synthetic zero

September 5th, 2009

I want to go over a fundamental conundrum in quantum mechanics which, while simple, suffices to illustrate an extremely thorny problem which has stumped physicists for the last century: the quantum measurement problem. There has been significant progress in resolving this problem (which I won’t detail below, although I will sketch out some of the earlier approaches physicists took to this), but there hasn’t been a definitive solution, yet.

I won’t get into the precise description of the experiment in question; I’ll try to keep it simple. The basic idea is you have two particles that are emitted from a source that fly off in opposite directions, let’s call these A and A’. We then measure these particles later, with instruments D and D’. An added spice factor is that we can rotate these instruments, and how we rotate them changes what they measure; we can say we’re measuring them along a certain axis; 0 degrees, 60 degrees, 90 degrees, etc., and furthermore D and D’ can only give one of two results, let’s call them + and -. Now, here’s the weird part.

Let’s say the two instruments D and D’ are both oriented at, say, 0 degrees. We then measure this property of particles A and A’, and it turns out that D and D’ always give the same result (in fact they always give the opposite result, but for simplicity we’ll just invert the measurements of one of the instruments so we can just say they’re always the same). The point is, they’re correlated 100% of the time.

Now, let’s say we start to rotate these instruments relative to each other. The more different the orientation of D and D’, the more often their measurements differ, statistically, until they’re exactly 90 degrees different and their measurements are not correlated at all.

Suppose we start with the hypothesis that all you need in order to understand the statistics of the measurements at D are some hidden property of A and hidden properties of the instrument D, and nothing else. Most importantly, how you orient D’ shouldn’t matter at all to what measurements you get at D. I won’t go through the math with you, but it turns out that in fact, if we assume this, we get a contradiction; that is to say, there is no way to account for the statistics of the measurements at D without considering how one set up the instrument D’. In other words, part of the “hidden property” of D would have to include the setup of the instrument D’ in order to account for the measurement correlations one gets between D and D’ (for more on this, please see this article on Bell’s Theorem.

Now it turns out there are a variety of ways of interpreting this and other similarly strange results from quantum mechanics, all of them radically different. One approach is to assume that the result you get at D depends not only on the particle A and the state of the measuring device D, but potentially the state of everything else in the universe for all time (i.e., including the future). This is a “realist” interpretation which holds that the particle A has a real position and momentum at all times, but it is governed by a “pilot wave” which depends on the state of the entire universe for all time; it is called Bohmian mechanics.

A more classic interpretation is called the Copenhagen Interpretation; in this interpretation a measurement is never actualized until an observer observes it.

Yet another interpretation which is favored by many physicists is called the Everett Many-Worlds Interpretation (there are many variants of this). In this interpretation, roughly speaking, when an observer observes something, at that moment the entire universe splits into different paths; one where the observer observes one measurement and one in which they observe another measurement. A variant of this is sometimes called “many minds”; that is to say, a mind is correlated with an observation, with which one can retrospectively project a past for that mind in that moment. These interpretations fundamentally revolve around a correlation between mind and an observation or set of observations, where particular observations have no realization without a mind to observe them, and furthermore there is a mututal dependency between a mind and a world (i.e., in some sense one could say that the mind, in this interpretation, arises together with a presumed universe of observations; that there are no independently existing objects whatsoever apart from minds, though one can speak of an independently existing universal quantum wavefunction that itself contains no separated objects, inherently.)

It is in this context that it’s important to think carefully about what we really mean when we talk about possible models or ways of thinking about the world; the pictures that physicists have been coming up with over the last century or so are incredibly bizarre, they question even things like whether space and time exist a priori, and whether any ordinary things can be said to exist apart from observers; they raise the possibility that mind and world arise together; one does not prefigure the other, etc. All of these are quite reasonable and plausible interpretations of quantum mechanics.

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