- #106
ShayanJ
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The Everett interpretation. But I think the current language in which we talk about it is a little misleading.
The state evolves with a unitary transformation ##\hat{C}(t)## obeyingstevendaryl said:Quantum mechanics violates either locality or separability in the above sense. This is shown by the EPR experiment. If Alice and Bob are in regions that are far removed from each other spatially, the evolution of the state of Alice's region depends on what happens in Bob's region.
vanhees71 said:The state evolves with a unitary transformation ##\hat{C}(t)## obeying
$$\mathrm{i} \dot{\hat{C}}=\hat{H}_1 \hat{C},$$
and the operators describing observables by one obeying
$$\mathrm{i} \dot{\hat{A}}=-\hat{H}_2 \hat{A},$$
where ##\hat{H}_1+\hat{H}_2=\hat{H}## is the Hamiltonian of the system. The split of ##\hat{H}## in two arbitrary self-adjoint operators ##\hat{H}_1## and ##\hat{H}_2## doesn't change anything in the physical predictions (probabilties for the outcome of measurements). It just defines the "picture of time evolution".
Can you specify what you mean by the last sentence? Are you referring to the partial traces, defining the states of the part of the system measured by Alice or Bob, respectively?
If yes, then of course you are right in a specific sense, and it also immediately follows that what's violated is separability and not locality (in the case of local relativistic QFTs) since the time evolution by construction (Hamilton density depends only on one space-time point and the microcausality property is fulilled for all local observables).
vanhees71 said:If yes, then of course you are right in a specific sense, and it also immediately follows that what's violated is separability and not locality.
(emphasis mine). Now you say yourself that this makes no sensestevendaryl said:If Alice and Bob are in regions that are far removed from each other spatially, the evolution of the state of Alice's region depends on what happens in Bob's region.
You are right as long as you don't specify what you mean by that, and it makes some sense, when you consider the standard example with an entangled photon pair, where A and B measure one of the two photons each, and the single-photon states are given by partial tracing the state over the other photon.stevendaryl said:You can't talk about the quantum state of a single region of space.
stevendaryl said:Suppose we have an anti-correlated twin pair, and Alice and Bob are each measuring particle spin along the z-axis. Let's suppose that Bob performed his measurement before Alice (but close enough that there is no possibility for light to travel from Bob to Alice before Alice performs her measurement). Then whether Alice gets spin-up depends on whether Bob got spin-up or spin-down.
vanhees71 said:For a local relavistic QFT you have locality of the interactions (as defined above) but inseparability due to entanglement.
Are you making a distinction between prediction and expectation?stevendaryl said:Now, we're trying to predict the state of ##A## at time ##t+\Delta t##. If the world is separable and local, then we don't need to check on the state of ##B, BN## or ##C## to make a prediction about the state of ##A##.
Fra said:Are you making a distinction between prediction and expectation?
In the Qbist and similar perspectives, the local agent (Alice) does not have any other choice but to form the expectation from available information.
/Fredrik
You have to specify what you mean by local, and a local relativistic QFT is local in a specific sense (Hamilton density a polynomial of the field operators and their derviatives at one space-time point and microcausality property for all local observables) and "non-local" in the same sense as any QT, and I think it's a good solution of the problem to specify the different sense of locality used here by calling the latter type "inseparability". Einstein made very clear that his quibbles with QT refer to "inseparability" and not so much on "non-locality".stevendaryl said:Yes, and in that sense, QFT is not local.
vanhees71 said:You have to specify what you mean by local
Yes, there is no objective state in Qbism. Also there locality follows from the construction, since any comparasions or is made on the information at hand of the local agent . This means any "external information", such as a phone call from Bob, has to be communicated to Alice first. And this communication is treated just like any other "measurement".stevendaryl said:I don't completely understand what the Qbist perspective is, but I don't think that there is any objective state of the universe in a Qbist interpretation. So it's not clear what locality means without a notion of state.
vanhees71 said:Einstein made very clear that his quibbles with QT refer to "inseparability" and not so much on "non-locality".
stevendaryl said:Now, we're trying to predict the state of ##A## at time ##t+\Delta t##. If the world is separable and local, then we don't need to check on the state of ##B, BN## or ##C## to make a prediction about the state of ##A##.
PeterDonis said:You appear to be using a different definition than the "appropriate" one I just referred to; your apparent definition seems to be saying that, since knowing B's measurement result gives us additional information about the probabilities for A's measurement result, we need to "check on the state" of B in order to make a prediction about the state of A. However, by this definition, it is equally true that we need to check on the state of A in order to make a prediction about the state of B. But those two claims, combined, would put us into a never-ending circle of checking on B to check on A to check on B to check on A to...
This is not an interpretation.StevieTNZ said:I trust in the consciousness causes 'collapse' (regardless if its physical or not) interpretation.
stevendaryl said:it just means that the evolution of the global state does not "factor" into evolution of local states
stevendaryl said:a very simple discrete-time cellular automaton analogy
PeterDonis said:This only makes sense if there is a "global state". It is not clear that there is one consistent with relativistic invariance.
This is not a valid analogy because the corresponding things in the QM case are regions of spacetime. Regions of spacetime don't "update" from one "time" to the "next". They just are. And the "neighbor" connections between them are one-way causal relations, not two-way "neighbor" relations.
stevendaryl said:Relativistic invariance doesn't prevent there from being a global state. The state would be frame-dependent, but I don't think that's a problem.
stevendaryl said:The state would be frame-dependent, but I don't think that's a problem.
stevendaryl said:For example, in flat spacetime, the classical (relativistic, but non-quantum) global state at time ##t## according to a Cartesian coordinate system ##(x,y,z,t)## would be provided by giving the values of ##\vec{E}## and ##\vec{B}## at each point ##(x,y,z)## at time ##t##, and the positions and locations of each particle at time ##t##.
stevendaryl said:Pick a "patch" of spacetime for which we can set up an inertial cartesian coordinate system ##(x,y,z,t)##. You split space up into boxes with dimensions ##\Delta x, \Delta y, \Delta z##. The state of one box at time ##t+\Delta t## depends on the state of that box and neighboring boxes at time ##t## (where "neighboring" means that some points in the neighboring box is less than or equal to ##c \Delta t##).
PeterDonis said:Again, this is not a valid analogy because your ##A##, ##AN##, ##C##, ##BN##, ##B## are not "boxes" in space, they are regions of spacetime. It makes no sense to talk about "updating the state" of a region of spacetime from one time to the next.
PeterDonis said:I don't see how it wouldn't be a problem, since "frame-dependent" is inconsistent with "relativistically invariant".
stevendaryl said:The cells correspond to regions in SPACE, not regions in SPACETIME.
stevendaryl said:Why does it matter if the notion of "state" is relativistically invariant, or not?
stevendaryl said:The point is simply that the "state" of any small region of space at time ##t + \Delta t## depends only the state of neighboring regions at time ##t## (where "neighboring" means the distance is less than ##c \Delta t##).
PeterDonis said:it doesn't seem like you actually need that notion of "state". Your "states" are really just "events" in spacetime (where "event" has the non-strict interpretation described in my previous paragraph), and you are simply saying that some states don't depend only on other states in their past light cones.
stevendaryl said:to understand what's going on in a small region, we need only consider that region and neighboring regions. QFT is not local in that sense.
PeterDonis said:Also, what, exactly, is supposed to "depend" on states not in the past light cone? It can't be just the A and B measurement results by themselves; the probabilities for each of those are dependent only on states in their past light cones. Only the statistical correlation between them can't be factorized, as above.
stevendaryl said:laws for the evolution of the global state
PeterDonis said:If the laws of physics are relativistically invariant, then there can't be any such "laws for evolution of the global state", since the global state is not relativistically invariant.
stevendaryl said:That is not true. I gave you a counterexample. If we define the "global state" to be the values of ##\vec{E}## and ##\vec{B}## at every point in space, together with the locations and positions of all particles, then classical relativistic theory gives you the evolution law for such a global state.
PeterDonis said:The evolution law you refer to, Maxwell's Equations, is not global, it's local.
stevendaryl said:The evolution of the global state factors into evolution equations in which the evolution of the local state only depends on nearby conditions.
PeterDonis said:I see what you are saying, and I don't think we disagree on the physics. I just don't think this way of describing it in ordinary language is useful; I think it's likely to cause more confusion than it solves.
stevendaryl said:The whole point is to say the sense in which classical electrodynamics is a local theory, but QM with entangled particles is NOT.
stevendaryl said:The whole point is to say the sense in which classical electrodynamics is a local theory, but QM with entangled particles is NOT.
stevendaryl said:Some people say that we should interpret "local" to mean the impossibility of FTL communication.