Is QM Inherently Non-local?

Sherlock

Does Special Relativity qualify?

vanesch

I don't understand this: A and B are time-like connected (A is in the past lightcone of B). C and B are time-like connected (C is in the future lightcone of B). How the hell can A and C then not be time-like connected ??
Imagine a material particle travelling from A to B (is possible: timelike), and have it then travel from B to C (is possible: timelike). So overall, a material particle travelled from A to C, no ?

Careful

Look Vanesh, A,B and C are spacetime REGIONS, you cannot speak about measurement theory for points since field operators are distributional, you need to smear it out by test functions (independently of this mathematical worry, locality in QFT must obviously also hold for observables living on such extended regions). I said that : A is in the past of B, this does not imply that B is in the future of A (this is however obviously true for points though). Moreover, sorry that I say this, it is a travesty to think that particles are points in QFT. To make everything crystal clear: I am not saying that it is impossible to construct a measurement theory which is consistent (although I am pretty much convinced it is impossible indeed), but it does not exist yet to my knowledge. Therefore, saying that superluminal signalling is excluded is unfounded.

Careful

Sorry, but you should better study QFT first before you make such comments... I am trying to raise a serious issue here: that is the lack of a consistent measurement theory for QFT which is compatible with the demands of special relativity.

DrChinese

Wow, you should consider starting a thread on this (as opposed to hijacking an existing one).

Sherlock

No offense intended. I saw your smily and thought I'd match it.

So there's no mathematically rigorous and consistent measurement theory for QFT in line with one of its principal components, SR -- and the possibility of superluminality in Nature can't be definitively ruled out. Ok.

Nothing said in this thread is ruling out the *possibility* of superluminality in Nature, afaik. However, the consensus seems to be that the considerations that go into considering whether to refer to QM as inherently non-local do not necessitate the assumption that there *is* superluminality in Nature either.

The problem of developing a consistent measurement theory for QFT which is compatible with the demands of special relativity is a problem for another thread. And I promise that I'll just sit back and watch that one.

As for the topic of this thread, I take it that you would consider quantum theory to be inherently non-local. Maybe one might say that it's kinematically, but not dynamically, non-local. But I think that such statements confuse the issue. The bases of quantum theory are local. It neither predicts ftl phenomena, nor does its formalism imply ftl phenomena.
Its principles do prohibit tracking the continuous evolution of quantum phenomena, thereby prohibiting hidden variable theories of the sort that would allow an explicitly local description of the phenomena responsible for the inequality-violating results of Bell tests.

Careful

Sorry this issue is relevant !! You cannot claim that QFT forbids signalling faster than with the speed of light when you do not have an appropriate measurement theory. Instead of being so defensive, look at it as a challenge : you should solve the problem, not me, I am convinced it is a waste of time anyway. If, on the other hand, you might surprise me, then I shall praise you.

Careful

HUH ????? You are claiming for some time now that you *cannot* signal faster than with the speed of light and now you say that it does not matter or that it violates it kinematically while a measurement process is clearly dynamical. Do you know the mathematical foundations of logic?

DrChinese

1. By that standard, we don't need threads at all. Everything in this subforum relates to QFT in SOME way.

2. Why would you ask me or any other person to expend effort for something you consider a waste of time?

Sherlock

The assumption that Nature obeys the principle of locality hasn't been falsified. Has it? Where did I say that it doesn't matter? The point is that, as far as is known, there are no superluminal phenomena in Nature. That doesn't mean that it's impossible for such phenomena to exist, does it? How would we know for sure?

That quantum theory is kinematically, but not dynamically, non-local is from something I read by H.D. Zeh.

Hurkyl

Careful:

I understand that the axioms of Algebraic Quantum Field Theory are derivable from doing things the ordinary way, and it's manifestly evident that in AQFT, that any space-like separated operators commute.

Careful

This is obvious and not the issue (I suspect you have to be careful when you take products of field operators and so on). What I say, is that this is not sufficient (while it is clearly sufficient in the case of two measurements). Check out the Sorkin 1994 paper. impossible measurements on quantum fields. THINK about it before you reply; I notice that Vanesh is thinking (or he is just absent for some reason, just noticed he was thinking).

Careful

Because YOU think QFT is a worthwile enterprise while I have a dozen of other reasons to dispose of it. Look, I am not saying that on this forum, research problems should be solved, but at least we should make the effort in trying to ask the right questions. If you take the Wightman axioms as true, then you need to develop a consistent measurement theory. Vanesh, a few mails ago, said that QM poses us with a riddle and started to argue why we should talk about the different options. Hereby, he assumed that it is a FACT that the Wightman axioms imply that no signalling faster than with the speed of light is possible (which is the crucial assumption for what follows in the entire conversation) without caring for an accurate measurement theory. Now, I transported the Copenhagen scheme to QFT and showed that this cannot be right. So you need to do better and I do not believe such effort it is meaningful in the end. If you would tell an engeneer for example that correlations beyond the lightcone exist in your theory, but you cannot measure them ,then he would mock you and say that your measurement apparatus sucks.

Careful

No, this assumption has not been fasfied by EXPERIMENT (although this is a very delicate issue and another piece of conversation). The question is whether your THEORY allows for processes FTL and that is NOT known for the moment. We never know for sure if processes FTL exist or not, but if this would be the case then we can forget about relativity and go back to eather theories. I must confess I BELIEVE that this cannot be, since it would be impossible for the justice departement to convict anyone of murder (he could argue that the person in question were killed in a tachyon crime commited by a third person in the future of the event itself). You can find this example in John Bell's book: no, the causality axiom is certainly more holy than anything else (this is certainly also the concensus although I do not like to use such arguments). You should not repeat what doctors write in books and realise that in research, there are many conflicting ideas written by equally qualified doctors. THINK for yourself, that is what Sherlock did, he was not a doctor but much sharper than dr. Watson however.

vanesch

Ah, so, if you allow me, we can in fact do things with A and C events (or small regions) and B an extended region somewhere in between, such that a part of B is in the future lightcone of A and a disjoint part of B is in the past lightcone of C.
Defining some observable a,b and c on each of these regions, we can then state:
[a,c] = 0
[a,b] is not 0
[b,c] is not 0
This case is in fact handled in "Modern Quantum Mechanics" by JJ Sakurai (p 33): the correlation between a and c is dependent on whether the b measurement is performed or not.
But, but: here our situation is subtly different:
the correlation of a and c IS NOT AVAILABLE to C because C is outside of the future lightcone of A. So what is only available to C is the REDUCED density matrix of the state, tracing out A and B (B also, because the result of B, being a region, is only available to an event which has the ENTIRE B in its past lightcone, let us call this event B', and B' must necessarily be outside the past lightcone of C). This is one of the reasons why it is in fact not necessary to consider extended regions, because their result of measurement can only become available at an event that has the ENTIRE region in its past lightcone (so only at that point one can say one has "performed the measurement" - if one insists on using the von Neumann picture ; me being an MWI-er, I insist on keeping everything unitary!).
Let us apply von Neumann's measurement scheme:
So you seem to claim that performing the measurement at a, or not, when the B measurement is performed, changes the outcomes of C ?
Let us take an initial state |psi> which is u|a+> + v|a->, |a+> and |a-> being the two eigenstates of A (and also of C, since they commute).
Now, if we perform the measurement at A, we have, with probability u^2, |a+> and with probability v^2, |a->
Now, if we perform the B measurement in the first case, we get, with probability
u^2 |(b+|a+)|^2 + v^2 |(b+|a-)|^2 the state |b+>
with probability u^2 |(b-|a+)|^2 + v^2 |(b-|a-)|^2 the state |b->
When C now performs its measurement (which is the same as A), we obtain:
with probability P_c(a+) =
(u^2 |(b+|a+)|^2 + v^2 |(b+|a-)|^2) |(a+|b+)|^2
+
(u^2 |(b-|a+)|^2 + v^2 |(b-|a-)|^2 ) |(a+|b-)|^2
the state |a+> (that will do, a- will be complementary).
On the other hand, if A does NOT perform his measurement, we have, for the B measurement:
|u(b+|a+) + v(b+|a-)|^2 probability to have b+ and
|u(b-|a+) + v(b-|a-)|^2 probability to have b-.
After C performs then his measurement, we have the probability at C to measure a+:
|u(b+|a+) + v(b+|a-)|^2 |(a+|b+)|^2 + |u(b-|a+) + v(b-|a-)|^2 |(a+|b-)|^2
The difference between both approaches (with A measurement and without A measurement) is then (we take u and v real):
Diff = u v ( (b+|a+) (a-|b+) + (a+|b+) (b+|a-) ) |(a+|b+)|^2
+ u v ( (b-|a+) (a-|b-) + (a+|b-)(b-|a-)) |(a+|b-)|^2
Writing this with U the unitary transformation matrix between the a set and the b set, we rewrite this as:
Diff = u v (U11 U11* U11 U21* + U12* U22 U12 U12* + CC)
If a is not to signal to c, this difference should vanish. Now, let us take that the basis transformation between the a set and the b set is unitary and unimodular (choice of overall phase):
U11 = x
U22 = x*
U12 = y
U21 = - y*
Now, after working this out I obtain:
Diff = u v (-x* x + y* y) (x y + x* y*)
which is, to my great surprise, not zero. I suspect I made an error somewhere...

vanesch

I checked my calculation and I don't seem to find an error.
If this is true, this is amazing:
We have an initial state |psi> to which a can, or can not, apply a measurement (decision of a).
b applies always his/her measurement.
c applies the measurement (which is the same, or compatible, with the one done by a) and looks at the probability to get a certain result.
This probability (of c) seems to depend on whether a decided to measure or not (and NOT on the outcome of a), although a and c are spacelike connected points, which would mean that there is a FTL phone from a to c (a can decide, or not, to measure A, and c sees his probabilities change).
I admit being puzzled. There must be some quirk I didn't get.
I suppose that the trick is the spread of the B measurement, which can only be completed at an event which has the entire B section in its past lightcone (probably von Neumann's projection should only apply at that moment - at least, only at that moment I could entangle, in an MWI view, a local observer with the system according to the B measurement), and that this B measurement then doesn't occur BEFORE C.
But I admit, again, to be puzzled !
cheers,
Patrick.

Tez

I simply dont understand what you mean. Are you intimating that our captors cannot make a local, independent random choice as to which question to ask, and that therefore the particles can know before they're seperated which question/measurement is going to come up? THis is the standard "no free will" loophole to Bell tests. And what is the "normal interpretation of a Bell test"?.

In case it wasn't clear, what I described is not an allegory - the game could be played by real prisoners and captors, and presuming the prisonors can carry concealed entangled particles and stern gerlach appartuses(!) their probability of being released goes up to 85%. And no, it doesn't allow for superluminal communication between the two prisoners, but it certainly would seem to require superluminal communication between the particles in order to achieve.

If you really don't see an issue with this, then perhaps you can outline how your understanding could help one tackle the question of why the probability of being released doesnt go up to 100%?