Provability of the provability or unprovability of QM interpretations

Question

It has been explained to me that it is impossible to prove or disprove a quantum interpretation because all quantum interpretations make the same predictions.

Is this accurate? Is there a seminal work proving this assertion? Are all possible predictions of QM known? If it's true by definition, then is it possible to prove absolutely that a proposed interpretation is an interpretation? Is it proven that QM alone is enough to describe the entire universe in entirety? And if not, couldn't there be a contradiction between an interpretation and something beyond, or emerging from QM?

Edit:

There have been some really interesting answers. I am surprised how divergent the thinking is on this subject. And that has made accepting an answer difficult. I thought I should take the opportunity to better convey the original questions now that I have the answers to relate them to.

(1) It seems that there is no generally agreed upon definition of an interpretation of a scientific theory, and, on top of that, the definitions people use, as they relate to QM, are further complicated by the strangeness of QM, and the long and complicated history of our progress in trying to understand it.

(2) It seems pragmatic (on the surface) to define what an interpretation of QM is by limiting interpretations, by definition, to make only the same predictions as QM does. However, it isn't clear to me how we can fully determine what predictions QM makes, and what predictions an interpretation of QM makes. To begin to approach this, you first need to approach the question of whether the theory of QM alone is enough to describe (in a formal mathematical sense), or generate, a given model of the universe. If that were accepted as an axiom, then you could approach the question of whether all observable manifestations of quantum systems are equivalent with respect to interpretation. Conversely, you could make the assumption that QM is not the complete causal picture to describe measurable reality. In this case, no matter how indirect, it would seem possible that a contradiction could arise between measurements and interpretations, without a contradiction arising between QM and the measurements. This question seems to be a problem for the domain of the formal sciences more so than the natural sciences.

However, the possibility of such a situation seems to only be taken half seriously, because QM and other theories in physics are typically assumed to be merely useful approximations, rather than true descriptions of reality itself. At least, we have no way to tell the difference through the scientific method. And in this view, contradictions between theories become moot.

On the other hand, logical consistency between multiple theories seems not entirely useless, since we can take that as a kind of evidence that there is likely to be unknown or hypothesized predictions that are strictly made jointly, by two or more theories together. For example, taking QM and GR together, and aiming for logical consistency, one may identify sets of testable predictions. Or further development of theories jointly consistent with a set of otherwise independent theories could be derived through formal sciences.

Despite this, ultimate observational limitations do make it impossible to determine what actually is consistent, since the unobservable, and uncomputable, could make anything possible (e.g. a simulation hypothesis). But, through formal mathematical methods, such as oracles, and the exploration of different sets of assumptions, one could explore many possibilities for consistent physical realities. To go from philosophy to theory of physics, you still need testability. But I'm not sure whether we know what is testable or not, for the same reasons described above.

Maybe this understanding (however flawed) can shed light on my questions and how they relate to one another, and the appropriateness or lack of appropriateness in referencing notions from formal science, in context.

Answer 1

Good question. They actually do not all make the same predictions. This is something that people say which isn't quite true.

Take, for example, spontaneous collapse models (like GRW). They have parameters which determine how likely the particle is to collapse. The space of possible parameters keeps getting smaller based on various experiments. You can see a graph which limits possible parameters in this paper, on page 6, for example.

Bohmian Mechanics is another example of an "interpretation" which does not give the same predictions as textbook QM. There is more than one example where they don't agree, but the most straightforward example is arrival times. Standard Quantum Mechanics doesn't make predictions for the distribution of arrival times of a particle at an apparatus because of the lack of a time operator. A few different methods have used quantum mechanics to come up with distributions nonetheless, by intuition rather than starting from the usual postulates of the theory, but they aren't all in agreement. Bohmian Mechanics gives yet another different distribution for arrival times, simply based on the time that the bohmian particle hits the screen. There are proposals for experiments which would test these differences. Such experiments can already be done using modern-day technology; see here for example. I'm really looking forward to concrete experimental evidence which confirms or disproves the bohmian approach to this one.

There are a lot of well-informed people who say that all interpretations give the same results, I would say that's not really scientific of them as it's not the case, and so of course there is no proof.

Answer 2

A note on terminology. Many posters in this thread seem to think that interpretation means something like: a story that is told about a particular physical theory, with the understanding that the map from interpretations to theories can be many-to-one. As far as I can tell this is not the standard usage in the field of foundations of quantum mechanics, which concerns itself with interpretations of quantum mechanics more than does any other field of research. In that field GRW theories are called interpretations on equal footing with Copenhagen and Everettian interpretations. See, for example, Wikipedia comparison between interpretations of quantum mechanics.

Rather, I would say the term "interpretation of quantum mechanics" includes a list of philosophical and theoretical-physical proposals which attempt to explain, understand, or resolve the quantum measurement problem. Some attacks on the problem are purely philosophical, starting from pure unitary evolution (such as Everett interpretations) or Copenhagen collapse theories, and some change the physics such as interpretations which postulate non-linear terms in the Schrodinger equation or spontaneous collapse.

It has been explained to me that it is impossible to prove or disprove a quantum interpretation because all quantum interpretations make the same predictions.

Is this accurate?

No it is not accurate. Objective collapse theories (These include Copenhagen interpretaion and GRW spontaneous collapse theories and others) postulate non-unitary evolution of the wavefunction at at least some points in time. This non-unitary evolution results in different predictions than, for example, Everettian interpretations which admit no non-unitary evolution, De Broglie-Bohmian mechanics which (for the sorts of systems about which they make predictions) are crafted so that they give the same dynamics as pure unitary evolution.

Is there a seminal work proving this assertion?

If there is it is wrong because the assertion is wrong. You can google around for stuff like "foundations of quantum mechanics" to find references in the literature about comparisons between different interpretations. You'll probably be interested in experiments which put bounds on parameters in spontaneous collapse theories such as @doublefelix has already pointed out.

Are all possible predictions of QM known?

Probably not.

If it's true by definition, then is it possible to prove absolutely that a proposed interpretation is an interpretation?

Meh..... the statement above is not true by definition so the rest of your sentence doesn't follow.. but that said, the second half of this sentence doesn't really make sense. You need to rephrase if you need more.

Is it proven that QM alone is enough to describe the entire universe in entirety?

No. The most notable example is the failure to unify quantum mechanics and general relativity.

And if not, couldn't there be a contradiction between an interpretation and something beyond, or emerging from QM?

Yes, it's certainly possible that we will discover phenomena (we already have) that are not consistent with our current understanding of quantum mechanics. These discoveries will force us to revise our physical theories as well as interpretations for quantum mechanics.

I'll also reiterate the point from @joseph h that you should unburden yourself of the terms "prove" and "truth" when thinking about physical theories. Here's a nice definition of science that sidesteps such epistemological issues. "Science is the process explaining our experience by generating theories and testing experimentally how consistent the theories are with our experience in order to enhance our ability to make accurate predictions about the future."

Answer 3

It has been explained to me that it is impossible to prove or disprove a quantum interpretation because all quantum interpretations make the same predictions.

The term "interpretations" characterizing a theory of quantum mechanics is used when the new theory interprets all the existing experimental data as well as the mainstream standard model does. This leave a window for predictions from the new theories for data not yet gathered, that might differentiate between the standard and the new.

It has been explained to me that it is impossible to prove or disprove a quantum interpretation because all quantum interpretations make the same predictions.

The statement is logically true for the case where a new theory's predictions are outside the present data base to be able to check whether it is just a mathematical interpretation or a new theory of particle physics.

Answer 4

The various quantum interpretations are different in many aspects, but they all attempt to explain how the mathematical formulation of quantum mechanics corresponds to reality. The basic mathematical ideas of quantum mechanics are built into (almost) all of them.

Forget about the words "true" and "proof" for now. We don't really prove things in physics or in any science, since physics is more about determining models that are consistent with reality, and can be modified. Proof would mean that our theories are truths without any room for doubt, and there is always doubt in physical theories. Especially when it comes to quantum interpretations.

Various quantum interpretations have different aspects, but the basic features, like the unitary evolution of quantum states and the Born rule, are built in to almost all interpretations. It can also be said that most of the different interpretations result from our inability to understand and quantify the measurement/collapse process.

There are of course "no-collapse" interpretations. Take, for example the "many-worlds" interpretation. This interpretation and collapse interpretations still share the same underlying mathematical features and result in the same experimental predictions, though they are different.

The pilot wave interpretation differs at a fundamental level to the predictions of many other interpretations, like the Copenhagen interpretation. The prior being deterministic and the latter being stochastic.

Is it proven that QM alone is enough to describe the entire universe in entirety?

Quantum mechanics on its own certainly could not describe the universe. Quantum mechanics describes how things happen microscopically, while the macroscopic universe is described by general relativity. We need a theory that would combine both. This is the work of those looking for quantum theories of gravity and even still, to truly describe the universe and all interactions, we would need grand unified theories. String theory appears to be a candidate for a GUT, though it is still far from being called a satisfactory GUT.

Answer 5

A theory makes predictions. An interpretation does not make predictions, although it may lead to a new theory. Textbook quantum mechanics is fully adequate. Any statement of new, beyond standard textbook predictions of QM constitutes a new theory.

Interpretations however can lead to paradoxes. If this is the case ultimately the interpretation must be rejected.

Answer 6

It's not exactly true that they all make the same predictions, it's mostly true that the Everett (Many Worlds) and Copenhagen (wavefunction collapse) interpretations make the same predictions about what we will observe experimentally.

The Everett interpretation says that all the possible outcomes of an experiment happen together, in superposition. We only seem to see one of them because we are quantum systems too, and what happens when we interact with another quantum system is that the wavefunctions become correlated, so interacting with a particle wavefunction spread across space turns the observer into a superposition of observers each seeing the particle at one point. The observer does not interact with the other versions of themself, and cannot see them or detect them in any way.

It is this last point that leads to the conclusion. The Everett interpretation says these other outcomes exist but are forever unobservable. The Copenhagen interpretation says these other outcomes magically vanish. Since they are unobservable, there is no possible way to tell if they do or not. The predictions about what we will observe are identical, the predictions about what actually happens are not.

That said, it's not quite true in principle, because of the issue of multiple observers, although we are a long, long way from being able to test it in practice. The wavefunction collapse interpretation has a problem with a universe in which there are multiple observers, because you can in principle put one of the observers in a box, and have the other observer outside the box treat it as a quantum system. This is the basic issue of Schrodinger's cat. Does the collapse happen when the cat makes the observation inside the box, or only when the human experimenter opens the box? It depends on what you think triggers collapse. If it's only human consciousness, then the cat can't. (And must therefore, according to the Copenhagen picture, directly experience fuzzy quantum reality.) If it's any sort of consciousness or perception, or if it's just a matter of size and complexity, then the cat can. But what about simpler systems? An ant? A bacterium? A nano-sized electronic sensor, with a microscopic molecular AI? A single electron?

We know that electrons can 'observe' one another - its state changes if it is electrostatically repelled by another electron. But when a single electron is sent through the apparatus of the double slit experiment, the electron passing through one slit does not repel the other instance of itself passing through the other slit. They are invisible to each other. But obviously, a single electron is down in the quantum realm and can't cause a collapse.

Experimentalists are gradually going up the size scale. So buckeyballs made of 60 Carbon atoms can be shown to exhibit quantum interference. There are other experiments where mechanical levers oscillate in quantum superposition. If you extend these experiments far enough, then eventually you may reach a point still small enough to show quantum superposition, but big enough and intelligent enough to answer questions about what it observed. Or quantum computing might one day be able to implement a 'human-level' AI in a verifiable quantum superposition.

The two interpretations thus differ on what a quantum-level system intelligent enough to 'observe' and thus collapse the wavefunction would see. Everett says we are all quantum systems already. Copenhagen presumably either thinks such a system would directly perceive and be able to describe the quantum-fuzziness of reality, or would lead to the mysterious vanishing of quantum interference in molecular-scale systems that similarly-sized non-intelligent systems still show.

But we're a long way off being able to do that, so for the time being these are metaphysical questions that cannot be experimentally tested. We are left only with more 'aesthetic' criteria. The Everett interpretation is local, causal, deterministic, complete, and realist. Wavefunction collapse is faster-than-light, backwards-in-time, probabilistic, and doesn't answer the fundamental question of what causes collapse, by what mechanism. It has problems with multiple observers, partial observations (like, when an observation of a particle's position collapses onto a point, why does the momentum uncertainty not go to infinity and cause it to ping away at close to lightspeed?), and creates a vaguely defined border between two domains of physical law: the quantum and the classical. By changing reference frame, I can shift my 'now' far away back and forth in time - does wavefunction collapse happen and unhappen when I do so? Normally, having a faster-than-light ontology would be enough to kill a theory, but the Copenhagen Interpretation has survived even this. Since they make nearly the same predictions about observations, and Everett is a local theory, it would be difficult if not impossible for wavefunction collapse to produce any observable and unambiguous causality-violating physical paradox.

Answer 7

It has been explained to me that it is impossible to prove or disprove a quantum interpretation because all quantum interpretations make the same predictions.

In physics$^1$ , the ultimate arbiter of truth are experiments. What the explanation meant was that all interpretations of quantum mechanics (QM) that make the same predictions for the outcomes of experiments, are indistinguishable.

Without going into the details of the various QM interpretations (of which I am no expert) like multi-world, pilot wave etc., from a purely semantic standpoint, this makes sense. If a new interpretation makes no differing predictions, it is equivalent to previous viewpoints and is as equally valid.

This is not to say that the underlying formalisms used by the varying interpretations are same or that such diversity has no advantage.

For e.g. consider the time when Schrodinger wave mechanics had just been invented. Heisenberg's matrix mechanics already existed and produced identical results, yet the new and distinct formalism provided new avenues for research and synthesis and a different approach to QM. Feynman's path integral approach later provided yet another refreshing viewpoint on the same.

Even though the above example isn't describing multiple QM interpretations, it provides a good analogy. It describes different formalisms that were indistinguishable in their consequences and therefore equally correct yet the varying treatments lead to new insights.

On the other hand, if two interpretations produce differing predictions, they aren't interpretations at all but different theories altogether. This means that the differing formalisms have differing fundamental axioms governing them and based on experiments, one set is superior than the other.

Is this accurate? Is there a seminal work proving this assertion? Are all possible predictions of QM known? If it's true by definition, then is it possible to prove absolutely that a proposed interpretation is an interpretation? Is it proven that QM alone is enough to describe the entire universe in entirety? And if not, couldn't there be a contradiction between an interpretation and something beyond, or emerging from QM?

This part of your question imo lacks focus, is vague and asks of several disconnected things at once.

Is this accurate? Is there a seminal work proving this assertion?

As discussed above, it is. Lack of experimental distinguishability between interpretations makes them equivalent, trivially so. The seminal body of work you inquire of exists, but it probes more interesting topics e.g. role of locality, contextuality, freedom of choice, loopholes in test experiments, determinism, measurement models, information theory etc.

Are all possible predictions of QM known?

What do you mean by all possible predictions? If you meant all possible theorems that can be proven given the fundamental QM assumptions, then no in theory and practice simply because there are infinitely many of them. If you meant all possible physics models that may be derived from them, then still no in theory and practice because there will always be more phenomenon yet to be modeled. If you meant fundamental laws of nature which ultimately underpin all phenomenon then yes in theory but no in practice.$^2$

If it's true by definition, then is it possible to prove absolutely that a proposed interpretation is an interpretation?

In theory two interpretations are equally valid as long as they predict the same true experimental outcome. That 'proves' an 'interpretation is an interpretation'. In practice, it may be more feasible to validate the consequences of one formalism than the other, making the harder-to-test theory undecidable.

In theory two interpretations which differ in their predictions are equally undecidable in terms of their validity. To repeat myself, only experiments are the arbiter of truth in physics. So for such interpretations, its impossible in theory but possible in practice (expt. limitations of the time notwithstanding) to prove which 'interpretation is an interpretation' and which isn't. However, as discussed later, these aren't different interpretations but rather different theories.

Is it proven that QM alone is enough to describe the entire universe in entirety?

We strongly suspect so. In theory all phenomenon may be reduced to manifestations of fundamental forces which are modeled in agreement with QM principles. Experimentally, this agreement has been verified, in some cases, to breathtaking accuracy.

However, to answer your question, an unequivocal no. IMO, it is not possible to prove in theory that no phenomenon exist which violate QM. Nor should it be - after all its a model of nature based on some assumptions and a consistent theory can't prove its own completeness.

Experimentally, at the current time, we do know of phenomenon for which we do not have a full fledged QM model. Apart from exotic beasts like dark matter to dusty giants like gravity, even full fledged quantum modelling of condensed matter systems is not available(or even some classical phenomenon for that matter). Yet, as I remarked earlier, we do not expect the would be future theories of such phenomenon to be non QM in nature. Suffice it is to say that any observations to the contrary would be more of a shock rather than a surprise.

In theory, we do expect the entire$^3$ universe to abide by the assumptions of QM. We expect this because we assume the universe is isotropic and homogeneous at cosmic scales. That along with the reductionist approach mentioned before, establishes that conclusion.

Experimentally, its impossible to verify this beyond the observable universe, within which, remarkably, it has stood the test of time and space.

And if not, couldn’t there be a contradiction between an interpretation and something beyond, or emerging from QM?

For interpretations that predict the same outcomes for experiments, no there can be no contradiction. Those which don't aren't interpretations but different theories altogether (e.g. extensions, weak forms of QM). For such distinct theories, in theory there should be a contradiction (that's what makes them different in the first place). In practice we have found none for any.

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$^1$ and perhaps all science

$^2$ even for gravity we expect there is some quantum theory of which GR is a classical limit, so even though we currently do not have an expt. verified quantum theory of gravity, we do not suspect the would be theories to be non QM in nature.

$^3$ as opposed to only some part and with the preceding discussion in mind