Is QM Inherently Non-local?

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vanesch said:
Well, the problem is that if you take quantum theory seriously, that's exactly what happens: your detector IS in two "mutually exclusive states" at the same time. That's what unitary evolution dictates, and it is the very founding principle of quantum mechanics.
This is called the superposition principle, and it is exactly the same principle that says that an electron in a hydrogen atom is both above and below the nucleus, and to the left and to the right of it, which are also "classically mutually exclusive states". This is exactly what the wavefunction is supposed to mean: the electron is in the state ABOVE the nucleus, is ALSO to the left of it, is ALSO to the right of it, and is ALSO below it, with the amplitudes given by the value of the wavefunction.
A quantum particle that impinges on a screen with several holes goes through the first hole, and ALSO goes through the second hole, and ALSO goes through the third hole.
And if you take this principle seriously all the way (that's what MWI does) then your particle detector SAW the particle, and DIDN'T see the particle. So on the display of the detector it is written "CLICK" AND it is written also "NO CLICK". And if you look at it, your eyes will BOTH see "click" and "no click". And your brain will BOTH register the information of the fact that your eyes saw "click" and that your eyes DIDN'T see click.
Only... you are only consciously aware of ONE of these possibilities.
Interference and the production of wave packets require the principle of linear superposition. Quantum theory is concerned with interference at the sub-microscopic level -- the level of interaction of the quantum disturbances themselves (including measuring device quanta). There is some relation to the physical reality of this level in QM's wave equation and wave functions wrt phases, phase relations, and amplitudes. It seems pretty certain that the details aren't in one to one correspondence with the physical reality of the sub-microscopic phenomena. Anyway, in order to say anything unambiguous about the quantum realm it's necessary to have these phenomena interact with macroscopic instruments.

The recorded (at a certain time) position of a particle at some location, or that a cat is alive (or dead) is unambiguous (and necessarily thermodynamically irreversible for the consistency of quantum theory). Afaik, quantum theory doesn't say that a detecting screen will detect an individual quantum in two different locations, or that a cat will be found to be both alive and dead. Measurement results are well defined values. Of course, in any set of many measurements of an identically prepared system, a detecting screen will have detected in many different locations, and the cat(s) will sometimes be alive and sometimes dead after a certain delta t from the opening of the radioactive material's enclosure.

vanesch said:
*IF* quantum theory as we know it applies to all the particles and interactions in this scheme (the atoms of the detector, of your eyes, of your brain etc...) then there is no escaping this conclusion. This is due to the fact that *ALL* interactions we know (electroweak, strong, except for gravity), are, as far as we know in current quantum theory, described by a UNITARY EVOLUTION OPERATOR.
So what are the ways out of this riddle ?
1) this is indeed what happens, and for some strange (?) reason, we are only aware of one of the states. This is the picture I'm advocating - unless we've good indications of the other possibilities.
2) this unitary evolution is a very good approximation which is in fact, slightly non-linear. this can be a minor modification to QM, or this can be just an indication that QM is a good effective theory for something totally different.
3) we've not yet included gravity. Maybe gravity will NOT be described by a unitary evolution operator.
4) there's maybe another interaction that spoils the strictly unitary evolution
5) somehow the act of observation (what's that ?) is a physical process that acts upon the wavefunction (that's the von Neumann view: but WHAT PHYSICS is this act of observation then ?) and reduces the state of whatever you're "observing".
I prefer number 5. The physics of the measurement process depends in part on the hardware that's doing the measuring, doesn't it? The wave equation for a free particle is different than for one that is interacting with some measuring device.
In the S-cat scenario, the measuring device includes whatever an emitted quantum disturbance interacts with that eventually amplifies the quantum disturbance and frees the poisonous gas, the poisonous gas itself, and the cat. The cat is the "pointer" or "clicker" of the device.

There is a problem in that quantum measurement processes are essentially uncontrollable and unpredictable. In the process of measuring the quantum disturbance, definite phase relations are destroyed, and the wavelike object that has been evolving unitarily is transformed into a particle-like object which eventually manifests macroscopically as a well defined value.

The problem doesn't really have to do with why we don't see the S-cat alive and dead, or a quantum particle here and there as a singular outcome of an individual measurement. It has to do with the fact that we can't see what's happening at the sub-microscopic level of the quantum disturbance itself.
 
  • #227
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Quote:
Originally Posted by Sherlock
Isn't Bell's general formulation for local realistic theories an exact definition?
P(a,b) = integral d lambda rho(lambda) A(a,lambda) B(b,lambda)
DrChinese said:
That is the separability requirement, also often referred to as "Bell Locality". It is also sometimes called "factorizability" which may or may not be the same thing, depending on your exact definition. Separability is sometimes defined as the following, where A and B are the two systems:

1) Each [system] possesses its own, distinct physical state.
2) The joint state of the two systems is wholly determined by these separate states.

But that does not include the "realistic" requirement which I call "Bell Reality". It is the requirement that there are values for observables which could have been measured alternately. "It follows that c is another unit vector..." from Bell, just after his (14). If you don't insert this assumption into the mix, there is no Bell Theorem.
That (realism) assumption is embodied in Bell's general lhv formulation (via the inclusion of lambda) isn't it?

Bell's locality requirement is based on the assumption that the statistics of two spacelike separated sets of detection events must be independent. But that assumption is wrong, because the statistics produced by two opposite-moving disturbances emitted by the same atom during the same transitional process and analyzed by a common measurement operator are going to be related.

Local realism seems to be disallowed for quantum theories, but locality as far as Nature is concerned isn't ruled out.
 
  • #228
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Bell, as the originator of these ideas, didn't disambiguate them. But since they turned out to be so very important a number of sharp thinkers have pondered them deeply and come up with the formulation Dr. Chinese sets forth.

It doesn't seem to me to be constructive to go back now and reassert Bell's original formulation as if it were some tablet of the Law handed down from on high. Ideas develop, even the ideas of great men.
 
  • #229
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Sherlock said:
Bell's locality requirement is based on the assumption that the statistics of two spacelike separated sets of detection events must be independent. But that assumption is wrong, because the statistics produced by two opposite-moving disturbances emitted by the same atom during the same transitional process and analyzed by a common measurement operator are going to be related.
This is something that you can see for yourself is quite different from the "Bell Reality" requirement. If you begin with Bell Locality (separability) as an assumption alone (and there is no unit vector c), you never get to Bell's Theorem as a conclusion. In fact, nothing at all strange happens except that you come to the conclusion that QM violates this (this is the point which ttn has made). You will NOT come to the conclusion that local realistic theories must respect Bell's Inequality. That is because the Inequality absolutely depends on the existence of the Bell Reality assumption.

What is not clear to me - and I know what Bell says - is whether or not the Bell Locality requirement is also necessary to arrive at Bell's Inequality. I think that it might be more accurate to say that parameter independence (PI) is a requirement but not outcome independence (OI) - where PI+OI=Bell Locality. Sure, it is in the proof and conventional wisdom is that it is a requirement. (And everyone knows how I feel about convention and QM. :bugeye: ) But here is a case where I personally feel that convention *may* be wrong. Suppose you deny separability - i.e. assume that there IS in fact a link between the outcomes at Alice and Bob (OI is false). Guess what, you can still end up with Bell's Inequality assuming PI alone! That shouldn't be possible if Bell Locality were necessary to the mix. By the way, PI is the requirement mentioned specifically in EPR - not OI.

If you are interested, I can explain the proof= of this in more detail. But I wouldn't bet my (:rofl: non-)reputation on it.
 
  • #230
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DrChinese said:
What is not clear to me - and I know what Bell says - is whether or not the Bell Locality requirement is also necessary to arrive at Bell's Inequality. I think that it might be more accurate to say that parameter independence (PI) is a requirement but not outcome independence (OI) - where PI+OI=Bell Locality. Sure, it is in the proof and conventional wisdom is that it is a requirement. (And everyone knows how I feel about convention and QM. :bugeye: ) But here is a case where I personally feel that convention *may* be wrong. Suppose you deny separability - i.e. assume that there IS in fact a link between the outcomes at Alice and Bob (OI is false). Guess what, you can still end up with Bell's Inequality assuming PI alone! That shouldn't be possible if Bell Locality were necessary to the mix. By the way, PI is the requirement mentioned specifically in EPR - not OI.
If you deny separability, then you're treating it like qm does, aren't you?
I'm not sure what you're getting at. What do you mean by "parameter independence"?
 
  • #231
DrChinese
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Sherlock said:
If you deny separability, then you're treating it like qm does, aren't you?

I'm not sure what you're getting at. What do you mean by "parameter independence"?
At some point (perhaps Jarrett?), it was noticed that "Bell Locality" (separability or factorizability) could be split into 2 different elements which have now come to be called Parameter Independence (PI) and Outcome Independence (OI). This is why I say BL=PI+OI.

Parameter Independence means that Alice's outcome is not affected by Bob's polarizer setting (i.e. how Bob chooses to measure his particle, which is his measurement parameter).

Outcome Independence means that Alice's outcome is not affected by Bob's outcome.

It is known that the Alice's local likelihood of a particular outcome does not change based on Bob's parameter or his outcome. However, knowledge of both Bob's parameter and Bob's outcome would in fact give you a more complete specification of the Alice's system. So that is why ttn (and many others) says oQM is not Bell local.

What I am trying to push - I think - is that if you assume parameter independence (and ignore outcome independence) and Bell Reality (let c be another unit vector...) then that is sufficient to lead to Bell's Inequality. Bell's inequality is violated in experiments, therefore either parameter independence or Bell Reality fails. oQM is a parameter independent theory (i.e. it is local in this specific limited respect), but does deny Bell Reality. Ergo it is realism, not locality, that needs to be sacrificed.

Keep in mind, in oQM you do not get a more complete specification of the system if you only specify Alice and/or Bob's parameters - you still get the same superposition until there is a measurement. So why do we want to even think about parameter independence as it relates to locality? In my mind, it is because you need parameter independence to match up to signal locality and therefore keep the concepts of relativity intact. But that is just one view.
 
  • #232
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Is space-time inherently classical ?

This could be the same question from another point of view?
Could it help to take this other pov?
 
  • #233
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DrChinese said:
At some point (perhaps Jarrett?), it was noticed that "Bell Locality" (separability or factorizability) could be split into 2 different elements which have now come to be called Parameter Independence (PI) and Outcome Independence (OI). This is why I say BL=PI+OI.
Parameter Independence means that Alice's outcome is not affected by Bob's polarizer setting (i.e. how Bob chooses to measure his particle, which is his measurement parameter).
Outcome Independence means that Alice's outcome is not affected by Bob's outcome.
It is known that the Alice's local likelihood of a particular outcome does not change based on Bob's parameter or his outcome. However, knowledge of both Bob's parameter and Bob's outcome would in fact give you a more complete specification of the Alice's system. So that is why ttn (and many others) says oQM is not Bell local.
What I am trying to push - I think - is that if you assume parameter independence (and ignore outcome independence) and Bell Reality (let c be another unit vector...) then that is sufficient to lead to Bell's Inequality. Bell's inequality is violated in experiments, therefore either parameter independence or Bell Reality fails. oQM is a parameter independent theory (i.e. it is local in this specific limited respect), but does deny Bell Reality. Ergo it is realism, not locality, that needs to be sacrificed.
Keep in mind, in oQM you do not get a more complete specification of the system if you only specify Alice and/or Bob's parameters - you still get the same superposition until there is a measurement. So why do we want to even think about parameter independence as it relates to locality? In my mind, it is because you need parameter independence to match up to signal locality and therefore keep the concepts of relativity intact. But that is just one view.
Thanks for your efforts DrChinese. I understand now what's meant by PI. This was Bell's "vital assumption". Since the quantum correlations in Bell tests are aggregates of individual joint measurements, each of which is initiated by a detection at either A or B, then it would seem that PI is equivalent to OI.

I agree with your conclusion that realism (but not necessarily locality) needs to be sacrificed. The reason that locality isn't necessarily disallowed is because the detection schemes that are necessary in order to produce correlations that violate a Bell inequality require that observations at A and B depend on each other. That is, while the settings at A and B are varied randomly, the pairings aren't random. The observations at A and B aren't independent so the statistics at A and B aren't independent -- and locality doesn't require that they be independent. So separable vs. non-separable formulation isn't local vs. non-local.
 

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