Many Worlds Interpretation and act of measuring

[bhobba]

Basis independence is also a theorem.

It isn't a theorem per-se. It's an assumption that goes into Gleason's theorem and may or may not be violated by hidden variables.

Thanks
Bill

 

[Derek Potter]

Fair comment. But if trickydicky is asserting that QM dynamics requires hidden variables then I should like him to say so.

 

[bhobba]

Fair comment. But if trickydicky is asserting that QM dynamics requires hidden variables then I should like him to say so.

It doesn't - see chapter 3 Ballentine.

Thanks
Bill

 

[Derek Potter]

The measurement problem actually has a number of parts - again the above reference gives the full detail. The part it doesn't explain without further interpretive assumptions is why we get any outcomes at all - which is the modern version of collapse. In MW it's of course trivial.

If it's trivial in MW then exactly the same reasoning must apply in a collapse theory. After all, collapse just takes the Many Worlds superposition and lops off the unwanted branches. MW relies on relative states - there is no obvious reason why a collapse theory should not express the superposition in the same terms.

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.

 

[bhobba]

If it's trivial in MW then exactly the same reasoning must apply in a collapse theory. After all, collapse just takes the Many Worlds superposition and lops off the unwanted branches.

It does more than that. It generally introduces non linearities that leads to actual collapse. But yes its trivial for collapse theories, and BM, and probably others I can't think of off the top of my head.

However, the theory needs to account for probability

I believe it does - but I won't be rehashing this whole thread to delve into it. If you want the detail get Wallace's book and make up your own mind.

Thanks
Bill

 

[kith]

The conceptual issue I have with MW is that once you think you have pinned down a state (and established world you are in) the state can often be described as a superposistion of states in another basis (so you don't know which world you are in). How to reconcile this?

The standard MWI doesn't simply associate a world with every term in a superposition (this would lead to interference between worlds).

The splitting into different worlds occurs when the interference between different states in a certain basis become negligible. The preferred basis and the decohering dynamics are results of interactions of the system with its environment. So looking at this from an external perspective, the splitting occurs when the dynamics lead to a certain kind of long-lasting and strong entanglement between the system and the environment.

 

[Derek Potter]

The standard MWI doesn't simply associate a world with every term in a superposition (this would lead to interference between worlds).

The splitting into different worlds occurs when the interference between different states in a certain basis become negligible. The preferred basis and the decohering dynamics are results of interactions of the system with its environment. So looking at this from an external perspective, the splitting occurs when the dynamics lead to a certain kind of long-lasting and strong entanglement between the system and the environment.

Of course decoherence must be taken into account in any interpretation but it is not fundamental to MWI. Everett's paper on relative states is perfectly clear - the worlds are different observer experiences (i.e permanent records but see below). Decoherence does not come into the interpretation.

[added] And yes, worlds do interfere. In MW it is meaningful to talk about worlds even if no observation is actually made, it is always meaningful to talk about what could have been observed, the interpretation is fully realist. Thus in the double slit experiment |left> interferes with |right> and we see the familiar bands.

 

[Derek Potter]

I believe it does - but I won't be rehashing this whole thread to delve into it. If you want the detail get Wallace's book and make up your own mind.

Yes, I believe it probably does. I believe Kastner to be mistaken and Carroll to be correct in this respect, but who am I to judge between warring titans? :)

 

[stevendaryl]

Of course decoherence must be taken into account in any interpretation but it is not fundamental to MW. Everett's paper on relative states is perfectly clear - the worlds are different observer experiences. Decoherence does notcome into it.

There is a basis issue, it seems to me, in Everett's relative state formulation of QM.

If you have a composite state |\Psi\rangle = \sum_{\alpha j} C_{\alpha j} |\alpha\rangle |j\rangle, where \alpha refers to states of the observer, and j refers to states of the system being observed, then we can define the "relative state" of the system relative to state |\alpha\rangle for the observer as follows:

|\psi_\alpha\rangle = \sum_j u_{\alpha j} |j\rangle

where u_{\alpha j} = C_{\alpha j}/\sqrt{P_\alpha}, and where P_\alpha = \sum_j C^*_{\alpha j} C_{\alpha j}

So that means that, to an observer in state |\alpha\rangle, it appears that the wave function of the system has "collapsed" into the state |\psi_\alpha\rangle. But that is relative to a particular choice, \alpha for the basis states for the observer.

 

[Derek Potter]

http://motls.blogspot.com.br/2014/07/many-worlds-pseudoscience-again.html
This article took all my doubts, It's pseudoscience...(If It's not pseudoscience, it's not really science either)
and BTW, schrodinger's cat to me is too much misunderstood, there is no magic.. bgaede explained it very well on youtube, he shows how simple is this experiment..
Now I can move on.. no magic here, Universe remains the same, and there is only ONE universe. which is the one we live in!

Unfortunately the whole point of Schrodinger's Cat is not to prove that there are many worlds but to prove that quantum superposition cannot be equated to Heisenberg fuzziness. The experiment amplifies the superposition of the particle to a macroscopic cat. You can deny it as much as you like, the superposition is implied by the linear Schrodinger equation and can only be circumvented by suspending linear evolution -generally by invoking wavefunction collapse. So far no-one has suggested a credible way of detecting this (or the suggestions fail when put to the test) and it should therefore be relegated to metaphysics. IMNSHO. :)

 

[Derek Potter]

There is a basis issue, it seems to me, in Everett's relative state formulation of QM.
If you have a composite state |\Psi\rangle = \sum_{\alpha j} C_{\alpha j} |\alpha\rangle |j\rangle, where \alpha refers to states of the observer, and j refers to states of the system being observed, then we can define the "relative state" of the system relative to state |\alpha\rangle for the observer as follows:
|\psi_\alpha\rangle = \sum_j u_{\alpha j} |j\rangle
where u_{\alpha j} = C_{\alpha j}/\sqrt{P_\alpha}, and where P_\alpha = \sum_j C^*_{\alpha j} C_{\alpha j}
So that means that, to an observer in state |\alpha\rangle, it appears that the wave function of the system has "collapsed" into the state |\psi_\alpha. But that is relative to a particular choice, \alpha for the basis states for the observer.

Quite so. The resolution of the basis issue depends on how the choice of basis is made (psuedo-random, free-will, quantum etc) but I think I covered all, ummm, bases in post #389, didn't I?

 

[stevendaryl]

Quite so. The resolution of the basis issue depends on how the choice of basis is made (psuedo-random, free-will, quantum etc) but I think I covered all, ummm, bases in post #389, didn't I?

I don't think so. When you say "Alice measured spin in the z-direction and found it was spin-up", what does that mean? Why does a certain measurement count as "measuring spin in the z-direction"? What I think it means is that the detector is set up so that:

1. If the particle has spin-up in the z-direction, then the detector will enter some state |U\rangle
2. If the particle has spin-down in the z-direction, then the detector will enter some state |D\rangle

But from linear quantum mechanics, it would follow that:

1. If the particle has spin-up in the x-direction, then the detector will enter some state |\tilde{U}\rangle = \frac{1}{\sqrt{2}} |U\rangle + \frac{1}{\sqrt{2}} |D\rangle
2. If the particle has spin-down in the x-direction, then the detector will enter some state |\tilde{D}\rangle = \frac{1}{\sqrt{2}} |U\rangle - \frac{1}{\sqrt{2}} |D\rangle

So to say that the detector is measuring spin in the z-direction is to say that |U\rangle, |D\rangle is somehow a more appropriate basis for describing the detector than the basis |\tilde{U}\rangle, |\tilde{D}\rangle. So that's saying that the detector (or the detector + the rest of the universe) has a preferred basis.

 

[Quantumental]

New paper exposing just how messy the question of ontology and coherence is in the MWI view: http://arxiv.org/abs/1504.04835

 

[Derek Potter]

I don't think so. When you say "Alice measured spin in the z-direction and found it was spin-up", what does that mean? Why does a certain measurement count as "measuring spin in the z-direction"? What I think it means is that the detector is set up so that:

1. If the particle has spin-up in the z-direction, then the detector will enter some state |U\rangle
2. If the particle has spin-down in the z-direction, then the detector will enter some state |D\rangle

But from linear quantum mechanics, it would follow that:

1. If the particle has spin-up in the x-direction, then the detector will enter some state |\tilde{U}\rangle = \frac{1}{\sqrt{2}} |U\rangle + \frac{1}{\sqrt{2}} |D\rangle
2. If the particle has spin-down in the x-direction, then the detector will enter some state |\tilde{D}\rangle = \frac{1}{\sqrt{2}} |U\rangle - \frac{1}{\sqrt{2}} |D\rangle

So to say that the detector is measuring spin in the z-direction is to say that |U\rangle, |D\rangle is somehow a more appropriate basis for describing the detector than the basis |\tilde{U}\rangle, |\tilde{D}\rangle. So that's saying that the detector (or the detector + the rest of the universe) has a preferred basis.

That's not what preferred basis means! You are using the word "prefer" in the sense that a mathematician may prefer to cast a problem in a particular basis for simplicity's sake. In QM "preferred basis" means that nature appears to prefer a particular basis. We now understand this to be due to the fact that some states are unstable against decoherence so the preferred basis is simply one comprising stable pointer states.

 

[stevendaryl]

That's not what preferred basis means! You are using the word "prefer" in the sense that a mathematician may prefer to cast a problem in a particular basis for simplicity's sake. In QM "preferred basis" means that nature appears to prefer a particular basis. We now understand this to be due to the fact that some states are unstable against decoherence so the preferred basis is simply one comprising stable pointer states.

That is exactly the sense of "preferred" that I was using. That's the reason I objected to your claim that

"...decoherence...is not fundamental to MW. Everett's paper on relative states is perfectly clear - the worlds are different observer experiences. Decoherence does not come into it."

Decoherence comes into play in talking about what an observer experiences, or what a device measures. An observer can only be said to "observe" something if by interacting with it, he's put into a state that is stable against decoherence.

 

[Derek Potter]

Decoherence comes into play in talking about what an observer experiences, or what a device measures. An observer can only be said to "observe" something if by interacting with it, he's put into a state that is stable against decoherence.

I do not agree. Alice can measure the spin again, this time in the x-basis. In MW she enters a superposition of observed-x-spin states. The superposition decoheres. Nobody cares or notices. It is still a superposition and within each component state her record or memory of the observation doesn't change. The only stability-against-decoherence that matters is where the observation detects interference. Decoherence of the observer's state is neither here nor there. At least, that's the way I see it, I'm open to being corrected.

 

[stevendaryl]

I do not agree. Alice can measure the spin again, this time in the x-basis.

What does it MEAN to say that Alice is measuring the spin in the x-direction (or the z-direction)? All she's doing is interacting with the spin, whatever direction it's in. How can you tell, by looking at Alice, and her detector, what direction she's measuring the spin relative to?

 

[Derek Potter]

What does it MEAN to say that Alice is measuring the spin in the x-direction (or the z-direction)? All she's doing is interacting with the spin, whatever direction it's in. How can you tell, by looking at Alice, and her detector, what direction she's measuring the spin relative to?

She interacts with the spin by means of a magnetic field that deflects the electrons. So the direction of measurement is defined by the direction of the field - the field that she sets up in order to choose the direction.

 

[stevendaryl]

She interacts with the spin by means of a magnetic field that deflects the electrons. So the direction of measurement is defined by the direction of the field - the field that she sets up in order to choose the direction.

I think you're still missing the point. Abstractly, you have a system with two possible "result states": |L\rangle corresponding to the electron deflecting left, and |R\rangle, corresponding to the electron deflecting right. So you set things up so that

1. If the electron were originally spin-up in the z-direction, then the result state will be |L\rangle
2. If the electron were originally spin-down in the z-direction, then the result state will be |R\rangle

Then by saying that the setup is a way of measuring spin in the z-direction, you are saying that the basis |L\rangle, |R\rangle is a preferred basis for the system (as opposed to, say \frac{1}{2} (|L\rangle \pm |R\rangle). The exact same setup could be said to be measuring spins in the x-direction:

1. If the electron were originally spin-up in the x-direction, then the result state will be \frac{1}{2} (|L\rangle +|R\rangle)
2. If the electron were originally spin-up in the x-direction, then the result state will be \frac{1}{2} (|L\rangle - |R\rangle)

Now, there is a reason why |L\rangle, |R\rangle is a preferred basis, compared with \frac{1}{2} (|L\rangle \pm |R\rangle), but it has to do with decoherence.

 

[stevendaryl]

She interacts with the spin by means of a magnetic field that deflects the electrons. So the direction of measurement is defined by the direction of the field - the field that she sets up in order to choose the direction.

I don't quite understand where you're coming from. I assume that you are aware of the issue of the "pointer basis" for measurement devices. My understanding is that decoherence is ultimately the explanation for such a pointer basis.

http://dieumsnh.qfb.umich.mx/archivoshistoricosmq/ModernaHist/Zurek b.pdf

 

[lucas_]

To what extend or how long (in months or years?) does each branch of the Many worlds varies. Remember in one world (branch) the cat can be alive, in one world it is dead. So in one world/branch Saddam Hussein is alive, in one branch he is dead. So in the branch he is alive, there is no ISIS. In the branch he is dead, there is ISIS. So it's normal in many worlds for the world histories even to vary?

 

[TrickyDicky]

Now, there is a reason why |L\rangle, |R\rangle is a preferred basis, compared with \frac{1}{2} (|L\rangle \pm |R\rangle), but it has to do with decoherence.

My understanding is that decoherence is ultimately the explanation for such a pointer basis.

Decoherence is just a narative for preferred basis-pointer basis, it doesn't solve the issue. But what Derek Potter seems to be saying and I agree with him in this case is that there is no preferred basis problem for spin. As he said in #408 measurement of spin is always relative to the magnetic field direction arbitrarily chosen, and therefore is well describe by the action of Spin(3) on a complex 2-dimensional column spinor. The specific direction of the axis is not what matters, just its relative position wrt the magnetic field setup or a previous outcome of an entangled partner.
Since there are only 2 possible mutually exclusive outcomes as defined by the spinor , there cannot be a preferred basis, basis orthonormality is guaranteed unlike the general vector state case where the preferred basis is indeed a problem not solved by decoherence..

 

[Derek Potter]

But what Derek Potter seems to be saying and I agree with him in this case.

Glad you said "in this case" - you had me worried for a moment

 

[Derek Potter]

I don't quite understand where you're coming from. I assume that you are aware of the issue of the "pointer basis" for measurement devices. My understanding is that decoherence is ultimately the explanation for such a pointer basis.
http://dieumsnh.qfb.umich.mx/archivoshistoricosmq/ModernaHist/Zurek b.pdf

That is my understanding too. Decoherence plays the same role in MW as in a canonical collapse theory.

 

[Derek Potter]

To what extend or how long (in months or years?) does each branch of the Many worlds varies. Remember in one world (branch) the cat can be alive, in one world it is dead. So in one world/branch Saddam Hussein is alive, in one branch he is dead. So in the branch he is alive, there is no ISIS. In the branch he is dead, there is ISIS. So it's normal in many worlds for the world histories even to vary?

Yes. In fact, although many of the possible histories are extremely unlikely, most, if not all, occur at some non-zero amplitude and all (presumably) feel equally real to their inhabitants who all think theirs is the only world until they discover MW.

 

[lucas_]

Yes. In fact, although many of the possible histories are extremely unlikely, most, if not all, occur at some non-zero amplitude and all (presumably) feel equally real to their inhabitants who all think theirs is the only world until they discover MW.

Do you realize that proponents of Many Worlds like Sean Carrol and many physicists are indeed believing there are other parallel worlds with alternative histories where Al Gore won the election instead of Bush?? Don't you think this is exactly the stuff of science fiction? Come on Guys?!

 

[stevendaryl]

Do you realize that proponents of Many Worlds like Sean Carrol and many physicists are indeed believing there are other parallel worlds with alternative histories where Al Gore won the election instead of Bush?? Don't you think this is exactly the stuff of science fiction? Come on Guys?!

Well, it's a boring notion of parallel worlds, in that there is no travel between alternate worlds (nor trade, nor internet messages). The lesson of decoherence is that when two alternatives become macrosopically distinguishable, then they no longer have any effect on each other (for all practical purposes).

 

[stevendaryl]

To what extend or how long (in months or years?) does each branch of the Many worlds varies. Remember in one world (branch) the cat can be alive, in one world it is dead. So in one world/branch Saddam Hussein is alive, in one branch he is dead. So in the branch he is alive, there is no ISIS. In the branch he is dead, there is ISIS. So it's normal in many worlds for the world histories even to vary?

Once two alternatives become macroscopically distinguishable, then of course the histories from that point on become distinguishable, as well. In one alternative, Schrodinger writes in his diary "Fluffy died today. I told the kids that he ran away from home to join a cat circus", and in the other, he writes "'I'm so relieved that Fluffy survived that stupid experiment. I don't know how I would have explained it to the kids if he had died."

 

[Derek Potter]

Do you realize that proponents of Many Worlds like Sean Carrol and many physicists are indeed believing there are other parallel worlds with alternative histories where Al Gore won the election instead of Bush?? Don't you think this is exactly the stuff of science fiction? Come on Guys?!

There is a big difference between MW and science fiction. SF is by definition fiction, either changing the known laws of nature or else introducing hypothetical scenarios. MW, however, is simply vanilla QM (linear evolution) without additional hypotheses. Indeed, if QM is correct then MW is unavoidable except by the science fiction-like ploy of adding extra postulates such as wavefunction collapse. Since MW explains the appearence of collapse, any such additional postulates are redundant and tend to get in the way of the theory unless fine-tuned to have no observable effect. For example the hypothetical collapse might be placed, hypothetically of course, during or immediately after decoherence. This makes it untestable. It also guarantees it has no explanatory value.

 

[Derek Potter]

Well, it's a boring notion of parallel worlds, in that there is no travel between alternate worlds (nor trade, nor internet messages). The lesson of decoherence is that when two alternatives become macrosopically distinguishable, then they no longer have any effect on each other (for all practical purposes).

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, leaving the substates intact.