How can one event affect another instantly over a distance

[ttn]

I used http://arxiv.org/abs/quant-ph/0002060 for a reference: QM does satisfy Bell Locality.

That conclusion is wrong. The problem is addressed explictly in Maudlin's book ("Quantum Non-Locality and Relativity"). For a shorter and very readable explanation of the point, see

http://arxiv.org/pdf/quant-ph/0408105

 

[Hurkyl]

Ah, the difference (I think) is where the assumption of outcome independence lies: in the reference I used, it was placed in the following text, stating that E(a, b, λ) = E(a, λ) * E(b, λ), but your reference puts the assumption into the equation itself.

 

[Hurkyl]

On the other hand, isn't relativistic QFT locally causal by the definition given by Bell in that paper?

IOW, given a state, isn't its value at a point in space-time completely determined by a slice of the backwards light-cone?

 

[ttn]

On the other hand, isn't relativistic QFT locally causal by the definition given by Bell in that paper?

IOW, given a state, isn't its value at a point in space-time completely determined by a slice of the backwards light-cone?

No, it isn't. That's a common misconception for the reason I mentioned earlier: texts on relativistic QFT (almost) never even mention the issue of measurement and the collapse postulate that is needed (yes, even in QFT) to ensure that measurements actually have definite outcomes.

One sees proofs in some QFT texts that the theory is "locally causal" (or so they say). This is usually a proof that space-like separated operators commute. But what this actually *means* is signal locality. This condition ensures that the theory cannot be used to transmit information faster than light. And in that sense, the theory is consistent with relativity. But in terms of the stronger locality condition (Bell Locality), QFT suffers from the same problem as regular old QM: measurements can have effects on the state attributed to distant locations (effects which change the probabilities for subsequent measurements at those distant locations, but in an unpredictable way that prevents these effects from being used to transmit information).

 

[Hurkyl]

The collapse postulate is an entirely separate issue from the kinematics.


We just have the cool theorem that says that these two algorithms:

(1) Let the system evolve
(2) Do a collapse to see what the two measurements were

and

(1) Let the system evolve
(2) Do a collapse to see what the first measurement is
(3) Let the collapsed system evolve
(4) Do a collapse to see what the second measurement is

are equivalent.


There is no non-locality in the evolution of the system. The non-locality is in the extraction of information, specifically that P(B|A) = P(B) for spatially separated measurements may be false, and the method of wavefunction collapse.

 

[ttn]

The collapse postulate is an entirely separate issue from the kinematics.

Well, they're not entirely separate. I mean, it's true that orthodox QM contains these two distinct rules for time-evolution of states. But if what we're assessing is the Bell Locality of that theory, we need to assess the whole theory -- not just half of it.

We just have the cool theorem that says that these two algorithms:

(1) Let the system evolve
(2) Do a collapse to see what the two measurements were

and

(1) Let the system evolve
(2) Do a collapse to see what the first measurement is
(3) Let the collapsed system evolve
(4) Do a collapse to see what the second measurement is

are equivalent.

That's too fast. Consider this: is the probability distribution for outcomes for the second measurement the same, regardless of whether or not the first measurement is made? According to QM, it isn't. Take the standard example of two spin 1/2 particles in a singlet state. If no measurement is made on the first particle (or, equivalently, before a measurement is made on the first particle), the probability for a z-spin measurement on particle 2 to have outcome "up" is 50%. But now suppose a z-spin measurement is made on particle 1, and suppose it has outcome "down." Now -- instantaneously -- the probability that a subsequent measurement of z-spin on particle 2 will yield result "up" jumps to 100%.

Now this alone doesn't mean that orthodox QM violates Bell Locality. It's only because the orthodox theory assumes the wave function description is *complete* -- i.e., according to OQM there is no way of understanding the sudden "jump" in probabilities for particle 2 as being the result merely of different available information (like we would have if the original description had been incomplete).

I don't know how clear that is; see the paper I referenced before (or Maudlin's book) for a better presentation.

But the main point is that your sketch of an argument above merely shows that QM is consistent with signal locality. It shows that the marginal probability for an outcome doesn't depend on choices made at spacelike separation. But *nevertheless*, the fact is that orthodox QM (and any other theory agreeing with its predictions) have a subtle, "hidden" kind of nonlocal causation. This cannot be used to build a telephone, but it's still a serious problem for serious Lorentz invariance.

There is no non-locality in the evolution of the system. The non-locality is in the extraction of information, specifically that P(B|A) = P(B) for spatially separated measurements may be false, and the method of wavefunction collapse.

The extraction of information is precisely where the nonlocality *isn't*. All the theories anyone takes seriously are "signal local". They can't be used to transmit information faster-than-light. But they all violate Bell Locality. (Well, leaving aside MWI, which I can't take seriously as a theory since it contradicts... everything else I know!)

 

[DrChinese]

But of course in this example you must conclude that reality is observer dependent--because as the basic premise of your argument you assume A = 0, B = 67.5.

I hold that Reality does not allow you to make this assumption, both A and B are what Reality has determined that they are independent of your assumption--they may in fact be A = 0.01 and B = 0.02 or any other infinite set of possibilities as the basic assumption. Unless all statistical a priori possibilities for A & B & C in your example reach a conclusion of "negative probability" any statement that Reality is in fact "observer dependent" is shown to be false...

Forgive me, I do not follow the logic of your argument. Can you explain further? (Generally, a single counter-example - such as the specific angle settings I provided - are sufficient to refute any hypothesis.)

 

[Hurkyl]

But now suppose a z-spin measurement is made on particle 1, and suppose it has outcome "down." Now -- instantaneously -- the probability that a subsequent measurement of z-spin on particle 2 will yield result "up" jumps to 100%.

No!

No matter what I do to the first particle, the distribution on the measurement of the second particle is always uniform.

What is not uniform is the distribution of the spin for the second particle, given a value for the spin of the first particle... the conditional probability.

No matter how analyze the problem, P(σ2 = up) = (1/2). What you're looking at is the fact P(σ2 = up | σ1 = down) = 1.


Actually, I should be somewhat more precise: if we let Ψ denote the initial state of the system, and Ψ0 denote a the singlet state, then:

P(σ2 = up | Ψ = Ψ0) = (1/2)
P(σ2 = up | σ1 = down and Ψ = Ψ0) = 1



Here's another way of looking at it:

If we're just looking at the universe near the detection of particle 2's spin (both in space and in time), then the portion of the wavefunction that is near the event does, in fact, tell us everything. We need to know nothing about what happens with particle 1 in order to get a complete description.

It's only when we look at both measurements (a non-local observation!) that we see non-locality.

Consider this experiment:

We have a black-box that will generate two particles. I have measuring devices A and B that will each measure the spin of the particles they see along the z-axis. A and B will then transmit a signal to C who will compare the two spins. (So that the comparison is performed locally!)

The backwards light-cone of the final measuring event does, in fact, tell us everything we need to know to analyze it.

 

[Sherlock]

So, that is the key assumption Bell attacked - that unmeasured spin components exist. They don't, as we now know from experiments.

This is just saying that data doesn't exist until it's produced by
the hardware. We don't need experiments to tell us this. It
follows from the definitions of the terms.

EPR was concerned with the idea that there's something
real moving from emitter to detector on both sides of the
biparticle setup (of course there is) -- and that these real
disturbances are related to each other due to their common
origin (of course they are), and that qm doesn't have much
to say about what is happening between the hardware (that
qm is an incomplete description of physical reality, which, of
course, it is).

... there is nothing special about Theta. The entangled (PDC-I) photons have identical polarization - if you measure it. They have identical wavelengths - if you measure it. They have opposite momenta, if you instead measure that. Etc. Theta is a number that is derived from one set of these fundamental properties of entangled particle pairs, and is completely dependent on how the observations are performed. If you measure both photons' positions, your Theta disappears entirely.

Theta is the angular difference between the settings of
the crossed linear polarizers. You 'derive' Theta by looking at
the polarizers. :-)

Theta is quite special indeed in the experiments where it's
determining the rate of coincidental detection. It defines the
observational context. It's the relevant independent variable.

The *variability* of the hidden parameter, Lambda, just doesn't
apply to the context where Theta is the determining variable.

In hypothesizing a hidden parameter relevant to the
biparticle, joint context, then that hidden parameter has
to be a constant -- such as a relationship between the
disturbances moving from emitter to the polarizers that
is essentially the same for all pairs.

At least, this is one way to straightforwardly approach
understanding the results without requiring some new
superluminally propagating thing.

I agree that for spin component tests, Theta acts as if it were real.
And as such, it leads you to believe that it is fundamental and a global variable.

What does this mean that Theta "acts as if it were real". :-)
Of course it's real, and of course it's a global variable.

Theta is a real (variable) orientation of the polarizer hardware,
defining the global measurement context.

But that view requires you to ignore the full range of possible
experiments that can be performed on the entangled particles.

Insofar as I'm concerned with what was actually done
in a particular experiment, I'll be ignoring the many other
things that might have been done but weren't. :-)

Recall that the basic delta(p)delta(q)>h of the HUP always applies.
Thus there are any number of permutations of experiments that
will yield any number of hypothetical alternate Thetas... are these
all real too? Or are they just numbers that act as if they
are real?

What are you talking about?

 

[ttn]

No!

Well, I agree with your analysis below, so I'm not sure exactly what you are disagreeing with. Let's see...

What is not uniform is the distribution of the spin for the second particle, given a value for the spin of the first particle... the conditional probability.

No matter how analyze the problem, P(σ2 = up) = (1/2). What you're looking at is the fact P(σ2 = up | σ1 = down) = 1.

That's right. The probability for a given outcome for particle 2 is different depending on whether you do or don't conditionalize on a certain event that is *not* in the past light cone of the measurement event in question. So that event (namely, the measurement on particle 1 having some particular outcome) should not (according to relativistic causality) be able to have any direct causal effect on the particle 1 measurement. Right?

Of course, as I noted before, in a normal situation one could always blame the correlations (i.e., the fact that the conditional probability P(2|1) is not equal to the marginal P(2)) on the fact that we had started with an incomplete description of the state of the two particles. If you say that, then there is, by assumption, some information that can be still learned about that state which will change the probabilities when we conditionalize on it. For example, if you have a theory in which "being in the singlet state" really means that the pair is *either* 1up-2down *or* 2up-1down with 50/50 probability either way, then there would be no nonlocality here. You could do a measurement on particle 1 and find out "it's up!", at which point you'd know that the pair had originally been in the state 1up-2down -- and hence also know that particle 2 will be found to be "down". So if the description of the state of the particles is initially incomplete, then the fact that the probability for one event changes when we conditionalize on the outcome of the other event, does *not* signal the presence of a non-locality.

But according to orthodox QM, the wave function is complete. (That doesn't mean it really is -- just according to that theory. And the consistency *of that theory* with Bell Locality is what we're assessing here.) So there is no way of interpreting the probability change as resulting from having winnowed down the prior state of the two particles more precisely. It was already as precise as it could be. In other words, *according to orthodox QM* there is no "common cause" explanation for the correlations, nothing in the past light cones of the two measurement events which is (even stochastically) responsible for the outcome. Hence, the measurement event on particle 1 -- which *apparently* affected the outcome for particle 2 -- *really does* affect the outcome for particle 2.

But (as I also said before) all of this is kind of beside the point. The main point I am making here is simply that orthodox QM violates Bell Locality, and there is no reasonably way to argue with that. It just does. You don't need any words or subtle arguments or anything -- you just look at the theory and ask whether or not it satisfies a certain mathematical condition. And it doesn't. OK? Orthodox QM violates Bell Locality. Now you're objecting that it doesn't make sense to call this condition a locality condition, because it involves only conditional probabilties, etc., etc. But then I don't understand what your point is. Is it that OQM really *doesn't* violate Bell Locality? Or that you don't think Bell Locality is accurately capturing relativity's prohibition on superluminal causation? Or that you think Bell Locality is poorly named? Or what?

Actually, I should be somewhat more precise: if we let Ψ denote the initial state of the system, and Ψ0 denote a the singlet state, then:

P(σ2 = up | Ψ = Ψ0) = (1/2)
P(σ2 = up | σ1 = down and Ψ = Ψ0) = 1

Yes, fine.

If we're just looking at the universe near the detection of particle 2's spin (both in space and in time), then the portion of the wavefunction that is near the event does, in fact, tell us everything. We need to know nothing about what happens with particle 1 in order to get a complete description.

There are several things wrong here. First off, the wave function for a 2 particle system isn't a wave in 3-D space, so it doesn't really make sense to talk about "the portion of the wf that is near [one particular] event".

But let's leave that aside and give your point as much benefit of the doubt as possible. So we have this wavefunction \psi_0 (the spin singlet state for two well separated spin 1/2 particles). You say that this wave function *alone* (and nothing about the distant particle or measurements on it) is sufficient to calculate probabilities for outcomes on each particle. OK, let's try that. So, suppose we measure the z-spin on particle 1. There's a 50/50 probability for an up/down outcome, right? And suppose (at spacelike separation) someone measures the z-spin on particle 2. There's also a 50/50 probability for an up/down outcome there, yes?

Are the outcomes correlated? According to your view, they can't be. There's nothing left to *correlate* them. The two measurements are just independent events. But this means that (eg) 25% of the time, Alice gets an "up" result and so does Bob. (50% of the time they get opposite results, and 25% of the time they both measure "down".) Right? But this contradicts the QM predictions! What this shows is that if you try to impose Bell Locality on orthodox QM, you *ruin* its correct predictions. This is precisely what is shown in that paper I mentioned before, quant-ph/0408105.

How does the actual theory (orthodox QM) get around this problem? That is, how does it manage to predict the right (perfectly anti-correlated) results for this kind of situation? Because of the collapse of the wave function. One of the two measurement events happens *first*, and this *causes* the wave function to collapse, so that the wave function on which subsequent measurements on the distant particle are based is no longer \psi_0, but something else -- an eigenstate of spin for which (as long as Bob measures along the z-direction) the outcome is fully determined (where before it wasn't). In short, Alice's measurement of z-spin of particle 1 causes Bob's particle to obtain a definite value for z-spin. I'm not saying it *really* causes this to happen -- just that this is what happens *according to orthodox QM*. OQM violates Bell Locality, in other words.

This, by the way, is just what was pointed out (unfortunately, in a not-too-clear way) by EPR. The collapse postulate in OQM implies (if you take the completeness doctrine seriously) a kind of action at a distance. So if you want to take relativity seriously, you should reject the completeness doctrine and look for some kind of local hidden variable theory. This is a perfectly valid argument, and the physics community should have been looking for a LHV theory until Bell proved in the 60's that one couldn't exist. It's rather depressing that hardly anyone bothered to look, and also depressing how few people understand what Bell actually proved.

It's only when we look at both measurements (a non-local observation!) that we see non-locality.

That's a silly position to take. If that's all that relativity forbids, then just about any wildly non-local theory would pass the test. For example, consider Newtonian gravitation in which the gravitational force exerted on one object depends on the properties of distant objects *right now*. So in principle you could make a pendulum in Tokyo swing a little bit by shaking your fist in Boston. Right? According to the theory, the gravitational effect of moving your fist *instantaneously* affects distant objects like the pendulum.

So would this count as relativity-violating non-locality according to you? Apparently not, since you wouldn't be able to find out what effect your fist-shaking had until you and your Japanese friend meet up later to compare notes. (I'm assuming that, say, airplane travel is still limited to the speed of light.) This view actually amounts to a kind of weird solipsism similar to what some advocates of the MWI hold. It says in effect that the outcomes (and all that implies, in particular that they are correlated in a way that can't be accounted for by anything in the past light cones) don't exist. All that exists is some belief inside the head of the person at C. But that, frankly, is crazy. No physicist should be willing to accept that the reason QM doesn't really conflict with relativity, is because we were wrong to think that experiments had outcomes that really existed, i.e., we were wrong to believe in an external world, i.e., solipsism is true. Not only is that position ridiculous on its face, it also undermines itself: the only basis that would justify going to such great lengths to save a principle like "relativistic causality" is a thorough realist basis. That is, it's only if you believe in an objective external physical world (and interpret relativity on that basis) that you would care enough about anything to try to save relativity. If you're a solipsist from the beginning, there no important issue regarding locality -- everything that seems to exist is just in your mind, so anything is just automatically local.

Consider this experiment:

We have a black-box that will generate two particles. I have measuring devices A and B that will each measure the spin of the particles they see along the z-axis. A and B will then transmit a signal to C who will compare the two spins. (So that the comparison is performed locally!)

The backwards light-cone of the final measuring event does, in fact, tell us everything we need to know to analyze it.

What exactly do you think this is supposed to prove? Surely it doesn't prove that orthodox QM is consistent with Bell Locality after all?

 

[DrChinese]

What does this mean that Theta "acts as if it were real". :-)
Of course it's real, and of course it's a global variable.

Theta is a real (variable) orientation of the polarizer hardware,
defining the global measurement context.

What are you talking about?

Entangled photons also have a wavelength, position, etc. These do not commute with spin components. According to the concepts and application of the HUP: if you measure any of these experimentally (before measuring the spin), the wavefunction collapses. Thereafter, the spin components are no longer correlated and that makes Theta meaningless. Theta's very existence is dependent on the observer. That is why I keep insisting that Theta acts as if it is real - when the experimental setup favors it. The stats of Theta are a derivable value.

 

[Sherlock]

Entangled photons also have a wavelength, position, etc. These do not commute with spin components. According to the concepts and application of the HUP: if you measure any of these experimentally (before measuring the spin), the wavefunction collapses. Thereafter, the spin components are no longer correlated and that makes Theta meaningless. Theta's very existence is dependent on the observer. That is why I keep insisting that Theta acts as if it is real - when the experimental setup favors it. The stats of Theta are a derivable value.

Ok ... but this is missing the point(s) I was trying to
make.

Consider setups of the sort (such as Aspect et al., 1982),
where Theta is real and where it determines the joint
results:

detector A <--- polarizer <--- emitter ---> polerizer --> detector B

Formulations of this setup that are based on Bell locality
aren't realistic, because the setup is a nonlocal one.
Changing the setting of the filter at A (or B) changes the
global variable, Theta, thus changing the result, (A,B).

The individual rates of detection at A and B don't change.

Saying that nature is violating locality because a nonlocal
context isn't amenable to a local description is misleading.
Saying that there are no hidden variables in nature because
results in a nonlocal context aren't determined by hidden
variables is misleading. Saying that qm is a nonlocal theory
incompatible with local hidden variable formulations is misleading.

This setup, emitter ---> polarizer ---> detector,
is a local one. Qm description of it is explicitly local,
and the accuracy of predictions could be enhanced by
supplementary local hidden variable information.

There are local and nonlocal contexts in our observations
of nature. Qm is either a local or nonlocal theory depending
on the context it's being applied to.

The word, "nonlocal", doesn't mean ftl or instantaneous
signal propagation. It refers to context. Nonlocal observational
contexts, by themselves, don't conflict with the postulates
of SR. One might infer that superluminal signalling of some
sort is causing the (A,B) results in the joint context. But that
inference isn't required. A and B are related to each other
via global parameters. The local origins of the spatially
separated components of Theta are there for anyone
to see. The origin of the hidden constant parameter,
ie., the entanglement at the level of the emitted optical
disturbances, is still an open question -- but it would be
very surprising if it were conclusively found that
the entanglement (at the submicroscopic level) is not due to
common origin or interaction, but rather to superluminal
signalling of some sort.

If one supposes that the common origin or interaction (that
researchers take such great pains in preparing) is producing
a hidden constant (ie., entangling the incident disturbances),
and then consider this hidden constant together with the observable
variable Theta, then the joint results make sense without the need
for signalling between A and B at spacelike separations.

 

[Sherlock]

It's only when we look at both measurements (a non-local observation!) that we see non-locality.

That's a silly position to take. If that's all that relativity forbids, then just about any wildly non-local theory would pass the test. For example, consider Newtonian gravitation in which the gravitational force exerted on one object depends on the properties of distant objects *right now*. So in principle you could make a pendulum in Tokyo swing a little bit by shaking your fist in Boston. Right? According to the theory, the gravitational effect of moving your fist *instantaneously* affects distant objects like the pendulum.

The terms "nonlocal" and "nonlocality" have various meanings. If one is using
these terms to refer to ftl signal propagation, then it's clearer to just use
"ftl signal propagation" (or some abbreviation thereof) rather than "nonlocal"
or "nonlocality".

The way that I'm using the term "nonlocality" isn't necessarily synonymous
with ftl signal propagation. It refers to system-dependent observational
contexts involving the counting/tracking of time-correlated, multiple events.
Such observational contexts aren't forbidden by relativity.

Gravitational behavior is, by definition, nonlocal behavior. Changes in
some part of a gravitational system affect the system as a whole, and insofar
as shaking your fist in Boston produces changes in the behavior of the
gravitational system which also includes a pendulum in Tokyo, then you
might say that you caused the pendulum changes. But, that would be
ignoring the system-dependent or context-dependent relationship between
the two events.

In typical biphoton Bell tests involving spacelike separated polarizers, what
is done at A does not affect the detection rate at B, and vice versa.
But changes in the polarizer setting at A (or B) do affect coincidence
rates.

Regarding Hurkyl's statement (which isn't silly, just not particularly
informative since it follows from a certain definition of the terms)
it's only when you look at (A,B) wrt Theta that predictable "nonlocal"
patterns emerge.

 

[DrChinese]

... Saying that qm is a nonlocal theory
incompatible with local hidden variable formulations is misleading.

This setup, emitter ---> polarizer ---> detector,
is a local one. Qm description of it is explicitly local,
and the accuracy of predictions could be enhanced by
supplementary local hidden variable information.

Your statement is misleading. There are no hidden variable descriptions local to any particle. The HUP insures this. Recall that any particle's attributes are influenced by the act of observation, and entangled particles are no different.

QM is explicitly non-local in that sense. There is no possibility of enhancing predictions using "supplementary local hidden variable information" as you assert.

I don't understand where you are going with this because it is 180 degrees opposite of the experimental results of Aspect (plus Bell).

 

[Sherlock]

Your statement is misleading. There are no hidden variable descriptions local to any particle. The HUP insures this. Recall that any particle's attributes are influenced by the act of observation, and entangled particles are no different.

I don't know what "there are no hidden variable descriptions local
to any particle" means. In qm, a click of the photon counter *is*
the photon. If you're just looking at a single photon detector, then
if you knew what was actually emitted and how it behaved prior
to hitting a filter and registering a click (or not), then you would
certainly be able to more accurately predict individual detection
patterns. Such prior knowledge of what are called local hidden
variables would be compatible with qm formulations of individual measurement setups. That is, wrt individual measurement
contexts that now produce random results, and which qm
describes accordingly, the qm description and resulting predictions
would be improved if you knew something more about the local
hidden variables determining the random results. Bell says
this in his paper.

QM is explicitly non-local in that sense. There is no possibility of
enhancing predictions using "supplementary local hidden variable
information" as you assert.

Bell asserts that in certain measurement contexts there is -- and I
agree with him.

I don't understand where you are going with this because it is 180 degrees opposite of the experimental results of Aspect (plus Bell).

The way I'm approaching an understanding of experimental
tests of Bell inequalities, and the meaning of Bell's analysis,
and the meaning of nonlocality and entanglement, and the
possibility of more realistic lhv descriptions, and ... etc.,
should be clear from my posts.

Bell showed that local hidden variables, if you knew them, would
enable you to make more accurate predictions of individual results.
He demonstrated that such lhv descriptions are compatible
with qm formulations for individual contexts.

However, such knowledge would not enable you to make
more accurate predictions of joint results. Why? Because,
as Bell showed, they aren't determining the joint results.

Ok so far?

 

[DrChinese]

Bell showed that local hidden variables, if you knew them, would enable you to make more accurate predictions of individual results.
He demonstrated that such lhv descriptions are compatible
with qm formulations for individual contexts.

However, such knowledge would not enable you to make
more accurate predictions of joint results. Why? Because,
as Bell showed, they aren't determining the joint results.

Ok so far?

No, this is absolutely false; and I am quite certain you should know better than to make such statements.

Bell's Theorem clearly shows that local hidden variables are incompatible with QM, and on this point there is really nothing ambiguous. You are completely off with regards to your characterization the entire EPR/Bell regime.

If there are hidden variables for one particle of a pair, then there are hidden variables for the other of the pair. That is the local realistic hypothesis by definition. Specifically, that unmeasured local hidden variables have existence independent of actual observation.

Bell has never, as far as I know, stated that a more complete specification of the system is possible beyond QM - per any actual science (theory or experiment). Perhaps he made a hopeful comment, I can't say. But I am quite certain he believed in the HUP all the way.

 

[cartuz]

How can one event affect another instantly over a distance if there is no absolute concept of simultaneity? In which reference frame does the cause have a "simultaneous" effect?

If we have two newspapers in two towns is the information to transmit instantly? Is the information is non-local in this case? I hope you are know the answer.

 

[Hurkyl]

I've had some time to think and work out exactly what I mean...

I assert that if you hypothesize that the QM description is complete that the only thing required to break is observation independence, and anything dependent on that assumption.

(Observation independence meaning that observations at spatially separated events are statistically independent)

In particular, I claim that Bell Locality is not dependent on observation independence, and is not required to be violated in an interpretation of QM that is assumed to be complete.

The derivation in ttn's reference applies observation independence in the derivation of the mathematical criterion, but I assert that the criterion is inequivalent to Bell locality when you reject observation independence.

Bell's definition of locality, taken from ttn's reference:

"A theory will be said to be locally causal if the probabilities attached to values of local beables in a space-time region ... are unaltered by the specification of values of local beables in a space-like separated region"

And that's true here, if by "local beable" I mean the restriction of the state of the system to a space-time region.

It is, of course, not true if by "local beable" I mean the spin of the particle around the z-axis.


I guess an important question is what Bell meant by "beable".



Some particular responses:

*according to orthodox QM* there is no "common cause" explanation for the correlations, nothing in the past light cones of the two measurement events which is (even stochastically) responsible for the outcome.

Surely the original emission of the pair of entangled particles counts as a "common cause"? It not only explains the distributions of the individual detections, but their joint distribution as well!

How does the actual theory (orthodox QM) get around this problem? That is, how does it manage to predict the right (perfectly anti-correlated) results for this kind of situation? Because of the collapse of the wave function.

Collapsing the wave function is merely a tool one might use: it is not a requirement. For example, the anti-correlation is simply the expected value of a particular operator.

That's a silly position to take. If that's all that relativity forbids, then just about any wildly non-local theory would pass the test. For example, consider Newtonian gravitation in which the gravitational force exerted on one object depends on the properties of distant objects *right now*.

I can do a measurement local to the pendulum that would detect the fact that the pendulum was being affected by something that wasn't local to the pendulum, so no, that doesn't pass my test.


Let me try and redo the point I was trying to make with my example: instead of looking externally at the problem, I can introduce a detector into the experiment that receives the results of the other two detectors says "anticorrelated" or "correlated".

Then, you don't have to posit any non-locality occurring (such as one of the measurements collapsing the wavefunction) to determine that the detector always says "anticorrelated".

 

[ttn]

Bell has never, as far as I know, stated that a more complete specification of the system is possible beyond QM - per any actual science (theory or experiment). Perhaps he made a hopeful comment, I can't say. But I am quite certain he believed in the HUP all the way.

The phrase "more complete specification of the system...beyond QM" refers to hidden variable theories, right?

Well then it's just outrageous to say that Bell never stated such a thing was possible. For about 20 years he was one of the only people to take Bohmian Mechanics seriously, i.e., to recognize clearly that Bohm's theory *existed* and that it was a *counterexample* to all the stale old claims that no hidden variable theories were possible. Indeed, Bell did a lot of work on this theory and moved it forward in several important ways. And of course his famous Theorem was inspired precisely by Bohm's hidden variable theory.

In any case, it is definitely not the case that Bell "believed in the HUP all the way" if that's supposed to mean he didn't recognize the possibility of hidden variable theories.

 

[ttn]

I assert that if you hypothesize that the QM description is complete that the only thing required to break is observation independence, and anything dependent on that assumption.

(Observation independence meaning that observations at spatially separated events are statistically independent)

I don't understand what you mean by "observation independence." By "observations" do you mean the *outcomes* of the experiments, or the fact that observations are made at all, or what?

I guess an important question is what Bell meant by "beable".

The best way to find out would be to read Bell's papers. Anybody even remotely interested in this topic should buy "Speakable and Unspeakable" and just start reading. Bell is an amazing writer. Some of the papers are quite technical, yes. But many if not most of them are extremely accessible, and extremely witty and fun to read.

Surely the original emission of the pair of entangled particles counts as a "common cause"? It not only explains the distributions of the individual detections, but their joint distribution as well!

No! It doesn't! The initial entangled wave function alone is *not* sufficient -- according to orthodox QM -- to calculate the correlations. That's precisely what is shown in quant-ph/0408105. If you get rid of the collapse postulate (which is where the Bell Locality violation arises) the correlations go away. Plus, without the collapse postulate, there is no clear algorithm in QM for calculating probabilities. (This is why the MWI people who want to do away with the collapse postulate are up a creek when it comes to making any contact whatsoever with observed Born rule probabilities.)

Collapsing the wave function is merely a tool one might use: it is not a requirement. For example, the anti-correlation is simply the expected value of a particular operator.

You might calculate an expectation value that way, yes. But that's not the same as accounting for the correlation on an event-by-event basis.

I can do a measurement local to the pendulum that would detect the fact that the pendulum was being affected by something that wasn't local to the pendulum, so no, that doesn't pass my test.

Yes, that's true. It's parallel to the following point about QM: if you had experimental access to the wave function associated with a given particle (in your lab, say), you would be able to detect a sudden change when somebody far away makes a measurement and collapses the wf. Or in Bohms' theory, if you had access to the local particle position (without disrupting the entangled wave function) you could watch it veer off when the far away guy makes a measurement.

I take all of this to support my original point: Bell Locality captures relativity's prohibition on superluminal causation just fine. A seriously relativistic theory should have no superluminal causation of any kind -- not just no superluminal causation that can be used to transmit information. A theory with superluminal causation that protects itself by saying you don't have experimental access to certain beables and hence can't directly observe the superluminal causation... still has superluminal causation!

Let me try and redo the point I was trying to make with my example: instead of looking externally at the problem, I can introduce a detector into the experiment that receives the results of the other two detectors says "anticorrelated" or "correlated".

Then, you don't have to posit any non-locality occurring (such as one of the measurements collapsing the wavefunction) to determine that the detector always says "anticorrelated".

So... are you arguing that there is no violation of Bell Locality because (all evidence to the contrary notwithstanding) nothing actually happens at space-like separation? Namely, there are no actual definite outcomes to the two experiments on the two sides -- there is only this "comparison" that happens later in the middle?

 

[DrChinese]

The phrase "more complete specification of the system...beyond QM" refers to hidden variable theories, right?

Well then it's just outrageous to say that Bell never stated such a thing was possible. For about 20 years he was one of the only people to take Bohmian Mechanics seriously, i.e., to recognize clearly that Bohm's theory *existed* and that it was a *counterexample* to all the stale old claims that no hidden variable theories were possible. Indeed, Bell did a lot of work on this theory and moved it forward in several important ways. And of course his famous Theorem was inspired precisely by Bohm's hidden variable theory.

In any case, it is definitely not the case that Bell "believed in the HUP all the way" if that's supposed to mean he didn't recognize the possibility of hidden variable theories.

I don't think he foresaw dropping the HUP, or re-instating EPR's conclusion that QM was incomplete. That was my point, and I am aware of his interest in BM.

 

[Hurkyl]

I don't understand what you mean by "observation independence." By "observations" do you mean the *outcomes* of the experiments, or the fact that observations are made at all, or what?

I'm talking about outcome independence from 0408105, but I misspoke. I agree entirely that Outcome Independence is violated.

The point I am trying to make is that, despite 0408105's claims, OI is not required by my reading of Bell Locality. But more importantly, even if I've completely misunderstood Bell, that my version of it is what's relevant for compatability with special relativity.

The initial entangled wave function alone is *not* sufficient -- according to orthodox QM -- to calculate the correlations. That's precisely what is shown in quant-ph/0408105.

Only if you assume OI, which 040815 does, since it wraps OI up in its criterion for locality. Specifically, OI was used in the derivation of (18). In other words, the article proves that completeness implies violation of OI.

(Well, I suppose it could mean violation of some of the other conditions instead, but I'm willing to grant those other ones)

You might calculate an expectation value that way, yes. But that's not the same as accounting for the correlation on an event-by-event basis.

Why isn't it? The correlation of two random variables is simply a number: it doesn't matter how you go about computing it.

Yes, that's true. It's parallel to the following point about QM: if you had experimental access to the wave function associated with a given particle (in your lab, say), you would be able to detect a sudden change when somebody far away makes a measurement and collapses the wf.

Only if you assume that wave function collapse is something that really happens to the system, rather than a mathematical trick.

Namely, there are no actual definite outcomes to the two experiments on the two sides -- there is only this "comparison" that happens later in the middle?

I take the idea of an "outcome" to be closely analogous with the concept of a "random variable" in statistics.

What I'm trying to emphasize is that nonlocality is an artifact of our external viewpoint on QM. Specifically, we can ask nonlocal questions.

So what I was trying to do is to replace the nonlocal question with a seemingly (to me) equivalent local question, "What is the output of the third detector?" Even better than that, I've turned it from an external question into an internal question.

If you only ask local questions, then all sorts of "problems" vanish. In particular, the question of outcome independence cannot come up.

I think this is an important point to make, since it emphasizes that things interpreted as nonlocality arise when answering nonlocal questions.

 

[Sherlock]

Bell's Theorem clearly shows that local hidden variables are incompatible with QM, and on this point there is really nothing ambiguous. You are completely off with regards to your characterization the entire EPR/Bell regime.

...

Bell has never, as far as I know, stated that a more complete specification of the system is possible beyond QM - per any actual science (theory or experiment) ...

Apparently there is something ambiguous about saying that
local hidden variables are incompatible with qm.

From page 196 of "On the Einstein Podolsky Rosen Paradox" Bell
writes "... there is no difficulty in giving a hidden variable account
of spin measurements on a single particle." Then he shows this
mathematically, concluding with ... "So in this simple case there
is no difficulty in the view that the result of every measurement
is determined by the value of an extra variable, and that the
statistical features of quantum mechanics arise because the value
of this variable is unknown in individual instances."

So what happens to these local hidden variables when
we incorporate these individual measurement events into
a correlational context involving other individual measurement
events at spacelike separations from these? Do the hidden
variables just vanish? Or is it simply that they aren't
determining the joint results?

 

[ttn]

The point I am trying to make is that, despite 0408105's claims, OI is not required by my reading of Bell Locality. But more importantly, even if I've completely misunderstood Bell, that my version of it is what's relevant for compatability with special relativity.

Well, Bell Locality is definitely the conjunction of OI and PI. There's no question about that.

However, I concede that it's at least a possible position to hold that Bell Locality is too strong -- that it requires more of a theory than relativity does, that relativity merely requires something weaker like "signal locality". Of course then one has to conede that theories such as OQM and BM (which are Bell Nonlocal but Signal Local) are consistent with SR.

Only if you assume that wave function collapse is something that really happens to the system, rather than a mathematical trick.

If (as Bohr claimed) the wave function is a complete description of the state of the system, then any change in the wf implies a change in the state of the system -- i.e., the collapse is "something that really happens to the system." Of course, one can reject this and view the collapse as merely an updating of our knowledge of the system. But to take that route is to reject the completeness claim. For us to be able to acquire additional knowledge of the state of the system (without any coincident change in the state of the system) is to discover that there were facts about the system that we didn't know about before.

In other words, to regard the collapse postulate as epistemological rather than physical is to advocate a hidden variable theory.

And then we're not really talking about "orthodox QM" anymore, are we?

 

[Hurkyl]

I assert that incompleteness is not a necessary conclusion, in the following sense:

The wave function allows us to compute the probability distribution on any measurement (and thus the conditional probabilities as well). One is not forced to assume that there is a reality beyond these distributions, thus one need not conclude that the QM description is incomplete.

(In other words, it's just like the fact a "random variable" never actually takes on any values: it's just a convenient fiction to assist the intuition. The probability distribution is all there is)

 

[ttn]

I assert that incompleteness is not a necessary conclusion, in the following sense:

The wave function allows us to compute the probability distribution on any measurement (and thus the conditional probabilities as well). One is not forced to assume that there is a reality beyond these distributions, thus one need not conclude that the QM description is incomplete.

This is wrong in an interesting way. In fact, it's wrong in precisely the same way that it's wrong to think that you can escape the apparent conflict between QM and SR by denying realism (which was suggested as a possibility on another thread).

The problem is this: "completeness" has a certain *meaning*. It means that some theory (or theoretical entity, like the wave function) captures *all* of the facts that pertain to a given system. It means our description doesn't leave anything out, doesn't miss anything that's really out there. So the very *claim* that the wf alone provides a complete description of the system, *presupposes* the external objective reality of the system. If there really is no system, then there's no possibility for the wave function (or anything else) to provide a complete description of *it*. ("It, brother?")

So, I guess, in a sense you are correct: if you deny that there's an external reality, it's not quite correct to say that the wf is *incomplete*. (That would commit the same error i just noted.) If there's no external reality, then there's simply no such issue as "completeness", so both terms ("complete" and "incomplete") become literally meaningless.

"Incompleteness" means that the wf fails to capture some relevant fact about the real system out there. (A complete description, if the wf is incomplete, would have to supplement the wf with some additional variables.) And that presupposes realism too, just as much as the concept of "completeness" does.

So where does this leave us? Well suppose we hold on to realism. Then, if you regard the collapse postulate as merely epistemological, as merely an updating of our knowledge (which doesn't coincide with any physical change to the system), then it would be correct to say that the wf is incomplete. Right?

But on the other hand, if you do drop the realism assumption (and retreat to solipsism or whatever) then *both* "completeness" and "incompleteness" are false. It's not true that the wf provides a complete description of the facts, nor is it true that the wf provides an incomplete description of the facts. There simply are no facts. Note finally how this is parallel to the locality issue. If someone objects that QM contradicts relativity's prohibition on superluminal causation, it is not a successful response to deny realism -- i.e., to deny that light exists, that the speed of light exists, that there is an external world with causal interactions in it, etc...

This is an important point, because Bohr is often interpreted as responding to EPR's claim that the wf was incomplete, by retreating to a kind of anti-realism. And it's important to grasp that this is not a successful response to that charge. In fact, the EPR argument is *valid*, so there is no successful response to it. Either you have to admit that OQM is incomplete, or that nonlocality is real, or you can deny realism and hence wipe both issues (completeness and locality) out. But then one can't come back and say "I refuted the charge that QM was incomplete or nonlocal; it's both complete and local." No, under the assumption of anti-realism, QM is *not* both complete and local. That's *false* because there's no world for QM to provide a complete description of, and no causal interactions in the world for QM to provide a local explanation of.

I hope that's somewhat clarifying...??

 

[DrChinese]

Apparently there is something ambiguous about saying that
local hidden variables are incompatible with qm.

From page 196 of "On the Einstein Podolsky Rosen Paradox" Bell
writes "... there is no difficulty in giving a hidden variable account
of spin measurements on a single particle." Then he shows this
mathematically, concluding with ... "So in this simple case there
is no difficulty in the view that the result of every measurement
is determined by the value of an extra variable, and that the
statistical features of quantum mechanics arise because the value
of this variable is unknown in individual instances."

I see the point you are making better now; however, it is out of context of the EPR and Bell progression.

1. Well before EPR, it was suspected that the observer "shaped" reality by what the observer chose to measure - but no one was sure. It was possible to see the HUP as due to our ignorance, and that future technogical improvements would cross the threshold of the HUP. So local reality was still a reasonable assumption. Local realistic interpretations of QM incorporating the HUP could be applied to single particles and would yield limits to our knowledge. That is what Bell is referring to in your quote above.

2. With EPR, it was shown that in the case of entangled particles, either QM is incomplete or there is not simultaneous reality to non-commuting variables. EPR could not say which, but they guessed that QM was incomplete. Either way, the conclusions applied to single particle interpretations - they simply used the entangled scenario as an example to demonstrate their ideas.

3. Bell came along and burst the bubble on EPR's guess as to local reality, showing it was not compatible with QM. The fact is: it is untenable to assert LR is compatible with QM - it is disproved by counterexample. The counterexample uses entangled particles, but the assumption it overturns applies generally.

QM's HUP requires limits to our knowledge about individual particles. Because of Bell, we know that it is not due to our ignorance - it is because those particles do not have local hidden variables present simultaneously. It is wrong to say that any LR theories are consistent with QM.

 

[vanesch]

The problem is this: "completeness" has a certain *meaning*. It means that some theory (or theoretical entity, like the wave function) captures *all* of the facts that pertain to a given system. It means our description doesn't leave anything out, doesn't miss anything that's really out there. So the very *claim* that the wf alone provides a complete description of the system, *presupposes* the external objective reality of the system.

Yup.

"Incompleteness" means that the wf fails to capture some relevant fact about the real system out there. (A complete description, if the wf is incomplete, would have to supplement the wf with some additional variables.) And that presupposes realism too, just as much as the concept of "completeness" does.

Ok.

So where does this leave us? Well suppose we hold on to realism. Then, if you regard the collapse postulate as merely epistemological, as merely an updating of our knowledge (which doesn't coincide with any physical change to the system), then it would be correct to say that the wf is incomplete. Right?

That's where I don't agree. After all, maybe you only consciously observe a part of the wavefunction (one term). The wavefunction is still real, and unprojected. Your relationship to the wavefunction is what makes you think it collapsed, because (by postulate) now you only consciously observe part of it. That's still some form of realism (less tangible, granted, because now largely unobservable: only one term will remain observable for your conscious observation). This doesn't mean that the wf description is incomplete, does it ? And it allows for a completely locally formulated interaction.

But on the other hand, if you do drop the realism assumption (and retreat to solipsism or whatever) then *both* "completeness" and "incompleteness" are false.

The "relative solipsism" that is needed in no way drops realism, does it ? It tells you what effects a realistic object has on your conscious observation. What could be more real ?

It's not true that the wf provides a complete description of the facts, nor is it true that the wf provides an incomplete description of the facts. There simply are no facts. Note finally how this is parallel to the locality issue. If someone objects that QM contradicts relativity's prohibition on superluminal causation, it is not a successful response to deny realism -- i.e., to deny that light exists, that the speed of light exists, that there is an external world with causal interactions in it, etc...

I think you jumped to the conclusion that because we only observe ONE TERM, that the rest isn't real for some reason. I don't see the reason for that. And if this is correct, then the WF DOES describe ENTIRELY reality (of which we only observe a part).
Also, if this is correct, there is no non-locality issue with Bell, because the remote measurement happened BOTH WAYS at once. Bob saw and Bob didn't see the detector click, at the same time. Only, when this Bob in a superposition gets to you, interference happens when he interacts with you, and out of it come the strange correlations of entangled pairs. So there is no objective probability to be assigned to whatever Bob is doing. There are only objective probabilities to be assigned to what YOU observe, on your worldline, because that's how you hop from interaction to interaction, and each time you only see part of what really happens - hence the probabilistic aspect in your observations, which comes from the hopping, and not from what happens out there (because EVERYTHING happens out there).

This is an important point, because Bohr is often interpreted as responding to EPR's claim that the wf was incomplete, by retreating to a kind of anti-realism. And it's important to grasp that this is not a successful response to that charge. In fact, the EPR argument is *valid*, so there is no successful response to it. Either you have to admit that OQM is incomplete, or that nonlocality is real, or you can deny realism and hence wipe both issues (completeness and locality) out.

I think you're missing the possibility that QM is complete, that locality holds, but that we only observe part of what is really out there, and that this partial observation is responsible for the probabilistic impression we have.

However, all you say is valid if you insist upon that what is observed is real and that the alternatives really didn't take place. Then, indeed, there's no way out. But if what's observed is part of what's real, and what you observe can be different from what I observe - different aspects of the same reality - then I don't see how you come to your conclusion. Except that you "find this silly" ...

 

[Sherlock]

I see the point you are making better now; however, it is out of context of
the EPR and Bell progression.

The point is this: we're talking about two different experimental
setups. One is detecting single particles, the other is correlating
detections of two particles. In the former, an lhv description is
not incompatible with qm. In the latter, an lhv description is
incompatible with qm (and experiment).

I'm asserting that the reason for this is because in the
individual setup an lhv is a factor in determining the results
(per Bell 1964), and in the correlational setup an lhc
(local hidden constant) is a factor in determining the results.

Showing that an lhv is not a factor in determining the
results in the correlational setup ( per Bell, 1964) does not
then mean that an lhv is not a factor in determining individual
results, or that lhv's don't exist.

The counterexample to local realism has only to do with the
correlational setup, but this is not a counterexample to
local realism for the simple reason that lhv's are just not
relevant to the joint results in the correlational setup.

So, I'll repeat my question that you didn't answer. :-)
What happens to these local hidden variables
when we incorporate these individual measurement
events into a correlational context involving other individual
measurement events at spacelike separations from these?
Do the hidden variables just vanish (along with local
reality)? Or is it simply that they aren't determining the
joint results?

If the lhv's simply aren't a factor in determining the joint
results, then isn't it incorrect to say that these setups
show that lhv's don't exist, or that there is no locally
realistic behavior occurring in these setups, or that lhv
descriptions of any setup are therefore ruled out?

 

[ttn]

1. Well before EPR, it was suspected that the observer "shaped" reality by what the observer chose to measure - but no one was sure. It was possible to see the HUP as due to our ignorance,

That's still possible, as shown by the extant hidden variable theories like Bohmian Mechanics.

So local reality was still a reasonable assumption. Local realistic interpretations of QM incorporating the HUP could be applied to single particles and would yield limits to our knowledge. That is what Bell is referring to in your quote above.

What is the source of this seemingly irresistable desire people have to associate locality and realism, as if there were only one issue: "local realism" vs everything else? Whether certain facts exist or not prior to observation, and whether a theory's dynamics respects relativity's prohibition on superluminal causation aren't the same question.

"Reality" is still a damn reasonable assumption. (Really, it's an axiom -- it is necessarily presupposed by any physics at all, and any attempt to deny it refutes itself.) If you mean something narrower, like whether spin-components are real properties (as opposed to "contextual" or "emergent" properties) of particles, well then you should be specific and not imply that somehow anything in QM refutes realism *generally*.

In regard to locality, it depends on what you mean. Signal Locality remains a reasonable assumption. Bell Locality is definitely violated.

Why lump all these together into one vague issue when really there are several distinct issues?

2. With EPR, it was shown that in the case of entangled particles, either QM is incomplete or there is not simultaneous reality to non-commuting variables. EPR could not say which, but they guessed that QM was incomplete.

The alternative you pose is simply the question of whether or not OQM is complete. (The EPR argument attempts to show that non-commuting properties like different spin components *do*, despite the orthodox eigenstate-eigenvalue link, possesses simultaneous definite values. Either they do and OQM is incomplete; or they don't and QM is complete. That's all that issue means.)

It's ridiculous to say that EPR *guessed* that QM was incomplete. This makes it sound like the entire content of the EPR argument is to pose a trivial dilemma (either X or not-X) and then to take a wild stab at answering. ("Ummm, I dunno, how about... not-X!??") The fact is, EPR actually had an *argument* for their conclusion. And the *premise* of this argument was: locality. So EPR didn't simply *guess* that maybe OQM was incomplete. They *proved* that OQM *has* to be incomplete if one insists on respecting locality. Or just saying the same thing differently, they proved that anyone who insists on treating OQM as complete has to contend with the fact that the theory is nonlocal.

3. Bell came along and burst the bubble on EPR's guess as to local reality, showing it was not compatible with QM. The fact is: it is untenable to assert LR is compatible with QM - it is disproved by counterexample. The counterexample uses entangled particles, but the assumption it overturns applies generally.

Now that is doubly ridiculous. Bell "burst the bubble on EPR's guess"?!??! What does this mean? Bell somehow refuted the EPR argument? He absolutely did not. What he showed is that the particular kind of theory lobbied for by EPR as a way of saving the locality principle in the face of the QM predictions (namely, a local hidden variable theory) couldn't work. Bell showed that the kind of theory Einstein probably hoped for couldn't exist, yes. But he didn't refute the EPR argument. It's still true that the completeness claim for QM entails nonlocality. (See quant-ph/0408105.) And Bell proved that the opposite claim -- that QM is *not* complete, that there are hidden variables -- also requires nonlocality. So locality fails. (BTW, by "locality" in this paragraph I mean "Bell Locality".)

QM's HUP requires limits to our knowledge about individual particles. Because of Bell, we know that it is not due to our ignorance - it is because those particles do not have local hidden variables present simultaneously. It is wrong to say that any LR theories are consistent with QM.

There you go again, conflating the issue of hidden variables with the issue of locality. Bell did *not* show that the HUP "is not due to our ignorance." He showed that if you want to have a theory in which the HUP is epistemological rather than fundamental, that theory will have to be nonlocal. EPR had already shown that if you regard the HUP as fundamental (i.e., as "not due to our ignorance") then the resulting theory (OQM) is nonlocal.

So it is totally misleading to say: "It is wrong to say that any L[ocal] R[ealistic] theories are consistent with QM." The correct statement is: "It is wrong to say that any [Local] theory is consistent with QM."

Neither Bell nor EPR nor their combination proves one way or the other whether or not there are hidden variables. The argument for these lies elsewhere (e.g., in the fact that a hv theory can solve the measurement problem).