# Is many-worlds interpretation only a philosophical matter?

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## Solution 1

My understanding of this kind of thing has evolved over time. I used to be convinced that interpretations were inherently untestable, but now I think that was an oversimplification.

To make the discussion more concrete, let's consider a set of axioms for quantum mechanics:

• (1) States are rays in a vector space over the complex numbers.

• (2) unitary evolution

You could add more to this list (observables are self-adjoint operators, completeness), but these are the main things that are important, and they are also things that everyone agrees on. This is all you need for the most austere versions of MWI, which I'll call MWI-basic.

If you want the Copenhagen interpretation, you need some more axioms:

• (3) Born rule

• (4) Measurement collapses the wavefunction.

So from the point of view of this kind of axiomatic development, CI is the same as MWI-basic plus additional axioms. One thing this tells us is that any experiment that disproves MWI-basic must also disprove CI.

It is certainly true that MWI-basic and CI are falsifiable. Any observation that falsifies 1 or 2 falsifies all of QM, and therefore falsifies both MWI-basic and CI.

I think the right way to look at this kind of thing is that CI is an approximation, and the approximation is good when the measuring instrument is macroscopic. When the measuring instrument is mesoscopic, the approximation is not perfect, and this is something that we can see. A nice example is Allahverdyan 2017. They simulate a measurement by a mesoscopic system, and they come up with all kinds of phenomena that actually do happen according to quantum mechanics, but that are not correctly described by CI. For example, there are time scales that emerge from the simulation, whereas (4) says collapse is instantaneous.

There are also more baroque versions of MWI, which we can refer to collectively as MWI-baroque. DeWitt gives a description of what I would call a baroque version of MWI:

This universe is constantly splitting into a stupendous number of branches, all resulting from the measurement-like interactions between its myriads of components. Moreover, every quantum transition taking place on every star, in every galaxy, in every remote corner of the universe is splitting our local world on earth into myriads of copies of itself.

This is also an approximation, and the approximation is not perfect. The approximation is valid if decoherence leads to a set of preferred states that are not "cat states," i.e., not coherent superpositions of different pointer states (like Schrodinger's cat). This approximation is good in the limit of large systems, for which the time scale for decoherence is very short. So MWI-baroque, like CI, is falsifiable, and is in fact false. Like CI, it's false for a mesoscopic measuring device.

So my current view on this is that we should stop talking about the Copenhagen and many-worlds "interpretations" and start talking about the "Copenhagen approximation" and the "splitting approximation" (the latter meaning MWI-baroque approximation).

Allahverdyan, Balian, and Nieuwenhuizen, "A sub-ensemble theory of ideal quantum measurement processes," 2017, https://arxiv.org/abs/1303.7257

## Solution 2

This question takes for granted an idea that is common among physicists, but is also false. The idea is that there are multiple interpretations of quantum mechanics that all make the same predictions. In reality, the so-called interpretations fall into three categories.

1. Alternatives to quantum mechanics that make different predictions, such as the pilot wave theory and spontaneous collapse theories like GRW:

2. Quantum mechanics without any modifications, which implies the existence of a structure that can sometimes be approximated as a collection of parallel universes (the Everett interpretation). Experimental tests can distinguish between the Everett interpretation and alternatives like pilot wave and GRW:

3. Theories that are too vague to work out their implications, with the result that they are not testable, such as the Copenhagen and statistical interpretations of quantum mechanics. Such theories fudge the issue of what exists in reality and so can't be used to make testable predictions since they are basically the same as saying "quantum mechanics applies, except when it doesn't".

The interpretations that are philosophical in a bad sense, i.e. - in the sense of being useless talk that obfuscates real problems, are in category (3) not in category (2).

## Solution 3

The very word interpretation means that it uses the same mathematics and interprets it in words differently. This means that there cannot be a difference in the calculated values in any experiment carried out in our labs, or observations fitted with the same mathematics.

It is futile to try and find either a validation or a falsification, as the mathematical structure is the same .

## Solution 4

It seems to me that a question is 'only' philosophical if its answer is essentially beyond physical proof.

Debates about the meaning of quantum theory are not inherently 'only' philosophical, since they include the search for testable implications. The fact that we have not yet found any scientific basis for proving MWI right or wrong doesn't mean that we never will.

That said, there are aspects of the debate that do have a philosophical nature. For example, you will find much discussion about the relative philosophical merits of various interpretations of QM, which bring into play principles such as Occam's razor. Opinion tends to dominate in those aspects of the debate, and one may take the view (as I do) that they are pointless and irrelevant from a physics perspective.

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Updated on March 30, 2020

Is many-worlds interpretation only a philosophical matter? It seems to me that we can't exclude a possible test for this hypothesis. I explain.

For superposition principle each world would follow the Schrodinger equation and then it seems impossible to distinguish if we collapsed in $$\psi_i$$ a wave function $$\psi=\sum_i\psi_i$$ or we ended up in a world where the state of the system is $$\Psi_i=\psi_{me}(i)\otimes\psi_i$$. This would be, at the multiverse level, just one state of the superposition $$\Psi=\sum_i\Psi_i$$ with all the other possible outcomes and their worlds. Also, if there are interferences enhancing some worlds and suppressing others, this would be testable only by someone experimenting on $$\Psi$$, at the multiverse level, then again invisible inside any world.

But if the interference cancels out completely some possible world, then we could be able to recognize that by statistical means. Suppose that I am doing a measure that can collapse $$\psi$$ in an eigenstate $$\psi_i$$ such that the world $$\psi_{me}(i)\otimes\psi_i$$ would be canceled out by interference with other worlds. Then, getting the eigenvalue of $$\psi_i$$ in the measure wouldn't be an evidence contrary to the many world hypothesis?

• probably_someone over 3 years
What's the probability of measuring the eigenvalue of $\psi_i$ in the other interpretations? If it's the same, then this doesn't distinguish anything.
MWI sets a completely different framework, it says that $\psi$ doesn't collapse at all. I have no idea why it calls itself an interpretation
• probably_someone over 3 years
Most of the modern solutions to the measurement problem also drop the idea of wavefunction collapse (because of things like time-reversibility issues). Besides the many-worlds interpretation, one other popular interpretation is that measurement means becoming entangled with the measurement device; the general phenomenon of entanglement with the environment is called "decoherence," for reference.
I agree, but it seems to me that many of these "interpretations" don't limit themselves to equivalent interpretation of the same formalism. Dropping the idea of the wave function collapse isn't just a philosophical speculation, as you say it can involve time reversibility, that is not so an exotic thing to be put at test
• probably_someone over 3 years
Do you know how to reverse the passage of time? I certainly don't. As such, "un-measuring" something is not at the moment possible to test, and it may never be. What decoherence and the many-worlds interpretation both do is explain why we observe wavefunction collapse while still being time-reversible.
But wave function collapse isn't reversible in the quantum theory, so whatever theory change this has also to change the math. Also, a way of testing time reversibility is "very simple", assuming unitary evolution we test cp conservation for example in an pure electrodinamical process
• probably_someone over 3 years
Can you explain precisely how an "un-measurement" can be done, then, in a regime where non-relativistic quantum mechanics (which is what we've been talking about) instead of quantum field theory (which has different philosophical issues) applies?
I proposed a test of the "interpretation" in my question. MWI assumes the same math as quantum theory (regardless non-relativistic or field theory I guess) at the multiverse level, but I claim this doesn't produce the same math on a single world
• probably_someone over 3 years
Your test requires experimentation "at the multiverse level," which may never be possible; also, you haven't demonstrated how "this doesn't produce the same math on a single world."
No, I consider only measures at the single world level, obviously. The test is an example (maybe wrong) of such a difference in math. Those who proposed the MWI should have demonstrated that it doesn't change the math so it's an interpretation and not a concurrent theory
• JimmyJames over 3 years
The Frauchiger-Renner thought experiment may be relevant. It is claimed that it shows that you cannot hold various interpretations as being equivalent: "'My take is likely to be that it kills wave-function-collapse or single-universe versions of quantum theory, but they were already stone dead'"
• alephzero over 3 years
"But if the interference cancels out completely some possible world, then we could be able to recognize that by statistical means." So you claim we can use statistics to demonstrate that something unobservable might have existed, except that it doesn't? Well, that still leaves five out of six impossible things to believe before breakfast ;)
• Shing over 3 years
I would argue: any interpretation is an attempt to give a complete picture, hence somewhere in the picture you can test (in principle).
• lurscher almost 3 years
well, when physicists claim that "information must be conserved due to unitarity", they actually mean that information is conserved in the multiverse, not individual observable slices. So in order for information conservation to be a meaningful concept, then the multiverse must also be
I know it calls itself an "interpretation", but it seems to me it pushes itself blatantly to the point of changing the math. If there isn't a collapse, then what prevents the worlds to interfere? Maybe I misunderstand what the interpretation is actually saying, but I read on wikipedia that even David Deutsch has proposed a test. I'm going to search the article
• anna v over 3 years
collapse is another interpretation, although I do not like the term, as the wavefunctionis not a balloon. In the end there are measurable quantities that have to be predicted , and those are the same, because the math is the same.
And how can we see that the math is the same? Is it so trivial that a unitary, continue and deterministic evolution of the supersystem can, somehow, be locally equivalent to the stochastic, discontinue, irreversible evolution predicted by the quantum theory?
It is futile to try and find either a validation or a falsification, as the mathematical structure is the same. This doesn't seem quite right to me. The Copenhagen interpretation involves the Born rule and wavefunction collapse. These are mathematical structures, and they are not present in MWI.
Thanks for the answer and the link. I'll meditate one ant try to understand the other. But I've to say I don't completely agree with your claim that any experiment that disproves MWI-basic must also disprove CI. The fact is that a theory as much austere as the MWI-basic would never be testable, because it doesn’t say anything about what a measure is. A slightly less austere version of it, that assumed that the measures we do happen (in some way) at the single world level, is already, in my opinion, distinguishable from CI by an ideal experiment of the kind I wrote above
@J.Ask: The fact is that a theory as much austere as the MWI-basic would never be testable, because it doesn’t say anything about what a measure is. I observe the energy levels of the hydrogen atom. This is a test of MWI-basic and doesn't depend in any way on the assumption that we have an inner product or a probability measure.
But you said any experiment. A fail of this test I agree that it would dispel both MWI-basic and CI, but I wonder if there are tests capable of dispel just MWI (in its slightly less basic versions)
• anna v over 3 years
@BenCrowell If it gives different measurement predictions, it is not an interpretation but a different theory. It is the numbers predicted that finally decide.It should not be called an interpretation.
@J.Ask: I'm claiming that CI is false. Therefore it's of no interest to look for some hypothetical test that disproves some version of MWI without disproving CI.
• JimmyJames over 3 years
I've always considered the term "waveform collapse" to mean "and then something happens" but if pilot wave and GRW make different predictions, why wouldn't that be testable?
• S. McGrew over 3 years
It's important to make it clear, as you did in the last comment, that you're "claiming that CI is false"; and it's equally important to make it clear that your earlier statement, "So MWI-baroque... is in fact false" is also your claim, asserted without proof.
• Steven Sagona over 3 years
I'm having trouble understanding your example. I am interested in interference of schodinger cat states too, but it's not clear to me exactly how to see their interference fringes. But I'm not exactly sure how the intereference happens here.
@S.McGrew: Not sure what you mean by "without proof." I gave an argument based on the theoretical paper by Allahverdyan. If you're just saying that that's not a universally accepted argument, then sure, I agree.
• S. McGrew over 3 years
OK, we're in agreement.
• S. McGrew over 3 years
In the example I gave, the interference is indirect: it is at the "A" end, among the particles that are entangled with the cats. If the "A" particles can interfere, they must be in mixed states. Because they are entangled with the cats, the cats, too, must be in mixed states.
• John McAndrew over 3 years
I don't believe wave-function collapse was ever a part of the Copenhagen interpretation; it was introduced by Von Neumann. Look at Jim Baggott's comments left on Not Even Wrong on this.
• alanf over 3 years
@JimmyJames They are testable. That was bad phrasing on my part. I've made an edit.
@JohnMcVirgo: I think both CI and MWI mean many different things to different people. CI doesn't just mean what Niels Bohr thought in 1927.
• isometry over 3 years
Excellent summary of how to tackle the quantum foundations question - thanks.
• JSorngard almost 3 years
But CI is not unitary (due to the presence of collapse), so having that assumption and saying that CI is obtained by adding more seems wrong to me.
• S. McGrew almost 3 years
Interference need not produce fringes: fringes relate to spatial interference.
• Steven Sagona almost 3 years
I just meant that I'm interested in seeing interference as a function of some variable (I didn't mean spacial interference specifically). If there's some superposition, there is some observation basis where you can see "interference" between the two states the quantum state is in a superposition of.
• Steven Sagona almost 3 years
I reread your answer, and I'm curious about what you are describing, but I don't exactly understand it. Could you perhaps go into more detail about what the mach-zender is doing to your cat state? Or maybe some kind of "blog" post might be helpful.
• S. McGrew almost 3 years
The basic idea is to do the Schroedinger's Cat experiment using two entangled particles (one in the box and one outside of the box) instead of the "traditional" radioactive particle. Then, because of entanglement, we have a way to know the cat's state without opening the box. If we can show that the particle outside the box is in a mixed state, then we know that the particle inside the box - and therefore the cat - is in a mixed state. The difficulty is that it takes a lot of particles (& cats) to prove the state is mixed.
• Steven Sagona almost 3 years
I would say that the details are a bit complicated that writing what the states are mathematically would be helpful. I'm not exactly sure what happens if you take a single particle in an entangled state and put in a MZI for one thing. Also, write that your goal is to conclude if the state is in a mixed state, but what does that conclude exactly?
• S. McGrew almost 3 years
Schroedinger's Cat is a "toy" version of the Many Worlds idea. If the cat is both dead and alive, its state is mixed. If you find that the cat is dead, you can't know if it's simply dead in all worlds, or if it's in a mixed state: alive in some worlds and dead in others. If you can repeat the experiment exactly a lot of times, checking the cat each time, you still don't know if it's in a mixed state. But a separate particle entangled with the cat can be prepared, and can (maybe) be proven to be mixed-state. The particle's state and the cat's state are (in a key sense) the same.
• anna v over 2 years
this answer of mine makes it more clear physics.stackexchange.com/questions/537614/…