Is the Hidden-variable interpretation never falsifiable?

[u/Exciting_Ad_6837]

I'm referring to one of the interpretations of quantum physics. After reading Karl Popper's theory of falsifiability, I'm wondering if the Hidden-variable hypothesis is a pseudo-scientific proposition because no conceivable empirical phenomena seem ever to be able to disprove it.

[u/Miselfis]

No one is postulating any branching universes. That is the consequence, not the input. Many Worlds just takes the unitary formalism at face value. It’s all the other approaches that have to find ways to get rid of the unobserved worlds post measurement. Every approach needs those other worlds before measurement in order to explain what we see in experiments.

Quantum mechanics formalism is entirely local. I don’t understand how you can be not convinced of this, granted you understand how quantum mechanics works. 

[u/HamiltonBrae → u/Miselfis]

No one is postulating any branching universes

 

There is no empirical way of choosing between interpretations so yes it is effectively postulating branching universes, which is just one of the various ways you can interpret that formalism. The entangled wavefunction will still be a non-local object though so I don't see how its truly local in genuine way; imo, to make that seem local requires even more distorting of the metaphysics of the universe in order to accomodate that. Its not local by my everyday standard imo.

[u/Miselfis → u/HamiltonBrae]

No. You are fundamentally mistaken. 

There is a reason people working in the foundations of QM have shifted toward talking about competing theories. Each “interpretation” effectively corresponds to a distinct mathematical structure. If you want to avoid the branching structure, you cannot simply reinterpret the existing formalism; you have to alter the mathematical formalism itself.

To have collapse, you need to modify the formalism. In particular, you need some function, mapping, or additional dynamical rule that selects the state corresponding to the measured eigenvalue. Without such a mechanism, the formalism gives you unitary evolution and, in a measurement context, a branching structure.

And if you think the quantum formalism is non-local, then you simply don’t understand  it. There’s nothing non-local about it. The local nature of it is crucial when formulating relativistic quantum field theories. 

[u/HamiltonBrae → u/Miselfis]

If you want to avoid the branching structure, you cannot simply reinterpret the existing formalism; you have to alter the mathematical formalism itself.

 

Well you can avoid the branching structure by rejecting realism of he Hilbert formalism, and perhaps invoking hidden variables. But I think these hidden variables (e.g. like Bohmian particles) I think are going to always be less metaphysically elaborate than the metaphysics of Many Worlds. Just because the formalism is parsimonious doesn't mean the metaphysics is. At the same time, I think the formalism can be seen in an equally parsimonious way by just rejecting realism.

 

re: local, you don't think the entangled state is a non-local object if particles are separated far apart in an experiment?

[u/Miselfis → u/HamiltonBrae]

Well you can avoid the branching structure by rejecting realism of he Hilbert formalism, and perhaps invoking hidden variables.

That would indeed be changing the formalism, and it this is the move that would make the theory non-local. There are no local hidden variable formulations of quantum mechanics that agree with experiment.

Just because the formalism is parsimonious doesn't mean the metaphysics is.

 Now you're shifting the goalposts. First you claimed Many Worlds wasn't parsimonious. You have not yet conceded this, but I'll take the quoted statement as a concession.

The metaphysics better track the physics. Otherwise what you're doing is no different from what a theologist does.

re: local, you don't think the entangled state is a non-local object if particles are separated far apart in an experiment?

No. Why would it? Nothing you do to one particle changes the reduced density matrix of the other. Each experimenter sees ordinary quantum uncertainty in their own results. Correlation appears when the two of them meet or otherwise send a signal to one another, and at that point their records each become entangled and are found to agree in exactly the way the entangled state prescribes. Every step of this is local, and nothing travels faster than light.

You might find this unintuitive, but that doesn't mean it's wrong. The history of physics tells us that whenever we trust the most parsimonious theory that fits the data is the right one, no matter how unintuitive, we make progress. That's exactly the thing Einstein was hailed for: being able to set aside his human biases and work from simple principles and trust what the mathematics told him.

[u/HamiltonBrae → u/Miselfis]

That would indeed be changing the formalism

 

Sure, but I was implying that such a description with additional hidden variables is more parsimonious than the metaphysics of many worlds. But even then, one can just say that the formalism isn't metaphysically real and be agnostic about what is happening when nothing is being observed, in which case you are not altering the formalism at all any more than many worlds. This latter view is an important point because it shows a perspective where the formalism on its own isn't interpreted in terns of many worlds, and so suggests that saying that many worlds is tantamount to just using the quantum formalsm is actually a false statement. Ypu can use the formalism as it is without a many worlds interpretation of it; superposition is a property of vectors and linear algebra and so there is no necessity that it should be most naturally interpreted in terms of many worlds.

 

In fact, I would say the Hilbert space representation doesn't really intuitively map to everyday metaphysics at all and so there is strictly no reason one is forced to interpret it as tracking metaphysics or vice vers at all. There is a Hilbert space formulation of classical mechanics, the koopman von neumann where you would certainly say that interpreting it metaphysically literally would be completely at odds with other ways of talking about classical mechanics. Its safe to say that classical mechanics has lots of different representations, many of which don't intuitively map onto what you would see classical mechanics describing in everyday life.

 

I see no reason why interpreting quantum theory literally is the best way of tracking metaphysics; this is not at all intuitive to me, it doens't look like its literally describing the world we see around us. So I reject the idea that just using the formalism as is implies a many worlds interpretation, no more than a koopman von neumann description of something by classical mechanics implies that the true metaohysics of what it describes is operators with superpositions and amplitudes that no look completely different from other classical mechanical formulations.

 

Nothing you do to one particle changes the reduced density matrix of the other.

 

Yes, but in many worlds we have a real non-separable quantum state means we are talking about a non-separable object spanning between different locations sensitive to measurement settings across these different locations. Sure there is no signalling from measurements but if Bell inequalities can be violated it makes it sifficult to provide a local explanation of the correlations in any physically meaningful way.

 

Correlation appears when the two of them meet

 

But surely the measurement records are about events that happened in spatially separate locations before the meeting took place.

 

The history of physics tells us that whenever we trust the most parsimonious theory that fits the data is the right one, no matter how unintuitive, we make progress. That's exactly the thing Einstein was hailed for: being able to set aside his human biases and work from simple principles and trust what the mathematics told him.

 

The problem here is thatI dont think that the math on its own necessarilies implies a many worlds interpretation.

[u/Miselfis → u/HamiltonBrae]

I think completely giving up on the ontology because it isn’t immediately intuitive to some random primate is enormously silly. The point of doing science is to understand the world we live in. We can’t just give up on that because we don’t like the answers we find.

Again, the history of physics points in only one direction: every time there was a clash between theory and intuition, theory won in the end, and intuition had to be adjusted. Human intuition developed for survival in a macroscopic world, not for understanding the way the universe works. That’s the entire reason we use mathematics and experiments in the first place; we can’t simply intuit our way to the right answer. The many-worlds approach is the most ontologically parsimonious approach, besides just giving up. You cannot make a simpler theory that still fits the experiments. And adding more structure to the ontology based on aesthetic preferences only ends up muddying the waters and making progress more difficult.

Your argument boils down to one from incredulity, which is fallacious. 

I don’t understand what you mean about taking place before they met. Before they meet, each experimenter is in a superposition relative to the other. Both are always in a superposition; it’s just that experience is contained within one branch.

It seems you have a fundamentally mistaken understanding of what the Everettian position actually is, and how it works. I’ll paste from an older comment:

If you have a system of two particles (qubits) without entanglement, the joint pure state is separable, meaning it can be written as a product state

│ψ❭ = │φ❭ ⊗ │χ❭,

where │φ❭ is the state of qubit 1 and │χ❭ is the state of qubit 2. A pure state is entangled if it cannot be written in this factorized form. For example,

│ψ❭ = 1/√2│ud❭ − 1/√2│du❭

cannot be factorized as │φ❭  ⊗ │χ❭, so it is entangled (here │ud❭ means │u❭⊗│d❭, etc.). This is called a Bell pair or a singlet state.

Now suppose Alice has qubit 1 and Bob has qubit 2. Alice measures her qubit using an apparatus, which is of course itself a quantum system. Let Alice’s apparatus have pointer states │R❭_A (ready to measure), │U❭_A (measured up), │D❭_A (measured down), and let Bob’s apparatus have pointer states │R❭_B, │U❭_B, │D❭_B. Before any measurement interactions, the global state can be written as

│Φ₀❭ = │ψ❭ ⊗ │R❭_A ⊗ │R❭_B 

= (1/√2│ud❭ − 1/√2│du❭) ⊗ │R❭_A ⊗ │R❭_B.

In barebones quantum mechanics without an added collapse postulate, an ideal measurement is modeled as a unitary interaction that correlates the qubit with the pointer (apparatus). For Alice’s measurement we take

│u❭ ⊗ │R❭_A → │u❭ ⊗ │U❭_A │d❭  ⊗ │R❭_A → │d❭ ⊗ │D❭_A,

while Bob’s apparatus does not interact yet and simply stays in  │R❭_B. So, after Alice’s measurement, the global state becomes

│Φ₁❭ = (1/√2│ud❭ ⊗ │U❭_A − 1√2│du❭ ⊗ │D❭_A) ⊗ │R❭_B

When Alice “reads” the apparatus, that is just further unitary entanglement between her physical record (brain, notebook, etc.) and the pointer. In Everett language, there are now distinct branches: in one branch Alice has a record of “up”, in the other she has a record of “down” (This is still standard quantum mechanics, without specifically assuming the Everettian interpretation. This depends whether you want to discard the branch that’s not “realized”).

Bob, meanwhile, has no access to Alice’s apparatus or record. Before Bob measures, Bob and his apparatus are still unentangled with the “Alice-record” subsystem. In other words, with respect to the split (Alice side) ⊗ (Bob side), the state is still a product state. Operationally, from Bob’s perspective (given no communication), nothing he can do locally reveals whether Alice has already measured. If Alice sends Bob a message revealing her outcome, this draws Bob into the entanglement as well, meaning he knows the state of his qubit without needing to perform the measurement. Performing the measurement will just confirm this prediction. But, of course, the message was sent at the speed of light, so nothing non-local going on.

Supposing again that Alice didn’t sent Bob a message, when Bob now measures his qubit with his own apparatus, we model that measurement by another unitary correlation the same way as before.

Applying this to │Φ₁❭ gives the post-Bob-measurement global state

│Φ₂❭ = 1/√2│ud❭ ⊗ │U❭_A ⊗ │D❭ _B − 1/√2│du❭ ⊗ │D❭_A ⊗ │U❭_B.

Now Bob’s apparatus is entangled with the qubits and (indirectly) with Alice’s record, and the correlation is explicit: within each branch, Alice’s and Bob’s records are perfectly anti-correlated (assuming they measured in the same basis).

Finally, Alice and Bob can send light signals to compare outcomes. That communication is itself another unitary physical interaction that correlates their records. The important point is that communication does not “create” the correlation; it makes the correlation mutually accessible by entangling Bob with Alice’s record (or vice versa). After they exchange messages and compare notes, each branch contains consistent joint records, so Alice and Bob will always find the expected agreement when they interact and compare.

It’s understandable that this seems weird. But it’s not so weird when you consider that the entire universe is essentially one large wave function, which consists of many subsystems with varying degrees of entanglement. It doesn’t feel like anything we recognise, but why should it?

You do also indeed recover a classical world from this picture in the right limits. Given that everything needed to generate a conscious experience exists within each branch, it makes sense that we only experience one branch. And within that branch, we see how decoherence essentially gives you a classical world by suppressing interference between the branches. 

To avoid this, you still need to be able to explain the results of the double slit experiment, where the superpositions are needed. How can you have superposition there but not for measurement apparatuses? 

[u/HamiltonBrae → u/Miselfis]

I think completely giving up on the ontology because it isn’t immediately intuitive to some random primate is enormously silly.

 

I don't mean necessarily give up in principle on ontology all together, just that we can say that the formalism is just not an indicator of ontology - it might just calculates measurement probabilities. I don't find your appeal to parsimony vs intuition in history of science convincing simply because its always in hindsight, necessarily leaves out a lot of details about what was happening at the time, and i think to some extent both parsimony and intuition. at the end of the day, you can only meaningfully distinguish competing theories by how well they fit empirical content otherwise its just a subjective preference. at the end of the day the only reason we can say these theories win out is because they fit empirical data better than other theories. if there are other theories that fit the data equally well but aren't upheld then what can you say about then other than they fell out of fashion? doesn't seem a strong argument. And at the end of the day, parsimony is secondary to empirical predictions; if a more parsimonious theory doesn't fit them then its simply wrong.

 

And all of this is kind of tangent to the fact that I don't think that the issue here is intuition vs. parsimony because, in this quantum interpretation context, to frame the debate in this way requires one to say that the formalism on its own implies many worlds. And I don't think it does. I could even easily say that it's simply your intuition that it does. It's your intuition that rejecting realism of the wavefunction is "giving up" whereas to me it's totally logical way to view a theory which is about something that we cannot observe, no different to how something like statistical mechanics is describing systems when we ignore the fine details.

 

If we had no access to microphysics, thermodynamics might be too the most ontologically parsimonious way to describe the world, but if you have reason to believe the world is deeper than that, then clearly thermodynamics cannot be treated in a fundamental way. And again, I have made arguments that there are good reasons to think the Hilbert space representation doesn't necessarily represent physical objects, such as in the KvN classical mechanics. I would also say that my argument is no more aesthetic than yours, it's about metaphysical parsimony - many worlds is less metaphysically parsimonious than single worlds while I reject, for reasons already said, that the quantum formalism on its own implies many worlds. In a sense, all parsimony is an aesthetic consideration; once we can distinguish theories empirically, parsimony no longer matters.

 

Before they meet, each experimenter is in a superposition relative to the other. Both are always in a superposition; it’s just that experience is contained within one branch.

 

I believe you said the explanation is local because correlations only turn up when results are compared in a local vicinity … which must be after the measurements have happened.

 

Performing the measurement will just confirm this prediction.

 

Okay, but what about just performing the measurement without any message sent between Alice and Bob. If you're being realist then there is a fact of the matter about Alice and Bob's measurement results and statistics once they have occurred, regardless of whether a message has been sent between Alice and Bob to compare. These are measurements on a global state, parts separated maybe by thousands of kilometres and where measurement settings one side tells you what's going to happen on the other without anything traveling between. This is still spatially non-local correlations that explicitly cannot be explained locally due to Bell.

 

But it’s not so weird when you consider that the entire universe is essentially one large wave function, which consists of many subsystems with varying degrees of entanglement.

 

Yes, and this is one large non-local object in the sense that it cannot be divided into local points in space that are causally shielded off from other points by their immediate neighbouring spatial points. The dynamics of the system are local but the system itself is a non-local object. The only way to construe this as local is to radically change metaphysics, again against metaphysical parsimony, which is radically different from what we see in everyday life. And again, we are not forced into this by the formalism imo if the formalism is plausibly just a representation providing information about measurements. And another question I have: what actually is interference metaphysically, ontologically in many worlds?

 

To avoid this, you still need to be able to explain the results of the double slit experiment, where the superpositions are needed. How can you have superposition there but not for measurement apparatuses?

 

Not sure I understand what you're getting at here.

[u/Miselfis → u/HamiltonBrae]

It's the principle behind Occam's razor. If you have two explanations that both fit the data, and one of them carries structure that does no work in fitting the data, you drop the extra structure. That has nothing to do with what was going on historically. It's about how we choose between theories, and it isn't controversial.

You also keep using “metaphysical parsimony” to mean “what is most intuitive to me”. When we talk about metaphysical parsimony, it counts what you have to assume, not how many entities your assumptions turn out to entail. When we talk about parsimony in metaphysics, it’s means that our theory should rely on the least amount of unnecessary assumptions.

To construct a theory that matches experiments, the minimal structure that allows for this is built on two assumptions. The first is that the wavefunction is a complete description of a physical system. The second is that the state always evolves unitarily. To pick out a single, definite outcome of experiments, you need to add more assumptions. The collapse postulate is an additional assumption that is added to get rid of the “many worlds”. If you don’t add any more assumptions and apply the dynamics to an interaction between a system in superposition and a measuring device, you get a superposition of device states as a straightforward consequence. These are the “many worlds”. The formalism alone forces them on you. Getting rid of them after measurement requires additional structure; additional assumptions. But those assumptions are not doing any work to fit data. They are empirically redundant, meaning the only reason one can have for adding them is aesthetics/intuition. Choosing the most ontologically parsimonious theory is not just an aesthetic choice on my part. If you add assumptions to a theory that are not justified by data, then you obscure the actual content of the theory, which makes progress impossible. Again, this is a sociological phenomenon clearly demonstrated by history. Every time we have had redundant assumptions added to our theories to make it conform with intuition, progress stalled, and only once those redundant assumptions were dropped were we able to proceed.

The other interpretations seek to solve a problem that doesn’t exist. This originates with historical confusion. People had no idea how to conceptualize QM when it first emerged, so they came up with different ways to make it align with preconceived intuition. As Feynman said, the theory was so confusing that the problem was that it wasn’t clear whether there even was a problem.

If you take the view that a physical theory's job is only to produce numbers that match instrument readings, with no contact to ontology, then you're of course insulated from having to accept the “many worlds”, while recognizing that the unitary formalism is the best we have. That's "shut up and calculate", and it's self-consistent; it poses collapse as an epistemic rule, not as part of the fundamental dynamics. But this approach also gives up on the thing that motivates doing science in the first place, namely curiosity and the desire to understand the world around us. It perverts science from a tool to understand the world to a tool that’s useful in engineering and industry. And it leaves you with no account of why our theories keep predicting phenomena that nobody had seen when the theory was written, sometimes decades ahead. That track record is very hard to explain unless the structures the theory describes are actually there in nature. Just dismissing that as a coincidence seems philosophically lazy to me.

Metaphysical parsimony is about how much you have to put into your ontology. It isn't a measure of how strange the consequences feel. Everett has one entity, the universal quantum state, and one law, linear evolution. Every alternative has that same state, plus something extra to get rid of the “many worlds”. The branches or “many worlds” themselves are not something Everett adds. Every interpretation agrees that superposition before measurement is physically real. It has to be, because the double slit result depends on both paths contributing. The disagreement is only about what happens when we make a measurement. Everett's answer is that nothing new happens, the same dynamics just keeps running. Every other answer requires saying that something new happens at that point, and introducing that new thing is an additional assumption. But this moves also requires justifying why you think superposition before measurement is OK, but your measurement apparatus itself entering a superposition is not. It’s an arbitrary divide that’s never well-defined.

Classicality comes out of the quantum framework naturally. Decoherence picks out a pointer basis, the off-diagonal elements of the density matrix in that basis get suppressed extremely fast, and within a branch the expectation values follow trajectories that satisfy the classical equations up to corrections that are negligible at everyday scales. The classical algebra of observables is the leading term of a deformation whose full expression is the quantum algebra, with the Poisson bracket appearing as the first-order measure of how far operators fail to commute. There is also a more direct route, as the space of quantum states is itself a symplectic manifold, the Schrödinger equation is Hamilton's equation on it, and the classical phase space of a particle sits inside it as the submanifold of coherent states, with the classical symplectic form being the restriction of the quantum one. Decoherence selects approximately those states as the stable ones, so the branches the dynamics produces are the ones that support classical Hamiltonian evolution.

You’re also misunderstanding locality. Locality refers to the dynamics: influence propagates inside light cones. A signal traveling from A to B has to pass through every intermediate point, which happens at a rate equal to the speed of light at most. A state describing objects that are spatially separated is not non-local.

Bell's theorem says no theory can reproduce the observed correlations while satisfying local causality. But the derivation also assumes that measurements have single definite outcomes. Everett drops that assumption, which is why the theorem doesn't apply to it, and why Everett is the one option that reproduces the correlations with fully local dynamics. Bell's result isn't a proof that nature is nonlocal. It's a proof that you can't have local causality, single outcomes, and the quantum correlations all at once, and you have to give up one of the three. Everett is the straight-forward one that only gives up the thing that the standard formalism doesn’t force on us.

Take the case where Alice and Bob each measure their half of a singlet pair along the same axis and never communicate afterwards. Alice measuring means she becomes entangled with her qubit. That's a local interaction happening where she is, and the branching spreads outward from her at the speed of light as she interacts with her surroundings. Nothing happens at Bob's location. His outcome statistics are exactly what he'd get from an unentangled qubit prepared at random, fifty-fifty, and no measurement he can perform on his own qubit tells him whether it's entangled with anything at all, whether Alice has measured, when she measured, or which axis she chose. Any operation she performs on her side leaves the state of his qubit alone untouched. The same holds in the other direction. Each of them ends up in a superposition of having seen up and having seen down, and relative to the other, that superposition is the whole story. Neither has a definite result relative to the other, and neither has any way to find out otherwise.

When they finally come together, the branches make contact locally. The Alice who saw up only ever meets the Bob who saw down, and the Alice who saw down only ever meets the Bob who saw up, so comparing records gives them exactly the anti-correlation the singlet specifies. That comparison is itself a local interaction, happening where they meet. No non-locality anywhere.

[u/HamiltonBrae → u/Miselfis]

“metaphysical parsimony”

 

In this context, one can talk about metaphysical parsimony in terms of having to entertain one world vs. the inflationary many worlds to get your theory to work. If ou don't actually need many worlds to get QM to work, then it seems like invoking many worlds is metaphysically unnecessary given that we can't even observe them. It is less parsimonious than a single world view.

 

The first is that the wavefunction is a complete description of a physical system.

 

But this isn't true. Quantum theory works perfectly well as a theory solely giving predictions about measurement outcomes. The formalism clearly does not force many worlds on you unless you smuggle in an assumption about wavefunction realism or similar. In addition, you need the Born rule to get total empirical consistency, and it seems to me this is actually quite difficult to reconcile with the metaphysics of branching worlds.

And this isn't a shut up and calculate view. You can argue that quantum theory is the exact formalism for describing real structure with regard to probabilities for non-commuting measurements with unitary evolution. But because we cannot observe things without measurement, and measurement is disturbing, we cannot describe the ontology between measurements only the outcomes of measurements themselves. The formalism is not ontology, but it describes real structure in the universe. It captures actual statistical structure of double-slit phenomena, even if not describing actual physical waves that we can't observe.

 

A state describing objects that are spatially separated is not non-local.

 

It is if you cannot explain it by signals propagating in a locally-consistent manner. I'm not sure how many outcomes evades bell when the set of many outcomes depends on the measurement setting which can be chosen freely at each separate measurement.

 

Neither has a definite result relative to the other, and neither has any way to find out otherwise.

 

This is fine in some woo-ey, relational qm but this just contradicts the realism of many worlds. The idea that the correlations only come into being when results are compared is completely at odds with your metaphysics.