# The Fundamental Difference in Interpretations of Quantum Mechanics

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 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 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.

Hi Peter:

I very much like the clarity of the dichotomy you present.

Sometimes I find myself comfortably accepting either of the two points of view at different times. The particular choice I make depends on my recognizing that the context makes one choice more convenient than the other. When I think about my practice of doing this, I interpret this as actually accepting both points of view at the same time, and when I do that I just ignore the apparent contradictions. I summarize this practice with the maxim:

Regards,

Buzz

Peter, when you write "physically real", do you refer to which definition of it?

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lightarrow

There is no precise definition of the term "physically real". That's part of what makes discussions of QM interpretations difficult: one is trying to go beyond the basic model of QM, which is expressed in math and has precise definitions, to interpretations that use ordinary language, where words do not have precise definitions.

Hi,

Nice article that shows a facet of epistemic (#1)/ontological (#2) duality. My understanding (and thus my point of view) is that the observer (humain being, measurements apparatus) interact with something that resist to us ("real in itself"), but can only capture the interaction effects and not the causes.

To buid a rational and complet interpretation, it seems to me that we need to dissect how we construct our knowledge from the effects we capture and then we have to take in acount all the humain process from ours first-person experience up to ours objectifications. Moreover It could be relevant to be aware of our blind spot when we made ours objectivations/reifications.

Best regards,

Patrick

Ok, and do you think that term, "physically real" refers only to physical quantities as position, momentum, spin components, etc, or even to something else? For example could I pretend that "physically real" is the "setting of the experiment" if it's prepared in a specific and reproducible way?

To which of the 2 "paradigms" you describes belongs this vision?

Thanks.

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lightarrow

What are the Interpretations of Classical Mechanics ?

The book by Laurence Sklar, Physics and Chance, discusses the philosophy of classical mechanics. But the subject have fallen out of fashion since it is known that classical mechanics fails completely in the subatomic domain.

Please read what I said in the article: I said that viewpoint #2 says that the

quantum stateis "physically real". In other words, the wave function/state vector/whatever you want to call it, a particular well-defined thing in the math, represents something "physically real". The quantum state is not position, momentum, spin components, etc. It's the particular well-defined thing in the math.In my opinion, part of the reason there is such scope for interpretations is that nobody actually KNOWS what Ψ means. Either there is an actual wave of there is not, and here we have the first room for debate. If there is, how come nobody can find it, and if there is not, how come a stream of particles reproduce a diffraction pattern in the two slit experiment? No matter which option you try, somewhere there is a dead rat to swallow. As it happens, I have my own interpretation which differs from others in two ways after you assume there is an actual wave. The first, the phase exp(2

πiS/h) becomes real when S = h (or h/2) – from Euler. This is why electrons pair in an energy well, despite repelling each other. Since it becomes real at the antinode, I add the premise that the expectation values of variables can be obtained there. The second is that if there is a wave, the wave front has to arrive at the two slits about the same time as the particle. If so, the wave must transmit energy (which waves generally do, but the dead rat here is where is this extra energy? However, it is better than Bohm's quantum potential because it has a specific value.) The Uncertainty Principle and Exclusion Principle follow readily, as does why the electron does not radiate its way to the nucleus. The value in this, from my point of view, is it makes the calculation of things like the chemical bond so much easier – the hydrogen molecule becomes almost mental arithmetic, although things get more complicated as the number of electrons increase. Nevertheless, the equations for Sb2 gave an energy within about 2 kJ/mol, which is not bad.True, but your article inherits an imprecise meaning directly from imprecision of "physically real". It would be unreasonable to expect any commentary on interpretations of QM to be free of all ambiguity, but in order to get the "general drift" of what you are saying it would be helpful to have examples of how , in your opinion, different concepts of the reality of the wave function lead to well-known interpretations of QM.

Even if we cannot precisely define "physically real" to the extent of proposing a physical test for it or a mathematical definition, it may be possible to agree on certain properties of "physically real" things. For example, thinking in terms of mathematics, if I grant that X and Y are physically real aspects of something then should I also say that any function f(X,Y) is also physically real? One would suspect the answer is "No". A tricky mathematician would have us consider the constant function f(X,Y) = 13. So perhaps the mathematical property of a physically real f(X,Y) should be that we can reconstruct the values of X and Y given the value of f(X,Y) or , more generally that we can reconstruct the values of X and Y from a given value f(X,Y) and values of some other functions of X and Y.

I don't understand that passage. For example, is the fact that a person is a resident of the state of Texas a physically real property of that person? Isn't belonging to the ensemble of Texans a real property of that single person? Would we define a physically real property of a person to be sufficient information to distinguish a unique person?