# 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 describes our knowledge or potential knowledge about the system; we use the state to predict the probabilities of different results for measurements we might choose to make of the system. Changes in the state represent changes in our knowledge about the system; for example, when we make a measurement and obtain a particular result, we update the state to reflect our knowledge of that result.

(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.)

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?

I thought cases 1 and 2 in the article already described that, but I'll give it another shot.

Case 1 says the state is not real; it's just a description of our knowledge of the system, in the same sense that, for example, saying that a coin has a 50-50 chance of coming up heads or tails describes our knowledge of the system–the coin itself isn't a 50-50 mixture of anything, nor is what happens when we flip it, it's just that we don't know–we can't predict–how it is going to land, we can only describe probabilities.

Case 2 says the state is real, in the same sense that, for example, a 3-vector describing the position of an object in Newtonian physics is real: it describes the actual position of the actual object.

I focus more on predictions than "interpretations."

One could have differing interpretations of Lagrangian, Hamiltonian, and Newtonian Mechanics (and I've met physicists who do argue one is right and the other two are "wrong"). However, all the predictions are the same.

The only interesting cases are where differing interpretations make different testable predictions. This is real science. Then we can perform an experiment to distinguish between them.

This is also my position, and in particular to understand how the choice of interpretation"implies" a certain research direction in the open questions, or even WHICH the open question are, such as unification of interactions. Then if a certain interpretations shows to provide a more fruitful "angle" to making progress, then that would be my "preferred" interpretation.

Lets note that this is a DIFFERENT selection strategy than those that think we need no modification to current theories, and that the preferred interpretation thus is some kind of "minimalist one". I fully agree that the minimalist selection principle makes sense if the interpretation served only the purposes of decreasing angst over understanding or not understanding the foundations..

/Fredrik

I often feel that the descriptor "real", would be better replaced in these discussions with "objective", or observer invariant.

Thus real would mean, that different observers should arrive at a consistent descriptions of the same system. And then it begs the question of explaining how does one make this "consistency check"? This is a bit like trying to compare angles of vectors living at different tangent planes or so. You need some kind fo "parallell transport".

As I see it, the consistency check is that the two systems making the inferences must physically interact/communicate. If they can do this without distorting the opinion of the other party, then they are consistent, and they have reached a consensus. And in many cases where there is an "apparent" disagreement, this is often identifed as an interaction term or force between the observers! And accounting for this, one can add some new interactions and recover a new elevated level of objectivity. This is also typically the situation that works fine in classical mechanics. And while we have observers also in classical mechanics, the fact that they typically easily reach a consensus of observations, is why the observations rarely are emphasised as of fundamental importance.

So unless we can define the interaction that constitutes the consistency check, the notion of "real" is not only slightly ambigous, it seems too undefined to be recommended.

/Fredrik

What I'm suggesting is that your give examples of the thesis of your article – that the two cases naturally divide the various interpretations- e.g. perhaps Case 2 leads to the Many Worlds or the Bohmian interpretation etc.

Parsing that definition seems to hinge on whether probabilities are "real". In your definition, must a physically real state be sufficient to produce a deterministic outcome ?

What aspect of that example is significant?

One feature of that example is that if point particle_1 has the same 3-vector as point particle_2 then particle_1 and particle_2 are the same particle. By contrast, if we are only given that particle_1 and particle_2 are both in a laboratory in Texas then, from that description, the names might refer to different particles.

Another aspect of that example is that we can measure the 3-vector associated with a particle. However, we could also determine whether a particle is in a laboratory in Texas, so the ability to measure the 3-vector seems not to be the outstanding feature of the example.

Perhaps, but that would fail to acknowledge the fundamental difference in interpretations which was the main topic of the article. :wink: I think all interpretations agree that the quantum state/wave function is observer invariant; that's not where the difference lies.

Ah, ok. If you want a quick categorization of some common interpretations, here it is:

Case 1: Copenhagen, ensemble

Case 2: Many worlds, Bohmian*

* – the Bohmian interpretation is kind of a special case, because it contains nonlocal hidden variables: the actual particle positions. The standard Bohmian interpretation considers these to be in principle unobservable, but it also considers the wave function–the "quantum potential"–to be real, which is why I put it in case 2.

But one could easily envision an extended Bohmian interpretation in which they were observable. This would amount to a new theory extending QM and making testable predictions that could distinguish it from standard QM, which would take it out of the topic area discussed in the article. Similar remarks apply to things like the GRW model, which adds an additional "objective collapse" process that makes different testable predictions from standard QM.

Sure, that's why I said we're dealing with vague ordinary language. I'm not trying to put a specific definition on the word "real". I'm just trying to say that, as far as I can tell, people who espouse Case 1 interpretations consider the quantum state to be like probabilities, and in common ordinary language usage probabilities do not describe the physically real state of anything; they just describe our knowledge (or the limitations thereof). If it helps, substitute "case 1 says the quantum state is like probabilities" for "case 1 says the quantum state is not real".

Case 2 interpretations of QM do not say a physically real state produces a deterministic outcome (that would contradict stan; they just say the quantum state is physically real. So I don't see how this helps to clarify anything relevant to this discussion.

Just what I said: case 2 interpretations treat the quantum state vector similarly to the way Newtonian physics treats the position 3-vector of a particle: it describes the physically real state of something.

I think you're making this more difficult that it needs to be. I'm not trying to be abstruse.

I am somewhat surprised this thread is allowed at all, since interpretations of QM is purely a philosophy of science/physics topic. This side discussion about the imprecision of language is a red herring, since there are already certain words in philosophy which have specified meanings to make clear distinctions, for example, physical is such a word. As was said before in post 5, the main distinction between interpretations of QM is precisely whether or not the state is itself ontic or epistemic; everything else (e.g. whether or not it is determistic or stochastic) is independent with regard to the ontic/epistemic distinction.

Moreover, some 'interpretations' of QM, in particular the collapse ones, are clearly not interpretations but incomplete extensions to or revisions of QM, i.e. alternative theories awaiting mathematical completion. It is here most clearly that philosophers of physics, i.e. physicists and other scientists focusing on these philosophical themes of their discipline by extending theories and placing extensions and alternative hypotheses in proper context, have contributed more to this aspect of physics than regular physicists have done so far.

This is an essential aspect of science which does not nearly get enough attention, mostly because in the practice of physics we don’t often explicitly run into such difficulties (implicitly is a whole different story) and therefore don't see the need for philosophical expertise. When we do however run into these difficulties, this kind of philosophical reevaluation of some theory is the correct method to take that actually can point the way forward. It is somewhat a matter of luck that in the early 20th, both Einstein and the founders of QM acknowledged this and so could end up discarding and reformulating core traditional principles of physics and so end up creating the correct mathematical formulations thereof, which we today refer to as relativity and QM.

Today we are somewhat priviliged that the philosophers of physics have already simplified and classified the different interpretations and also given instructions on how to proceed. It is tragic that not many physicists have been willing to listen. In any case, the only way physicists can do more in advancing our understanding of QM deeper than what the philosophers of physics have done so far, is by actually creating new mathematical theories based on or incorporating those ideas from first principle, with hopefully one of the resulting mathematical theories being self-consistent and simultaneously not being trivially equivalent to QM itself.

The collapse theories tend to be of this variety, but their dynamical formulations to this day remain mathematically incomplete. Somewhat unfortunate is that the domain of physics concerned with critical phenomenon, of which the mathematical theory is very much a theory of principle, has become somewhat directly associated with condensed matter physics, which is itself a collection of constructive theories. This is unfortunate because the mathematical methods required by the theoreticians to derive these theories from first principles are precisely the mathematical methods taught to condensed matter physicists except in a very different context and with a completely different purpose.

Peter,

thank you for condensing this debate to two simple alternatives. I think, following Einstein and Bohr, we can make this dilemma even simpler. The question is: "Does God really play dice?"

If your answer is "no", then you have to complain

But if you are OK with God playing dice, then there is nothing wrong with the probabilistic behavior of Nature. All these quantum events are simply unpredictable. So, existing quantum mechanics does a good job at describing this unpredictability. If somebody asks you why the electron hit this particular place on the screen, you can simply reply: "I don't know and don't care. It was just random."

I think, with this thought all of us should rejoice: we finally came to a satisfying end of the scientific quest (at least in this particular direction). We don't have to keep unraveling the never-ending chain of cause-and-effect relationships. Because we came to the class of quantum events, which don't have causes, since they are truly random. Congratulations everyone!

Eugene.