## By his bootstraps

 “By His Bootstraps” (1941) was a science fiction story in which a man acquired a time machine from a future version of himself. This is an example of an acausal loop because the time machine need never be invented.

In my last Physics in a Nutshell, I started a series about quantum mechanics by addressing its first strange feature: the fact that quantities can be multivalued yet restricted to whole numbers, like a light switch that is both on and off but never halfway on.

The second weird thing about quantum mechanics is that it takes as much liberty with time and causality as is logically possible. Time travel, as it is usually presented in fiction, is full of logical paradoxes. Suppose you go back in time and prevent yourself from inventing a time machine. Without a time machine, you can’t go back to make the change, and an infinite regress ensues. But there is another way of changing history that isn’t impossible, merely contrived: Suppose you go back and teach yourself how to invent a time machine, retroactively making the trip possible. Heinlein’s novella “By His Bootstraps” worked this way, and in a sense, so did Sophocles’ “Oedipus Rex.”

If quantum processes are taken literally as sequences, they resemble constructive time loops. The simplest example is the mutual repulsion of charged particles (the reason hair stands up on a dry day). Two charged particles repel each other because one emits a photon, recoiling from the photon’s momentum, and the other catches it, recoiling the other way. However, they never miss — the pitcher doesn’t throw the ball unless the catcher catches it. If viewed at relativistic speeds (charged particles in an accelerator, for instance), the catcher’s catch can even precede the pitcher’s throw, with the photon traveling backward between them. The same process, viewed by two different observers, happens in a different time order.

More complex examples demonstrate this more conclusively. The lesson physicists have drawn is that a quantum process is not a sequence of independent steps, but an undivided cloth that entirely happens or entirely does not happen. Oedipus would not have married his mother if he were not trying to avoid the prophecy that he would do so, and the prophecy would not have been uttered if he did not do so. The whole process can happen without inconsistency, and it can also not happen without inconsistency.

On a human scale, closed time loops would seem to imply a lack of free will, but the randomness of quantum events prevents us from drawing simple philosophical conclusions. Even though experiments on coupled processes have been scaled up such that measurements on one side of a workbench predict outcomes on the other, the sequence of messages is strictly random and cannot be influenced by the experimenter. Thus, we can’t use this to communicate with or change the past. Quantum processes are as acausal as is logically possible, and no more.

In the next article, I will talk about waves, particles and the strange fact that matter at microscopic scales appears to be both.

Jim Pivarski