Undergrad In which cases does superposition lead to splitting of worlds?

[entropy1]

I don't know how to understand this:

• Suppose we measure the spin of an electron with apparatus M. M can yield spin-up or spin-down. According to MWI, M briefly becomes in superposition of measuring spin up and spin down. Extremely quick however, M gets split by the splitting into two universes, in one of which M yields spin-up and in the other spin-down.
• Now, if we split a photon with a half-silvered mirror, then the photon will become in superposition of being let through and being reflected:
• 

So, what I don't understand is why in the first case, superposition leads to two worlds, and in the second case it doesn't. What do I not understand correctly?

 

[PeterDonis]

According to MWI, M briefly becomes in superposition of measuring spin up and spin down. Extremely quick however, M gets split by the splitting into two universes, in one of which M yields spin-up and in the other spin-down.

This is not a correct description of what the MWI says. The MWI says that M becomes entangled with the electron, so that the wave function of the joint system of M + electron has two terms that correspond to "electron spin up, M measures spin up" and "electron spin down, M measures spin down". This is properly described as entanglement, not superposition, because superposition is basis dependent, but the entanglement of M and the electron is not.

if we split a photon with a half-silvered mirror, then the photon will become in superposition of being let through and being reflected

Yes, but this in itself does not entangle the photon with anything and no measurement occurs. Superposition is an appropriate term here.

what I don't understand is why in the first case, superposition leads to two worlds, and in the second case it doesn't.

What leads to two worlds in the first case is not superposition; it's the entanglement of the electron with M.

 

[entropy1]

Ok thanks! So suppose we take the second case with a photon in superposition following two paths simultaneously. Suppose we put detection measuring devices on both paths, Ma and Mb. Does that mean that if Ma detects the photon, Mb doesn't detect it, and vice versa? And does that depend on spacetemporal ordening of Ma and Mb?

 

[Michael Price]

Another way of viewing the MWI splitting issue is to decree that splits only happen at entropically irreversible events, where ΔS >> k. If there is the possibility of significant future interference terms then the world(s) have not split or decohered from each other. A photon going through/reflecting off a half-silvered mirror is not an entropic event. The photon being detected by a photomultiplier, or caught on camera, is an irreversible event.

 

[entropy1]

The photon being detected by a photomultiplier, or caught on camera, is an irreversible event.

As perhaps a digression, what puzzles me in the second case is, if Ma detects the photon, Mb doesn't and vice versa. This seems to me a kind of entanglement, not between particles, but perhaps between measuring devices (Ma/Mb). Is this correct?

 

[Michael Price]

As perhaps a digression, what puzzles me in the second case is, if Ma detects the photon, Mb doesn't and vice versa. This seems to me a kind of entanglement, not between particles, but perhaps between measuring devices (Ma/Mb). Is this correct?

Entanglement is not half as whacky or interesting as it is made out to be. Entanglement is the consequence of most many particle interactions, and is absolutely bog-standard QM. Yes, the states of Ma and Mb are correlated (or entangled, if you prefer) with each other - if one measuring device records the photon then the other can't. But is that so Earth shattering?

 

[entropy1]

Yes, the states of Ma and Mb are correlated (or entangled, if you prefer) with each other - if one measuring device records the photon then the other can't. But is that so Earth shattering?

Well, it seems to me that one of the apparatusses doesn't know what the other measures, and yet their outcomes correlate. Ma and Mb can be setup spacelike separated. And I guess the photon, when in superposition of paths, travels no definite path. So there had to be some (FTL) communication between Ma and Mb, right? Just tell me if the wavefunction solves te paradox . Would be appreciated.

UPDATE: I realize that Ma doesn't have control over what its measurement outcome wil be, and likewise Mb, so that no information can be transferred FTL. So this is the solution to the paradox I think. However, this superposition seems to behave as an entanglement!

 

[Vanadium 50]

According to MWI, M briefly becomes in superposition of measuring spin up and spin down. Extremely quick however, M gets split by the splitting into two universes, in one of which M yields spin-up and in the other spin-down.

That's not what MWI says. Where and what did you read that's what it does?

 

[entropy1]

That's not what MWI says. Where and what did you read that's what it does?

It's my own recollection.

 

[PeterDonis]

So suppose we take the second case with a photon in superposition following two paths simultaneously. Suppose we put detection measuring devices on both paths, Ma and Mb. Does that mean that if Ma detects the photon, Mb doesn't detect it, and vice versa?

Yes, and that also destroys any interference between the two paths, so it changes the expected output after the second beam splitter. If both paths are open, all photons end up detected at just one detector (D2 in the case you illustrate, if I've understood the input state correctly). If only one path is open, each photon has a 50-50 chance of going to each detector.

 

[PeterDonis]

it seems to me that one of the apparatusses doesn't know what the other measures, and yet their outcomes correlate. Ma and Mb can be setup spacelike separated.

Yes, this is called "quantum nonlocality", and there is a huge amount of literature on it, including many PF threads, some quite recent. (Search on "quantum nonlocality" or "Bell's theorem" using the PF search feature.) It is well confirmed experimentally, and it is indeed highly counterintuitive. (Note: with only a single photon, you can't actually demonstrate quantum nonlocality; see my next post.)

So there had to be some (FTL) communication between Ma and Mb, right?

Not in the sense of being able to send information FTL; quantum nonlocality does not allow you to do that. The correlations between the measurements can violate the Bell inequalities, but you can't use them to send information, because in order to confirm that the correlations did in fact violate the Bell inequalities, each of the measurement results have to be communicated to some central location via ordinary slower than light means.

 

[PeterDonis]

Ma doesn't have control over what its measurement outcome wil be, and likewise Mb, so that no information can be transferred FTL.

Yes.

this superposition seems to behave as an entanglement!

No; if you only have a single photon in the apparatus at a time, there is no entanglement, because there's only one photon. You need at least two photons to have entanglement. The single photon case is actually simple enough that it can be described by an ordinary local model that does not violate the Bell inequalities. To get Bell inequality violations, you have to have a setup where you start with two entangled photons and then make spacelike separated measurements on them.

 

[Michael Price]

Well, it seems to me that one of the apparatusses doesn't know what the other measures, and yet their outcomes correlate. Ma and Mb can be setup spacelike separated. And I guess the photon, when in superposition of paths, travels no definite path. So there had to be some (FTL) communication between Ma and Mb, right? Just tell me if the wavefunction solves te paradox . Would be appreciated.

UPDATE: I realize that Ma doesn't have control over what its measurement outcome wil be, and likewise Mb, so that no information can be transferred FTL. So this is the solution to the paradox I think. However, this superposition seems to behave as an entanglement!

Yes, it is entanglement, and the two measuring devices are already spacelike separated. The two measuring devices can be arranged so the photon's wavefunction passes both simultaneously, which is when the splitting occurs. In one world Ma records a photon, but not Mb. In the other world Mb records a photon and not Ma.
'Timeline' is probably a better word than 'world'. Timelines split and diverge when things happen.

 

[PeterDonis]

it is entanglement

To be clear for the OP's benefit, you are talking about entanglement of the photon with the measuring devices. In my previous post, I was only talking about entanglement of photons with other photons. Both are valid cases of entanglement, but they should be distinguished because entanglement with measuring devices is what, according to the MWI, causes splitting into multiple "worlds" (I agree that "worlds" is not the best term).

 

[Michael Price]

To be clear for the OP's benefit, you are talking about entanglement of the photon with the measuring devices. In my previous post, I was only talking about entanglement of photons with other photons. Both are valid cases of entanglement, but they should be distinguished because entanglement with measuring devices is what, according to the MWI, causes splitting into multiple "worlds" (I agree that "worlds" is not the best term).

To be clear, yes, I agree.

 

[bhobba]

(I agree that "worlds" is not the best term).

Indeed - Gell-Mann has trouble with it as well:


As do I

Interesting side - I think many people here are wary of discussing Lubos Motol's views on things - he can be, how to put it, rather 'prickly'. But like me he is very keen n Gell-Mann's view of QM:
https://motls.blogspot.com/2014/09/murray-gell-mann-on-foundations-of.html
Sad day of course that Murray Gell-Mann died recently. Everyone justifiably admires Feynman and his rather different 'personality' revealed in Surely Your Joking Mr Feynman - Murray used to call it Feynman's book of jokes - but I do not think that's quite true of the second book which had some profound things to say about his time on the Challenger disaster. But sadly not as many had Gell-Mann on the same pedestal. They were great friends and collaborators at first, but the relationship soured a bit towards the end due to Feynman's quirks annoying Murray. But Feynman was unwavering in his scientific admiration for Gell-Mann - on a number of occasions calling him the greatest living physicist. Great praise indeed for a great man.

Thanks
Bill

 

[Michael Price]

Indeed - Gell-Mann has trouble with it as well:


As do I

Interesting side - I think many people here are wary of discussing Lubos Motol's views on things - he can be, how to put it, rather 'prickly'. But like me he is very keen n Gell-Mann's view of QM:
https://motls.blogspot.com/2014/09/murray-gell-mann-on-foundations-of.html
Sad day of course that Murray Gell-Mann died recently. Everyone justifiably admires Feynman and his rather different 'personality' revealed in Surely Your Joking Mr Feynman - Murray used to call it Feynman's book of jokes - but I do not think that's quite true of the second book which had some profound things to say about his time on the Challenger disaster. But sadly not as many had Gell-Mann on the same pedestal. They were great friends and collaborators at first, but the relationship soured a bit towards the end due to Feynman's quirks annoying Murray. But Feynman was unwavering in his scientific admiration for Gell-Mann - on a number of occasions calling him the greatest living physicist. Great praise indeed for a great man.

Thanks
Bill

Gell-Mann is misrepresenting Everett.
First he says Wheeler suggested the MWI idea to Everett, which is not true. In fact Wheeler was never that keen on the idea, although he thought it deserved a decent analysis and was supportive of Everett's work. But Everett was not happy with the way Wheeler forced him to rewrite his published synopsis.
Second, Gell-Mann says Everett was only interested in QM as a problem, not as a physicist, moving swiftly on to other military problems. In fact Everett was very bitter (as recent biographies testify) about MWI's reception and left physics in disgust. Working for the WSEG was also a way of avoiding the draft.