A topic that continually comes up in discussions of quantum mechanics is the existence of many different interpretations. Not only are there different interpretations, but people often get quite emphatic about the one they favor, so that discussions of QM can easily turn into long arguments. Sometimes this even reaches the point where proponents of a particular interpretation claim that anyone who doesn’t believe it is “idiotic”, or some other extreme term. This seems a bit odd given that all of the interpretations use the same theoretical machinery of QM to make predictions, and therefore whatever differences there are between them are not experimentally testable.

In this article I want to present what I see as a fundamental difference in interpretation that I think is at the heart of many of these disagreements and arguments. I take no position on whether either of the interpretations I will describe is “right” or “wrong”; my purpose here is not to argue for either one but to try to explain the fundamental beliefs underlying each one to people who hold the other. If people are going to disagree about interpretations of QM, which is likely to continue until someone figures out a way of extending QM so that the differences in interpretations become experimentally testable, it would be nice if they could at least understand what they are disagreeing about instead of calling each other idiots. This article is an attempt to make some small contribution towards that goal.

The fundamental difference that I see is how to interpret the mathematical object that describes a quantum system. This object has various names: quantum state, state vector, wave function, etc. I will call it the “state” both for brevity and to avoid adopting any specific mathematical framework, since they’re all equivalent anyway. The question is, what does the state represent? The two fundamentally different interpretations give two very different answers to this question:

(1) The state is only a tool that we use to predict the probabilities of different results for measurements we might choose to make of the system. Changes in the state represent changes in the predicted probabilities; for example, when we make a measurement and obtain a particular result, we update the state to reflect that observed result, so that our predictions of probabilities of future measurements change.

(2) The state describes the physically real state of the individual quantum system; the state allows us to predict the probabilities of different results for measurements because it describes something physically real, and measurements do physically real things to it. Changes in the state represent physically real changes in the system; for example, when we make a measurement, the state of the measured system becomes entangled with the state of the measuring device, which is a physically real change in both of them.

(Some people might want to add a third answer: the state describes an ensemble of a large number of similar systems, rather than a single system. For purposes of this discussion, I am considering this to be equivalent to answer #1, because the state does not describe the physically real state of a single system, and the role of the ensemble is simply to enable a frequentist interpretation of the predicted probabilities.)

(Note: Originally, answer #1 above talked about the state as describing our knowledge of the system. However, the word “knowledge” is itself open to various interpretations, and I did not intend to limit answer #1 to just “knowledge interpretations” of QM; I intended it to cover all interpretations that do not view the state as directly describing the physically real state of the system.)

The reason there is a fundamental problem with the interpretation of QM is that each of the above answers, while it contains parts that seem obviously true, leads us, if we take it to its logical conclusion, to a place that doesn’t make sense. There is no choice that gives us just a set of comfortable, reasonable statements that we can easily accept as true. Picking an interpretation requires you to decide which of the obviously true things seems more compelling and which ones you are willing to give up, and/or which of the places that don’t make sense is less unpalatable to you.

For #1, the obviously true part is that we can never directly observe the state, and we can never make deterministic predictions about the results of quantum experiments. That makes it seem obvious that the state can’t be the physically real state of the system; if it were, we ought to be able to pin it down and not have to settle for merely probabilistic descriptions. But if we take that idea to its logical conclusion, it implies that QM must be an incomplete theory; there ought to be some more complete description of the system that fills in the gaps and allows us to do better than merely probabilistic predictions. And yet nobody has ever found such a more complete description, and all indications from experiments (at least so far) are that no such description exists; the probabilistic predictions that QM gives us really are the best we can do.

For #2, the obviously true part is that interpreting the state as physically real makes QM work just like all the other physical theories we’ve discovered, instead of being a unique special case. The theoretical model assigns the system a state that reflects, as best we can in the model, the real physical state of the real system. But if we take this to its logical conclusion, it implies that the real world is nothing like the world that we perceive. We perceive a single classical world, but the state that QM assigns is a quantum superposition of many worlds. We perceive a single definite result for measurements, but the state that QM assigns is a quantum superposition of all possible results, entangled with all possible states of the measuring device, and of our own brains, perceiving all the different possible results.

Again, my purpose here is not to pick either one of these and try to argue for it. It is simply to observe that, as I said above, no matter which one you pick, #1 or #2, there are obvious drawbacks to the choice, which might reasonably lead other people to pick the other one instead. Neither choice is “right” or “wrong”; both are just best guesses, based on, as I said above, which particular tradeoff one chooses to make between the obviously true parts and the unpalatable parts. And we have no way of resolving any of this by experiment, so we simply have to accept that both viewpoints can reasonably coexist at the present state of our knowledge.

I realize that pointing all this out is not going to stop all arguments about interpretations of QM. I would simply suggest that, if you find yourself in such an argument, you take a moment to step back and reflect on the above, and realize that the argument has no “right” or “wrong” outcome, and that the best we can do at this point is to accept that reasonable people can disagree on QM interpretations and leave it at that.