Interpretations vs. Non-Interpretations (e.g. Ensemble)

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  • #1
Recall the famous "Shut up and calculate interpretation". Should it be called an interpretation? The content of the interpretation is "don't interpret quantum mechanics". I argue that for certain purposes it would make sense to distinguish between interpretations (like Many Worlds and Copenhagen) and non-interpretations (like Shut up and calculate), because the real interpretations actually have nontrivial content in that they characterize the mechanics of the model. What I mean is that Copenhagen and Many Worlds say "this is what the waves/particles/fields are doing, including when we're not measuring them," and thus they're making assertions about the mechanics of these objects, including individual particles. In the other branches of physics besides quantum, physicists use the term "Mechanics" to refer to descriptions that apply to individual particles, whereas they use the term "Statistical Mechanics" to refer to the descriptions that only apply to ensembles of particles. So there are only two options for theories of mechanics: they are either Mechanics or Statistical Mechanics. To make the distinction more clear, from now on I will call Statistical Mechanics by the name "Ensemble Mechanics", and I will call Mechanics by the name "Individual Mechanics".

For some background, consider the development of classical statistical mechanics, especially the contributions of Ludwig Boltzmann. Boltzmann was able to derive all the correct equations of thermodynamics, but much of his work focused on connecting the statistical/thermodynamic descriptions with the underlying individual mechanics. His efforts to relate the statistical equations to Newtonian mechanics were a kind of "interpetation"--he wanted an explanation of "this is what the individual waves/particles/fields are doing", and he actually managed to develop the classical kinetic theory of gasses which relates thermodynamic variables with classical particle motions pretty successfully, even though we now know the real underlying mechanics are quantum.

Back to my main point: is the Ensemble Interpretation an interpretation or a non-interpretation? The Ensemble Interpretation says that Quantum Mechanics is actually only applicable to ensembles of identically prepared waves/particles/fields. So in this interpretation it would be better to call the theory "Quantum Ensemble Mechanics" rather than "Quantum Individual Mechanics". But we could ask the same question as Boltzmann, "what are the underlying individual mechanics that give rise to quantum ensemble mechanics?" The ensemble interpretation offers nothing to answer that question. For that question, it is equivalent to Shut up and calculate. The ensemble interpretation would likewise fail to answer the afformentioned question "what are the individual waves/particles/fields doing?"

However, Copenhagen and Many Worlds state that quantum mechanics is actually Quantum Individual Mechanics; i.e. it is the fundamental rule for what each and every individual particle is doing. So they actually do answer interpretive questions.

For this reason I think the Ensemble interpretation is a non-interpretation like Shut up and calculate.

For the record, though, I am not advocating any interpretations over any others. There is no scientific evidence for or against any of them, so it is perfectly legitimate to believe Ensemble, Many Worlds, Copenhagen, Shut up and calculate, or any of the others. In this post I am only attempting to characterize and group together these different alternatives.
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It seems to me on the one hand, there are opinions about the things we measure in the lab and try to predict with our theories (traditional interpretations), and on the other hand, there are the opinions about the nature of the theory (as opposed to the "things" the theory talks about). You could call the first group, the "theory-is interpretations" and the other group, the "theory-ought interpretations".

Some jumping off points to clarify my ideas:

Theory oughts:
"Quantum mechanics is intended to describe..."
... the interaction between observer and observed?
... the statistics of ensembles of particles?
... the probability of measurement outcomes of particular experiments?

Theory is's:
"When we measure an observable, what happens is..."
... the state collapses?
... we become entangled with the system?
"What quantum entanglement means physically..."
and so on

The ensemble and SUAC "interpretations" are statements about what quantum theory is indented to describe and how it should be used, whereas more traditional "interpretations" (i.e. Copenhagen, Many-Worlds, Pilot Wave, etc) are statements about the thing(s) Quantum mechanics is alleged to describe.

Good question, though
  • #3
For this reason I think the Ensemble interpretation is a non-interpretation like Shut up and calculate.
There seems to be a bit of confusion about this - I have seen posts where people claim the Ensemble interpretation is a non interpretation because it doesn't tell us what is really going on.

Think about it for a minute though. Things like what's really going on are value judgements on how you think the world works and to a large extent depends on what you think reality is. These are very deep philosophical questions there is no agreement on by a long shot - millenia of philosophical discourse has led to no consensus. Take your statistical physics analogy. You are assuming, because the ensemble view of statistical physics also talks about ensembles it must be like those. That is a specific interpretation of reality - reality does not have to oblige. The outcomes of observations may be the fundamental reality - end of story. To put it another way - you can ask the question you posed - but the answer may be - there aren't any - get used to it.

The Ensemble interpretation is an interpretation that takes as fundamental the outcome of and existence of observations. Other interpretations such as consciousnesses causes collapse even doubt that. This is modeled by a specific interpretation of probability - the so called ensemble interpretation (outside QM its called the frequentest interpretation). It is the most common one and extensively used in applied math - but is not the only one (there is the so called subjectivist or Bayesian view):

Assumptions are being made here, assumptions not implied by the formalism. They are minimalist assumptions to be sure - but assumptions they are.

Copenhagen believes the state is fundamental (not real - but fundamental) and probabilities enter as degrees of subjective knowledge about the outcomes of observations. This leads to a different view of probability more in line with Bayesian view:
'The subjective view, that the wave function is merely a mathematical tool for calculating the probabilities in a specific experiment, has some similarities to the Ensemble interpretation in that it takes probabilities to be the essence of the quantum state, but unlike the ensemble interpretation, it takes these probabilities to be perfectly applicable to single experimental outcomes, as it interprets them in terms of subjective probability.'

It too is a minimalist interpretation but a bit different to the Ensemble.

Both could reasonably be thought of as shut up and calculate because they are so minimal but assumptions are still being made. In fact that's my view of shut up and calculate - interpretations with very few assumptions beyond the formalism. I suppose however shut up and calculate is taking the formalism at face value without any assumptions. I however have a slight issue with that because most applied mathematicians stick to the ensemble interpretation of probability so there is really an interpretation implicitly being made.

MWI goes a bit further and actually thinks the state exists out there in a real sense and in my view goes beyond a minimalist one. It's very beautiful mathematically and some say it's QM taken literally, but in assuming the reality of the state it is making a definite non minimalist assumption.

Of course Bohm is most definitely non minimalist - it takes the state as very real indeed.

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