EPR paradox and prediction time

[jk22]

If we suppose we have an entangled pair in position/momentum and, following the argument, we measure position of particle A. We get a result let say xA.

Then we want to predict the measurement of position of B, so up to now we have not measured particle B, but we know it's wave-function is a delta in -xA.

Since we have to carry the information from A to B, the wave-function in B evolved into a gaussian spreading wave-packet.

Then we measure the position of B and we get xB which is now not forcedly -xA even if it is the most probable.

So that in this case, we cannot predict the outcome of measurement of B with certainty (or exactness) when we compare with measurement in A.

If we program the measurement time of A and B, they have to be simultaneous, but this would mean relatively to a reference frame. If let say one frame of measurement is moving, then the events are no more simultaneous depending on the frame, so that the wave-function spread out again according to Schroedinger's equation, hence the prediction with certainty is not possible neither ? Even if for the latter case I don't really understand in which frame the evolution arises. Maybe somebody could clear it up, thanks.

 

[UltrafastPED]

IIRC, the original paper did not consider relativity; so the measurements would all be with reference to the "lab" frame.

No actual measurement technique was proposed.

 

[jk22]

Ok. I had another point that disturbs me, the source is submitted to the uncertainty principle, so it is possible that particle A "arrives" not exactly at the same time as particle B ?

 

[UltrafastPED]

That would be a measurement problem, it seems to me.

For most EPR examples a conserved quantity is used; this is why you can predict the second measurement from the first one.

But position is not a conserved quantity. What is there to predict?

 

[DrChinese]

A and B do not particularly arrive at a point at the same time even when so routed.

There is no sense in which the state of A and the state of B are in any way affected by the order of measurements on A and B. Essentially, there are no frame type considerations.

 

[DevilsAvocado]

If we program the measurement time of A and B, they have to be simultaneous, but this would mean relatively to a reference frame. If let say one frame of measurement is moving, then the events are no more simultaneous depending on the frame, so that the wave-function spread out again according to Schroedinger's equation, hence the prediction with certainty is not possible neither ? Even if for the latter case I don't really understand in which frame the evolution arises. Maybe somebody could clear it up, thanks.

Ok. I had another point that disturbs me, the source is submitted to the uncertainty principle, so it is possible that particle A "arrives" not exactly at the same time as particle B ?

Welcome to the club jk22!
It's a great joy to see that also you have found the Holy Grail of Questions, to put meaning and substance to our short little lives here on planet Earth!

Seriously, this is my favorite question, because it nails down the tension between QM & SR/GR in a nice little package that can be studied in a lab, without black holes or big bangs present.

However, I wish I could answer the question without bringing in the issue of interpretations, but I'm afraid there is no other way to handle this neat Catch-22 (today).


Short answer:

• In QM interpretations that are epistemic (i.e. that deals only with knowledge) there are no [big] problems. Stuff happens, the equations works, and things only become real when we measure them (some even question the later).
  
  
• In QM interpretations that are ontic (i.e. that infer a microscopic physical reality/factual existence) there are BIG problems.
  
  
• In QM interpretations that are time-symmetric there are no problems at all (except if someone kills your juvenile and unmarried grandfather ).

Long answer:
As you see, this only becomes a real issue for QM interpretations that are ontic, as for example Bohmian mechanics.

This is what professor Lee Smolin has to say about the issue, in his latest book Time Reborn:

Could there be a hidden-variables theory compatible with the principles of relativity theory? We know that the answer is no. If there were such a theory, it would violate the free-will theorem—a theorem implying that there’s no way to determine what a quantum system will do (hence no hidden-variables theory) as long as the theorem’s assumptions are satisfied. One of those assumptions is the relativity of simultaneity.

The aforementioned theorem of John Bell also rules out local hidden-variable theories—local in the sense that they involve only communication at less than the speed of light. But a hidden-variables theory is possible, if it violates relativity.

As long as we’re just checking the predictions of quantum mechanics at the level of statistics, we don’t have to ask how the correlations were actually established. It is only when we seek to describe how information is transmitted within each entangled pair that we need a notion of instantaneous communication. It’s only when we seek to go beyond the statistical predictions of quantum theory to a hidden-variables theory that we come into conflict with the relativity of simultaneity.

To describe how the correlations are established, a hidden-variables theory must embrace one observer’s definition of simultaneity. This means, in turn, that there is a preferred notion of rest. And that, in turn, implies that motion is absolute. Motion is absolutely meaningful, because you can talk absolutely about who is moving with respect to that one observer—call him Aristotle. Aristotle is at rest. Anything he sees as moving is really moving. End of story.

In other words, Einstein was wrong. Newton was wrong. Galileo was wrong. There is no relativity of motion.

This is our choice. Either quantum mechanics is the final theory and there is no penetrating its statistical veil to reach a deeper level of description, or Aristotle was right and there is a preferred version of motion and rest.

Note: Some has gone through the roof for Smolin implying that maybe Einstein, Newton and Galileo was wrong. However, this is a popular science book, and there are no rigorous theories or anything else even close to proving or suggesting that this is the actual case. The premises – our choice – is what Smolin talks about (within current knowledge), nothing else.

So, there is no question that EPR-Bell brings BIG problems for ontic QM interpretations, and personally I just love it – very exciting times!

And to make it even more thrilling, Experimental test of non-local quantum correlation in relativistic configurations has already been done (moving "passive detector") and EPR-Bell/QM survived the test!

The conclusion in the paper above is that the experiment challenges our description of "measurements" and "concept of states", and the "projection postulate" (wave function collapse) has got another blow as a description of a real physical phenomenon.

What I would like to know, is how epistemic QM interpretations deals with the (entangled) shared wavefunction theoretically. Afaik, there can only be one "break up" of the entanglement, and even if there is no FTL signaling going on, there is a change in quantum states (where order should be crucial).

Does anyone know how this is solved theoretically (in epistemic interpretations)?

 

[jk22]

What I would like to know, is how epistemic QM interpretations deals with the (entangled) shared wavefunction theoretically. Afaik, there can only be one "break up" of the entanglement, and even if there is no FTL signaling going on, there is a change in quantum states (where order should be crucial).

Does anyone know how this is solved theoretically (in epistemic interpretations)?

What I could learn from quantum axioms is that it teaches us "nothing" about how to solve this, there is a non-separable initial wave-function, singlet state proportional to |+->-|-+>.
And when measured along the same axes, the final separable state is either |+-> or |-+>, but there is no indication of how the collapse happens.

I don't know if a theory will ever go beyond this to explain how the collapse happen, i.e. if there is FTL (which would not agree with SR) or other hidden variables from the source, but this was shown by Bell's Thm not to be the case. So which possibilities still remains ? I don't see.

If it's epistemic, then there is no reality behind the singlet state, it's a way to describe that results have same probabilities and that there is perfect anti-correlation.

BTW we see that the final and initial wf are not the same, hence there is a disturbance, whereas EPR speaks of prediction without disturbing the system as a condition for the existence of elements of reality.

Maybe it's really a end-story, and no other explanation than quantum formalism exists for this phenomenon...

 

[Ookke]

I don't know if a theory will ever go beyond this to explain how the collapse happen, i.e. if there is FTL (which would not agree with SR) or other hidden variables from the source, but this was shown by Bell's Thm not to be the case. So which possibilities still remains ? I don't see.

I don't see either, but maybe the concepts of spacetime do not really apply to quantum world. So maybe things like distance, time interval or order of events do not have any meaning there. This sounds a bit crackpot, but in a sense, quantum entanglement could be something that happens in another "plane of existence", and we are just interpreting that phenomenon using concepts that don't really fit. Like asking if information needed for perfect anti-correlation is contained in hidden variables or transmitted FTL at the time of measurement. Maybe both are wrong. This is indeed very interesting area to study.

 

[aphirst]

This sounds a bit crackpot, but in a sense, quantum entanglement could be something that happens in another "plane of existence", and we are just interpreting that phenomenon using concepts that don't really fit.

My understanding of 'textbook', de Broglie-Bohm(-like), and Everett(-like) QM and QFT is that, other details aside, evolution of \Psi is 100% local... in configuration space at the very least. I would be utterly unsurprised if many 'realist' theoretical physicists consider, at least in some sense, consider configuration space to be more 'fundamental' than 3/4-space; and that (loosely speaking) nonlocality in 3/4-space (or the appearance of it via correlations) is just an artefact of 3/4-space itself being emergent.

Clearly there are issues with views like this, not limited to the fact that it is not at all obvious that configuration-space should be so clearly arranged into triplets/quadruplets, to so nicely yield our space(time) structure.

In any case, it would certainly be fruitful for us in the long term to try to find many different ways to formalise and conceptualise what we can describe quantitatively, along with further studying the means by which we humans 'understand' things, so as potentially to find an explanatory framework which can mesh with our base intuitive tendencies in a useful manner; rather than simply being content to say that reality is "different" or "not compatible" with our "natural" intuitive conceptual structure.

 

[Ookke]

In any case, it would certainly be fruitful for us in the long term to try to find many different ways to formalise and conceptualise what we can describe quantitatively, along with further studying the means by which we humans 'understand' things, so as potentially to find an explanatory framework which can mesh with our base intuitive tendencies in a useful manner; rather than simply being content to say that reality is "different" or "not compatible" with our "natural" intuitive conceptual structure.

Agreed, we definitely should seek those. I just meant that spacetime (which is one construct among others) may not be good way to approach QM.

 

[RUTA]

Agreed, we definitely should seek those. I just meant that spacetime (which is one construct among others) may not be good way to approach QM.

Or, it could be that a spacetime perspective is *exactly* what is needed to understand quantum physics. For example, the refraction of light between points in two different media can be understood dynamically or spatiotemporally. Dynamically, the light takes a path through space that is governed instant by instant by its immediate environment. Spatiotemporally, the light's entire path is one of least time between emission and reception points. This difference is reflected (NPI) in the contrasting formalisms -- dynamics uses differential equations while spatiotemporality uses path integrals. We perceive and therefore think in terms of the former, understanding the latter as a mere "math trick." But, what if the fundamental rule of reality/physics is actually cast as a path integral that doesn't necessitate a corresponding differential equation dealing with localized objects in space? In that case, dynamics is just an approximation that works statistically akin (formally) to the manner by which thermodynamical concepts like temperature and pressure arise statistically from statistical mechanics. And, quantum physics is giving us the distribution of events in that "dynamical, statistical background." The confusion/mystery of quantum physics then arises because one assumes the ontology of the dynamical background is fundamental, i.e., that phenomena are to be understood fundamentally via objects or substances distributed in space changing configurations as a function of time. Once you realize that the true fundamental understanding is given by a "spatiotemporally holistic rule" and dynamics only holds statistically, then the outcomes of quantum physics aren't "mysterious" at all. With this interpretation, one is motivated to search for new fundamental physics, i.e., the spatiotemporally holistic rule whence both quantum physics and general relativity, arguably an advantage over interpretations like "shut up and calculate" :-)

 

[DevilsAvocado]

What I could learn from quantum axioms is that it teaches us "nothing" about how to solve this, there is a non-separable initial wave-function, singlet state proportional to |+->-|-+>.
And when measured along the same axes, the final separable state is either |+-> or |-+>, but there is no indication of how the collapse happens.

I don't know if a theory will ever go beyond this to explain how the collapse happen, i.e. if there is FTL (which would not agree with SR) or other hidden variables from the source, but this was shown by Bell's Thm not to be the case. So which possibilities still remains ? I don't see.

If it's epistemic, then there is no reality behind the singlet state, it's a way to describe that results have same probabilities and that there is perfect anti-correlation.

BTW we see that the final and initial wf are not the same, hence there is a disturbance, whereas EPR speaks of prediction without disturbing the system as a condition for the existence of elements of reality.

Maybe it's really a end-story, and no other explanation than quantum formalism exists for this phenomenon...

You're right. As long as we only talk about the deterministic wavefunction, evolving as predicted by theory – there are no problems at all – and there are no 'magical' correlations either, as we have not performed any measurements!

The crux of the matter, is that we try to solve an 'interpretational issue', with another 'ad hoc' interpretation, i.e. the Born rule P=|\phi|^2.

In current situation there can be no theoretical explanation for the ERP-Bell correlations that goes beyond the 'interpretational stage' and give a 'complete' description all the way, as Steven Weinberg explains:

The difficulty is not that quantum mechanics is probabilistic — that is something we apparently just have to live with. The real difficulty is that it is also deterministic, or more precisely, that it combines a probabilistic interpretation with deterministic dynamics.

Work to do...?

 

[DevilsAvocado]

I don't see either, but maybe the concepts of spacetime do not really apply to quantum world. So maybe things like distance, time interval or order of events do not have any meaning there. This sounds a bit crackpot, but in a sense, quantum entanglement could be something that happens in another "plane of existence", and we are just interpreting that phenomenon using concepts that don't really fit. Like asking if information needed for perfect anti-correlation is contained in hidden variables or transmitted FTL at the time of measurement. Maybe both are wrong. This is indeed very interesting area to study.

Yes maybe... what I can't understand (due to ignorance) is how one could ever 'avoid' the results of EPR-Bell by introducing "separate strange worlds"...

EPR-Bell measurement data are classical in their nature and right in front of our noses – in this world.

 

[DevilsAvocado]

[...] , arguably an advantage over interpretations like "shut up and calculate" :-)

[Since I can't solve the Schrödinger equation]

This looks like a tasty offer... were can I buy a member card!?

[Ah, now I know, your last paper that I forgot to read, sorry... ]

 

[jk22]

EPR-Bell measurement data are classical in their nature and right in front of our noses – in this world.

In this sense it maybe has to be wondered what the measurement data for Bell are, since it is assumed that the measurement result of B+B' are considered as to be 2,0,-2, whereas the eigenvalues of B+B' are +/-√2

So I wonder if the experimentalist can design a circuit in which the measurement outcomes are 2,0,-2 and another where it's this algebraic value ?

 

[Ookke]

arguably an advantage over interpretations like "shut up and calculate" :-)

I don't like "shut up and calculate" either, this is far too interesting for that

EPR-Bell measurement data are classical in their nature and right in front of our noses – in this world.

Only the outcomes are, not the underlying mechanism why correlation is what it is. In relativity it's said that light does not experience time, maybe quantum effects do not experience it either.

 

[DevilsAvocado]

In this sense it maybe has to be wondered what the measurement data for Bell are, since it is assumed that the measurement result of B+B' are considered as to be 2,0,-2, whereas the eigenvalues of B+B' are +/-√2

So I wonder if the experimentalist can design a circuit in which the measurement outcomes are 2,0,-2 and another where it's this algebraic value ?

I'm not sure I understand the question...

Depending on the cut-angle of the BBO crystal in the SPDC process, it generates two types of Bell states, Type I and Type II, which means that for Type I the photons share the same polarization |HH\rangle + |VV\rangle and for Type II they are orthogonally polarized |HV\rangle + |VH\rangle, which means that if Alice & Bob use a BBO Type I crystal and set their polarizers at same angle they will always get the same results i.e. [1, 1] or [0, 0], whereas if they use a BBO Type II they will always get opposite results i.e. [1, 0] or [0, 1]*.

*[1] means the photon went through the polarizer, [0] means stopped.

To get more reliable data, instead of a polarizer, a polarizing beam splitter (PBS) is used which handles both through/stop (1/0).

I guess you can design a circuit to do basically anything with the registered incoming photon, including showing a Green vs Red Muppet for different polarizations...

There's an interactive explanation of the EPR-Bell experiment in the http://www.didaktik.physik.uni-erlangen.de/quantumlab/english/.

 

[DevilsAvocado]

Only the outcomes are, not the underlying mechanism why correlation is what it is.

Yup, and: Outcomes = Measurement = Supreme Court of the Scientific Endeavor

If we start dealing with measurements as "yada yada not the real deal"... where are we then...?

 

[aphirst]

Yup, and: Outcomes = Measurement = Supreme Court of the Scientific Endeavor

If we start dealing with measurements as "yada yada not the real deal"... where are we then...?

Arguably in the same place we've been several times before in scientific history, where we've thought that we had a complete description of reality (with a few tiny holes that will surely be patched up soon...), before eventually some bright spark works out that something underneath helps explain something new (or something old in new ways), and then how to measure its constituents.

It doesn't seem like much of a stretch to at least consider such a possibility: that there are fundamentally measurable underlying mechanics, but that we're too stuck in our old formalisms to work out how. It would seem arrogant to presume that has not been measured necessarily equates to is unmeasurable in principle, if only because similar claims could have been made in pre-quantum physics which we can now say would have been abjectly false.

I might almost go so far as to say that any serious physical theory should actually presume that it is manifestly incomplete, for humbleness' sake. Or, to avoid creating an intellectual environment where the only option people have is to try to fit the square peg of 'new data/phenomena' into the round hole of 'current, complete, true theory'.

Obviously committing to any particular sub-quantum theory can't currently be justified by experiment. But considering physics to only be about "measurements" very seriously begs the question measurements of what?

TL;DR: "Can't see it, isn't there" might be a useful heuristic for dismissing extraneous supernatural guff, but there are countless now-observed entities/phenomena which would have been (and were!) dismissed before the right experiments were devised (or even possible!), so what makes anyone think that quantum physics is going to be fundamentally immune to this?

 

[DevilsAvocado]

My understanding of 'textbook', de Broglie-Bohm(-like), and Everett(-like) QM and QFT is that, other details aside, evolution of \Psi is 100% local... in configuration space at the very least.

The de Broglie–Bohm theory is explicitly nonlocal (as are all ontic QM interpretations), to be compatible with empirical data.

I would be utterly unsurprised if many 'realist' theoretical physicists consider, at least in some sense, consider configuration space to be more 'fundamental' than 3/4-space;

More fundamental?? To me, this is when things go wrong. Science is about understanding and constructing explanatory models (approximations) of this world – not to build a "Mathematical Heaven" that's stands above everyone and everything, representing the Ultimate Platonic Truth.

This is not science – science has to be refutable by experiments.

I know there are guys like Max Tegmark who propose the Mathematical Universe Hypothesis. Question: How do you test the validity of MUH? With a calculator? What has Gödel to say about that?

and that (loosely speaking) nonlocality in 3/4-space (or the appearance of it via correlations) is just an artefact of 3/4-space itself being emergent.

This is exactly what I'm talking about; in order to preserve the good ol' Local Realism, we're introduced to a "magical world" of buzzwords and "stuff" that just "pops out" to make everything right again. If I have to choose between "spooky action at a distance" and "emergent disasters" – I choose the spooky stuff, no doubt, it seems less spooky...

Clearly there are issues with views like this, not limited to the fact that it is not at all obvious that configuration-space should be so clearly arranged into triplets/quadruplets, to so nicely yield our space(time) structure.

I think "issues" is an understatement.

[...] rather than simply being content to say that reality is "different" or "not compatible" with our "natural" intuitive conceptual structure.

Do you for real mean that an "explanation" that state a mathematical configuration space to be more fundamental than the world we live in (which is degraded as "emergent") – as natural, intuitive and conceptual??

Arguably in the same place we've been several times before in scientific history, where we've thought that we had a complete description of reality (with a few tiny holes that will surely be patched up soon...), before eventually some bright spark works out that something underneath helps explain something new (or something old in new ways), and then how to measure its constituents.

It doesn't seem like much of a stretch to at least consider such a possibility: that there are fundamentally measurable underlying mechanics, but that we're too stuck in our old formalisms to work out how. It would seem arrogant to presume that has not been measured necessarily equates to is unmeasurable in principle, if only because similar claims could have been made in pre-quantum physics which we can now say would have been abjectly false.

With all due respect, I think you're missing the point – Bell's theorem does not represent a "measurement problem", it proves something much more fundamental, by both theory and experiments.

At least one of these options has to be abandoned to be compatible with QM theory & experiments:

• Locality
• Realism^[1]
• Free will^[2]

^[1] One way to 'give up' classical realism is by Holism & Nonseparability, where the spin of the entangled photons is not a property of each photon, RUTA can tell you more about this.
^[2] I.e. give up our freedom to choose (random) settings, which would conduce to Superdeterminism.

Observing the violation of Bell's inequality tells us something about all possible future theories; they must all comply with the options above, in the same way as Newton's apple will always fall in same direction at same speed, no matter what scientific theory may come in the future.

I might almost go so far as to say that any serious physical theory should actually presume that it is manifestly incomplete, for humbleness' sake.

If you mean that science cannot and should not represent "The Ultimate Final Truth", then yes.

Obviously committing to any particular sub-quantum theory can't currently be justified by experiment. But considering physics to only be about "measurements" very seriously begs the question measurements of what?

This is not what I am saying. A scientific theory must be refutable (in contrast to mysticism/religion), and the only way to refute a theory is by experiments.

Do you know any other way??

[...] so what makes anyone think that quantum physics is going to be fundamentally immune to this?

Do you conceive the possibility of someone ever measuring Newton's apple going in opposite direction, at twice the speed? (Disclaimer: excluding fleeting local Micro Black Holes )

 

[aphirst]

The de Broglie–Bohm theory is explicitly nonlocal (as are all ontic QM interpretations), to be compatible with empirical data.

I am more than aware of this, which is exactly why I had said locality in configuration space, because that's what I meant. So I don't see the relevance of your objection?

Also, saying "to be compatible" is a bit of a disingenuous representation, as if to say that it's necessarily some sort of epicyclic fudge.

More fundamental?? To me, this is when things go wrong. Science is about understanding and constructing explanatory models (approximations) of this world – not to build a "Mathematical Heaven" that's stands above everyone and everything, representing the Ultimate Platonic Truth.

This is not science – science has to be refutable by experiments.

I know there are guys like Max Tegmark who propose the Mathematical Universe Hypothesis. Question: How do you test the validity of MUH? With a calculator? What has Gödel to say about that?

For this portion I have little idea how this relates to what I originally said. I don't recall at any point saying that "the universe is fundamentally maths, and doesn't actually exist"...?

Do you for real mean that an "explanation" that state a mathematical configuration space to be more fundamental than the world we live in (which is degraded as "emergent") – as natural, intuitive and conceptual??

Saying things like "than the world we live in" is just affirming the consequent (normal space is fundamental, therefore normal space is fundamental, kinda thing). Compared to a Gallilean geometry, Minkowski space is a seemingly more abstract space. It seems like youir point could be directly applied to people (either now or in the past) who would want to insist that only "normal 3-space-plus-time" exists and that anything is "just maths, but not reeeally there".

Also, "natural, intuitive, and conceptual" are notoriously difficult to agree on, and surely shouldn't in-and-of-themselves presume to be deciding factors in discussions of what is fundamental (a point which I get the impression you would have made in response to me if I had happened to mention the same).

This is exactly what I'm talking about; in order to preserve the good ol' Local Realism, we're introduced to a "magical world" of buzzwords and "stuff" that just "pops out" to make everything right again. If I have to choose between "spooky action at a distance" and "emergent disasters" – I choose the spooky stuff, no doubt, it seems less spooky...

EDIT: I appreciate that we have differing opinions about whether or not it makes sense for spatial nonlocality to be explicable by taking the configuration-space representation as more fundamental, but I'd at least reiterate that we are in fact talking about the same thing (quantitatively, and empirically, if not conceptually), and point out that despite what you might have mistakenly thought while reading my post, that I am not a proponent of Local Realism. You've probably been thrown off by my making a distinction between spatial-locality and configuration-space locality.

I'll omit the part about Bell's theorem, since we do actually agree, I'm just not sure how your reply related to what I said.

Observing the violation of Bell's inequality tells us something about all possible future theories; they must all comply with the options above, in the same way as Newton's apple will always fall in same direction at same speed, no matter what scientific theory may come in the future.

Do you conceive the possibility of someone ever measuring Newton's apple going in opposite direction, at twice the speed? (Disclaimer: excluding fleeting local Micro Black Holes )

It should have been obvious that my point was just an elaboration on the fact that, eventually, we have tended to find scenarios which look as if they ought to be described by our current laws, but then aren't - and need something new. Older theories usually remain valuable approximations within some limited domain.

If you mean that science cannot and should not represent "The Ultimate Final Truth", then yes.

It certainly shouldn't represent itself as having it, but it should definitely constantly try to get closer. Deciding either way on whether such a Truth does or does not actually exist seems premature, though I'll happily admit for the record's sake that I am inclined to think that one does.

This is not what I am saying. A scientific theory must be refutable (in contrast to mysticism/religion), and the only way to refute a theory is by experiments.

Do you know any other way??

All I was saying was that "we haven't done an experiment to demonstrate the limitedness of X theory" doesn't automatically imply that "such an experiment is impossible in principle". Demonstrating the latter, if true, takes a fair amount of effort; and is still only valid if the physical theory you use to derive it is also fully true.

---

I kind of get the feeling that your responses have been trying to imply things about what I said/meant which weren't there at all; as if I'm supporting some sort of anti-scientific spiritualistic "knowledge"-gaining process, or some other trivially-deconstructible naive viewpoint.

 

[DevilsAvocado]

I kind of get the feeling that your responses have been trying to imply things about what I said/meant which weren't there at all;

No, not at all, but if you read your latest reply carefully, you will see that it's full of contradictions.

I think you've have to decide, for yourself, if you accept the result/consequences of Bell's theorem, or not. You say you do – but argue as if you don't.

A thread about the EPR paradox is all about Bell's theorem – which should be obvious...

 

[jk22]

I'm not sure I understand the question...

If we want to check Bell's theorem we would need a double canal setup like :


https://drive.google.com/file/d/0B9pGxyM9yy2fWjZvWnlwRVZaR0E/edit?usp=sharing

What I don't understand is that if we "measure" the sum of A+B it should give results plus or minus √2, whereas if we measure A outcome, it's 1 or -1 ? So how to check this in a lab ?

 

[jk22]

In fact i revised the question : considering the EPR paradox :

-) two particles are created at a source at time zero with the entangled wavefunction delta(x1+x2)

-) the particles fly away a distance L in time t to reach the detectors A and B

From this it follows that inbetween the wavefunction evolved from a delta to a gaussian.

Hence it is not possible to predict the measurement result at a certain distance.

 

[Derek Potter]

The delta function can be transformed into a sum of every possible spatial frequency by a Fourier transform, each of which is a different momentum state. So the wavefunction represents a superposition of all possible momenta These will be the same magnitude but in opposite directions. The magnitude is not predictable. The momentum determines the position later on. We can only ever observe one state so although the wavefunction has dispersed we don't see the gaussian distribution, we just see a particular position. We have observed one and only one momentum state with a single value of x1 = -x2 at the later measurement. So measuring x1 does tell you x2. Hope you can make sense of that.

 

[jk22]

The momentum determine the position later on.

If you know the momentum then the position is not determined so what is meant here ?

What i mean is not that we see the gaussian distribution but we have not forcedly x1=-x2 at later times

 

[Derek Potter]

The momentum determines where the particle goes.

 

[jk22]

That is in the classical picture. In the epr case the momentum and the position wavefunctions become a gaussian as soon as t is bigger than initial time.

 

[Derek Potter]

Superposition.

 

[jk22]

we can visualize the quantum phase-space as being pixelized in small cells of the size in the magnitude of hbar sothat the trajectory is fuzzy the momentum does not imply a trajectory uniquely.

 

[Derek Potter]

We are talking about different things. If my answer is not helpful, forget it.

 

[jk22]

I think it points to a discrepancy between the description in words and in formulas in the epr paradox.

Epr considers two particles interacting, hence at the same place in the text. Then it describes this state with the wavefunction delta(x1+x2). In the latter the 2 particles are not at the same place so imo there lack a time evolution to describe the system between the pair creation and the measurement.