Causality and the timeline

In relation to your engagement in these areas from a philosophical-halakhic and sometimes also physical perspective, I wondered what you would think of Avshalom Elitzur’s following argument regarding our ability to talk about causal relationships in relation to the timeline in the world of relativity theory (I apologize in advance for the length of the passage):
“To understand how such a reversal is possible, let us introduce into the discussion another question concerning the essence of modern physics: Is our world completely governed by causality? In other words, is every event that occurs in the universe, even the movement of a tiny particle, absolutely determined by what preceded it? This question – in Einstein’s famous phrase, “Does God play dice” – is an unsolvable question and we will not pretend to rule on it here, but we cannot help but comment with astonishment on the fact that in all the vast literature discussing the arrow of time and the passage of time, there is almost no reference to the question of causality, although even a non-scientist will immediately intuitively feel that the two questions are closely related to each other.

Figure 8b Figure 7a illustrates this claim. This is a computer simulation depicting the motion of billiard balls. At the bottom right, you can see a group of billiard balls arranged in a triangle, until another ball hits them and scatters them in all directions (top right). Clearly, entropy has increased in this process. On the left side of the image, you can see a space-time diagram of the process, that is, the trajectories of the balls in space-time.
In Figure 7b, we have reversed the direction. In the simulation, which we invite all who are interested to witness (—www), the balls were commanded to reverse their directions of motion at the final stage. In no time, the mess will reorganize into a beautiful triangle that will emit a single ball back to where it came from. On the left, again, appears a space-time diagram of the reversed process.
What has just been said is almost trivial, and every beginning student knows it, and yet, almost none of the physicists who discuss the question of the origin of the arrow of time have paid attention to it: in a world that is not completely causal, process A is certainly possible, while process B is doomed to failure. Here is Figure 8a: We repeated the first process with the addition of a slight “fake” – we moved one of the balls slightly during the experiment. The result: the entropy increased this time too. In Figure 8b, we introduced the fake into the reverse process, which was supposed to decrease entropy, and the result was disastrous: from the moment of intervention, disorder took over again and destroyed the entire reversal.
In the formulation accepted by physicists, it is stated as follows: A normal process, one whose entropy increases with time, is insensitive to the initial conditions, while those rare processes whose entropy decreases with time are extremely sensitive: any such process requires infinitely precise initial conditions, and any deviation from these conditions will cause it to revert to a normal, entropy-increasing process. Yakir Aharonov expressed this principle succinctly: If we take one worm out of a person’s grave, then no time reversal of the processes occurring in the grave will bring him back to life.
True, this is well known, but this principle has an immediate implication for the nature of time: given a closed system that has a single non-causal event, then, regardless of the initial conditions of that system, its entropy will increase, starting from that event, in both directions! The impression obtained is that although the arrow of time in that system initially pointed in the opposite direction to that of the universe, from the moment the non-causal event appeared, the cosmic arrow of time returned and took control of the system again, even though the system is completely isolated from this location (Figure 9).
From this logically follows an equally far-reaching conclusion for the entire universe: if there is even one non-causal interaction somewhere, the entire universe is not asymmetric in time. Hence, the conventional way of reading the history of the universe is correct, while the inverted way (version 0) is absurd.
So there remains only a small question: is the universe we live in causal? Of course, this is no small question at all, and we have already said that it is beyond our ability. But someone did decide this question, and he is none other than the famous Stephen Hawking. This good man firmly claims that the laws of nature allow for the existence of fundamental indeterminism, that is, a process that is not causal. All we can say in the margins of his remarks is that this claim contradicts his second claim, that 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 challenged causality, but in fact this is not accurate. The formalism of quantum theory, that is, its system of laws, preserves causality. True, given a certain quantum state, A, we can only predict the probabilities of 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 outcome based on knowledge of the cause. This is the “hidden variables” hypothesis that Einstein toyed with in the hope of disproving quantum theory, but today, not only has it not been proven but has also been limited (such as John Bell’s proof that such hidden variables would act at a distance, ostensibly contrary to the theory of relativity), and yet most physicists believe in it.
Physicists rely on a principle called in professional language the “unitary conservation hypothesis,” which in everyday language can be formulated as the principle of information conservation. For example, if we throw a book into a fire, the information written in the book does not disappear completely. It is preserved in the photons (particles of light) that come out of the fire. It is impossible to recover this information with today’s technology, but in principle this information has not been lost, but has only been mixed with a huge amount of information that appears to us to be nothing more than random noise. The extent to which such information can be recovered is a technological question and nothing more. In the eyes of theoretical physics, information never disappears.
And now, more than twenty years ago, Hawking announced that there is a case in which unitarity is not preserved, that is, a process in which information disappears completely, and does not just mix with noise. This process is the evaporation of a black hole. Physicists had known for a long time that when a black hole is formed, everything that falls into it – bicycles, bananas, members of Knesset – will lose all its physical properties (color, shape, smell, etc.) and will change only the three only physical properties of the black hole: mass, angular momentum, and electric charge. There is, ostensibly, a clear loss of information here, but physicists assumed that the lost properties of the objects that fell into the black hole remain hidden within it, beyond the reach of the visible universe. And here came Hawking, following a hint from Jacob Bekenstein of the Hebrew University, and proved that black holes evaporate in a surprisingly simple quantum process. We will not repeat the details of the process – they are clearly explained in “A Brief History of Time.” What is important for our purposes is that the particles emitted from the black hole and causing its collapse are created on its edges, far from the bicycles, bananas and MKs that were swallowed into its center. Here, Hawking said, there is a real loss of information. While the photons coming out of the fire still preserve the content of the book, the photons coming out of the edges of a black hole cannot preserve any of the properties of the bodies that were swallowed far into its center. Thus, at the end of the black hole, all the information that was swallowed into it will completely disappear.
And here is the irony: For many years, Hawking and Penrose have been arguing about the origin of the arrow of time. Hawking, the younger of the two, actually takes the conservative position (Chapter 0), while Penrose, as we have seen, puts forward the more daring hypothesis (Chapter 0). This long-running debate (which, like the famous debate between Einstein and Bohr, was conducted out of friendship and mutual admiration), was conducted on public stages and was recently even published as a book. But throughout this entire debate, Penrose did not notice how Hawking unknowingly presented him, again and again, with the argument that supports his own approach!
The logic here is quite simple. Let us imagine two closed systems. One of them undergoes a normal evolution, 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 a sufficient time and check its entropy, we find that the entropy has increased. This is not surprising: if Hawking’s hypothesis is correct, the particles into which the black hole evaporated could not preserve information about the objects previously swallowed by the black hole. Thus, the evaporation of the black hole simply added to the entropy of the system, in the same way as the single disturbance in Figure 7a that disrupted the causal chain.
The second system would be the exact inverse of the first system: a closed system in which the states and momentums of all particles are pre-coordinated with the utmost precision so that its entropy would decrease over time (coffee mugs heating up, the dead rising from their graves, and all the other antics we mentioned). Here too, the amounts of matter and the length of time allocated to the system would be sufficient for the formation and evaporation of a black hole. When we open the system at the end of the experiment, we find that the time reversal has failed: the entropy has increased in this case as well.
The reason is clear: the information-destroying effect of the black hole destroyed the pre-arranged adjustments with which the initial state was prepared. This process is analogous to the case we saw in Figure 7b, with the difference that the causality failure caused by the black hole affects not just one particle but many particles.
And so, as the lawyers say, We rest our case. If even one completely non-deterministic event occurred somewhere in the universe—be it the evaporation of a black hole, the yawning of a cat, or the tears shed by a housewife after peeling an onion—then the causal relationships throughout the universe lose their time symmetry. Such an event is equivalent to the perturbation we introduced in 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 we mentioned in Chapter 0, and in this way we can finally establish that past events cause future events and not vice versa. We would like to reiterate 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. Any severely non-causal event is treated as the slight perturbation we have caused in the trajectory of the billiard balls. Because of it, a beautiful triangle turning into a jumble of bullets (or, in our world, coffee cups getting cold and people getting old and dying) is possible, while the reverse process requires well-thought-out and ongoing intervention from a higher power.
From this point, where conventional physics must enlist miraculous coincidences, there are only two ways to return to science. On the one hand, it is possible that Hawking and his ilk may turn out to be wrong and that information is preserved even in the evaporation of a black hole (an idea recently supported by string theory, which attempts to provide a detailed description of black holes). We of course hope that this will not be the case, but for now we can only wait and see what day brings. On the other hand, if it turns out that Hawking was right, then the conservative argument presented at the beginning of this article also collapses, namely that future events exist alongside present and past events just as the northern gates exist alongside the southern ones. And if so, if the future does not exist, the theory that time is subject to becoming will return and force physics to exceed its current limits.