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By Root 762 0

the effect is subtle because ‘getting the job’ and ‘not getting the job’ makes a big difference to our lives and one cannot easily imagine a scenario where they lead to identical future Universes (remember, we should only add amplitudes that lead to identical outcomes). So in that case, getting and not getting the job do not interfere much with each other and our perception of the world is as if one thing has happened and not the other. However, things become more ambiguous the less dramatic the two alternative scenarios are and, as we have seen, for interactions involving small numbers of particles summing over the different possibilities is absolutely necessary. The large numbers of particles involved in everyday life mean that two substantially different configurations of atoms at some time (e.g. getting the job or not) are simply very unlikely to lead to significantly interfering contributions to some future scenario. In turn, that means we can go ahead and pretend that the world has changed irrevocably as a result of a measurement, even when nothing of the sort has actually happened.

But these musings are not of pressing importance when it comes to the serious business of computing the probability that something will happen when we actually carry out an experiment. For that, we know the rules and we can implement them without any problems. But that happy circumstance may change one day – for now it is the case that questions about how our past might influence the future through quantum interference simply haven’t been accessible to experiment. The extent to which meditations on the ‘true nature’ of the world (or worlds) described by quantum theory can detract from scientific progress is nicely encapsulated in the position taken by the ‘shut up and calculate’ school of physics, which deftly dismisses any attempt to talk about the reality of things.

Anti-matter

Back in this world, Figure 10.3 shows another way that two electrons can scatter off each other. One of the incoming electrons hops from A to X, whereupon it emits a photon. So far so good but now the electron heads backwards in time to Y where it absorbs another photon and thence it heads into the future, where it might be eventually detected at C. This diagram does not contravene our rules for hopping and branching, because the electron goes about emitting and absorbing photons as prescribed by the theory. It can happen according to the rules and, as the title of the book suggests, if it can happen, then it does. But such behaviour does appear to violate the rules of common sense, because we are entertaining the idea that electrons travel backwards in time. This would make for nice science fiction, but violating the law of cause and effect is no way to build a universe. It would also seem to place quantum theory in direct conflict with Einstein’s Theory of Special Relativity.

Figure 10.3. Anti-matter … or an electron travelling backwards in time.

Remarkably, this particular kind of time travel for subatomic particles is not forbidden, as Dirac realized in 1928. We can see a hint that all may not be quite as defective as it seems if we reinterpret the goings-on in Figure 10.3 from our ‘forwards in time’ perspective. We are to track events from left to right in the figure. Let’s start at time T = 0, where there is a world of just two electrons located at A and B. We continue with a world containing just two electrons until time T1, whereupon the lower electron emits a photon; between times T1 and T2 the world now contains two electrons plus one photon. At time T2, the photon dies and is replaced by an electron (which will end up at C) and a second particle (which will end up at X). We hesitate to call the second particle an electron because it is ‘an electron travelling back in time’. The question is, what does an electron that is travelling back in time look like from the point of view of someone (like you) travelling forwards in time?

To answer this, let’s imagine shooting some video footage of an electron as it travels in the vicinity of a magnet, as