“We have a different kind of awareness about what might happen than we have of what probably has happened”

In physicist Richard P. Feynman’s fifth lecture at Cornell University in 1959 he entertained for a moment the question of ‘what distinguishes the future from the past?’. His lecture sets out with the following primer:

It is obvious to everyone that the phenomena of the world are evidently irreversible. I mean, things happen that do not happen the other way. You drop a cup and it breaks, and you sit there a long time waiting for the pieces to come together and jump back into your hand. If you watch the waves of the sea breaking, you can stand there and wait for the great moment when the foam collects together, rises up out of the sea, and falls back farther out from the shore - it would be very pretty!

Of course, as Feynman proceeds to point out: this would never happen in the real world. In fact, if one played a video in reverse of this happening in the early days of cinema, the spontaneous reaction of the crowd would likely be laughter — an indication of its surreal nature.

“Even without an experiment, our very experiences inside are completely different for past and future”

Why is so that the progression of still water transformed into breaking waves is so perfectly natural, but the transformation of waves that have broken reversed into their previous state of perfect stillness is absurd? Why do we think of the future and past as different?

We remember the past, we do not remember the future. We have a different kind of awareness about what might happen than we have of what probably has happened.

Indeed, as Feynman points out, the difference between future and past manifests itself in us psychologically, even though we are unable to precisely describe why. We find it absurd to think that we could influence our past, yet still mostlybelieve in free will as it regards to the future.

The past and the future look completely different psychologically, with concepts like memory and apparent freedom of will, in the sense that we feel that we can do something to affect the future, but none of us believe that there is anything we can do to affect the past.

A lack of belief in our ability to affect the past manifests itself in our emotions too, such as in remorse and grief as well as in our faith in the converse, hopes and dreams. This perfectly distinguishes the past and the future for us, psychologically. However, how can we interpret the same distinction physically?

Irreversibility

“Things are reversible only in the sense that going one way is likely, but going the other way, although possible, would not happen in a million years”

Now if the world is made of atoms, and we too are made of atoms and obey physical laws, the most obvious interpretation of this evident distinction between past and future, and this irreversibility of all phenomena, would be that some laws, some of the motion laws of the atoms, are going one way - that the atom laws are not such that they can go either way.

As Feynman next proclaims “there should be somewhere in the works some kind of principle that Uxles only make Wuxles, and never vica versa, and so the world is turning from Uxley character to Wuxley character all the time — and this one-way business of the interactions of things should be the thing that makes the whole phenomena of the world seem to go one way”.

Yet, as he points out, we have not yet found what it is that does this. What is it in nature’s laws that provides the “arrow of time”?

“The movie should work the same going both ways, and the physicist who looks at it should not laugh”

The Law of Gravitation

Take the law of gravitation. “Every particle attracts every other particle in the universe with a force that is directly proportional to the product of their masses and inversely proportional ot the square of the distance between their centers”:

If I have a sun and a planet, and I start the planet off in some direction, going around the sun, and then I [record a video of it], and run the film backwards and look at it, what happens? The planet goes around the sun, the opposite way of course, keeps on going around in an ellipse. The speed of the planet is such that the area swept out by the radius is always the same in equal times. In fact, it just goes exactly the way it ought to go. It cannot be distinguished from going the other way.

So, the law of gravitation is of such a kind that the direction does not make any difference. From the perspective of the law, playing back the wave forwards or backwards in time makes no difference. Nobody laughs.

The laws of electricity and magnetism are the same, also time reversible. As are the laws describing the nuclear reaction and as far as we can tell, beta decay.

Complexity

As Feynman points out, if we look a little bit closer, we however soon realize that the above interpretation does not capture all of the picture:

If we look at our planets moving around the sun more carefully, we soon find that all is not quite right. For example, the Earth's rotation on its axis is slightly slowing down. It is due to tidal friction, and you can see that friction is something which is obviously irreversible.

That is, the frictional effect is the result of the enormous complexity that arises from the interaction between the jiggling atoms of two substances coming together. Reversibility at this scale, in this domain, is not as straightforward as are the reversibility of the motion of planets.

Thought Experiment: The Water Tank

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 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 colour uniformly distributed throughout.

Now, would we expect the two fluids to ever separate back to blue and white again? As Feynman points out, we could do something to separate them, but we would most certainly never expect them to do so spontaneously. This gives us some clue. If we run a movie of the experiment backwards, we are surprised to see a mixed substance separate.

Now, if we magnify the picture even more, what do we expect to see? We expect to see giggling molecules of (for the sake of the thought experiment) blue and white color, interacting in a jittery motion. The extent of their jiggering is dependent on their temperature:

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 "luke blue".

Watch a video of any one of the billions and billions of collisions and you will witness the atoms come together and bounce off one another. Run the film backwards, and ask yourself, “do the atoms behave any differently when we play the movie backwards rather than forwards?” Ask a physicist and he will tell you that no, the interactions played backwards are happening according to the laws of physics. Their interaction is reversible. Atomic collisions are reversible, even if the sum of billions of such collisions are not.

The Nature of Future and Past

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. That is the answer.

And so, as Feynman proclaims, the distinction between events in the past and events the future, “the arrow of time” may indeed be as simple as the distinction between extremely unlikely events, and relatively much higher probability events. The blue and white waters could separate, as if we were playing the movie backwards, as if we were moving back in time, but that event is simply so unlikely that in our universe, such events do not take place often enough for it to be probable for us to see them in our comparetively short lives.

“Things are reversible only in the sense that going one way is likely, but going the other way, although possible, would not happen in a million years”

Interpreting Events at Micro and Macro Scales

Now if I put a box around my experiment, so that there were only four or five molecules of each kind in the box, as time went on they would get mixed up. But I think you could believe that, if you kept watching, in the perpetual irregular collusions of these molecules, after some time - not necessarily a million years, maybe only a year - you would see that, accidentally they would get back more or less to their original state, at least in the sense that if I put a barrier through the middle, all the whites would be on one side and all the other blues on the other.

Reimagining Feynman’s experiment at a much smaller scale, we would not find ourselves surprised to see that at some time after their separation is removed, the four blue molecules find their way back to the right side and visa versa for the whites.

“It is not impossible. However, the actual objects with which we work have not only four or five blue and whites. They have four or five million, million, million, million, which are all going to get separated like this.”

And so, Feynman concludes, the apparent irreversibility of nature does not arise from the irreversibility of the fundamental physical laws; it comes from the characteristic that if you start with an ordered system and add the irregularities of nature, the “bouncing of molecules”, then

“The thing goes one way.”

Those interested in reading more about Feynman’s views on causation and the arrow of time are encouraged to acquire the book “The Character of Physical Law” (1965)