Question

Given your engagement with these areas from the philosophical-halakhic angle, and sometimes also the physical one, I wondered what you would think about the following argument by Avshalom Elitzur regarding our ability to speak about causal relations with respect to the timeline in a world governed by relativity theory (apologies in advance for the length of the passage):
“To understand how such a reversal could be possible, let us introduce into the discussion another question touching the foundations of modern physics: is our world governed completely by causality? In other words, is every event that occurs in the universe—even the motion of the tiniest conceivable particle—determined absolutely by what preceded it? This question—in Einstein’s famous formulation, ‘Does God play dice?’—is an unresolved one, and we will not presume to decide it here. But we cannot help noting, with some astonishment, that in the vast literature dealing with the arrow of time and the passage of time, there is almost no reference to the question of causality, even though even a non-scientist will immediately feel intuitively that the two questions are closely connected.

Figures 7A and 8B illustrate this claim. This is a computer simulation describing the motion of billiard balls. At the bottom right one can see a group of billiard balls arranged in a triangle, until another ball strikes them and scatters them in all directions (upper right). Clearly, entropy increased in this process. On the left side of the picture one can see a spacetime diagram of the process, that is, the trajectories of the balls in spacetime.
In Figure 7B we reversed the direction. In the simulation, which we invite anyone interested to view (—www), the command was given to the balls at the final stage to reverse the directions of their motion. Very quickly, the mess reorganizes itself into a neat triangle that ejects a single ball back to the place from which it came. On the left, again, appears a spacetime diagram of the reversed process.
What we are now saying is almost trivial, and every beginning student knows it, yet almost none of the physicists discussing the origin of the arrow of time notices it: in a world that is not completely causal, process A is entirely possible while process B is doomed to fail. Here is Figure 8A: we repeated the first process with a slight ‘forgery’—we moved one of the balls a little during the experiment. The result: entropy increased this time as well. In Figure 8B we introduced the forgery into the reverse process, which was supposed to lower entropy, and the result was disastrous: from the moment of the intervention, disorder took over again and destroyed the entire reversal.
In physicists’ usual formulation, it would be said like this: a normal process, one whose entropy rises with time, is not sensitive to initial conditions; but those rare processes whose entropy decreases with time are extremely sensitive: every such process requires incomparably precise initial conditions, and every deviation from those conditions will cause it to revert back into a normal, entropy-increasing process. Yakir Aharonov expressed this principle neatly: if we remove one worm from a man’s grave, then no time-reversal of the processes occurring in the grave will bring him back to life.
True, everyone knows this, but this principle has an immediate implication for the nature of time: given a closed system in which there is one non-causal event, then regardless of that system’s initial conditions, its entropy will go on increasing, from that event onward, in both directions! The impression one gets is that although the arrow of time in that system initially pointed in the opposite direction from that of the universe, from the moment the non-causal event appeared, the cosmic arrow of time returned and reasserted control over the system, even though the system is completely isolated from that universe (Figure 9).
From this there follows, logically, an equally far-reaching conclusion about the universe as a whole: if there exists anywhere even one interaction that is not causal, then the entire universe is not time-symmetric. Hence the usual way of reading the history of the universe is the correct one, whereas the reversed way (version 0) is absurd.
Only one small question remains, then: is the universe in which we live causal? Of course, this is not a small question at all, and we have already said that it is beyond our ability. But there was someone who did decide this question, and it was none other than the famous Stephen Hawking. This good man insists that the laws of nature permit the existence of fundamental indeterminism, that is, a process that is not causal. All we are saying on the margins of his remarks is that this claim contradicts his second claim, according to which there is no fundamental arrow of time.
First, a note on the status of causality in physics today. It is commonly thought that quantum theory has already undermined causality, but in fact that is not precise. The formalism of quantum theory—that is, its system of laws—preserves causality. True, given a certain quantum state, A, one can predict only probabilities for the states B and C that will follow it. But this does not rule out the possibility that B or C were predetermined by A, and only our lack of knowledge prevents us from predicting the effect on the basis of knowledge of the cause. This is the hypothesis of ‘hidden variables,’ which Einstein toyed with in the hope of refuting quantum theory. But today it has not only not been proved, it has even been constrained (for example by John Bell’s proof that such hidden variables would act at a distance, apparently contrary to relativity), and nevertheless most physicists believe in it.
Physicists rely on a principle known in professional language as ‘the hypothesis of unitarity conservation,’ which in everyday language can be formulated as the principle of information conservation. Thus, for example, if we throw a book into a bonfire, the information written in the book does not disappear completely. It is preserved in the photons (particles of light) emerging from the fire. It is indeed impossible to reconstruct that information with present-day technology, but in principle the information has not been lost; it has only become mixed with an enormous quantity of information that appears to us as nothing more than random noise. How far such information can be reconstructed is merely a technological question and nothing more. In the eyes of theoretical physics, information never disappears.
Now, more than twenty years ago Hawking announced that there is one case in which unitarity is not preserved—in other words, a process in which information really disappears, completely, and not merely gets mixed with noise. That process is the evaporation of a black hole. Physicists had known long before that when a black hole forms, everything that falls into it—bicycles, bananas, members of Knesset—loses all its physical properties (color, shape, smell, etc.) and changes only the black hole’s three physical properties: mass, angular momentum, and electric charge. Here there appears to be a clear loss of information, but physicists assumed that the lost properties of the objects that fell into the black hole remained hidden inside it, beyond the reach of the visible universe. Then Hawking came, following a hint from Yaakov Bekenstein of the Hebrew University, and proved that black holes evaporate through a marvelous and simple quantum process. We will not repeat the details of the process—they are clearly explained in A Brief History of Time. What matters for our purposes is that the particles emitted from the black hole and causing its demise are created at its boundary, far from the bicycles, bananas, and Knesset members swallowed into its center. Here, said Hawking, there is genuine loss of information. Whereas the photons emerging from the fire still preserve the content written in the book, the photons emerging from the edge of a black hole cannot preserve anything of the properties of the bodies swallowed far away in its center. And so, when the black hole is exhausted, all the information swallowed into it disappears completely.
And here is an irony: for many years Hawking and Penrose have been conducting an argument about the origin of the arrow of time. Hawking, the younger of the two, actually takes the conservative position (chapter 0), whereas Penrose, as we have seen, advances the bolder hypothesis (chapter 0). This long debate (which, like the famous argument between Einstein and Bohr, was conducted in friendship and mutual admiration) took place on public stages and was even recently published as a book. But throughout this whole debate, Penrose did not notice how Hawking was repeatedly, unwittingly, handing him the very argument that supports his own approach!
The logic here is utterly simple. Let us imagine two closed systems. One of them undergoes normal development, so that its entropy increases with time. Let us give the system enough mass and time to allow a black hole to form and evaporate. When we open the system after sufficient time and examine its entropy, we will find that the entropy has increased. That is not surprising: if Hawking’s hypothesis is correct, the particles into which the black hole evaporated could not preserve the information about the objects previously swallowed by the black hole. Therefore, black-hole evaporation simply added to the entropy of the system, in a way identical to that of the single disturbance in Figure 7A that disrupted the causal chain.
The second system will be the exact reverse of the first: a closed system in which the states and momenta of all the particles are pre-coordinated with maximal precision so that its entropy decreases with time (cups of coffee getting warmer, the dead rising from their graves, and all the other absurdities we mentioned). Here too the quantities of matter and duration of time allotted to the system will be enough for a black hole to form and evaporate. When we open the system at the end of the experiment, we find that time reversal has failed: entropy increases in this case as well.
The reason is clear: the information-destroying effect of the black hole destroyed the prearranged correlations with which the initial state had been prepared. This process parallels the case we saw in Figure 7B, except that the failure of causality caused by the black hole affects not just one particle but many particles.
And with that, as lawyers say, we rest our case. If anywhere in the universe there occurred even a single event that is not completely deterministic—be it the evaporation of a black hole, the yawn of a cat, or tears shed by a housewife after peeling an onion—then the causal relations throughout the universe lose their time symmetry. Such an event is equivalent to the disturbance we introduced into the trajectory of a single billiard ball: over time it affects all other events. In this way we can rule out the possibility that we live in a reversed universe of the kind mentioned in chapter 0, and thus we can finally determine that events in the past cause events in the future and not the other way around. We want to emphasize again the simplicity of this argument: if determinism is correct, the universe is no different from the billiard table in Figure 6 except in the number of its components. Every event that is seriously non-causal is equivalent to the slight disturbance we introduced into the motion of the billiard balls. Because of it, a neat triangle turning into a jumble of balls (or, in our world, cups of coffee cooling and people aging and dying) is possible, whereas the reverse process requires carefully calculated and ongoing intervention by a higher power.
From this point, where standard physics must recruit miraculous coincidences, there are only two ways back to science. On the one hand, it may turn out that Hawking and those like him are mistaken and that information is preserved even in black-hole evaporation (an idea recently supported by string theory, which tries to provide a detailed description of black holes). We of course hope this will not be the case, but for now all that remains is to wait and see what the future brings. On the other hand, if it turns out that Hawking was the one who was right, then the conservative claim presented at the beginning of this article also collapses—namely, that future events exist alongside present and past events just as the cities of the north exist alongside the cities of the south. And if so, if the future does not exist, then the theory that says time is in a state of becoming returns, and physics will be forced to go beyond its current boundaries.”