You are right that these are just "words", in the sense that their meaning is not defined precisely. Indeed, this is why MWI is a branch of philosophy of physics, and not a branch of mathematical physics. But I don't think that it makes it completely useless. Many important aspects of human life cannot be precisely defined (e.g. emotions or ethics), but any insight on them can be very useful.martinbn said:But this is just quantum mechanics. The interpretation is supposed to say what a world is and what it means for them to be thought as separate.
It seems that these are just words, which are useless and misleading.
vanhees71 said:We should clarify this point, because I think it's wrong what you claim. The collapse in the usual meaning of textbooks claims that the interaction of the measured system with the measurement device (a local interaction according to local relativistic QFT) acts instantaneously over the entire space, which is contradicting itself, because that would mean the interaction is not local. In the mathematical foundations, however it is built in that the interaction is local. So collapse cannot be part of relativistic local QFT.
Demystifier said:So neither space behind cosmological horizon of GR nor other worlds of MWI are physical. Yet, somehow you feel that space behind horizon is more "acceptable" than other worlds of MWI. Still, you cannot explain why exactly do you feel so. Am I right?
Demystifier said:You are right that these are just "words", in the sense that their meaning is not defined precisely. Indeed, this is why MWI is a branch of philosophy of physics, and not a branch of mathematical physics. But I don't think that it makes it completely useless. Many important aspects of human life cannot be precisely defined (e.g. emotions or ethics), but any insight on them can be very useful.
A similar idea has been brilliantly expressed by (my avatar) Bertrand Russell:
"Physics is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover."
If you want to use Schrödinger equation, you must live with the fact that it predicts unobservable parts of wave function, because there is decoherence. There is nothing speculative or vague about that.vanhees71 said:If I want to use GR I must live with the fact that it predicts unobservable parts of spacetime, because there are horizons.
Demystifier said:If you want to use Schrödinger equation, you must live with the fact that it predicts unobservable parts of wave function, because there is decoherence. There is nothing speculative or vague about that.
vanhees71 said:But it's a contradiction to the very foundations! So how can it be acceptable at all?
I mean unobservable after the update of the probability distribution.vanhees71 said:What do you mean by "unobservable parts of wave function"? ##|\psi|^2## is the probability distribution for the position of the particle, and that's measurable by preparing an ensemble and detecting particles as a function of position. I think our discussion becomes weirder and weirder... :-(.
Then I have a new probability distribution according to a new state-preparation procedure. So what?Demystifier said:I mean unobservable after the update of the probability distribution.
vanhees71 said:QFT, as it is formulated and used on the Standard Model, realizes the "no faster than light signalling" by the (probably) stronger assumption of local interactions, and I'm discussing this standard flavor of relativistic QFT. I'm not aware of any alternative successful formulation of relativistic QT. Are you denying that particles interact? Why then does the Standard Model work better than many HEP people like?
Likewise, I can "cut out" the space behind the horizon and get a new spacetime. So what?vanhees71 said:Then I have a new probability distribution according to a new state-preparation procedure. So what?
Demystifier said:Likewise, I can "cut out" the space behind the horizon and get a new spacetime. So what?
In the spacetime case, the cutting is not described by Einstein equation. In the probability distribution case, the transition from the old to the new probability distribution is not described by the Schrödinger equation. So what?
The meaning is in the eyes of the beholder. (For instance, I know people who will say that category theory doesn't carry any additional meaning. Or those who will say that transfinite numbers don't carry any additional meaning.)martinbn said:When I said useless I meant useless because they don't carry any additional meaning.
Yes.martinbn said:It seems that a world is a summand in a certain representation of the wave function, perhaps associated to a basis. And separate means that they are orthogonal (or nearly so). That is just substituting words.
You missed the crucial meta-physical assumption of MWI that there is only wave function and nothing but the wave function. If that assumption is correct, then all other objects we observe (tables, chairs, galaxies, space, time) must be a part of the wave function. The collection of all objects that we can observe is called "the world". But wave function contains separated parts which we cannot observe, so it makes sense to call them "other worlds".martinbn said:I thought that each "world", when separate, comes with their own space and time, hence the choice of the word. Otherwise why not call it terms or something like that.
Here you tacitly assume that the particle (just like galaxy) exists all the time, and has some position at any time, despite the fact that the position is not measured at all times. But this is a hidden-variable assumption, and Bell theorem implies that such an assumption implies action at a distance. One of the motivations for MWI is to avoid action at a distance.martinbn said:But you can see galaxies disappear behind the horizon. If the there is no space-time there, it means that matter must vanish. It is not the same with the wave function. If a particle goes through a Stern-Gerlach apparatus, there is just one particle, it is found either up or down. And if it is found up, nothing went down. So, saying that the "world" in which it is down doesn't exist is very different from saying that nothing beyond the horizon exists.
That is very different. If you use a new word for something that already has a name, what new does this bring? Except, of course, possible confusion. You agreed that terms and orthogonal is fine, then worlds and separate is useless. That's what I meant by useless.Demystifier said:The meaning is in the eyes of the beholder. (For instance, I know people who will say that category theory doesn't carry any additional meaning. Or those who will say that transfinite numbers don't carry any additional meaning.)
You missed the crucial meta-physical assumption of MWI that there is only wave function and nothing but the wave function. If that assumption is correct, then all other objects we observe (tables, chairs, galaxies, space, time) must be a part of the wave function. The collection of all objects that we can observe is called "the world". But wave function contains separated parts which we cannot observe, so it makes sense to call them "other worlds".
Demystifier said:Here you tacitly assume that the particle (just like galaxy) exists all the time, and has some position at any time, despite the fact that the position is not measured at all times. But this is a hidden-variable assumption, and Bell theorem implies that such an assumption implies action at a distance. One of the motivations for MWI is to avoid action at a distance.
1. A model that is using only local interactions can not model correct statistics for entangled particle measurements.vanhees71 said:QFT, as it is formulated and used on the Standard Model, realizes the "no faster than light signalling" by the (probably) stronger assumption of local interactions
vanhees71 said:This is nonsense. QED is modelling all the quantum optical experiments with entangled photon pairs correctly, and that's the paradigmatic example of a local relativistic QFT! You must not mix up local interactions (a basic assumption of relativstic QFT) and long-ranged correlations described by entangled states. The latter are of course possible in QFT. What all this has to do with active vs. passive (Poincare?) transformations, I don't know.
Can you give reference to example of QED model for polarization entangled photon measurements at different measurement angles?vanhees71 said:QED is modelling all the quantum optical experiments with entangled photon pairs correctly, and that's the paradigmatic example of a local relativistic QFT!
rubi said:I think vanhees is right about the incompatibility of the collapse with relativity. However, it's not because of locality, but rather because of the incompatibility with the Poincare group. There is an interplay between time evolution, translations, rotations and boosts, which is encoded in the Poincare group relations and its Lie algebra. In quantum theory, compatibility with relativity is guaranteed by the use of unitary representations of the (centrally extended universal cover of the) Poincare group. If you claim that collapse is compatible with relativity, you must explain in what sense it is supposed to satisfy the Poincare group relations (representation theory won't work, since it is a non-linear operation) and then show that it actually satisfies them. I don't think anyone has done this and I don't see how it is supposed to work. For example, in the Poincare group, two time evolutions always commute, but projectors of non-commuting observables don't commute in general. How do you resolve this issue? Another example: There is a Poincare group element corresponding to a time translation followed by a Lorentz boost. What is the Poincare group element corresponding to a collapse followed by a boost?
Yes.martinbn said:Ok, those other worlds, do they have things that could be observed (tables, chairs, galaxies, space, time)? It seems that the answer must be yes.
Ah, by space and time you mean a 4-dimensional manifold, right? Well, that space and time is not shared and not in the domain D. The shared space and time in D has much more dimensions. In the simplest description this number of dimensions is 3N+1, where N is at least of the order of ##10^{80}##.martinbn said:So, do they come with their own space and time? Or are the space and time shared? Since there is just one wave function it must be that space and time are unique, they are the domain of the wave function. But in my world, where I can observe things, I have access to all of space and I observe things only in some places (say a particle whent up). The other worlds will have observers that observe other things elsewhere (a particle went down). Yet, it there is just one space where all this happens.
It should also be pointed out that motion faster than light is not in contradiction with relativity (unless some additional assumptions are taken). See e.g.atyy said:Well, why don't you show that collapse is not compatible with relativity? While I know of know proof that it is, all particular cases I know of show that it relativity is not violated, eg. http://arxiv.org/abs/0706.1232
Then there must be some other assumption you are tacitly taking. I am not sure what it is, so please explain to me in your own words: What exactly do you mean by "particle" and how exactly is it related to the "wave function"? From that I will probably know why MWI does not make sense to you and which of your assumptions should be questioned in order to make sense of MWI. (Unless you already decided that MWI does not make sense, in which case there is no point in bothering.)martinbn said:No, I only assume that at one given moment of time(when detected) the particle can exists at one place only.
You are the one who claims that collapse is compatible with relativity, so you are obliged to prove it. What are your answers to the questions I askes in my previous post? How can collapse be compatible with relativity despite non-commutativity of projections?atyy said:Well, why don't you show that collapse is not compatible with relativity?
Your paper addresses some paradoxes, but it doesn't prove the compatibility. Compatibility with relativity means that full Poincare symmetry is somehow implemented. If this can be done, then you should be able to answer the two questions that I askes in my previous post. Moreover, I'd like to see the mathematical implementation of the Poincare group.While I know of know proof that it is, all particular cases I know of show that it relativity is not violated, eg. http://arxiv.org/abs/0706.1232
You keep repeating your personal theories that aren't in accordance with accepted science. If PF were serious about its rules, you should have been banned by now. QM is fully compatible with locality. One can embedd the QM probabilities in a local classical probabilistic model (https://arxiv.org/abs/1412.6987), so the compatibility with locality is established at full rigor.zonde said:1. A model that is using only local interactions can not model correct statistics for entangled particle measurements.
2. A model that can model correct statistics for entangled particle measurements has to involve non-local interactions.
This follows from Bell theorem and other similar theorems or counter examples.
I have impression that QFT corresponds to the second case. I don't know why you believe there is nothing non-local in QFT but I suppose that you are imagining that it's possible to arrive at correct statistics for entangled particle measurements using only passive transformations of any non-local element of QFT (state in Fock space) while it actually requires active transformations.