Aspect/Innsbruck Interpretation which respects SR locality

[Hans de Vries]

--
--

EPR experiments seem to show a significantly higher
correlation rate in the detection of separated photons which
are in an entangled state. From the measured correlation we
may or may not want to draw very fundamental conclusions.

One such a far reaching conclusion would be that our world
is fundamentally non-local and that "action on a distance"
is possible. This would be in serious friction with the Special
Theory of Relativity.

Rather then saying that QM predicts non-locality we need to
be more specific and state that the correlations measured
predict non-locality, that is, if all other alternative local
explanations are exhausted.

The most successful Quantum Field Theory, The Standard Model
which unifies the Electromagnetic, Weak and Strong forces does
not need "action on a distance". Path integrals do not "jump
space" and respect Special Relativity.

Some of the champions of the Standard Model have a strong
preference for local theories. For instance Gerard ‘t Hooft:
http://www.phys.uu.nl/~thooft/quantloss/sld020.htm

--------------------------------------------------

I would like to show an example of how a purely local
interpretation can give a much higher correlation equal
to the results of the Aspect and Innsbruck experiments
without the need for action on a distance.

I will discuss first the “Bell Inequality” case, the non-local
QM case and then the local alternative. I’ll use an example
based on the Wollaston Prism which is used in most if not
all EPR experiments.

The Wollaston Prism splits a light beam in two beams, one
horizontally and one vertically polarized. A single photon
is said to exit at either the horizontal or vertical output, but
never at both.

--------------------------------------------------

We will look at the case where the two entangled photons at
A and B are both polarized at 45 degrees with respect to the
Wollaston prisms:


The Bell inequality case: It is presumed that the photon at
A has a 50:50 % chance to exit at the horizontal or vertical
output and the same is true for the photon at B. However,
the outcome at A and B are presumed to be completely
independent even though the particles are entangled.
The correlation is calculated to be 50%

The non-local QM case: It is presumed that the photon at
A has a 50:50 % chance to exit at the horizontal or vertical
output. However when it exits at for instance the vertical
output then “action on a distance” causes the photon at B to
be also vertically polarized as a result of the measurement at A.
The correlation is assumed to be ~100%

The alternative local model: We presume that both photons
share a property because they are entangled. They are more
equal then other seemingly equal photons. If the photon at
A leaves at the horizontal output then B will generally also leave
at the horizontal output because they share this property.
Although different photons will exit at different sides, entangled
photons will typically leave at the same side resulting in a
correlation of ~100%

--------------------------------------------------


This would mean that the selection process at the Wollaston
Prism is not entirely random anymore but became predeter-
mined by the property at the place where the photons became
entangled.

This then requires a property to be explained. One possibility
I came across stems from the fact that fundamental photons
(spin 1 bosons) are either left or right circular polarized.
So called linear polarized single photons as presumed in the
EPR experiments can not be fundamental since they would
have spin 0.

Linear polarized photons must be considered to be a combination
of a photon with spin up and a photon with spin down. This now
introduces extra degrees of freedom. These degrees of freedom
may be random for arbitrary photons but equal for entangled
photons coming from a PDC.

The particular constitution of the up and down photon may make
the difference in the birefringent beam splitter where a choice
is forced for the 45% polarized combination to exit at either the
horizontal or vertical polarized output.

--------------------------------------------------

This example just goes to show that one should exhaust
all possible local explanations before such far reaching
conclusions as non-locality can be made with certainty.

It’s my opinion that the above alternative should be
disproved convincingly in order to prove non-locality.


Regards, Hans


PS. The difference in correlation in the actual Aspect and
Insbruck experiments is not as high as here stated because
several things are going on at the same time. The photons
are assumed to be superposition states and various different
angles are used randomly (0, 22.5 45 and 67.5 degrees)

 

[vanesch]

One such a far reaching conclusion would be that our world
is fundamentally non-local and that "action on a distance"
is possible. This would be in serious friction with the Special
Theory of Relativity.

The statement that EPR experiments indicate that "quantum mechanics is inherently non-local" is over-stretched. The unitary part of quantum mechanics is (as you point out, in the standard model for example) perfectly local. What is non-local is the projection postulate, when applied too early. In a many-worlds like context, nothing non-local is going on, and this explains also in a quite natural way why we can "see correlations which point to nonlocality after the fact" but that we can never observe them "in real time" and have to wait for the sub-lightspeed signal in order to find it out.

So if you take the attitude that QM only predicts statistics, then there is not really a problem, because nothing "inherently nonlocal" happened. The only thing that is disproved by Bell's inequalities is that these statistics cannot be generated by an underlying local realist model.
If you take the attitude that QM describes physically what happens (my preference) and take the Hilbert space as something physical, then what goes wrong is the collapse at a distance: so simply don't collapse, and you're ok too.

cheers,
Patrick.

 

[vanesch]

I would like to add the following:
If the EPR situation hadn't been motivated by Einstein's viewpoint, and successively by Bell's work, then the experiment could be interpreted in a totally different way, being a "proof" of macroscopic entanglement and not a "proof of non-locality".

Let us imagine that Einstein never insisted on an underlying mechanism that would generate the statistics (hidden variable model) - or for that matter, that Einstein wasn't such a heavy-weight in physics, and that Schroedinger was the "big guy" to whom everyone was paying attention.
Schroedinger (and his cat) claimed somehow that you couldn't have macroscopic superpositions of classical situations "because of the absurdity of the idea" (a cat which is dead and alive at the same time). In fact, Schroedinger understood very well that the unitary evolution of QM automatically lead to entanglement of macroscopic systems.

And let us imagine that an experiment would then be set up to show that even people can be in macroscopic superpositions. How would one try to do that ? How could we verify that Alice is in an entangled state ? The simplest way would be to entangle Alice with a microscopic system which is entangled with another system, of which we know it cannot influence Alice, because it is miles away, in a bunker 50 m underground. And in order to check whether Alice is really entangled, you let her come down later into the bunker, and see if she can interfere with that second microscopic system.
So what do you do ?
You generate 2 entangled particles (say, 2 photons), and "keep one in the bunker" and send off another one to Alice, miles away.

So we have:
|photonspins> = (|bunkerz+>|farawayz-> - |bunkerz->|farawayz+>)|alice0>

(this state is such that we can take z to be any direction)

She "measures" something about the faraway photon (say the spin component in the z-direction), which comes down to entangling her, locally, with that spin component. So we have now Alice in an entangled state:

|bunkerz+>|farawayz->|alicez-> - |bunkerz->|farawayz+>|alicez+>

This is the kind of state Schroedinger objected to. Note that to obtain the state, there has only been a LOCAL interaction at Alice's place, between her and the faraway photon.
|alicez-> is the Alice who saw a z- state, and |alicez+> is the Alice who saw a z+ state.

Now, how could we find out whether this superposition is total nonsense or not ? Let us let Alice INTERFERE with the state of the bunker photon !

So the two states of Alice now take the train, and come down to the bunker. In doing so, she gets extra correlated with a lot of environment, like the guy in her compartment to whom she shows her notebook etc... So you can now take on the situation in which |alicez-> stands in fact not only for alice, but also for the guy in the train and everything which gets correlated with her. It doesn't matter.

If Alice now comes into the bunker, and she decides to measure the spin of the other photon, which is still whirling around in optical fibers, if she's in an entangled state, she will get an interference result which shows in her correlations between her notebook of the faraway photon and the local bunker photon.
So Alicez- will work with the |bunkerz+> state and find accordingly the correct correlations, while Alicez+ will work with the |bunkerz-> state and will also find the correct correlations. So in both cases, Alice will realize she finds correlations with the state she's supposed to find *as if she collapsed the wavefunction* at a distance during her first "measurement". But in fact, her two states interfered with the bunker photon ! And of course, locally in the bunker, nothing "collapsed" when she did the other measurement !

So this experiment, which shows interference between the Alice states in her notes, shows us that we have to take the macroscopic superpositions seriously. This could have been the aim of the experiment.

If you take quantum mechanics seriously, you don't even need the Bell inequalities to prove the point. The very fact that Alice, if she measures the z-components everywhere, always finds perfect anticorrelation, indicates already her superposition. This is the outcome when you stay within the framework of QM, but you wonder whether it makes sense to talk about macroscopic superpositions.

But you then might find the objection that *maybe we don't know, but the photons DO carry hidden variables with them giving you the outcomes for the spins*. And in fact, the original "entanglement" of the two photons just meant a correlation of the hidden variables, like the classical example with a red and a black marble in two bags: if you know that there is a red marble in YOUR bag, you automatically know that there must be a black marble in the other bag. Note that saying that already gets us out of the scope of QM, because it means that the initial entanglement of the two photons is just an expression of a correlation of underlying hidden variables. It is at that point that Bell's inequalities show us that for certain combinations of choices of measurement by Alice, you cannot find hidden variables which could generate you the same correlations in her notebooks.

You can even increase the power of the experiment in proving that macroscopic entanglements must exist, by using 2 human beings, Alice and Bob, who measure simultaneously some spin components: Bob in the bunker, and Alice far away, and then they both take the train and meet in some intermediately located railway station.
Then it is the entangled Bob state which interferes with the entangled Alice state, and out come a superposition of "bob and alice" product states which have correct notes.

At no point in this discussion, locality has been put in doubt. What has been studied is whether macroscopic superpositions make sense, and the experiment gives strong hints that yes, you have to take macroscopic superpositions into account, if you do not want to "collapse wavefunctions" at 50 miles, 700 meter underground, in a bunker, and of which we never got any theoretical nor experimental indication.
Of course, if you INSIST on that collapse because you cannot stand the idea of macroscopic superpositions, you get into all kinds of weird ideas,such as non-locality, signalling back in time, and so on. But if you accept QM AS IT IS, there is no problem.

cheers,
Patrick.

 

[gptejms]

Hans,
Given my little knowledge of QFT,I've the following question.
Could we assume the following picture for a linearly polarized photon:-it is a mixture of two one-photon states,one left circularly polarized and another right circularly polarized with equal probability amplitudes for both the states?
If yes,then the following question arises:-if such a photon is passed thru a polarizer how do you calculate the probability of it passing thru a polarizer?Do you first calculate the prob. amplitudes for the two states passing thru the polarizer,add them and then square to get the probability or you calculate the probabilities for the two states and simply add them?
The former looks to me the right thing to do.If yes,one needs to re-do the EPR calculations and see what we get.

 

[vanesch]

Hans,

If you only want Hans to reply, then ignore my message

Could we assume the following picture for a linearly polarized photon:-it is a mixture of two one-photon states,one left circularly polarized and another right circularly polarized with equal probability amplitudes for both the states?
If yes,then the following question arises:-if such a photon is passed thru a polarizer how do you calculate the probability of it passing thru a polarizer?Do you first calculate the prob. amplitudes for the two states passing thru the polarizer,add them and then square to get the probability or you calculate the probabilities for the two states and simply add them?
The former looks to me the right thing to do.If yes,one needs to re-do the EPR calculations and see what we get.

Ha, you hit the nail on its head. The question is, again and again: when do we use the Born rule ?
If you consider the first case, namely you calculate the coefficient of the vector component that gets through the polarizer, then you postpone the use of the Born rule - and that's what you should do.
If you apply the Born rule BEFORE the polarizer, then you calculate the individual probabilities.

Let's have a look: we take right-polarized photon |r> ; left : |l>
we take linear x-polarized light: |x> and y-polarized light |y>

we have that |r> = 1/sqrt(2) ( |x> + i |y>)
and : |l> = 1/sqrt(2) (|x> - i |y> )

You can inverse easily these two linear equations:

|x> = 1/sqrt(2) (|r> + |l> )
|y> = - i /sqrt(2) (|r> - |l> )

Let us assume we have an |x> state. You consider somehow the r/l base as more fundamental, so we say that |x> is a superposition of |r> and |l>.

probability to be in the |r> state: 1/2 and probability to be in the |l> state: 1/2. That's applying Born's rule, and you transform in fact the superposition into a statistical mixture.
But this goes terribly wrong !
Namely, what's the probability of an |r> state to be x-polarized ? It is 1/2.
Same for an |l> state. So how much of our original |x> state gets through an x-polarizer ??
1/2 x 1/2 + 1/2 x 1/2 = 1/4 + 1/4 = 1/2

So x-polarized light only gets half through an x-polarizer ? ERROR !

No, you have to work with the Hilbert states. An |x> state is an eigenstate of the polarizer measurement, which has eigenvalue 1 for |x> and eigenvalue 0 for |y>. So an |x> state, being an eigenvector, will get through it 100%.

cheers,
Patrick.

 

[gptejms]

Thanks vanesch for your imp. input.
Coming back to Hans:-it's amply clear that for a state like |x>,the prob. amplitude for the photon to pass thru a polarizer directed along |x'>, at an anlgle \theta to |x>,is <x'|x> = \cos \theta---the probability is \cos^2 \theta--i.e. Malus' law is satisfied in this quantum scenario.For the classical case,treatment as in posts in the thread 'Bell's theorem and negative probabilities' stands.So nothing new really arises by considering left/right circular polarizations of a photon.

 

[DrChinese]

1. EPR experiments seem to show a significantly higher correlation rate in the detection of separated photons which
are in an entangled state. From the measured correlation we
may or may not want to draw very fundamental conclusions.

One such a far reaching conclusion would be that our world
is fundamentally non-local and that "action on a distance"
is possible. This would be in serious friction with the Special
Theory of Relativity.

Rather then saying that QM predicts non-locality we need to
be more specific and state that the correlations measured
predict non-locality, that is, if all other alternative local
explanations are exhausted.

2. The Bell inequality case: It is presumed that the photon at
A has a 50:50 % chance to exit at the horizontal or vertical
output and the same is true for the photon at B. However,
the outcome at A and B are presumed to be completely
independent even though the particles are entangled.
The correlation is calculated to be 50%

3. This would mean that the selection process at the Wollaston
Prism is not entirely random anymore but became predeter-
mined by the property at the place where the photons became
entangled.

Regards, Hans

1. I agree: this is actually exactly what the Bell Theorem leads us to... but many folks cannot see how we could get the correlations without locality being violated. So they assume non-locality is observed. But that is not strictly a consequence of Bell. Reality - as we commonly understand it - may not be an accurate way to look at the universe. I.e. it's a local non-realistic universe rather than a non-local realistic universe.

2. I do not follow you here. Bell clearly contemplated that local reality (LR) yielded identical predictions to QM, not different ones.

3. I couldn't follow your logic on this one. As I understand it, you are saying that we are measuring something different than a spin 1 particle. But how does that make the Bell Theorem conclusion - no local hidden variables - disappear?

 

[vanesch]

I.e. it's a local non-realistic universe rather than a non-local realistic universe.

Right ! The issue is not locality, but "realism" (in the classical sense). But if you push in realism by all means, then it looks like locality is violated, causality is violated and all this in such a way that... you cannot really violate causality or locality


cheers,
patrick.

 

[DrChinese]

Right ! The issue is not locality, but "realism" (in the classical sense). But if you push in realism by all means, then it looks like locality is violated, causality is violated and all this in such a way that... you cannot really violate causality or locality


cheers,
patrick.

Yes, I am glad you said that. I think it is also interesting that the same kind of spooky actions that happen in an EPR setup - i.e. instantaneous collapse of the wave function - also happen in plenty of other situations in which locality isn't an issue. Presumably, covering up one slit in a double slit experiment immediately changes something at the other slit. (And no one has a cow about that even though it is no different.) So the point is that EPR tests really show nothing surprisingly new, they just show it so well!

 

[Caroline Thompson]

--
--EPR experiments seem to show a significantly higher
correlation rate in the detection of separated photons which
are in an entangled state. From the measured correlation we
may or may not want to draw very fundamental conclusions.

In view of the various loopholes in the experiments, whether or not the observed correlation is incompatible with local realism is debatable. I'm interested, though, in your point about Wollaston prisms not necessarily splitting even light polarised at 45 deg 50-50. I'm beginning to accumulate evidence, not so much from EPR experiments as from other quantum optics ones, that the behaviour of the light may be influenced by the phase difference between the horizontal and vertical components. This applies only when the source is a PDC one, but in practice this means nearly every recent quantum optics experiment.

I'm afraid I have little use for the "photon" concept, or for the idea that plane polarised light is always formed by the addition of right and left circularly polarised waves. PDC outputs are sometimes polarised exactly vertically or exactly horizontally, but sometimes, I believe, both at once. In these cases, the phase difference between the two components is undeniably critical to the way the light splits at a Wollaston prism. The matter is mentioned in a footnote to Weihs et al's report of their 1998 Bell test at Innsbruck -- it comes from the standard classical theory of light. [I discuss how this may explain Weihs' results in http://arxiv.org/abs/quant-ph/9912082.]

There may, though, be other subtle properties of the light and of the prism that influence the proportion in which the energy of an individual pulse of light it is split. The prism is actually a pair of prisms, with carefully-engineered layers of dielectric or metal, of thickness 1/2 or 1/4 wavelength, between the them. The behaviour of the light may well be influenced by its exact wavelength, with 50-50 splitting occurring only when that wavelength exactly matches the one for which the prism was designed.

No time for more ...

Caroline

http://freespace.virgin.net/ch.thompson1/

 

[DrChinese]

I'm interested, though, in your point about Wollaston prisms not necessarily splitting even light polarised at 45 deg 50-50. I'm beginning to accumulate evidence, not so much from EPR experiments as from other quantum optics ones, that the behaviour of the light may be influenced by the phase difference between the horizontal and vertical components. This applies only when the source is a PDC one, but in practice this means nearly every recent quantum optics experiment.

...

There may, though, be other subtle properties of the light and of the prism that influence the proportion in which the energy of an individual pulse of light it is split. The prism is actually a pair of prisms, with carefully-engineered layers of dielectric or metal, of thickness 1/2 or 1/4 wavelength, between the them. The behaviour of the light may well be influenced by its exact wavelength, with 50-50 splitting occurring only when that wavelength exactly matches the one for which the prism was designed.

This argument deftly diverts us from the essence of the experimental results (which do not support local realism and do support the predictions of QM). If there was no correlation observed, this might be meaningful. But since we see strong correlations, this issue is totally meaningless. It doesn't matter what kind of splitter is used as long as efficiency is high. And it also doesn't matter is there is some anisotropy. There cannot be "accidental" agreement due to a local polarizer bias in this kind of setup.

 

[Hans de Vries]

I would like to add the following:
If the EPR situation hadn't been motivated by Einstein's viewpoint, and successively by Bell's work, then the experiment could be interpreted in a totally different way, being a "proof" of macroscopic entanglement and not a "proof of non-locality".

In a similar sense I've got the feeling that, If Einstein, Podolsky and
Rosen would have been familiar with the Fourier Interpretation of
Heisenberg's Uncertainty Relation, we not would have the hidden
variables so much in the in the center of the discussion.

From the EPR paper on DrChinese's website:

From this follows that either (1) the quantum-mechanical description
of reality given by the wave function is not complete or (2) when the
operators corresponding to two physical quantities do not commute
the two quantities cannot have simultaneous reality. For if both
of them had simultanous reality-and thus definite values-these values
would enter into the complete description.

So it's either (1) Hidden Variables or (2) No "simultaneous reality"


Regards, Hans

 

[Hans de Vries]

Hans,
Given my little knowledge of QFT,I've the following question.
Could we assume the following picture for a linearly polarized photon:-it is a mixture of two one-photon states,one left circularly polarized and another right circularly polarized with equal probability amplitudes for both the states?
If yes,then the following question arises:-if such a photon is passed thru a polarizer how do you calculate the probability of it passing thru a polarizer?Do you first calculate the prob. amplitudes for the two states passing thru the polarizer,add them and then square to get the probability or you calculate the probabilities for the two states and simply add them?
The former looks to me the right thing to do.If yes,one needs to re-do the EPR calculations and see what we get.

The complication I see is the nature of the birefringent Calcite of the
Wollaston Prisms. It has a different diffraction index for horizontal and
vertical polarized light. (n_E = 1.4864, n_O = 1.6585) which means that
the speed of light depends on the polarization of the photons. Now
what will be the effect on a circular polarized photon (spin up or down) ?



http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/cdopt.html

Regards, Hans

 

[vanesch]

Now
what will be the effect on a circular polarized photon (spin up or down) ?

This is classical optics
Remember the quarter wavelength plates which transform linearly polarized light under 45 degrees into circularly polarized light ?

It is quite straightforward:

If |pol> is your incoming polarization, then you write |pol> in the x-y basis:
|pol> = a |x> + b |y>

|x> will follow the evolution with a refractive index n_x, and |y> will follow the evolution with a refractive index n_y.

This means that you can calculate how many wavelengths w_x have been gone through for the x-part (from the incoming surface of your optical device to the outgoing surface), and idem for w_y. Each component will then get a phase factor equal to exp(i 2 pi w_j), so the outgoing polarization is:

|pol-out> = a exp(i 2 pi w_x) |x> + b exp( i 2 pi w_y) |y>

( I use here QM notation, but the calculation is identical in classical optics of course).

Exercise: pure |x> will remain pure |x> and pure |y> will remain pure |y> (both get a phase factor: some optical path length).

Exercise: 1/4 wavelength plate:
incoming linear polarized under 45 degrees:
|pol> = 1/sqrt(2) (|x> + |y>)

quarter wavelength: w_x = n ; w_y = n + 1/4

thus: |pol-out> = 1/sqrt(2) ( |x> + i |y>)

circularly polarized light (due to the i)

Exercise: 1/2 wavelength plate:
incoming linear polarized under 45 degrees:
|pol> = 1/sqrt(2) (|x> + |y>)

w_x = n ; w_y = n + 1/2

|pol> = 1/sqrt(2) (|x> - |y>)

linearly polarized light which is 90 degrees rotated with incoming polarization!

Optics is fun.

cheers,
Patrick.

 

[Caroline Thompson]

This is classical optics
Remember the quarter wavelength plates which transform linearly polarized light under 45 degrees into circularly polarized light ? ...

Quite. This classical optics is what I was talking about.

Caroline

 

[caribou]

Right ! The issue is not locality, but "realism" (in the classical sense). But if you push in realism by all means, then it looks like locality is violated, causality is violated and all this in such a way that... you cannot really violate causality or locality

You just reminded me of something Murray Gell-Mann and Jim Hartle said about EPR. Here's the quote, the italics are theirs.

This behaviour, although unfortunately called "non-local" by some authors, involves no non-locality in the ordinary sense of quantum field theory and no possibility of signaling outside the light cone. The problem with the "local realism" that Einstein would have liked is not the locality but the realism. Quantum mechanics describes alternative decohering histories and cannot assign "reality" simultaneously to different alternatives because they are contradictory.

That's from their paper, Quantum Mechanics in the Light of Quantum Cosmology, the first paper to describe their Decoherent Histories work to clarify quantum theory. It's not freely available online but I have a scanned copy.

If you haven't read their work on this already, then I think you'll find it very interesting. Hartle introduces some parts of their work here in a different paper that talks about the two-slit experiment:

http://arxiv.org/abs/gr-qc/9210006

 

[JesseM]

The statement that EPR experiments indicate that "quantum mechanics is inherently non-local" is over-stretched. The unitary part of quantum mechanics is (as you point out, in the standard model for example) perfectly local. What is non-local is the projection postulate, when applied too early. In a many-worlds like context, nothing non-local is going on, and this explains also in a quite natural way why we can "see correlations which point to nonlocality after the fact" but that we can never observe them "in real time" and have to wait for the sub-lightspeed signal in order to find it out.

How is "locality" defined in the context of quantum theory? This isn't obvious to me if you represent a system's state as a vector in Hilbert space. For a classical field, each point in space is assigned a force vector, and "locality" basically means that the direction and magnitude of the vector at a given point in spacetime depends on the vectors at all the points in its past light cone, but does not depend on the vectors at points outside the past light cone. Can a system's quantum state be described by assigning some mathematical entity (analogous to the force vector) to each point in space, with "locality" having the same sort of meaning?

 

[vanesch]

How is "locality" defined in the context of quantum theory? This isn't obvious to me if you represent a system's state as a vector in Hilbert space.

The Hilbert space state is of course not local, in the same way as a point in classical phase space is not "local". By local is meant only that physical processes only work on the components of the tensor product of spaces which correspond to systems which are local.
So if we have a general state in the space H1xH2xH3 where system 1, described by H1, is far away, and H2 and H3 are systems in each other's neighbourhood, then the general state:

a |u1>|u2>|u3> + b |v1>|v2>|v3>

undergoing a local physical process involving H2 and H3
can only change |u2>|u3> into something else and |v2>|v3> into something else, according to the same unitary transformation U23.
Locally at "23" you cannot do anything about u1 or even know anything about it ; it is completely transparant to the physics at "23".
I think this is what is generally meant with locality: an interaction can only influence the part of the description which corresponds to local systems.

cheers,
Patrick.

EDIT: I should point out maybe that what I think is understood by "locality" is "the ability to influence, through interaction" and not "the description of the state of the universe". In fact, in pre-relativistic physics, locality might have been a philosophically satisfying, but not strictly necessary requirement. It is relativity which makes "locality" equivalent to "causality". And causality is a much harder thing to sacrifice.
But all this has only to to with *interactions*. So as long as interactions only influence that part of the state description which has to do with the locally available systems, I think one can conclude that the theory is "local" in the sense required by relativity and causality.

So in quantum theory, the state description is not local, but the interactions satisfy locality, at least as long as one doesn't apply the projection postulate. The projection postulate is bluntly non-local ; so if the projection postulate is part of the possible sets of interactions in nature, then there is a real problem with causality ; and it is THIS thing which people are always talking and writing about. But - as I tried to point out several times - you don't need to apply that postulate non-locally: you can wait until you arrive at your final, local, measurement of the correlations (after Bob and Alice came together to compare their notebooks). And if you do so, all the mystique of the non-locality of QM drops. The mystery is not so much in the fact that it could have been non-local (and hence non-causal), but in that the inherent mechanism in QM is such that it is non-local and non-causal, but that each time you would like to USE that non-locality to make a faster-than-light phone, somehow there is a conspiracy in the theory that forbids you to do so.
If you understand that there is also a non-a-causal explanation to the EPR experiments (with Alice and Bob in entangled states), then this "conspiracy" is easily explained.

EDIT2:
the fact that you want to assign numbers to each local system (for instance, through fields) which will then determine completely (deterministically or stochastically) what will happen to that local system, I would call that "realism", in that there is a complete description of the local system which corresponds to its "real behaviour".

For instance, Newton's theory of gravity is realist but non-local (the "real state" of each particle is locally described by its velocity and (of course) its location) but gravity works at a distance.
Maxwell's electromagnetism is realist and local (all you need to know locally about the state of the EM field is given by the local values of E and B ; and they influence each other only through their derivatives).
Quantum theory is non-realist but local.

 

[vanesch]

basically means that the direction and magnitude of the vector at a given point in spacetime depends on the vectors at all the points in its past light cone, but does not depend on the vectors at points outside the past light cone.

A more formal answer: yes, in QFT, field operators which correspond to spacetime events which are space-like connected, commute. This is the requirement of locality in QFT. It comes down to what I said in my previous post: an interaction, depending on the field operators at A, will not influence any component of the state vector at B.

cheers,
Patrick.

 

[Hans de Vries]

2. I do not follow you here. Bell clearly contemplated that local reality (LR) yielded identical predictions to QM, not different ones.

Let's see. are you assuming here that for the case of 45 degrees Bell
and entangled QM should be equal? That is, in the electron LR theory
of Bell?

The two differences here are
1) is that were looking at photons.
2) is that both a and b have equal angles.

So we have the 0 degrees case here. See figure 4 of Aspect
http://www.drchinese.com/David/EPR_Bell_Aspect.htm
and figure 3. of Caroline's paper which shows the idealized QM and LR
curves. http://arxiv.org/abs/quant-ph/9903066

3. I couldn't follow your logic on this one. As I understand it, you are saying that we are measuring something different than a spin 1 particle. But how does that make the Bell Theorem conclusion - no local hidden variables - disappear?

If a linear polarized photon is a composition of a spin up and a spin
down particle then there are extra degrees of freedom to combine
them. These extra degrees of freedom may be random in general but
equal in the two entangled particles.

The extra degrees of freedom may also influence the outcome of the
measurement and thus increase the correlation well beyond what is
shown in figure 3 of Caroline's paper for the LR case.

Caroline's calculation for the LR case assumes that the only thing they
have in common is the polarization angle.


Regards, Hans

 

[Hans de Vries]

In view of the various loopholes in the experiments, whether or not the observed correlation is incompatible with local realism is debatable. I'm interested, though, in your point about Wollaston prisms not necessarily splitting even light polarised at 45 deg 50-50. I'm beginning to accumulate evidence, not so much from EPR experiments as from other quantum optics ones, that the behaviour of the light may be influenced by the phase difference between the horizontal and vertical components. This applies only when the source is a PDC one, but in practice this means nearly every recent quantum optics experiment.

I'm afraid I have little use for the "photon" concept, or for the idea that plane polarised light is always formed by the addition of right and left circularly polarised waves. PDC outputs are sometimes polarised exactly vertically or exactly horizontally, but sometimes, I believe, both at once. In these cases, the phase difference between the two components is undeniably critical to the way the light splits at a Wollaston prism. The matter is mentioned in a footnote to Weihs et al's report of their 1998 Bell test at Innsbruck -- it comes from the standard classical theory of light. [I discuss how this may explain Weihs' results in http://arxiv.org/abs/quant-ph/9912082.]

There may, though, be other subtle properties of the light and of the prism that influence the proportion in which the energy of an individual pulse of light it is split. The prism is actually a pair of prisms, with carefully-engineered layers of dielectric or metal, of thickness 1/2 or 1/4 wavelength, between the them. The behaviour of the light may well be influenced by its exact wavelength, with 50-50 splitting occurring only when that wavelength exactly matches the one for which the prism was designed.

No time for more ...

Caroline

http://freespace.virgin.net/ch.thompson1/

Thanks, Caroline.

I will have a look at this Weihs story. If you have more info on
this kind of specifics on the exact functioning of the PDC's used
or the Wollaston prisms, please let me know.


Regards, Hans

 

[JesseM]

EDIT2:
the fact that you want to assign numbers to each local system (for instance, through fields) which will then determine completely (deterministically or stochastically) what will happen to that local system, I would call that "realism", in that there is a complete description of the local system which corresponds to its "real behaviour".

For instance, Newton's theory of gravity is realist but non-local (the "real state" of each particle is locally described by its velocity and (of course) its location) but gravity works at a distance.
Maxwell's electromagnetism is realist and local (all you need to know locally about the state of the EM field is given by the local values of E and B ; and they influence each other only through their derivatives).
Quantum theory is non-realist but local.

But if one favors the Everett interpretation, then under this interpretation quantum theory would be realist--the wavefunction of the universe would be a complete description of the universe at any given moment. As you say in your post, it would also be "local" in the sense that observers can't transmit information faster than light, but would there be any way to break up the state of the whole wavefunction into a bunch of local chunks of information, in the way that the state of a whole classical field can be broken up into information about the force vectors at each point in space?

I came across this paper which seems to argue (although I may be misunderstanding) that you can get such a local description of the universe's state if you use the Heisenberg picture, where it's the operators that change over time rather than the wavefunction:

In the Everett interpretation the nonlocal notion of reduction of the wavefunction is eliminated, suggesting that questions of the locality of quantum mechanics might indeed be more easily addressed. On the other hand, while wavefunctions do not suffer reduction in the Everett interpretation, nonlocality nevertheless remains present in many accounts of this formulation. In DeWitt’s (1970) often-quoted description, for example, “every quantum transition taking place on every star, in every galaxy, in every remote corner of the universe is splitting our local world on Earth into myriads of copies of itself.” Contrary to this viewpoint, others argue (Page, 1982; Tipler, 1986, 2000; Albert and Loewer, 1988; Albert, 1992; Vaidman, 1994, 1998, 1999; Price, 1995; Lockwood, 1996; Deutsch, 1996; Deutsch and Hayden, 2000) that the Everett interpretation can in fact resolve the apparent contradiction between locality and quantum mechanics. In particular, Deutsch and Hayden (2000) apply the Everett interpretation to quantum mechanics in the Heisenberg picture, and show that in EPRB experiments,1 information regarding the correlations between systems is encoded in the Heisenberg-picture operators corresponding to the observables of the systems, and is carried from system to system and from place to place in a local manner. The picture which emerges is not one of measurement-type interactions “splitting the universe” but, rather, producing copies of the observers and observed physical systems which have interacted during the (local) measurement process (Tipler, 1986).

Likewise, in this paper by the same author, I think he's arguing that the Everett interpretation of quantum field theory can also be understood in terms of information encoded in purely local operators:

In the Everett interpretation, correlations between the two experimenters’ results are not at issue; rather, a different question of causation arises. According to Everett, both possible outcomes, spin-up and spin-down, occur at each analyzer magnet and, at the conclusion of the experiment, there are two copies of each experimenter.2 When they compare their respective results using some causal means of communication, Alice-who-saw-spin-up only talks to Bob-who-saw-spin-down, and Alice-who-saw-spin-down always converses with Bob-who-saw-spin-up. What is the mechanism which brings about this perfect anticorrelation in the possibilities for exchange of information between the Alices and the Bobs?

Deutsch and Hayden(21) have identified this mechanism. In the Heisenberg picture of quantum mechanics, the properties of physical systems are represented by time-dependent operators. When two systems interact, the operators corresponding to the properties of each of the systems may acquire nontrivial tensor-product factors acting in the state space of the other system. These factors are in effect labels, appending to each system a record of the fact that it has interacted with a certain other system in a certain way.(22) So, for example, when the two particles in the EPRB experiment are initially prepared in the singlet state, the interaction involved in the preparation process causes the spin operators of each particle to contain nontrivial factors acting in the space in which the spin operators of the other particle act. When Alice measures the spin of one of the particles, the operator representing her state of awareness ends up with factors which act in the state space of the particle which she has measured, as well as in the state space of the other particle. The operator corresponding to Bob’s state of awareness is similarly modified. When the Alices and Bobs meet to compare notes, it is these factors which lead to the correct pairing-up of the four of them.

The amount of information which even a simple electron carries with it regarding the other particles with which it has interacted is thus enormous. In Ref. 22 I termed this the problem of “label proliferation,” and suggested that the physical question of how all this information is stored3 might receive an answer in the framework of quantum field theory.

More generally, quantum field theory is a description of nature encompassing a wider range of physical phenomena than the quantum mechanics of particles; it is therefore of interest to investigate the degree to which the conceptual picture of the labeling mechanism for bringing about correlations at a distance in a causal manner accords with the field-theoretic formalism.

Indeed, there is a simple line of argument which leads to the conclusion that Everett interpretation Heisenberg-picture quantum field theory must be local. The dynamical variables of the theory are field operators defined at each point in space, whose dynamical evolution is described by local (Lorentz-invariant, in the relativistic case) differential equations. And the Everett interpretation removes nonlocal reduction of the wavefunction from the formalism. So how can nonlocality enter the scene?

This argument as it stands is incorrect, but it can be modified so that its conclusion, the locality of Everett-interpretation Heisenberg-picture quantum field theory, holds. What is wrong is the following: While it is certainly true that operators in Heisenberg-picture quantum field theory evolve according to local differential equations, it is not in general true that all of the information needed to determine the outcomes and probabilities of measurements is contained in these operators. Initial-condition information, needed to determine probabilities, resides in the time-independent Heisenberg-picture state vector. Since not all information is carried in the operators, is incorrect to argue that the local evolution of the operators implies locality of the theory.

However, as discussed in Sec. 4 below, it turns out to be possible to transform from the usual representation of the Heisenberg-picture field theory to other representations in which the operators also carry the initial-condition information. So, in these representations, the simple argument above for the locality of Heisenberg-picture quantum field theory is valid. Bear in mind that in these representations the use of the Everett interpretation still is crucial for the theory to be local. As mentioned above, the Everett interpretation removes a source of explicit nonlocality in the theory (wavefunction collapse); it “defangs” the Bell argument that, notwithstanding the explicitly local transfer of information in the operators, something else of a nonlocal nature must be going on; and it provides labeling as an alternative to the “instruction set” mechanism which in single-outcome interpretations appears as the only explanation for correlations-at-a-distance and which is what ultimately leads to Bell’s theorem. This last issue of instruction sets and labels is no different in field theory than in first-quantized theory, and is discussed in Ref 22. In field theory as in first-quantized theory, interaction-induced transformations of Heisenberg-picture operators (field operators, of course, in the field theory case—see e.g., eq. (154) below) serve to encode the label information.

 

[vanesch]

but would there be any way to break up the state of the whole wavefunction into a bunch of local chunks of information, in the way that the state of a whole classical field can be broken up into information about the force vectors at each point in space?

Hi !

Thanks for these papers. The first one I knew of, the second I'll have to read ; but in any way it comes rather close to the view I have concerning the locality (the *dynamical* locality) of QM. I should look closer at the formalism, but I would be surprised that a simple switch from the Schroedinger to the Heisenberg picture would solve the issue of the non-holisitic aspect of the theory in its description ; after all, they are mathematically equivalent !

But I think that on the issue of the "locality" required by relativity, all should be clear (in that it is satisfied in QM, so that nothing physically happens "at a distance"). No FTL telephone.

Concerning the Everett-like interpretations, I think it is hard not to consider them. When I say everett-like, I mean the idea that macroscopic systems can be in a superposition of classical states ; I do not think however that the Everett program itself will ever work out (that we can derive an "effective Born rule" from unitary QM) ; I'm convinced that there is some 'real physics' in the Born rule itself. People like Penrose think it has something to do with gravity - but everything done recently in that area seems to point out to the contrary ; namely that gravity will not alter the superposition principle.

cheers,
Patrick.

 

[vanesch]

But if one favors the Everett interpretation, then under this interpretation quantum theory would be realist--the wavefunction of the universe would be a complete description of the universe at any given moment.

The problem is that then, every physical theory is realist (the word looses its meaning). After all, no matter what theory, its formalism will be "real" in the Platonic sense and is the "machinery that produces the numbers I observe", so the "real description" of the universe.

I saw "realism" as a more constrained way, in that "what is observed is really there, locally encoded in the thing we're observing". So if I see an electron with a spin-up, because that's what my detector says, then I say that there really is an electron with a spin up, and it is spin up even if I wouldn't have observed it. And that's of course NOT possible in QM. The only thing that QM says is that the part of my state that corresponds to my conscient observation that I experience is entangled with the part of the electron's state that has spin up, but there can (or cannot) be other parts of the electron's state that are different (say, spin down), but of which I will never hear again. So the "realism" has shifted from "it is really there" to "a relationship between me, my observations, and part of what's there".


cheers,
Patrick.

 

[DrChinese]

Let's see. are you assuming here that for the case of 45 degrees Bell
and entangled QM should be equal? That is, in the electron LR theory
of Bell?

The two differences here are
1) is that were looking at photons.
2) is that both a and b have equal angles.

So we have the 0 degrees case here. See figure 4 of Aspect
http://www.drchinese.com/David/EPR_Bell_Aspect.htm
and figure 3. of Caroline's paper which shows the idealized QM and LR
curves. http://arxiv.org/abs/quant-ph/9903066

Hans,

I looked at the references. Here is my point:

a. The Local Realist (LR) position in 1935 was that the predictions of QM were correct, but was not a complete specification of the system. Therefore P(QM)=P(LR) and the curve Caroline shows as the LR curve in her paper was not representative of the general LR position at that time. Perhaps there was a camp back then that predicted her LR curve 1/8+1/4cos^2\theta but I am completely unaware of that from a historical perspective.

b. After Bell showed the flaw in the above thinking (i.e. that LR could NOT successfully mimic QM), there have clearly been some folks who have tried to develop alternatives. It is true that the 1/8+1/4cos^2\theta fits nicely into the area which falls within the Inequalities and fits with the concept that there is no entanglement. I don't recall seeing a single reference to such predictions FOR ENTANGLED PHOTONS other than Caroline's references to it. I am not saying they aren't out there, I just haven't seen them once in looking at plenty of books and papers on the subject.

c. The obvious explanation of that to me is that there has never been any serious support for that position, given the existence and success of QM. A review of the usual EPR test papers will show that the comparision of experimental results is always between the QM prediction and the bounds of the Bell Inequality being tested. The "LR predicted" value is never presented because there is no such commonly accepted value. That would change if future experiments yielded a different set of results.

 

[JesseM]

The problem is that then, every physical theory is realist (the word looses its meaning). After all, no matter what theory, its formalism will be "real" in the Platonic sense and is the "machinery that produces the numbers I observe", so the "real description" of the universe.

I saw "realism" as a more constrained way, in that "what is observed is really there, locally encoded in the thing we're observing". So if I see an electron with a spin-up, because that's what my detector says, then I say that there really is an electron with a spin up, and it is spin up even if I wouldn't have observed it. And that's of course NOT possible in QM. The only thing that QM says is that the part of my state that corresponds to my conscient observation that I experience is entangled with the part of the electron's state that has spin up, but there can (or cannot) be other parts of the electron's state that are different (say, spin down), but of which I will never hear again. So the "realism" has shifted from "it is really there" to "a relationship between me, my observations, and part of what's there".


cheers,
Patrick.

At one point when I was thinking about how the Everett interpretation could explain the results of the EPR experiment in a local realist way, I came up with the following analogy to show how in principle an Everett-like interpretation could do this:

say Bob and Alice are each receiving one of an entangled pair of photons, and their decisions about which spin axis to measure are totally deterministic, so the only "splitting" necessary is in the different possible results of their measurements. Label the three spin axes a, b, and c. If they always find opposite spins when they both measure their photons along the same axis, a local hidden-variables theory would say that if they choose different axes, the probability they get opposite spins must be at least 5/9 (assuming there's no correlation between their choice of which axes to measure and the states of the photons before they make the measurement). I forgot what the actual probability of opposite spins along different axes ends up being in this type of experiment, but all that's important is that it's less than 5/9, so for the sake of the argument let's say it's 1/3.

So suppose Bob's decision will be to measure along axis a, and Alice's decision will be to measure along axis c. When they do this, suppose each splits into 6 parallel versions, 3 measuring spin + and 3 measuring spin -. Label the 6 Bobs like this:

Bob 1: a+
Bob 2: a+
Bob 3: a+
Bob 4: a-
Bob 5: a-
Bob 6: a-

Similarly, label the 6 Alices like this:

Alice 1: c+
Alice 2: c+
Alice 3: c+
Alice 4: c-
Alice 5: c-
Alice 6: c-

Note that the decision of how they split is based only on the assumption that each has a 50% chance of getting + and a 50% chance of getting - on whatever axis they choose, no knowledge about what the other one was doing was needed. And again, only when a signal traveling at the speed of light or slower passes from one to the other does the universe need to decide which Alice shares the same world with which Bob...when that happens, they can be matched up like this:

Alice 1 (c+) <--> Bob 1 (a+)
Alice 2 (c+) <--> Bob 2 (a+)
Alice 3 (c+) <--> Bob 4 (a-)
Alice 4 (c-) <--> Bob 3 (a+)
Alice 5 (c-) <--> Bob 5 (a-)
Alice 6 (c-) <--> Bob 6 (a-)

This insures that each one has a 2/3 chance of finding out the other got the same spin, and a 1/3 chance that the other got the opposite spin. If Bob and Alice were two A.I.'s running on classical computers in realtime, you could simulate Bob on one computer and Alice on another, make copies of each according to purely local rules whenever each measured a quantum particle, and then use this type of matching rule to decide which of the signals from the various copies of Alice will be passed on to which copy of Bob, and you wouldn't have to make that decision until the information from the computer simulating Alice was actually transmitted to the computer simulating Bob. So using purely local rules you could insure that, after many trials like this, a randomly-selected copy of A.I. Bob or A.I. Alice would record the same type of statistics that's seen in the Aspect experiment, including the violation of Bell's inequality.

Note that you wouldn't have to simulate any hidden variables in this case--you only have to decide what the spin was along the axes each one measured, you never have to decide what the spin along the other 2 unmeasured axes of each photon was.

Now, I realize that the various Everett interpretations are not so straightforward--in my computer simulation above, probability has a clear frequentist meaning, while the problem of getting a notion of "probability" out of any version of the Everett interpretation is notoriously difficult, and perhaps it can't work at all without tacking on extra assumptions. Still, I got the impression that this was the general type of explanation that Mark Rubin was aiming for in his papers, where each observation creates a local splitting of the observer, but the observations of spatially separated observers are only mapped to each other once a signal has had the chance to pass between them.

 

[chronon]

The alternative local model: We presume that both photons share a property because they are entangled. They are more
equal then other seemingly equal photons.

This sounds to me like a standard local hidden variables theory. As such it would have to obey Bell's inequality, and so disagrees with the results of the Aspect experiments.

I have to say that I do tend towards believing in local realism (although I don't like the 'realism' bit, see http://www.chronon.org/Articles/localreal.html),and I hope for either the success of Caroline Thompson's attack on the statistics of the experiments, or for an explanation in terms of subluminal (but maybe 'spooky') transfer of information between the detectors. But I don't see Hans' model as succeeding.

 

[Hans de Vries]

This sounds to me like a standard local hidden variables theory. As such it would have to obey Bell's inequality, and so disagrees with the results of the Aspect experiments.

The word "hidden variables" is always used in combination with non-
commuting quantities. This is not the case here with the extra degrees
of freedom.


Regards, Hans

 

[chronon]

The word "hidden variables" is always used in combination with non-
commuting quantities. This is not the case here with the extra degrees
of freedom. Regards, Hans

So "hidden variables" means something else, and as I've said I don't like the term "realist" being used for this.

The problem is that then, every physical theory is realist (the word looses its meaning).

Indeed. I don't think that the words "non-realist theory" have any meaning.

But let's be clear about what Bell tells us. Suppose we have two detectors A and B with experimenters who are free to choose the settings of the detectors. If Bell's inequalities are violated, then any model which agrees with the results must have something corresponding to information exchange between A and B.

 

[JesseM]

But let's be clear about what Bell tells us. Suppose we have two detectors A and B with experimenters who are free to choose the settings of the detectors. If Bell's inequalities are violated, then any model which agrees with the results must have something corresponding to information exchange between A and B.

But the information exchange doesn't necessarily have to be faster than light--see my thought-experiment above involving two simulated experimenters, Alice and Bob who split into multiple copies when they make a measurement, and the simulation doesn't have to decide which Alice-copy is mapped to which Bob-copy until there has been time for a signal moving at light speed to pass between them. The Everett interpretation isn't as simple as this, but the thought-experiment shows that in principle you can have a local realist theory (without hidden variables, though) in which the Bell inequalities are violated.

 

[vanesch]

But let's be clear about what Bell tells us. Suppose we have two detectors A and B with experimenters who are free to choose the settings of the detectors. If Bell's inequalities are violated, then any model which agrees with the results must have something corresponding to information exchange between A and B.

Yes, and that something is the state of the observer which goes from A to B to check the correlations!
The trick is that for the observer at A (the one, for instance who will do the travelling), there IS NO DEFINITE RESULT at B as long as he didn't go there to check. It is when you insist on the definiteness of the remote result, before you can check it, that *something corresponding to information exchange* must travel FTL between A and B. But if all that is done at B remains in a superposition until A checks it (and it is only at that moment that A can verify the correlation), then it is whatever travels from A to B (or from B to A, or from A to X and B to X) that carries with it "the information needed", which corresponds to the "choice of the partial statevector" that has been made when A had to decide on which branch its sentient experience was now going to live (according to Born's rule).

When, however, you insist on the "reality" of the measurement at A and the "reality of the measurement" at B, and you insist on the fact that every correlation must have a causal origin, then yes, "something" must travel from A to B and from B to A forward and backward in time. But as that "reality" cannot be checked by a real transmission of information FTL, that "something" remains very vague! It is then left to the opinion of the interpreter to accept such a "something" which will never have any verifiable influence and call it collapse at a distance, or to accept that there is not such a "something" but that macroscopic objects, such as persons, can exist in superposed states.
My preference goes to the second possibility. Not because I find this exciting or so, but because it introduces the least new elements in the existing theory ; especially the necessary introduction of a "something" which communicates at a distance but in such a way that we will never be able to use it to communicate at a distance, relativity obliging, and which happens or not, according to whether a physical process is called a measurement or an interaction.


cheers,
Patrick.

 

[chronon]

Yes, and that something is the state of the observer which goes from A to B to check the correlations!
The trick is that for the observer at A (the one, for instance who will do the travelling), there IS NO DEFINITE RESULT at B as long as he didn't go there to check.

But what if there are two experimenters one at A and one at B? If they then get together to compare results, you seem to be claiming that the one from A could say to the one from B. "Yes, I realize that you claim to have made a definite measurement at B, but from my point of view that wasn't a real event. In fact you are just part of a superposition which only resolved itself when we met."

You say you think this involves the least new elements, but it still needs "something" which causes our minds to divide when faced with a superposition, which I find far less acceptable than a non-local influence.

 

[vanesch]

You say you think this involves the least new elements, but it still needs "something" which causes our minds to divide when faced with a superposition, which I find far less acceptable than a non-local influence.

This is indeed a matter of personal opinion, and you hit the nail on its head: I think that this is the true content of the physics of the Born rule and that you cannot leave it out and derive it from strictly unitary QM. So you can say that unitary QM is the physics of the universe, and the Born rule is the physics of the mind. It is just a personal, maybe strange, but - I think - coherent viewpoint. But it has one practical consequence, or almost so: if you take that viewpoint, you will not bother trying to make a FTL telephone with entangled states, trying to use "collapse at a distance" in order to force somehow what is proven not to be able to exist in QM

Now if you *really* want my personal opinion, I don't take my opinion very seriously, but take it just as a means to reason in QM, as it stands. It avoids me a lot of traps which are often invited by the smalltalk that goes into EPR and quantum erasure papers, and which come down (IMHO) to applying the Born postulate too early.
One thing is sure in QM: when you apply the Born postulate only COMPLETELY AT THE END of your calculation, for the quantity that you want to plot in your paper, you NEVER make an error. If you apply it earlier, you can get away with it if you are very careful. If you apply it too early, you have an FTL telephone and you made an error against QM theory.

I am completely open on the seriousness with which you have to take all this. If indeed, say, gravity DOES somehow induce the collapse in QM, then this changes completely the picture. But I wasn't talking about an interpretion of _that_ hypothetical theory of which I'm even not aware of the formalism. I'm talking about a way of seeing _current_ QM theory. What *really* happens, I just don't know, and I think that everybody who claims to know is fooling him/herself.


cheers,
Patrick.

 

[vanesch]

But what if there are two experimenters one at A and one at B? If they then get together to compare results, you seem to be claiming that the one from A could say to the one from B. "Yes, I realize that you claim to have made a definite measurement at B, but from my point of view that wasn't a real event. In fact you are just part of a superposition which only resolved itself when we met."

Exactly ! As seen from the "I" experience of A.
The "I" experience seems to require that it can only observe a product state of the self and the rest of the universe ; call it the "self-awareness" or whatever. It seems not to support entanglement with the universe. So that "I" experience HAS to choose when it undergoes a physical interaction which entangles its physical structure with something else, and that choice is dictated by the Born rule.

So if A and B are two friends, and they get apart, do an EPR experiment and then come together, there's a possibility that the "I" experience of A now talks to the CLONE of B, while B's "I" experience is now in another branch. There's no way for A to find out that he's now separated from his friend forever, and has to deal with a clone

Try to explain that to your wife/girlfriend when cheating on her

cheers,
Patrick.

 

[chronon]

I think you can put it this way:

If the Bell inequalities are still violated when you have two experimenters choosing the detector settings at spacelike separation,
then either
(1) Your model must have something corresponding to FTL communication
or
(2) Your model must include the minds of the experimenters

I agree that this is a matter of personal opinion, but I can think of several arguments against (2)

(a) You are trying to model a system consisting of lasers and detectors. Why should you need to bring in the unrelated subject of mental workings.

(b) It moves towards non-falsifiability. If results disagree with your model you can keep the model, just change what the experimenters minds end up believing.

(c) It can be seen as a delaying tactic. By introducing mental workings, which we are unlikely to understand for several decades, it means we can go on using hand-waving arguments.

you will not bother trying to make a FTL telephone with entangled states, trying to use "collapse at a distance" in order to force somehow what is proven not to be able to exist in QM

I think people will always try to use the results to make an FTL telephone. In case (1) you can think that maybe you can utilise the underlying FTL information transfer, but in case (2) you can think that maybe the recipient gets a random signal but you can arrange things so that you end up in the universe when they get the message you sent.

 

[vanesch]

I think you can put it this way:

If the Bell inequalities are still violated when you have two experimenters choosing the detector settings at spacelike separation,
then either
(1) Your model must have something corresponding to FTL communication
or
(2) Your model must include the minds of the experimenters

I would agree with you if these two options were all there was to it. But it is not!

In (1), you still must explain me why the photodetector cannot be described by the unitary evolution of the schroedinger equation describing the photo detector processes. If the essential process is photo-emission (in a photomultiplier), then we perfectly know how that works, through unitary evolution.
So the "measurement problem" still stands unsolved: what physical processes are "measurements" (and don't follow the Schroedinger equation, but follow the Born rule and the projection postulate), and what physical processes are "interactions" following unitary evolution ? When is the emission of an electron by an impinging photon a measurement (and hence will collapse a wave function through a yet unknown FTL process), and when is it a physical process that could still in principle be used to do further QM with ?
And on top of that you have to invent an FTL transmission in the past in such a way that you cannot use it.

In (2), you can say that you know that already: it is the Born rule.
So in (2), you essentially solve the measurement process issue and you do not need to invent an FTL communication.

So the options are:

(1) Your model must have something corresponding to FTL communication AND you must STILL explain in what a measurement is physically different from an interaction.

(2) Your model of the minds of the experimenters is given by the Born rule.

I think that (2) is much closer to the actual formalism than (1). In fact, (1) expects a NEW theory, with new physics in it. Indeed, whenever the exact physical process responsable for the distinction between a measurement and an interaction is found, it will be possible to determine that experimentally (even if our current technology is maybe not yet up to it), because it will be IMPOSSIBLE in principle to obtain superpositions in that case. An application of the Born rule implies that you fix the basis in which you "measure", while unitary evolution let's you free to work in any basis.

I had a similar discussion in another thread here. Look at your photodetector, say, a PM. You will probably agree with me that it is the electron emission from the photocathode that is the "measurement process". All the rest is amplification.
So, you say, when a photon impinges on a photocathode, there is a relatively high probability that an electron is emitted. But what, in this process, is not unitary ? In what "photon basis" do we now apply the Born rule ? I think it is quite obvious that it is the standard "photon" basis of Fock space (there is no photon, or there is 1 photon, or there are 2 photons...). Does this then mean that in all interactions of light with a metal, we have to work in that basis and apply the Born rule ?
Hell no ! If that were the case, a metal surface wouldn't work as a mirror ! Indeed, to do so, you need to have a coherent light state (a superposition of Fock states) interact with the sea of electrons, in order for them to emit another coherent state which is the reflected beam. So now suddenly, the preferred basis is the basis of coherent states ?
You will then say: no, it is when a photon is "absorbed" that you apply the Born rule in the Fock basis. But isn't the mirror action an absorption and coherent re-emission of the coherent states by the sea of electrons then ?
Ah, you will say: it is when ENERGY is transferred between the EM field and the electrons that you have to apply the Born rule. But (ok, I failed to come up with the correct complete calculation) if that were true, stimulated emission couldn't amplify coherent states in a laser then !

And this is the case each time when you analyse a "measurement device". Each time you think you've found the pivotal process that "does the measurement" you can find situations where very similar interactions are necessarily described by unitary processes and superpositions have to remain so in order to be correct. So why, in some cases, do these processes "collapse" the wavefunction and send out their FTL signals, and not in other cases ?

So maybe there ARE indeed physical processes that collapse the wavefunction, and maybe there ARE then FTL messages sent out. But you agree with me that that is a whole lot of new physics to be added, so we're not talking about an *interpretation* of QM anymore. It is only in such a setting that (1) makes sense.

cheers,
Patrick.

 

[gptejms]

Have logged in after a couple of days and need to catch up with what has been going on.Firstly what is FTL?Also let me ask what is IMHO---seen this quite commonly used in physicsforums.
Coming to the discussion between vanesch and chronon,there was a thread 'Does decoherence solve the measurent problem?' in s.p.r. which is relevant to the present discussion.Decoherence as you know knocks off the off-diagonal elements of the density matrix.So you are left with the diagonal elements each with its own probability.This probability I think is like a classical probability--for a two state system,you'll find some systems in state |1> and some in state |2>.True you have only one system to make measurement on,but this does not imply that the system continues to be in a superposition of the two states.
Besides,in 'most' decoherence situations,the coherent superposition is short lived because of dissipation and the system mostly ends up in the state of lower energy.So does decoherence not solve the measurement problem?

 

[vanesch]

True you have only one system to make measurement on,but this does not imply that the system continues to be in a superposition of the two states.
Besides,in 'most' decoherence situations,the coherent superposition is short lived because of dissipation and the system mostly ends up in the state of lower energy.So does decoherence not solve the measurement problem?

FTL = Faster Than Light
IMHO = In My Humble Opinion

Concerning decoherence, it solves *part* of the measurement problem, namely the "preferred basis" problem. But it doesn't solve the "projection postulate" problem, however, it gives an interesting property about it.
Note also that in order to apply decoherence theory, you place yourself already in a MWI like situation, otherwise it has no meaning !

In order to apply decoherence theory, you assume that unitary quantum mechanics is strictly correct upto the macroscopic level, so that your macroscopic measurement instruments become entangled with the states of the microsystem under study.

Typically, you consider the begin situation:

System : (a |s1> + b |s2> + c |s3> )

Measurement: |m0> (ignorance state)

Environment: |e0> (not yet interacted).

The physics of the system and the measurement apparatus is then such that the Hamiltonian of it leads to an entanglement:

(a |s1> |m1> + b |s2> |m2> + c |s3> |m3>)

Here, the "m" states are the so-called pointer states of the measurement device.
They are supposed to indicate macroscopically what is the value of the measurement under study. So for example, it could be a spin-z measurement on the system.
But you see the arbitrariness of the procedure: If I would have written my original system state in another basis, which is a linear combination of |s1> |s2> and |s3> then I would find "pointer states" that are linear combinations of m1, m2 and m3, and my "z-spin" measurement apparatus would work just as well as a "y-spin" measurement apparatus.

It is here that decoherence theory comes to rescue, by showing that, when the measurement apparatus interacts with the environment, there will be only one way to write this:
|m1> |e1> + |m2> |e2> + |m3> |e3>
in a way that is stable against remixture (so that the Hamiltonian of the interaction m-e takes on a block-diagonal form in the m-e basis).

As such, the m-basis is NOT arbitrary anymore, but is determined by the Hamiltonian of the interaction measurement system - environment (and corresponds to what we call "classical states").
Once this is fixed, we also see that our trio s-m-e now takes on the form:

a |s1>|m1>|e1> + b |s2> |m2> |e2> + c |s3> |m3> |e3>

This is to where decoherence theory brings you: that the interaction between a macroscopic measurement system and the environment leads to a unitary evolution of the system which can only be written in one way.

But you now still have to apply the Born rule in order to say:

with probability |a|^2 I measured s1 (through the pointer state m1), and now my state is to be considered to be |s1> |m1> |e1>

This last part is still a mystery which is NOT explained by any physical interaction. In fact, it cannot, because all physical interactions are described by unitary transformations which are linear, so you can never pick out one component of a superposition that way.

But decoherence theory is important because it tells you that, IF YOU ARE GOING TO APPLY THE BORN RULE at the end of your calculation, you can just as well apply it in the pointer basis from the moment you will seriously interact with the environment (where the pointer basis comes down to the states that are stable against further mixture with the environment). So it allows you the mathematical shortcut which is always applied: "and we measure the position of the electron |psi(x)|^2 ... " without having to plunge into the details of your measurement apparatus and all that.
So that's why people say that decoherence theory solves the measurement problem FAPP (for all practical purposes). But it doesn't solve it in principle, because it USES it at the end of the calculation.

cheers,
Patrick.

 

[ppnl2]

Pardon a quick question.

Hans talks about a pair of photons that are phase entangled at 90 degrees and polarized at 45 degrees. Is that possible?

Usually when you talk about entangled photons they are randomly polarized. How can you know they are polarized at 45 degree and also entangled at 90 degrees?

I don't think it affects what he said much. Its just that something about the way he said it seemed wrong. But I get confused easily.

 

[chronon]

In (1), you still must explain me why the photodetector cannot be described by the unitary evolution of the schroedinger equation describing the photo detector processes.

I agree that in (1) we are still left with the (local) measurement problem. However, I think that the real mystery in quantum theory is nonlocality, and that the measurement problem is minor in comparison. Several possibilities have been proposed, and the main reason they are rejected seems to be that they don't also deal with nonlocality. (Actually, the real measurement problem I see is that people have convinced themselves that they can calculate much more than is in fact the case; see http://www.chronon.org/Articles/shut_up_and_calculate.html)

So in (1) we still have some work to do, but I would maintain that this is also the case with (2), as you then have to include the behaviour of the human mind in your theory - not a trivial matter. Even if you have a simplified model of minds splitting, you have to explain why they split in the way they do, essentially giving the same problem as in (1).

 

[gptejms]

Vanesch,let's take a specific example e.g. the double slit experiment with electrons.Before I make any measurement,the electron is in state a|1> + b|2> and there are off-diagonal elements a^*b and ab^*.Now I make a measurement(with a gamma ray microscope) at slit 1 and find that the electron passes thru it.Let me denote my state by |m>---since this is a macroscopic state I don't expect it to change significantlyby detection of an electron(may be some microscopic changes take place which have recorded the fact that the electron has passed).Upon my measurement,the electron decoheres(due to interaction with the gamma photon) from the state a|1>+b|2> to |1> and a becomes equal to 1 and b=0.Not only the off-diagonal elements go to zero,but also only one of the diagonal elements survives.What is your environment in this case--why do you need it all?

What is your version of the above experiment?

 

[vanesch]

I agree that in (1) we are still left with the (local) measurement problem. However, I think that the real mystery in quantum theory is nonlocality, and that the measurement problem is minor in comparison. Several possibilities have been proposed, and the main reason they are rejected seems to be that they don't also deal with nonlocality.

Well, it is hard to accept non-locality which implies non-causality through relativity, especially when it is not strictly necessary (after all, in the QM formalism, there is no real FTL communication (information transmission allowed). But I still claim that the really big problem in QM is the measurement problem. After all, it is not that because you cannot explicitly, without approximations, CALCULATE several measurement processes, that you cannot know that they must be unitary. If they have a Hamiltonian description, then they ARE unitary.

So in (1) we still have some work to do, but I would maintain that this is also the case with (2), as you then have to include the behaviour of the human mind in your theory - not a trivial matter. Even if you have a simplified model of minds splitting, you have to explain why they split in the way they do, essentially giving the same problem as in (1).

No, I really don't, if I say that the essence of their behaviour is given by the Born rule. I don't have to say WHY it follows the Born rule, it is a fundamental postulate, just as the unitary evolution is a fundamental postulate.

Fundamental postulate I: "The universe evolves according to the Schroedinger equation" i hbar d/dt psi = H psi

Fundamental postulate II: "a sentient being gets its subjective experiences of its interactions with the universe through random assignment to one term in the superposition according to the Born rule". Decoherence insures me that this basis is well-defined.

As such, I didn't have to touch at all at the formalism of QM. I just fixed *where* the Born rule had to be applied, and because it doesn't correspond to a physical process but a subjective mental one, I don't have the difficulty of having at the same time a unitary description of it, as would be the problem if ever I fixed the Born rule application earlier in the measurement chain.

I really think it is the minimally invading interpretation in the formalism of QM.
Moreover, I get as a bonus that I do not need any extra non-local stuff.

cheers,
Patrick.

 

[vanesch]

Upon my measurement,the electron decoheres(due to interaction with the gamma photon) from the state a|1>+b|2> to |1> and a becomes equal to 1 and b=0.

This is not a unitary process. After all, a unitary operator is linear:

U (a |1> + b|2> ) = a U |1> + b U |2>

So there's no way to change these a and b through unitary processes. THIS is the central problem of the measurement process. You can make your physical process as complicated as you want, you cannot get away with the fact that the time evolution operator will be a linear operator on the states, and that, by definition, superpositions survive the application of U.

cheers,
Patrick.

 

[gptejms]

I expected you to tell what the environment is,and to give a more detailed explanation where you would include the states of the observer |m1>,|m2> etc.(and possibly also of the environment).
Anyway,coming to your objection.For an atom radiating, the state is a(t)|e> + b(t)|g> and a(t) goes from 1 to 0 and b(t) from 0 to 1---isn't this a unitary process?
Coming back to my double slit experiment,upto what state does decoherence take the initial superposition a|1>+b|2> to?

 

[vanesch]

I expected you to tell what the environment is,and to give a more detailed explanation where you would include the states of the observer |m1>,|m2> etc.(and possibly also of the environment).
Anyway,coming to your objection.For an atom radiating, the state is a(t)|e> + b(t)|g> and a(t) goes from 1 to 0 and b(t) from 0 to 1---isn't this a unitary process?
Coming back to my double slit experiment,upto what state does decoherence take the initial superposition a|1>+b|2> to?

I'm a bit confused by what you say ; so let's first get tuned :-)
In your previous message, you wrote things I don't understand:

Before I make any measurement,the electron is in state a|1> + b|2> and there are off-diagonal elements a^*b and ab^*.Now I make a measurement(with a gamma ray microscope) at slit 1 and find that the electron passes thru it.Let me denote my state by |m>---since this is a macroscopic state I don't expect it to change significantlyby detection of an electron(may be some microscopic changes take place which have recorded the fact that the electron has passed).

I don't know what you mean with this off-diagonal elements a^*b ... ?

If you "make a measurement and find" you leave already the superposition. Normally, you would say that your gamma ray microscope interacts with your electron, and would get into the state:

a |1> |gammamicroscope_saw_electron> + b |2> |gammamicroscope_didnt_see electron>

Also, your *macroscopic state* after having observed the display of the gamma microscope, is significantly different according to whether you saw or didn't see it. In fact, chances are these are orthogonal states.
Indeed, if you write your state as:
|stateofmyfirstproton>|stateofmysecondproton>...|stateofmylastneutron>
it is sufficient for ONE SINGLE PROTON to be at a slightly different place between two possibilities for your entire states to be orthogonal to each other.

So the end state is:
a |1> |gammamicroscope_saw_electron>|yousawdisplayred> + b |2> |gammamicroscope_didnt_see electron> |yousawdisplaygreen>

cheers,
patrick.

 

[gptejms]

I'm a bit confused by what you say ; so let's first get tuned :-)
In your previous message, you wrote things I don't understand:



I don't know what you mean with this off-diagonal elements a^*b ... ?

|\psi&gt; = a|0&gt; + b|1&gt;

density matrix \rho is
\rho = |\psi&gt;&lt;\psi|,<br /> so &lt;0|\rho|1&gt; = ab^* and &lt;1|\rho|0&gt; = a^*b
These off-diagonal elements go to zero by the act of measurement.Decoherence also leads to decay of the off-diagonal elements--i.e. why it's said to provide a solution to the measurement problem.

So the end state is:
a |1> |gammamicroscope_saw_electron>|yousawdisplayred> + b |2> |gammamicroscope_didnt_see electron> |yousawdisplaygreen>

So do you mean that the off-diagonal elements survive as such in this mega-superposition?

 

[vanesch]

|\psi&gt; = a|0&gt; + b|1&gt;

density matrix \rho is
\rho = |\psi&gt;&lt;\psi|,<br /> so &lt;0|\rho|1&gt; = ab^* and &lt;1|\rho|0&gt; = a^*b
These off-diagonal elements go to zero by the act of measurement.Decoherence also leads to decay of the off-diagonal elements--i.e. why it's said to provide a solution to the measurement problem.

Ah, ok, it was about the components of the density matrix associated with this statevector.

So do you mean that the off-diagonal elements survive as such in this mega-superposition?

Yes, of course they survive, _in the densitymatrix of the entire system_, including the environment. They have to, by unitarity.
What happens is that when you now calculate the LOCAL DENSITY MATRIX, limited to the system, by taking the partial traces, in this LOCAL density matrix the off-diagonal elements become zero.

Let us limit the description to:

a |1> |gammamicroscope_saw_electron>|yousawdisplayred> + b |2> |gammamicroscope_didnt_see electron> |yousawdisplaygreen>, and let us include the gammamicroscope state in the "you saw" state, to simplify notation:

a |1> |yousawelectron> + b |2> |youdidntsee>

The overall densitymatrix, in the basis:

|1>|yousaw> , |1>|youdidntsee>, |1>|yourotherstates...> ...
|2> |yousaw> , |2>|youdidntsee>,|2>|yourotherstates...> ...

takes on the form of 4 blocs:


rho_11 rho_12
rho_21 rho_22

with rho_11 the coefficients of |1>|you..><1|<you...| in |state><state| ;
rho_12 the coefficients of |2>|you...><1|<you...|
etc...

The coefficient a b* appears off-diagonal in rho_21, in the term:
|1>|yousaw><2|<youdidntsee|

The coefficient a^2 appears in rho_11 on the diagonal:
|1>|yousaw><1|<yousaw|

etc...

To get back to the local density matrix, we have to take the traces of these 4 component matrices (that's what partial tracing out means).

So you see that the trace of rho_11 will essentially be a^2,
that the trace of rho_12 and rho_21 will be 0 (because a b* appears off-diagonal) and that the trace of rho_22 will essentially be b^2.

Of course, the evolution of the states |you...> will make the off-diagonal components wiggle, but if the |you...> space is big enough, they will never gain significant components on the diagonal.

So you see that after tracing out, the LOCAL density matrix is reduced to:

|a|^2 0

0 |b|^2

If the entanglement is perfect, as the state describes. But this is a PARTIALLY TRACED OUT density matrix, and in order for this to be interpreted as probabilities, you in fact USE already the Born rule, saying that you have summed over the probabilities of all the potential exclusive cases of the environment. That's why this local density matrix is called an "improper mixture", because it behaves as a statistical mixture only if:
- we limit ourselves to the local observables
- we have assumed the Born rule for the total system

This is decoherence in a nutshell...

cheers,
Patrick.

 

[vanesch]

I would like to add something, concerning this partial tracing out. Imagine I have 2 systems, one with 2 states |1> and |2> and another one with 3 states, |a>,|b> and |c>.
We construct the tensor basis:

{|1>|a>, |1>|b>,|1>|c>,|2>|a>,|2>|b>,|2>|c>}

Let us assume that we have a pure, but entangled state |psi>, written in this basis, and given by the 6-tupel {u_1a, u_1b...,u_2c} (with u_xx complex numbers, and normalized).

Imagine now that we have an observable which only observes something on system 1. This means that it can be written as: O x 1 (tensor product of operators), and let us imagine that O has as eigenstates |1> and |2>, with eigenvalues o1 and o2. This means that the eigenstates of Ox1 are:
|1>|a>, |1>|b> and |1>|c> with eigenvalue o1
and
|2>|a>, |2>|b> and |2> |c> with eigenvalue o2

The probability of having eigenvalue o1 is the sum of the probabilities of having |1>|a>, |1>|b> and |1>|c> , so this will be |u_1a|^2 + |u_1b|^2 + |u_1c|^2.

And that is nothing else but the trace of the 1-1 block in the overall density matrix |psi><psi| as you can easily verify.
What is very important is that a trace is invariant under a change of basis. So if we would have taken another basis for the H2 system we would find exactly the same trace of the 1-1 block. And this is the proof that the measurement on system 2 (choosing another basis for the second system) has no influence on the local measurement O.

But you also see that in order to give a meaning to this partial trace, we had to apply the Born rule on the 6-state space H1 x H2 ; once these were probabilities, we could then sum them.

The off-diagonal elements in the local density matrix play a role when we have a local observable O which doesn't diagonalize in the |1>, |2> basis. You can work the algebra out if you want to, it is a bit tedious.

cheers,
Patrick.

 

[gptejms]

Excellent posts---cheers Patrick!
So is this your conclusion:-decoherence 'theory'(I see some people call it a theory) assumes Born's rule in its derivation,so it really does not explain much.Use Born's rule to get at a local/reduced density matrix that does not have off-diagonal elements;then say since you now have only a statistical mixture you have solved the measurement problem--the argument is flawed.Is this what you are saying?
Because of interactions with measuring device/environment,the phase information gets dispersed,but is never lost.Superpositions stay---so MWI kind of thing is needed(?).But my problem is:-once you have included the measuring device as well as the environment(which includes one who wrote down the wavefunction,plus everyone else) into your wavefunction,who is left to make a measurement?

 

[vanesch]

Excellent posts---cheers Patrick!

Thanks

So is this your conclusion:-decoherence theory(I see some people call it that way) assumes Born's rule in its derivation,so it really does not explain much.Use Born's rule to get at a local/reduced density matrix that does not have off-diagonal elements;then say since you now have only a statistical mixture you have solved the measurement problem--the argument is flawed.Is this what you are saying?

No, decoherence people, like Zeh, realize this and say this also. Decoherence DOES show us something, namely the "preferred basis", the one in which the product states remain product states that way under time evolution ; this is determined by the character of the interaction between the system and the environment, and always leads to a basis of states which "looks classical" (like position states for particles ; or coherent field states for EM fields). THAT is the real contribution of decoherence.
It allows you to make the shortcut of applying the Born rule on the system level instead of having to work out the complicated QM of the interaction with the measurement instrument.
But, as you say, considering that it solves the measurement problem is based upon circular reasoning.

Because of interactions with measuring device/environment,the phase information gets dispersed,but is never lost.Superpositions stay---so MWI kind of thing is needed(?).But my problem is:-once you have included the measuring device as well as the environment into your wavefunction,who is left to make a measurement,collapse the wavefunction?

Hehe, you're beginning to see the issue ! Who's left ? My way to solve it is:
my consciousness is left :-) But you got to the gist of the problem I think.

cheers,
Patrick.