that means.
One of the most bizarre ideas about the nature of time is the one that comes out of the Special Theory of Relativity, and was the reason Einstein made the comment he did: the block universe. I first ran into the block universe model not from Einstein but from physicist Brian Greene's phenomenal four-part documentary The Fabric of the Cosmos, and it goes something like this. (I will append my usual caveat that despite my bachelor's degree in physics, I really am a layperson, and if any physicists read this and pick up any mistakes, I would very much appreciate it if they'd let me know so I can correct them.)
One of the most mind-bending things about the Special Theory is that it does away with simultaneity being a fixed, absolute, universal phenomenon. If we observe two events happening at exactly the same time, our automatic assumption is that anyone else, anywhere in the universe, would also observe them as simultaneous. Why would we not? But the Special Theory shows conclusively that your perception of the order of events is dependent upon your frame of reference. If two individuals are in different reference frames (i.e. moving at different velocities), and one sees the two events as simultaneous, the other will see them as sequential. (The effect is tiny unless the difference in velocities is very large; that's why we don't experience this under ordinary circumstances.)
This means that past, present, and future depend on what frame of reference you're in. Something that is in the future for me might be in the past for you. This can be conceptualized by looking at space-time as being shaped like a loaf of bread; the long axis is time, the other two represent space. (We've lost a dimension, but the analogy still works.) The angle you are allowed to slice into the loaf is determined by your velocity; if you and two friends are moving at different velocities, your slice and theirs are cut at different angles. Here's a picture of what happens -- to make it even more visualizable, all three spatial dimensions are reduced to one (the x axis) and the slice of time perceived moves along the other (the y axis). A, B, and C are three events, and the question is -- what order do they occur in?
As you can see, it depends. If you are taking your own velocity as zero, all three seem to be simultaneous. But change the velocity -- the velocities are shown at the bottom of the graph -- and the situation changes. To an observer moving at a speed of thirty percent of the speed of light relative to you, the order is C -> B -> A. At a speed of fifty percent of the speed of light in the other direction, the order is A -> B -> C.
So the tempting question -- who is right? what order did the events really occur in? -- is meaningless.
Probably unnecessarily, I'll add that this isn't just wild speculation. The Special Theory of Relativity has been tested hundreds, probably thousands, of times, and has passed every test to a precision of as many decimal places as you want to calculate. (A friend of mine says that the papers written about these continuing experiments should contain only one sentence: "Yay! Einstein wins again!") Not only has this been confirmed in the lab, the predictions of the Special Theory have a critical real-world application -- without the equations that lead directly to the block universe and the relativity of simultaneity, our GPS systems wouldn't work. If you want accurate GPS, you have to accept that the universe has some seriously weird features.
So the fact that we remember the past and don't remember the future is still unexplained. From the standpoint of physics, it seems like past, present, and future are all already there, fixed, trapped in the block like flies in amber. Our sense of time flowing, however familiar, is the real mystery.
But I'd better wrap this up, because I'm running out of time.
Whatever that means.