there is causal invariance, then ultimately all these different histories must in a sense be equivalent. And with this constraint, if one breaks some process into parts, there will typically be no simple way to describe how the effect of these parts combines together.

And for at least some purposes it may well make sense to think explicitly about different possible histories, combining something like amplitudes that one assigns to each of them. Yet quite how this might work will certainly depend on what feature of the network one tries to look at.

It has always been a major issue in quantum theory just how one tells what is happening with a particular particle like an electron. From our experience with everyday objects we might think that it should somehow be possible to do this without affecting the electron. But if the only things we have are particles, then to find out something about a given particle we inevitably have to have some other particle—say a photon of light—explicitly interact with it. And in this interaction the original particle will inevitably be affected in some way.

And in fact just one interaction will certainly not be enough. For we as humans cannot normally perceive individual particles. And indeed there usually have to be a huge number of particles doing more or less the same thing before we successfully register it.

Most often the way this is made to happen is by setting up some kind of detector that is initially in a state that is sufficiently unstable that just a single particle can initiate a whole cascade of consequences. And usually such a detector is arranged so that it evolves to one or another stable state that has sufficiently uniform properties that we can recognize it as corresponding to a definite outcome of a measurement.

At first, however, such evolution to an organized state might seem inconsistent with microscopic reversibility. But in fact—just as in so many other seemingly irreversible processes—all that is needed to preserve reversibility is that if one looks at sufficient details of the system there can be arbitrary and seemingly random behavior. And the point is just that in making conclusions about the result of a measurement we choose to ignore such details.

So even though the actual result that we take away from a measurement may be quite simple, many particles—and many events—

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From Stephen Wolfram: A New Kind of Science [citation]