Many Worlds Interpretation and act of measuring

[stevendaryl]

Since all states evolve independently of each other in a linear system, different alternatives can't affect each other whether macroscopically distinguishable or not. Whether decohered or not. Whether eigenstates or not. Heck, they don't even have to be orthogonal. Interference is not one state affecting another but a single superposition evolving. The interference is visible in the state of the observer if he repudiates the boring preferred basis of |left>,|right> and insists on using $\frac{1}{2} (|L\rangle \pm |R\rangle)$

Suppose that the system is in a superposition of states $|A\rangle + |B\rangle$. You want to know what the probability of winding up in state $|C\rangle$ is. Well, it could be zero, even if there is a nonzero chance of state $|A\rangle$ evolving into $|C\rangle$ and a nonzero chance of state $|B\rangle$ evolving into $|C\rangle$. That's because the two amplitudes could undergo destructive interference. So in that case, it would be weird to think of this situation as two independent possible worlds, one in which the system is in state $|A\rangle$ and another in which the system is in state $|B\rangle$. Or so it seems to me.

 

[Jilang]

Wouldn't there need to four possible worlds in that case covering each of the four possible histories?

 

[Derek Potter]

Suppose that the system is in a superposition of states $|A\rangle + |B\rangle$. You want to know what the probability of winding up in state $|C\rangle$ is. Well, it could be zero, even if there is a nonzero chance of state $|A\rangle$ evolving into $|C\rangle$ and a nonzero chance of state $|B\rangle$ evolving into $|C\rangle$. That's because the two amplitudes could undergo destructive interference. So in that case, it would be weird to think of this situation as two independent possible worlds, one in which the system is in state $|A\rangle$ and another in which the system is in state $|B\rangle$. Or so it seems to me.

I understand that, but it is a mistake (or so it seems to me! ). The A outcome-world and the B outcome-world continue merrily on their way even though their sum is locally zero. It can't be zero everywhere or unitarity (-ness?) would be violated so we are looking at constructive interference somewhere else. It's no different from two beams of coherent light crossing each other.

 

[stevendaryl]

I understand that, but it is a mistake (or so it seems to me! ). The A outcome-world and the B outcome-world continue merrily on their way even though their sum is locally zero. It can't be zero everywhere or unitarity (-ness?) would be violated so we are looking at constructive interference somewhere else. It's no different from two beams of coherent light crossing each other.

I'm just saying that if you think of A, B and C as "possible worlds", then such destructive interference could make world C impossible (zero probability) even though it seems possible from the point of view of world A, and it seems possible from the point of view of world B.

I don't know what you mean by "zero everywhere". Unitarity will just imply the existence of some other world, say $D$ that will take up the slack from the fact that C is no longer possible.

 

[Derek Potter]

Wouldn't there need to four possible worlds in that case covering each of the four possible histories?

Not sure which four cases you mean but in general there are as many worlds as there are possible histories. That's "possible at the most microscopic level" so naturally the number of world branches is usually infinite. Bush vs Gore was dominated, we presume, by classical causes so the range of possibilities was mostly [Bush], [Gore], but there was also a non-zero but tiny possibility of me being elected even though I didn't stand - through a bizarre quantum fluctuation. On this view one outcome was almost certain and one was vanishingly unlikely though nobody knew it at the time because we only had political news to guide us. Had we known the quantum state of the voters we would have known that [Gore] was extremely unlikely, though maybe not as unlikely as [Potter]. In MW there is a world for each quantum state though sometimes people lump all similar macroscopic states together as a single world, as you are doing. This may make the picture more appealing but it obscures the quantum statistics.

 

[Derek Potter]

D is the constructive interference term. Its can only take up the slack if A and B evolve to C plus D, it can't just watch A B and C from afar off and puff itself up to compensate when C disappears!
added: To put it another way if |A> evolves to +|C> and |B> evolves to -|C> then does this not mean that |A> = -|B>? So A and B are not alternatives but are the same state with zero total amplitude from the beginning.

 

[Derek Potter]

Jilang - sorry, mistook your meaning and now can't delete post #425

 

[Jilang]

Not sure which four cases you mean but in general there are as many worlds as there are possible histories.

Yes I think so, but this is all new to me:
1) A evolves to C
2) A doesn't evolve to C
3) B evolves to C
4) B doesn't evolve to C

 

[Jilang]

LOL, you can delete my post #428 then.

 

[Derek Potter]

Quite! :) Leaving aside whether Steve's point is right or not, do you get the idea of a vast tree of branching states each of which is subjectively different to the oberserver/inhabitants?

 

[Jilang]

No. As the observer I just don't know what world I am in (yet).

 

[Derek Potter]

And the other quantum states in the superposition - where are they and what happens to those slightly different and not-so-slightly different versions of you represented by the components of the wavefunction that were there a moment ago?

Sascha Vongehr got a lot of stick for posting a question designed to shock people into realizing how bizarre QM is - no fudging the issue. He envisaged a revolting, horrific scenario which I won't reproduce here and which, by QM, *could* happen and therefore, by QM, *does* happen in at least one world and which, by QM, is just as real as the relatively humdrum world(s) we think to be normal. Do we care? Should we care? The physics is clear unless wavefunction collapse occurs and there is no evidence for that, just our prejudices.

On the other hand the Hard Problem does let us speculate whether the other versions of us are conscious. Nature is (according to MW) profligate with physical worlds, perhaps it is parsimonious with consciousness? We just don't know.

 

[RUTA]

This paper just appeared in Weekly Papers on Quantum Foundations 17 at IJQF http://arxiv.org/abs/1504.04835. It may be of interest to this thread.

 

[Rajkovic]

have you thought how funny is to discuss and get deep into something that doesn't exist? NO? So I present you ---> MWI

 

[stevendaryl]

have you thought how funny is to discuss something that doesn't exist? Yes! so, I present you ---> MWI

Any time someone discusses theoretical physics, there is a possibility that they are discussing something that doesn't exist. Get used to it.

 

[Nugatory]

This paper just appeared in Weekly Papers on Quantum Foundations 17 at IJQF http://arxiv.org/abs/1504.04835. It may be of interest to this thread.

It's been a while since I've read a properly deadpan understatement... from the abstract of this paper we have "We conclude that much remains to be done to clarify and specify Everett's approach".

 

[TrickyDicky]

have you thought how funny is to discuss and get deep into something that doesn't exist? NO? So I present you ---> MWI

Yes, I have.
It is also a bit sad if you realize that there are(and have been for many years) more than enough elements in the mathematical physics literature to not even consider this discussion. But there are few things harder than going against intellectual mendacity and mendicity, so indeed it is better to take it with humor.

 

[RUTA]

I just finished reading http://arxiv.org/pdf/1504.04835v1.pdf and I agree with the author's conclusion:

*************************************************************************************************************
After 50 years, there is no well-defined, generally agreed set of assumptions and postulates that together constitute ‘the Everett interpretation of quantum theory.’ (Kent, 2010, p. 307.)

This assessment, I believe, has been substantiated in this paper with respect to multiplicity: Are worlds physically splitting, or does the split happen only in the mind? Do worlds split locally or globally, instantaneously or on some other space-time hypersurface? Are worlds generated upon any entanglement-producing interaction, or only when macroscopic objects or apparatus are involved? Do worlds split or bifurcate? Do they occupy the same physical space-time or do they involve extra dimensions? These and others are all questions on which different investigators disagree, or even questions that have received different answers at different times from the same investigator.
*************************************************************************************************************
I also think MW is going to have a big problem with quantum gravity, because each different possible configuration will have a different spacetime metric per GR. That's not typically a problem for QM because the difference in energy deposited in different detectors is too small to have a measureable effect on the metric per GR. But, in MW those different outcomes are all realized so the difference in energy distribution will compound. Since these differences have been compounding since the Big Bang, at this stage in the evolution of the universe the spacetime metric between "branches" should in many cases be significant. So, for example, it seems to me that the Hilbert space for Wheeler-deWitt would not accommodate MW because the states are all connected in time in MW whereas one would have distinct spacetime manifolds and metrics in Wheeler-deWitt Hilbert space. In any event, I don't understand why MW is so popular in foundations. It's a mess.

 

[Derek Potter]

It's been a while since I've read a properly deadpan understatement... from the abstract of this paper we have "We conclude that much remains to be done to clarify and specify Everett's approach".

Everett's formulation of quantum superpositions in terms of relative states seems to be clear enough. Why does his personal opinion of the ontologicy matter to us 60 years on? Or why does it impinge on the economy of MW that decoherence plays the same role and is explained the same way, with the same residual issues, in MW as in a canonical collapse theory?

 

[Derek Potter]

But, in MW those different outcomes are all realized so the difference in energy distribution will compound. Since these differences have been compounding since the Big Bang, at this stage in the evolution of the universe the spacetime metric between "branches" should in many cases be significant. So, for example, it seems to me that the Hilbert space for Wheeler-deWitt would not accommodate MW because the states are all connected in time in MW whereas one would have distinct spacetime manifolds and metrics in Wheeler-deWitt Hilbert space. In any event, I don't understand why MW is so popular in foundations. It's a mess.

If you're right then the problem doesn't away in any interpretation that admits of superposed states even momentarily. However, I don't know why it is a problem if each state defines its own manifold. Obviously it all becomes much more complicated but that's going to happen in any theory that includes GR.

 

[Derek Potter]

Any time someone discusses theoretical physics, there is a possibility that they are discussing something that doesn't exist. Get used to it.

I believe the point was not that the Many Worlds may not exist but that they definitely don't. This has been proven by very clever mathematicians. Only mediocre dullards like Sean Carroll still give it head room. Apparently.

 

[Derek Potter]

I just finished reading http://arxiv.org/pdf/1504.04835v1.pdf and I agree with the author's conclusion:

*************************************************************************************************************
After 50 years, there is no well-defined, generally agreed set of assumptions and postulates that together constitute ‘the Everett interpretation of quantum theory.’ (Kent, 2010, p. 307.)

This assessment, I believe, has been substantiated in this paper with respect to multiplicity: Are worlds physically splitting, or does the split happen only in the mind? Do worlds split locally or globally, instantaneously or on some other space-time hypersurface? Are worlds generated upon any entanglement-producing interaction, or only when macroscopic objects or apparatus are involved? Do worlds split or bifurcate? Do they occupy the same physical space-time or do they involve extra dimensions? These and others are all questions on which different investigators disagree, or even questions that have received different answers at different times from the same investigator.

The RSF was not made by hypothesising multiple universes. It expresses vanilla QM in terms of a superposition of observations. So the questions amount to asking when the superposition occurs. And the answer to that is that superposition is not a physical event, it's a change of basis. At what "point" does an electron prepared with spin-z = 1 "become" one with |spin-y =1> superposed with |spin-y = -1>? The states are the same! MW does not require multiplicity of universes that physically split apart. Everett actually warned against interpreting MW that way. Instead the worlds are simply the way the universe appears to the observer, meaning he/she sees all possible outcomes. The superposition of x-spins exists even before the beam splitter. That is not to trivialise the ontology of MW but to emphasise how profoundly weird *any* superposition actually is. We are all Schrodinger Cats.

 

[StevieTNZ]

I believe the point was not that the Many Worlds may not exist but that they definitely don't. This has been proven by very clever mathematicians. Only mediocre dullards like Sean Carroll still give it head room. Apparently.

"My advice to any heartbroken young girl is to pay close attention to the study of theoretical physics. Because one day there may well be proof of multiple universes," Hawking answered.

"It would not be beyond the realms of possibility that somewhere outside of our own universe lies another different universe. And in that universe, Zayn is still in One Direction."

http://www.stuff.co.nz/entertainmen...hope-to-one-direction-fans-missing-zayn-malik

I haven't seen any proof that many worlds don't exist due to the some Mathematicians. I've even seen an article that would test many world's interacting - http://phys.org/news/2014-10-interacting-worlds-theory-scientists-interaction.html

 

[Rajkovic]

I agree with Derek, MWI Is bull****But Derek, what do you mean by "We are all Schrodinger Cats" ?

 

[atyy]

However I tentatively disagree about its being trivial in MW. Yes, some outcome occurs by definition and that part is trivial. However, the theory needs to account for probability - otherwise it cannot even say why Schrodinger doesn't always see a dead cat. As far as I understand it, Gleason's Theorem shows that a measure of probability exists. Hence if there is a probability rule it must be the Born Rule. I believe this is Kastner's objection to the claims of MW: that MW assumes probability in order to justify applying Gleason's theorem and is thus circular. Carroll seems to think this objection is wrong.

As described, the objection is wrong, because certainty is a type of probability. In other words, deterministic theories are a subset of probability theories.

 

[Derek Potter]

http://www.stuff.co.nz/entertainmen...hope-to-one-direction-fans-missing-zayn-malik
I haven't seen any proof that many worlds don't exist due to the some Mathematicians. I've even seen an article that would test many world's interacting - http://phys.org/news/2014-10-interacting-worlds-theory-scientists-interaction.html

I'm not impressed by the MIW articles - they are a bit elementary even by my standards so it's hard to tell what the point is. If it is yet another non-linear tweak to QM, then as far as MW is concerned it may be a big "so what?" But if it can describe physics in terms of classical worlds and get quantum wave mechnaics (all the i.hbar stuff) to emerge from the model than it is not QM but something sub-quantum. And that would be a wonderful breakthrough.

 

[Derek Potter]

Sorry, I guess I should have said "Irony Alert" in big bold red letters. Of course MW is not rubbish and of course I do not believe for a moment that it can be debunked mathematically or that Sean Carroll is a dullard!

 

[Derek Potter]

As described, the objection is wrong, because certainty is a type of probability. In other words, deterministic theories are a subset of probability theories.

I don't agree, of course. The alternative to probability is not certainty or determinism. The alternative to probability is the absence of probability. You appear to be thinking of determinism as admitting multiple possibilities but superselecting one actual outcome ("sprinkling the magic fairy dust of existence on one state" as it has rudely been described). The determinism of wave mechanics doesn't allow different possibilities at all: C follows from B follows from A. There is no concept of P_a=1 since there are no other outcomes to consider.

 

[Derek Potter]

I agree with Derek, MWI Is bull****
But Derek, what do you mean by "We are all Schrodinger Cats" ?

Well, hang on. I am here trying to distinguish between the Many Worlds principle and the various Many Worlds Interpretations. MW as such is inescapable in linear Wave Mechanics i.e. Schrodinger evolution. The depictions of the worlds that occur in popular presentations are often misleading to the point of being downright BS, and typically lead to meaningless questions like "when does the universe split?" Nevertheless a superposition in a subsystem (the cat) invariably leads to different alternatives being actualized as far as another subsystem (the scientist) is concerned.

We are all Schrodinger cats. Everyone and everything is just a perspective on the underlying state. The perspective is created by our senses working on the so-called preferred basis, the near-classical set of outcome possibilities that are stable against decoherence. Thus not only is Schrodinger's cat alive and dead at the same time, so are we. All the silly alternative history scenarios that people bring up are actualized with respect to their particular observers in their own worlds.

 

[Quantumental]

We are all Schrodinger cats. Everyone and everything is just a perspective on the underlying state. The perspective is created by our senses working on the so-called preferred basis, the near-classical set of outcome possibilities that are stable against decoherence. Thus not only is Schrodinger's cat alive and dead at the same time, so are we. All the silly alternative history scenarios that people bring up are actualized with respect to their particular observers in their own worlds.

Prove it then and win a Nobel Prize.

So far there is pretty much no agreement amongst even supporters of MWI in terms of how to solve preferred basis problem and Born Rule problem. Yougot no solution either. You sounds borderline religious with this dogmatic "WE ARE"

 

[RUTA]

If you're right then the problem doesn't away in any interpretation that admits of superposed states even momentarily. However, I don't know why it is a problem if each state defines its own manifold. Obviously it all becomes much more complicated but that's going to happen in any theory that includes GR.

What would superposition look like in Wheeler-deWitt? Each Hilbert space vector would represent a single spacetime manifold, metric and stress-energy tensor with no "meta" time dependence, i.e., the vector would not change or evolve.

If you're a psi-epistemist, then you might view MW as simply supplying the time-evolved 3D embedded view of a subset of all flat spacetime solutions in Wheeler-deWitt. In that sense, MW actually fits nicely with quantum gravity.

I'm sure MWers have considered this, so I was hoping someone here might explain it :-)

 

[stevendaryl]

Prove it then and win a Nobel Prize.

So far there is pretty much no agreement amongst even supporters of MWI in terms of how to solve preferred basis problem and Born Rule problem. Yougot no solution either. You sounds borderline religious with this dogmatic "WE ARE"

I think your tone is way out of line. There is nothing "religious" about what Derek said.

There is a tendency in physics discussions for people to be insultingly certain about subjects that are understood the least. People don't understand the foundations of quantum mechanics, the meaning of measurement, the origin of probabilities very well at all, but everyone has a strong opinion that other people's views are nonsense.

Everett's original paper about MWI was mostly about exploring the question: What if in quantum mechanics we treat the measuring device (or observer) quantum-mechanically? That's not only a non-silly thing to ask, it seems required if we are to take quantum mechanics seriously as a foundation for physics. MWI in this sense is the insistence that there NOT be anything magical going on in the measurement process. That's an assumption, but it's hardly a "religious" assumption.

 

[Quantumental]

I think your tone is way out of line. There is nothing "religious" about what Derek said.

My tone is a replication of his own tone. He is being condescending to everyone that isn't a member of his 'MWI religion' here by calling them "silly". He has already stated that it *is* true, with no solution to the current problems and absolutely no evidence.

 

[stevendaryl]

My tone is a replication of his own tone. He is being condescending to everyone that isn't a member of his 'MWI religion' here by calling them "silly". He has already stated that it *is* true, with no solution to the current problems and absolutely no evidence.

You're way out of line. What he's describing is not "religious".

 

[Quantumental]

You're way out of line. What he's describing is not "religious".

CLAIMING that something unprovable that directly disagrees with observation IS TRUE is indeed the definition of 'borderline religious'