I What is the current status of Many Worlds?

[lukephysics]

Schrodingers equation says there are many worlds, but can’t there be an equally explanatory equation that drops the many worlds since they seem unnecessary?

I guess none of this matters really anyway since schrodingers and qm works anyway.

 

[Jarvis323]

Suppose we have a two-electron system with electrons A and B in the singlet state:

$$
\frac{1}{\sqrt{2}} \left( \ket{A}_\text{up} \ket{B}_\text{down} - \ket{A}_\text{down} \ket{B}_\text{up} \right)
$$

Are there "many" electron A's and "many" electron B's in this state?

Whatever your answer is to this question, the answer will be the same to the question you asked that is quoted above.

If you want to ask this kind of question, why not go further and ask if there are any electrons in this state. All there are that I see are arrangements of black pixels. And if I could probe your mind, maybe I'd see some wrinkles where this state lives. If we say the wave function is real, it is already a statement about something that is a level of abstraction beyond (or below) just the mathematics. So isn't looking at the mathematics to understand what MWI means only half the picture.

 

[vanhees71]

In the financial case, only one of the possible outcomes in the PDF actually occurs. In many worlds, all of the possible outcomes occur.

Can you tell me, how to get into that very universe, where the content of my account is spontaneously doubled by some event on the stock market? SCNR.

 

[vanhees71]

What does standard QM say about the states of individual subsystems that are entangled? (The "subsystems" could just be two electrons, instead of an electron and a measuring device.)

If you have a quantum system that can be separated in two subsystems $A$ and $B$ the Hilbert space of the system is described as the product of the two Hilbert spaces of the subsystems $\mathcal{H}=\mathcal{H}_A \otimes \mathcal{H}_B$. Let $|u_j \rangle \in \mathcal{H}_A$ and $|v_k \rangle \in \mathcal{H}_B$ be complete orthonormal systems (CONSs) then $|w_{jk} \rangle=|u_j \rangle \otimes |v_k \rangle$ are a CONS in $\mathcal{H}$.

If the quantum system is prepared in some state $\hat{\rho}$ then the states of the subsystems are described by the reduced statistical operators $\hat{\rho}_A$ and $\hat{\rho}_B$, defined by taking the partial traces over the respective other subsystem:
$$\hat{\rho}_A = \sum_{j,k,l} |w_{kj} \rangle \langle w_{kj}|\hat{\rho}|w_{lj} \rangle |u_k \rangle \langle u_l |$$
and analogously for $\hat{\rho}_B$.
If you know the state of the complete system all subsystems take unique states defined by these "reduced statistical operators".

Take, as a simple example, the spin-singlet state of a system of two spins 1/2. Then
$$\hat{\rho}=|\Psi \rangle \langle \Psi|$$
with
$$|\Psi \rangle=\frac{1}{\sqrt{2}} (|1/2,-1/2 \rangle-|-1/2,1/2 \rangle).$$
It's a simple exercise to find that for this "Bell state" the subsystems are maximally indetermined, i.e., the corresponding particles are precisely unpolarized,
$$\hat{\rho}_A=\hat{\rho}_B=\frac{1}{2} \hat{1}.$$

That you don't know what state each system is in until you measure it? I'm not asking about standard QM. I'm asking if there is any reality to all this multiple worlds view or is it just math. Seems to me you are saying it is just math. If it is just math then why are physicists like DeWitt saying such misleading nonsense like every interaction branches the universe?

This is an enigma to me too, but usually when physicists enter the terrain of fuzzy philosophy, "misleading nonsense" is likely to occur (just an observation ;-)). For me the greatest progress of the thinking of mankind was the idea to strictly separate the "hard sciences" from the fuzzy "humanities" in the renaissance when modern natural sciences started to be developed.

 

[Jarvis323]

This is an enigma to me too, but usually when physicists enter the terrain of fuzzy philosophy, "misleading nonsense" is likely to occur (just an observation ;-)). For me the greatest progress of the thinking of mankind was the idea to strictly separate the "hard sciences" from the fuzzy "humanities" in the renaissance when modern natural sciences started to be developed.

For me, this line of thinking is highly confusing. The entire goal of philosophy is to make things not fuzzy. The thing that changed in the renaissance wasn't separating philosophy from science, it was to establish concrete philosophical foundations for science. This was also the time when we began to established concrete philosophical foundations for mathematics. The revolution in science was due to a breakthrough in philosophy, not an abandonment of it.

 

[WernerQH]

This is an enigma to me too, but usually when physicists enter the terrain of fuzzy philosophy, "misleading nonsense" is likely to occur (just an observation ;-)). For me the greatest progress of the thinking of mankind was the idea to strictly separate the "hard sciences" from the fuzzy "humanities" in the renaissance when modern natural sciences started to be developed.

It seems some people desperately try to make sense of MWI. Using stict logical deduction, it is of course possible to "derive" an infinity of absurd conclusions from just one nonsensical assumption.

 

[bob012345]

Suppose we have a two-electron system with electrons A and B in the singlet state:

$$
\frac{1}{\sqrt{2}} \left( \ket{A}_\text{up} \ket{B}_\text{down} - \ket{A}_\text{down} \ket{B}_\text{up} \right)
$$

Are there "many" electron A's and "many" electron B's in this state?

Whatever your answer is to this question, the answer will be the same to the question you asked that is quoted above.

My answer is no, of course not. I would not regard this wavefunction as involving two A electrons and two B electrons. The wavefunction is over states of the electrons. You seem to be saying to regard the MWI wavefunction in the same way. That makes sense to me. Going back and forth further about what MWI adherents really believe is counterproductive at this point. I found an essay by a Princeton physicist;

https://arxiv.org/pdf/1801.08587.pdf

Thanks for the discussion!

 

[PeterDonis]

If you want to ask this kind of question, why not go further and ask if there are any electrons in this state. All there are that I see are arrangements of black pixels.

"Electron" in this case is simply a name for the degrees of freedom referred to by the symbols $A$ and $B$. So of course there are electrons in this state. There are "electron A" degrees of freedom, and "electron B" degrees of freedom. They're right there in the wave function.

Of course when we write down a wave function like this, we are usually making some implicit assumption about how the degrees of freedom in the state correspond to measurements--for example, we might relate the "electron A" degrees of freedom to some measurement made by Alice, and the "electron B" degrees of freedom to some measurement made by Bob. That is not a matter of any particular QM interpretation; it's a matter of the basic math and how it relates to measurements. If you can't relate the math to measurements in some way, you can't test the theory's predictions.

isn't looking at the mathematics to understand what MWI means only half the picture.

For any interpretation, as I said, there has to be a grounding in the math. Otherwise it isn't an interpretation of QM to begin with.

For the MWI in particular, there is a sense in which "the math is all there is", because the central claim of this interpretation is that the wave function is real, and it's the only thing that's real. But I agree that advocates of the MWI have to do more than just point at the wave function to explain why they think the interpretation makes sense.

 

[PeterDonis]

My answer is no, of course not. I would not regard this wavefunction as involving two A electrons and two B electrons. The wavefunction is over states of the electrons.

That is my view as well.

You seem to be saying to regard the MWI wavefunction in the same way.

Yes. And then the challenge for MWI advocates is to explain how this can possibly be consistent with our experiences, since when we observe or measure something we experience a definite result having occurred. The MWI has to say that all of the possible results occurred, but it's not clear to start with what that means, since in an entangled state like the ones we have been looking at, it seems like nothing has "occurred"--neither subsystem is in a definite state at all.

The original "relative state" viewpoint explained this by saying that, for each subsystem, each of the possible results occurs relative to the corresponding result for the other subsystem. So it would say that in the singlet state, two results have occurred: "electron A up, electron B down" and "electron A down, electron B up". (Actually, since the development of decoherence theory, even a "relative state" interpretation would no longer say this, since no decoherence has occurred for two electrons in the singlet state. But it would still work for any case that does involve decoherence, which certainly includes any macroscopic measurement or any observation by a human.) This is still a change in the meaning of the term "occurs", since it no longer corresponds to a subsystem having a definite state period--now it only requires the subsystem to have a relative state with respect to another subsystem with which it is entangled.

The "many worlds" viewpoint, however, wants to make a stronger claim, one that seems to amount to there actually being multiple "copies" of each subsystem, one in each "world"--but, as we've seen, if we take such statements literally they are obviously false since that's not how entangled states in QM work. So the "many worlds" viewpoint still has to fall back on something like a "relative state" formulation when challenged, while trying to make the stronger-sounding "many worlds" claims whenever it can get away with it. As you can see from this description of mine, I am not a many worlds proponent myself (as I've already said).

 

[AndreiB]

Wave function is fundamental but not ontic, in the same sense in which Hamiltonian in classical mechanics is fundamental but not ontic.

Why is the Hamiltonian fundamental in classical mechanics? Newton was fine without it. Is Bohm's interpretation fine without the wave function?

 

[AndreiB]

Can you tell me, how to get into that very universe, where the content of my account is spontaneously doubled by some event on the stock market? SCNR.

You don't need to get there. There is a "you" there already. So, just be happy for him!

 

[AndreiB]

In this spirit of confusion I'd love to hear what the thoughts on Many Worlds are in 2021 by everyone here at PF.

As far as I know there is no way to derive Born's rule in MWI, so the theory cannot make any predictions. There is no way to ascribe any meaning for probabilities in MWI.

 

[Demystifier]

Why is the Hamiltonian fundamental in classical mechanics? Newton was fine without it. Is Bohm's interpretation fine without the wave function?

You can define classical mechanics without Hamiltonian $H(x,p)$, but then you need something equivalent, e.g. the force function $F(x)$. The wave function is something similar, the closest classical analogy of the wave function is in fact the Hamilton-Jacobi function $S(x,t)$.

 

[AndreiB]

You can define classical mechanics without Hamiltonian $H(x,p)$, but then you need something equivalent, e.g. the force function $F(x)$. The wave function is something similar, the closest classical analogy of the wave function is in fact the Hamilton-Jacobi function $S(x,t)$.

So you can replace the wave function with a force that acts instantaneously between particles?

 

[Demystifier]

So you can replace the wave function with a force that acts instantaneously between particles?

No, in Bohmian mechanics you can't really do that. Bohmian mechanics is a law for the velocity, not for the acceleration.

 

[AndreiB]

No, in Bohmian mechanics you can't really do that. Bohmian mechanics is a law for the velocity, not for the acceleration.

OK, so if you modify Newton's second law so that the "force" does not determine the acceleration, but the velocity of the particle can you replace the wave function?

 

[Demystifier]

OK, so if you modify Newton's second law so that the "force" does not determine the acceleration, but the velocity of the particle can you replace the wave function?

Replace with what? I think nobody found such a mathematical object yet.

 

[AndreiB]

Replace with what? I think nobody found such a mathematical object yet.

You claimed that the wave function is not ontic. That means that it should be possible to describe it in terms of something else which is ontic. Or maybe we have a different understanding of what ontic means. Would you consider the forces in Newtonian mechanics as ontic?

 

[PeroK]

For me, this line of thinking is highly confusing. The entire goal of philosophy is to make things not fuzzy. The thing that changed in the renaissance wasn't separating philosophy from science, it was to establish concrete philosophical foundations for science. This was also the time when we began to established concrete philosophical foundations for mathematics. The revolution in science was due to a breakthrough in philosophy, not an abandonment of it.

This is such a travesty that I couldn't let it go.

The philosopher Henri Bergson, who didn't understand and wouldn't accept relativity, blocked Einstein receiving a Nobel prize for the theory of relativity.

https://nautil.us/issue/35/boundaries/this-philosopher-helped-ensure-there-was-no-nobel-for-relativity

Bergson himself got the Nobel prize for Literature (!) in 1927 and - like other philosophers - battled against the progress of science and mathematics in the mistaken belief that their own supreme intellect and powers of pure thought outweighed that of mathematics and empirical science.

Ironically, of course, any decent undergraduate of physics or mathematics can understand the theory of SR in six weeks or so. That's what it took me.

The lesson is clear: if you want to make progress in science and mathematics, you have to ditch philosophy and the philosophers and their non-existent powers to know the world through pure thought alone.

 

[martinbn]

My view on the many worlds is that, when it talks about many worlds existing and many copies of everything, it is just a pile of words. On the other hand the idea of a relative state interpretation without the philosophical nonsense is very atractive.

 

[Demystifier]

You claimed that the wave function is not ontic. That means that it should be possible to describe it in terms of something else which is ontic. Or maybe we have a different understanding of what ontic means. Would you consider the forces in Newtonian mechanics as ontic?

I would not consider the forces in Newtonian mechanics as ontic. $F(x)$ is nomological, as is the wave function.

 

[Demystifier]

My view on the many worlds is that, when it talks about many worlds existing and many copies of everything, it is just a pile of words. On the other hand the idea of a relative state interpretation without the philosophical nonsense is very atractive.

What's the "relative state interpretation without the philosophical nonsense"? Do you have a reference?

 

[martinbn]

What's the "relative state interpretation without the philosophical nonsense"? Do you have a reference?

I didn't say the relative state interpretation. I said a relative state interpretation.

 

[Morbert]

I think MWI as a project was completed by Consistent histories.

MWI showed us how decoherence can let us assign probabilities to possible worlds/histories, and how QM treats these possibilities on equal footing apart from their probabilities.

But you need an exotic ontology underlying these probabilities. Consistent histories showed us i) how we can recover our intuitive understanding of these probabilities as likelihoods for mutually exclusive alternatives, as opposed to needing all alternatives to actually exist, and ii) How to more rigorously quantify the decoherence between worlds.

 

[vanhees71]

The paper defining the original relative-state interpretation by Everett or rather the version of Everett's view revised due to the advice of his thesis adviser J.A. Wheeler, who was a declared Bohr disciple, is

https://doi.org/10.1103/RevModPhys.29.454

 

[Demystifier]

I didn't say the relative state interpretation. I said a relative state interpretation.

What's a relative state interpretation without philosophical nonsense?

 

[PeterDonis]

Can you tell me, how to get into that very universe, where the content of my account is spontaneously doubled by some event on the stock market?

Sure, just invest in the right stock.

 

[*now*]

RQM involves relative states. This is an early paper, there could be further developments since,
https://link.springer.com/article/10.1007/BF02302261
Published: August 1996
Relational quantum mechanics
Carlo Rovelli
International Journal of Theoretical Physics volume 35, pages1637–1678 (1996)
Abstract
I suggest that the common unease with taking quantum mechanics as a fundamental description of nature (the “measurement problem”) could derive from the use of an incorrect notion, as the unease with the Lorentz transformations before Einstein derived from the notion of observer-independent time. I suggest that this incorrect notion that generates the unease with quantum mechanics is the notion of “observer-independent state” of a system, or “observer-independent values of physical quantities.” I reformulate the problem of the “interpretation of quantum mechanics” as the problem of deriving the formalism from a set of simple physical postulates. I consider a reformulation of quantum mechanics in terms of information theory. All systems are assumed to be equivalent, there is no observer-observed distinction, and the theory describes only the information that systems have about each other; nevertheless, the theory is complete.
https://arxiv.org/abs/quant-ph/9609002

 

[Jarvis323]

This is such a travesty that I couldn't let it go.

The philosopher Henri Bergson, who didn't understand and wouldn't accept relativity, blocked Einstein receiving a Nobel prize for the theory of relativity.

https://nautil.us/issue/35/boundaries/this-philosopher-helped-ensure-there-was-no-nobel-for-relativity

Bergson himself got the Nobel prize for Literature (!) in 1927 and - like other philosophers - battled against the progress of science and mathematics in the mistaken belief that their own supreme intellect and powers of pure thought outweighed that of mathematics and empirical science.

Ironically, of course, any decent undergraduate of physics or mathematics can understand the theory of SR in six weeks or so. That's what it took me.

The lesson is clear: if you want to make progress in science and mathematics, you have to ditch philosophy and the philosophers and their non-existent powers to know the world through pure thought alone.

You're talking about groups of arrogant Philosophers, not Philosophy.

There have also been arrogant groups of medical doctors that rejected the merits of hand washing with tragic consequences. The solution wasn't to abandon medicine.

Philosophy has given us the scientific method, formalization of computation, logic, and axiomatic systems in mathematics.

You really want scientists to ditch the scientific method, and you want mathematicians to ditch logic and axioms?

You can't expect to make progress by reason and intelect alone, but how much progress can you make without it at all?

 

[PeterDonis]

You're talking about groups of arrogant Philosophers, not Philosophy.

Even Philosophers should recognize this logical fallacy, namely No True Scotsman.

Philosophy has given us the scientific method, formalization of computation, logic, and axiomatic systems in mathematics.

Nope. None of those things were given to use by Philosophy. The scientific method, to the extent that term even has a definite meaning, was given to us by scientists. Formalization of computation, logic, and axiomatic systems was given to us by mathematicians. The fact that some of the people who contributed to those things also billed themselves as philosophers does not mean Philosophy gets to take credit for those things.

You really want scientists to ditch the scientific method, and you want mathematicians to ditch logic and axioms?

This is another logical fallacy that even Philosophers should recognize, namely the Straw Man.