Time Travel. A History

Except when we start to consider order and chaos, organization and randomness. The second law applies not to individual entities but to ensembles. The molecules in a box of gas comprise an ensemble. Entropy is a measure of their disorder. If you put a billion atoms of helium into one side of a box and a billion atoms of argon into the other side and allow them to bounce around for a while, they will not remain neatly separated but will eventually become a uniform—random—mixture. The probability that the next atom you find at a given place will be helium, rather than argon, will be 50 percent. The process of diffusion is not instantaneous and it runs in one direction. As you watch the distribution of the two elements, past and future are easily distinguishable. “A random element,” said Eddington, “brings the irrevocable into the world.” Without randomness, the clocks could run backward.

“The accidents of life” is the way Feynman liked to put it: “Well, you see that all there is to it is that the irreversibility is caused by the general accidents of life.” If you throw a cup of water into the sea, let time pass, and dip your cup back in, can you get the same water back? Well, you could—the probability is not zero. It’s just awfully small. Fifteen billiard balls could smash around a table and finally come to a stop in a perfect triangle—but when you see that happen, you know that the film has been reversed. The second law is a probabilistic law.

Mixing is one of those processes that follow the arrow of time. Unmixing takes work. “You cannot stir things apart,” says Stoppard’s Thomasina—entropy explained in five words. (Her tutor, Septimus, replies, “No more you can, time must needs run backward, and since it will not, we must stir our way onward mixing as we go, disorder out of disorder into disorder until pink is complete, unchanging and unchangeable, and we are done with it for ever.”) Maxwell himself wrote:

Moral. The 2nd law of Thermodynamics has the same degree of truth as the statement that if you throw a tumblerful of water into the sea, you cannot get the same tumblerful of water out again.

But Maxwell predated Einstein. For him, time required no particular justification. He already “knew” that the past is past and the future still to come. Now matters are not so simple. In 1949, in a essay titled “Life, Thermodynamics, and Cybernetics,” Léon Brillouin said:

Time flows on, never comes back. When the physicist is confronted with this fact he is greatly disturbed.

To the physicist, it feels that a troublesome gap lies between the microscopic laws, where time has no preferred direction, because the laws are reversible, and the macroscopic world, where the arrow of time points from past to future. Some are content to say that fundamental processes are reversible and macro-scale processes are mere statistics. This gap is a disconnect—a lapse in explanation. How do you get from one place to the other? The gap even has a name: the arrow of time dilemma, or Loschmidt’s paradox.

Einstein admitted that the problem disturbed him at his moment of greatest understanding, in the creation of the general theory of relativity—“without my having succeeded in clarifying it.” In a diagram of the four-dimensional space-time continuum, let’s say that P is a “world-point” lying between two other world-points, A and B. “We draw a ‘time-like’ world-line through P,” suggested Einstein; “does it make any sense to provide the world-line with an arrow, and to assert that B is before P, A after P?” Only when thermodynamics enters the picture, he concluded—but he also said that any transfer of information involves thermodynamics. Communication and memory are entropic processes. “If it is possible to send (to telegraph) a signal from B to A, but not from A to B, then the one-sided (asymmetrical) character of time is secured, i.e. there exists no free choice for the direction of the arrow. What is essential in this is the fact that the sending of a signal is, in the sense of thermodynamics, an irreversible process, a process which is connected with the growth of entropy.”

In the beginning, therefore, the universe must have had low entropy. Very low entropy. It must have been in a highly ordered state, which is also an extremely improbable state. This is a cosmic mystery. Ever since, entropy has grown. “That is the way toward the future,” said Feynman, years later, when he was a famous man assembling his knowledge of physics into textbook form.

That is the origin of all irreversibility, that is what makes the processes of growth and decay, that makes us remember the past and not the future, remember the things which are closer to that moment in history of the universe when the order was higher than now, and why we are not able to remember things where the disorder is higher than now, which we call the future.

And in the end?

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