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Entropy and the Irreversibility of Time

The following is an excerpt from “The Character of Physical Law” by Richard Feynman

Begin quote:

I will take a simple example. Suppose we have blue water, with ink, and white water, that is without ink, in a tank, with a little separation, and then we pull out the separation very delicately. The water starts to separate, blue on one side and white on the other side. Wait a while. Gradually the blue mixes up with the white, and after a while the water is ‘luke blue’, I mean it is sort of fifty-fifty, the color uniformly distributed throughout. Now if we wait and watch this for a long time, it does not by itself separate...

That gives us some clue. Let us look at the molecules. Suppose that we take a moving picture of the blue and white water mixing. It will look funny when we run it backwards, because we will start with uniform water and gradually the thing will separate -- it will be obviously nutty. Now we magnify the picture, so that every physicist can watch, atom by atom, to find out what happens irreversibly -- where the laws of balance of forward and backward break down. So you start, and you look at the picture. You have atoms of two different kinds (it’s ridiculous, but let’s call them blue and white) jiggling all the time in thermal motion. If we were to start at the beginning, we should have mostly atoms of one kind on one side, and atoms of the other kind on the other side. Now these atoms are jiggling around, billions and billions of them, and if we start them with one kind all on one side, and the other kind on the other side, we see that in their perpetual irregular motions they will get mixed up, and that is why the water becomes more or less uniformly blue.

Let us watch any one collision selected from that picture, and in the moving picture the atoms come together this way and bounce off that way. Now run that section of the film backwards, and you find the pair of atoms moving together the other way and bouncing off this way. And the physicist looks with his keen eye, and measures everything, and says, ‘That’s all right, that’s according to the laws of physics. If two molecules came together this way, they would bounce off this way’. It is reversible. The laws of molecular collision are reversible.

So if you watch too carefully you cannot understand it at all, because every one of the collisions is absolutely reversible, and yet the whole moving picture shows something absurd, which is that in the reversed picture the molecules start in the reversed condition -- blue, white, blue, white, blue, white -- and as time goes on, through all the collisions, the blue separates from the white. But they cannot do that -- it is not natural that the accidents of life should be such that the blues will separate themselves from the whites. And yet if you watch this reversed movie very carefully every collision is okay.

Well you see that all there is to it is that the irreversibility is caused by the general accidents of life. If you start with a thing that is separated and make irregular changes, it does get more uniform. But if it starts uniform and you make irregular changes, it does not get separated. It could get separated. It is not against the laws of physics that the molecules bounce around so that they separate. It is just unlikely. It would never happen in a million years. And that is the answer. Things are irreversible only in a sense that going one way is likely, and going the other way, although it is possible and is according to the laws of physics, would not happen in a million years. It is just ridiculous to expect that if you sit there long enough the jiggling of the atoms will separate a uniform mixture of ink and water into ink on one side and water on the other...

And so the apparent irreversibility of nature does not come from the irreversibility of the fundamental physical laws; it comes from the characteristic that if you start with an ordered system, and have the irregularities of nature, the bouncing of molecules, then the thing goes one way. (pp.105-107)

...I do not know if you have ever had the experience -- I have -- of sitting on the beach with several towels, and suddenly a tremendous downpour comes. You pick up the towels as quickly as you can, and run into the bathhouse. Then you start to dry yourself, and you find that this towel is a little wet, but it is drier than you are. You keep drying with this one until you find that it is too wet -- it is wetting you as much as drying you -- and you try another one; and pretty soon you discover a horrible thing -- that all the towels are damp and so are you. There is no way to get any drier, even though you have many towels, because there is no difference in some sense between the wetness of the towels and the wetness of yourself. I could invent a kind of quantity which I could call ‘ease of removing water’. The towel has the same ease of removing water from it as you have, so when you touch yourself with the towel, as much water comes off the towel on to you as comes from you to the towel. It does no mean there is the same amount of water in the towel as there is on you -- a big towel will have more water in it than a little towel, but they have the same dampness. When things get to the same dampness then there is nothing you can do any longer.

Now the water is like the energy, because the total amount of water is not changing. (If the bathhouse door is open and you can run into the sun and get dried out, or find another towel, then you’re saved, but suppose everything is closed, and you can’t get away from these towels or get any new towels.) In the same way if you imagine a part of the world that is closed, and wait long enough, in the accidents of the world the energy, like the water, will be distributed over all the parts evenly until there is nothing left of one-way-ness, nothing left of the real interest of the world as we experience it...

Incidentally, the thing that corresponds to the dampness or the ‘ease of removing water’ is called temperature, and although I say when two things are at the same temperature they get balanced, it does not mean they have the same energy in them; it means that it is just as easy to pick energy off one as to pick it off the other. Temperature is like ‘ease of removing energy’. So if you sit them next to each other, nothing apparently happens; they pass energy back and forth equally, but the net result is nothing. So when things have become all of the same temperature, there is no more energy available to do anything. The principle of irreversibility is that if things are at different temperatures and are left to themselves, as time goes on they become more and more at the same temperature, and the availability of energy is perpetually decreasing.

This is another name for what is called the entropy law, which says the entropy is always increasing. But never mind the words; stated the other way, the availability of energy is always decreasing. And that is a characteristic of the world, in the sense that it is due to the chaos of irregular molecular motions. Things of different temperature, if left to themselves, tend to become the same temperature. If you have two things at the same temperature, like water on an ordinary stove without a fire under it, the water is not going to freeze and the stove get hot. But if you have a hot stove with ice, it goes the other way. So the one-way-ness is always to the loss of the availability of energy. (pp.113-115)

End quote

”The Character of Physical Law” is a transcript of a series of seven lectures Feynman gave at Cornell University in 1964. Feynman’s description of the irreversibility of natural phenomena, and how it relates to entropy, describes an important part of chaos theory, which was not formalized until 1975, when Benoit Mandelbrot published “The Fractal Geometry of Nature”. A container of blue and white water, such as Feynman describes, is a complex dynamic system. As Feynman states, each molecular collision is perfectly reversible, but the phenomenon as a whole is not.

When Feynman talks about imagining “...a part of the world that is closed, and wait long enough, in the accidents of the world the energy, like the water, will be distributed over all the parts evenly until there is nothing left of one-way-ness, nothing left of the real interest of the world as we experience it...”, he says something very important about the nature of time. Time travel has always been a popular subject for science fiction writers, and some scientists have gone so far as to say that the concept does not break the laws of special relativity. But if we see the temporal ramifications of Feynman’s lecture, we see that the whole idea of time travel is absurd.

What is time? Simply put, time is a tool we use to measure the passage of events. Events do not go backward, so we cannot experience time backward. If we take any closed system, it will progress from an ordered state to one of disorder, uniformity. Feynman’s container of ‘luke blue’ water will never separate into blue and white again, and a thousand monkeys with typewriters will never re-create the complete works of Shakespeare, or even Dickens (“It was the best of times, it was the... blurst of times?! Stupid monkey!” --C.M. Burns).

That is not to say that there is no order being created in the universe. I have in front of me a very random-looking collection of letters on my keyboard, and from them I am creating a complex, very ordered sequence of those letters as I write this essay. Elsewhere in the world, people are building bridges, plants are synthesizing glucose, and DNA is creating replicas of itself from molecules which are forming from base elements. Throughout the universe, stars are igniting, galaxies are forming and clustering together into truly immense structures.

If we were to eliminate all external energy flows from any part of the universe, no matter how big, thus making it a closed system, we would see a net increase in entropy. But is the universe itself a closed system? There is much evidence to suggest that it is not. As our ability to see deeper into the universe increases, we see larger and larger structures in space, structures that formed in the presence of an external magnetic field. There is no reason to suppose that we have reached the upper size limit of these structures; every time someone says we have, we discover something larger. Right now, only 10,000 galaxies (out of billions) have been mapped. Next year, Margaret Geller, the astronomer who discovered the ‘Stickman’ and the ‘Great Wall’ will start the largest sky survey ever done; she will map 50,000 galaxies over the course of several years (Discover, p. 59). As her project unfolds, it is likely she will discover huge, new structures.

Another bit of evidence that suggests an open universe is the Hubble redshift. If it does represent a universal expansion, and if we have measured the speed accurately, the universe is expanding much too rapidly for gravity to cause a ‘big crunch’. If the energy of expansion came from the collapse of a previous universe, therefore, our present universe is analogous to a ball that bounces higher than the height from which it is dropped. (Big Bang, Part Two).

It therefore seems likely that the universe is receiving energy from beyond the bounds of what we can see. The observable universe does not appear to be ‘winding down’, as a closed system must, following the law of entropy. Instead it appears to be ‘winding up’. Everywhere in the universe, we see matter building into complex structures, and energy flowing in complex patterns. Does this contradict the law of entropy? No! If we look at the individual parts of these structures, we see energy becoming disordered and uniform, even though the overall structures are becoming more ordered and separate. And the tendency toward increasing order on this large scale is just as irreversible as the tendency toward disorder on the smaller scale. Stars do not diffuse into clouds of plasma, and galaxies do not dissolve into evenly distributed collections of stars, any more than humans do not decay into smelly bags of mostly water.

Who knows what lies on the next level in the cosmic hierarchy? Maybe Margaret Geller will show us by Clarke’s infamous year...


George Beckingham. “Big Bang: You’re Dead!” The Frontier, Tripod, 1994, 1995, 1996.

Richard Feynman. “The Character of Physical Law” New York: The Modern Library, 1994. (A transcript of seven lectures given at Cornell University in 1964)

Benoit Mandelbrot. “The Fractal Geometry of Nature” New York: W.H. Freeman and Company, 1983.

The Simpsons, unidentified episode.

Star Trek, unidentified episode.

Gary Taubes. “Beyond the Soapsuds Universe” Discover, (Disney Publishing), August 1997.

Entropy and the Irreversibility of Time, copyright 1998 by George Beckingham