Can the following explain randomness in quantum events?

[Idunno]

Hi, I was just wondering if the following can be viewed as an explanation for randomness in quantum events. My knowledge of quantum physics is not all that good. I've got a bit of philosophical bent, which is the source of my interest. Anyways...

Assume that when particles interact, what determines what will happen is based on the information available to the particles that interact. It's hard not to write this in anthropomorphic terms, so I'll just give up and write it with words like "decide", "sense", and so on. Another way to put this assumption is that particles "sense" their environment (presumably through their wavefunction) and, based on what environment they "sense", they mutually "decide" what to do next (or you could say nature "decides" what to do next). So the outcome of quantum particle interactions is determined by the information available to the particles.

Now assuming this to be true, it seems to me, as ignorant as I am, that this could explain why quantum interactions are unpredictable. Let me explain why.

If the above assumption is true, then it seems to follow that each particle "senses" a different environment from every other particle, that is, the set of information for every particle is different from every other particle. This would be because (1) every particle is in a different location from every other one, so they all "see" a different field than each other. (2) Each has different light cones, so they all have different information from each other. Therefore no particle can "sense" what another particle can "sense". You cannot duplicate the exact field that one particle "senses", even if you painstakingly build an environment to be the same, as there are just too many particles out there.

Now, further supposing that what the particle(s) will "decide" to do depends sensitively on the environment they can "sense", it would seem that there would be no way to predict what it will do, simply because we will always have incomplete information. Hence, in this view, what will happen is determined by the information the particles have, but is not determinable by us, because we don't have that information, and can't have it.

So, in this view, it seems to me that you cannot expect to be able to predict what a particle will do, because you will never have the requisite information. So then you would expect to find what will happen next to be undeterminable, and a particle "choosing" a random outcome out of a set of possibilities would seem intuitive. At least it does to me, and I hope I have made no logical error here. :)

When you put an instrument near a particle, the instrument (which is just another collection of particles) cannot measure the same enviromnment that the other particle, as it is not in the same place and does not have the same light cone.

So I hope that my idea is clear, and I'm interested to know what people think. I have not seen this idea before and argument before, so I thought I'd ask those who know more than I do. I don't know what this would mean for other weird aspects of quantum mechanics, but it seems to fit this aspect. One thing I just thought of that might defeat this idea is if you put two particles on opposite sides of a third, then maybe this would be enough information to know what the third is "sensing". So maybe that defeats this idea, Idunno. :)

 

[julcab12]

Just a regular science spectator. If you want to understand and eventually learn QM. I 'll advice you to follow the experiments first and find axioms that are consistent to it. Remember to set aside locality for now. Classical randomness is bound by (local)constraints so it is easy to account for hidden variables/randomness from ignorance while on Quantum randomness is simply -- weird and challenges our sensibility like spin, superposition and entanglement (unless compensated by some interpretations which is heavily discussed here in this forum). Contextuality vs non contextuality.

 

[Paul Parnell]

You seem to be describing a hidden variable theory. Hidden variables can work but only if you allow faster than light communication. You need to look up and understand Bell's inequality in order to understand why.

 

[julcab12]

I'm describing Hidden variable in a local setting i.e a coin flip; in comparison to a quantum object which is experimentally verified to be different (photon polarization experiment) or simply a violation of locality in addition to non correlation. Anyways from what i understand (correct me if I am wrong). I'm always drawn to the idealization that information doesn't travel like our usual perception of local traveling from point A to B in time. Instead; I'm thinking that information in QM is a spread out field and any changes between distances happens instantaneously creating that illusion of communication and our detectors registered it as photons instead of some form of wavelets.

 

[Idunno]

I think that's consistent with what I'm suggesting Julcab12. I kind of intuitively think of entanglement phenonmenon like you do, as being the result of "one object" changing, if that makes sense. IF, as you say, the object's information is spread out, then it appears to have faster than light communication (of a sort).

I don't know if this is a hidden variables theory or not, I'd just like to know if it's plausible, and logically leads to where I think it does. Is this idea (that the information available to the interacting particles determines the outcome) out there in regular physics?

Just to add to this, the way I understand why macroscopic objects typically do not display quantum behaviour is due to the fact that there is usually no one wavefunction for the entire object. A macroscopic object is a collection of many bound atoms, all of which are interacting with each other. The wavefunctions of all the atoms in a rock are interacting with each other - basically cancelling each other out. Hence for a rock, there is no one single wavefunction that determines its interaction, creating a new type of object (an object without a wavefunction), that does not behave in a QM manner. However, for something like a Bose Einstien condensate, the wavefunctions of the particles all "agree" with each other, creating a collective object with a single wavefunction that will display QM behaviour.

This is of course all a hand-wavey explanation, but I'd just like to know how much sense it makes. How correct of a view is this for why macroscopic objects do not display QM behaviour?

 

[the_pulp]

I am also an amateur of quantum physics but I always thought something like this. I also think that this does not violate locality necessarily. I think that if we admit retrocausality, your idea can coexist with locality (see time symmetric interpretations). Please someone with more knowledge of bell theorem and this subject correct me if I'm wrong.

 

[Nugatory]

I don't know if this is a hidden variables theory or not, I'd just like to know if it's plausible, and logically leads to where I think it does.

"Hidden variable" is the general term applied to all models in which the apparent randomness is explained by something the particles "know" that we don't - so yes, you have a hidden variable model here. It is not plausible, for the reason that Paul Parnell gave above.

Just to add to this, the way I understand why macroscopic objects typically do not display quantum behaviour is due to the fact that there is usually no one wavefunction for the entire object...How correct of a view is this for why macroscopic objects do not display QM behaviour?

Not very correct. No matter how many or how few particles make up a quantum system, the wave function belongs to the system as a whole - there's one wave function for the entire system. For example, the wave function for a two-electron system is written $\psi(x_1,x_2,t)$ to give the probability amplitude for finding one electron at position $x_1$ and the other at position $x_2$ at a given time. For most macroscopic systems most of the time, the wave function evolves in a way that makes quantum effects like interference extremely improbable very quickly. For more information, you could google for "quantum decoherence" or try David Lindley's layman-friendly and math-free book "Where does the weirdness go?"

 

[Idunno]

"Hidden variable" is the general term applied to all models in which the apparent randomness is explained by something the particles "know" that we don't - so yes, you have a hidden variable model here. It is not plausible, for the reason that Paul Parnell gave above.

Ok, so it is hidden variable theory. Why is a non local hidden variable theory not plausible?

I had a few more thoughts, the first is: doesn't every physicist implicitly believe that the information available to the particles determines what they will do?

I say this because of the use of fields in physics. As far as I can gather, the "action at a distance" problem was bothersome to Newton and to everyone else, so when fields were invented, they were regarded as a solution to this bothersome problem. It seems quite implausible that a particle could react to something without it the information being somehow transferred to it, and a field does this, be it gravitational, electromagnetic, or whatever.

So, if fields are a necessary part of physics, and they transfer information to a particle, then is it not implicit that a particle must "react" to the information at hand? Is it not implicit that the information available to a particle determines what the particle will do?

If so, then why is it surprising that we cannot determine what a particle will do? We cannot ever have the information that a particle can "see". So why would we ever expect to know what it will do? Hence the intrinsic uncertainty of QM should not be suprising.

Not very correct. No matter how many or how few particles make up a quantum system, the wave function belongs to the system as a whole - there's one wave function for the entire system. For example, the wave function for a two-electron system is written $\psi(x_1,x_2,t)$ to give the probability amplitude for finding one electron at position $x_1$ and the other at position $x_2$ at a given time. For most macroscopic systems most of the time, the wave function evolves in a way that makes quantum effects like interference extremely improbable very quickly. For more information, you could google for "quantum decoherence" or try David Lindley's layman-friendly and math-free book "Where does the weirdness go?"

Thanks for that, Appreciated.

One more half baked idea I hope people won't mind commenting on: Assuming this idea to be true, that the information available to particles determines what they will do, can this explain why the wavefunction collapses when a measurement is made?

My thought on this question was: if you take seriously the idea that a particle has information about its surroundings, then it must have some sort of "map" of its surroundings. presumably, the particle has nothing to do if its map is correct. However, when it's map is in error, it must choose how to respond. My thought is, at that moment, the wavefunction collapses, as the particle is forced to "decide" on a value. Wavefunction collapse would correspond to the particle coming across wrong information of its surroundings, corresponding to what we call a "measurement".

So, how does that sound? I am simply trying to form an intuitive understanding of all the weird aspects fo quantum phenonemon, hope it makes some sense... :)

 

[gill1109]

Ok, so it is hidden variable theory. Why is a non local hidden variable theory not plausible?

I had a few more thoughts, the first is: doesn't every physicist implicitly believe that the information available to the particles determines what they will do?

There exists a non local hidden variable theory which exactly reproduces quantum mechanics: it's called Bohmian theory. Most people do not like it very much. One problem with it is that it assumes a preferred global frame of reference. So it is not Lorentz invariant. Other people worry about its conspiratorial nature: there are hidden connections between everything, acting instantaneously across time and space, but you can't do anything with it except violate Bell inequalities.

I'm sure that every human being implicitly believes that the information available to "particles" determines what they will do. This picture of the world has been engrained in our primate brains by evolution. And it worked fine with regards to science ... till quantum mechanics came along. So for the last hundred years we have all been rather confused ...

 

[Nugatory]

Ok, so it is hidden variable theory. Why is a non local hidden variable theory not plausible?

In your first post you're described the particles behaving according to the "information available to them" and noted that that information is different for two reasons: the particles are at different locations so experience different fields; and there's different stuff in their different past light cones. Those are the defining characteristics of a local - as opposed to non-local - theory and Bell's theorem shows that no local hidden-variable theory can be consistent with quantum mechanics. (If you are not already familiar with Bell's theorem, you might try http://www.drchinese.com/Bells_Theorem.htm, maintained by our own @DrChinese).

A non-local theory is one in which particles can be influenced by events outside their past light cone and by the values of fields at other locations. Such a theory is not precluded by Bell's theorem, but it also doesn't seem to be at all what you had in mind.

Usually when people go looking for hidden variable theories, they're doing so for the reason you gave: they're trying to form an intuitive understanding of all the weird aspects of quantum phenomenology. Unfortunately, non-locality is one of those weird aspects and there's no escaping it - a hidden variable theory must be non-local and therefore at least as weird and counter-intuitive as QM itself.

 

[the_pulp]

Usually when people go looking for hidden variable theories, they're doing so for the reason you gave: they're trying to form an intuitive understanding of all the weird aspects of quantum phenomenology. Unfortunately, non-locality is one of those weird aspects and there's no escaping it - a hidden variable theory must be non-local and therefore at least as weird and counter-intuitive as QM itself.

Reference https://www.physicsforums.com/threads/can-the-following-explain-randomness-in-quantum-events.829691/

I insist that I don't agree with this. From my amateur understanding of Bell Theorem: Hidden Variables + Causality==>Non Locality. You still can have hidden variables + Locality if you dismiss Causality (see time symmetric interpretation of quantum mechanics). Moreover, rejecting Causality restores much of the time symmetry that is usually lost in the colapse based interpretations (where things are divided between what happens before and after the measurement). Dr Chinnese usually writes a lot about this interpretation. I hope he (or whoever with more profesional background than me) can back (or correct) my understanding.

Thanks!

 

[DrChinese]

From my amateur understanding of Bell Theorem: Hidden Variables + Causality==>Non Locality. You still can have hidden variables + Locality if you dismiss Causality (see time symmetric interpretation of quantum mechanics). Moreover, rejecting Causality restores much of the time symmetry that is usually lost in the colapse based interpretations (where things are divided between what happens before and after the measurement).

I would agree with that (and agree with Nugatory too). In fact, the "Hidden Variables + Causality==>Non Locality" argument is what pushes a lot of folks towards the Bohmian outlook.

But the rejection of causality works too. Because of the advent of various entanglement swapping experiments - which appear to violate causality in many cases - I have come to see the rejection of causality in a more favorable light. So now I don't see one view as "less weird" than the other. Still comes back to personal preference.

 

[Nugatory]

I insist that I don't agree with this.

That's fair - there's more than one sensible definition of locality. A goodly number of episodes of violent agreement (such as this one, and I do mean "violent agreement" ) could be avoided by clearly enumerating the properties of the class of theories that is being described instead of just saying "local" or "non-local".

IIn his first published proof of the theorem, Bell was quite clear about what he meant by locality and non-locality: the probability distributions for the observations can or cannot be written in a particular form. If we are being precise, we wouldn't say that Bell's theorem precludes "local hidden variable theories", we'd say that it precludes "theories in which the probability distribution can be written in the form Bell assumed"... Although as a matter of history, that definition happens to coincide with what the EPR authors would have considered a respectable and acceptable LHV theory.

 

[gill1109]

That's fair - there's more than one sensible definition of locality. A goodly number of episodes of violent agreement (such as this one, and I do mean "violent agreement" ) could be avoided by clearly enumerating the properties of the class of theories that is being described instead of just saying "local" or "non-local".

IIn his first published proof of the theorem, Bell was quite clear about what he meant by locality and non-locality: the probability distributions for the observations can or cannot be written in a particular form. If we are being precise, we wouldn't say that Bell's theorem precludes "local hidden variable theories", we'd say that it precludes "theories in which the probability distribution can be written in the form Bell assumed"... Although as a matter of history, that definition happens to coincide with what the EPR authors would have considered a respectable and acceptable LHV theory.

Here's a nice quote from Bell (1981) "Bertlmann's socks": "It is notable that in this argument nothing is said about the locality, or even localizability, of the variable lambda. These variables could well include, for example, quantum mechanical state vectors, which have no particular localization in ordinary space-time. It is assumed only that the outputs A and B, and the particular inputs a and b, are well localized.

There is a nice theorem (due to A. Fine, about 1980 I believe) going in the opposite direction: suppose we have a Bell-CHSH type experiment, loophole-free, and the 16 empirical joint probabilities of all outcome pairs given all setting pairs P(A, B | a, b) satisfy all 8 CHSH inequalities (exchange A for B, + for -, 1 for 2, and so on...). Then there is a local hidden variables model for the experiment which exactly reproduces all those probabilities, according to which: at the source a random choice is made of one of the 16 deterministic local models, specifiying in advance both of Alice's outputs for each of Alice's outcomes, and both of Bob's outputs for each of Bob's inputs. Here is one of the 16: if Alice chooses setting a = 1 then the outcome A will be +1, if Alice chooses setting a = 2 the outcome will be A = -1, if Bob chooses setting b = 1 the outcome will be B = -1, if Bob chooses setting b = 2 the outcome will be B = -1. The two particles go to the two measurement settings taking their instruction with them, and follow them there slavishly.

 

[georgir]

I can not even begin to comprehend what you guys mean by "reject causality" and still have "locality". How do you even define locality without causality?

Isn't the whole definition of "locality" that you can not have a relation between space-like separated events without a common time-like separated cause for them?

 

[Michel_vdg]

I would agree with that (and agree with Nugatory too). In fact, the "Hidden Variables + Causality==>Non Locality" argument is what pushes a lot of folks towards the Bohmian outlook.

The conclusion in this paper nicely discribes many of these issues and talks about 'realism' vs. 'locality':

A Rigorous Analysis of the CHSH Inequality Experiment When Trials Need Not Be Independent

Sometimes it is claimed that it is not locality, but realism that must be abandoned. However, there is some debate about whether realism is a well-defined, required concept in the context of Bell experiments ...

http://arxiv.org/pdf/1311.3605v2.pdf - (299kb)

 

[the_pulp]

I can not even begin to comprehend what you guys mean by "reject causality" and still have "locality". How do you even define locality without causality?

Reference https://www.physicsforums.com/threads/can-the-following-explain-randomness-in-quantum-events.829691/

In amateur terms:

Locality is that the things that affect myself now are only the things that are nearby.
Causality is that the things that affect myself now are only things that happened in the past. If you are nearby myself and you decide, one second after I blinked, that you are going to jump, if we don't reject causality, my decsion to blink (before) was not affected by your decision to jump (after). If we reject causality, it may be possible that your decision to jump in the future influenced my decision to blink in the past.

This crazy correlation is one of the possible explanationes of crazy stuff like entanglement (where it is usually said that two "entangled" particles are influenced by each other instantly, no matter how far away they are). Rejecting causality, it could be said, in layman terms, that "the measurement made here with particle A does not necesarily affects instantly to the particle B that is 100 kilometres away. It can happen that the information produced by my measurement can travel back in time to the moment where the particles A and B were together being entangled, and then travel forward to the future of particle B until the actual time where the measurement over this particle is being made 100 kilometres from myself."

I think that this crazy idea is less crazy than rejecting hidden variables or locality, but as DrChinese said, it's a matter of taste.

There are several nice papers about it nowadays. Try in google "weak measurements", "Time symmetric interpretation", "Aharonov"...

two nice papers are (both from Ognyan Oreshkov and Nicolas J. Cerf):

Operational quantum theory without predefined time arXiv:1406.3829v3 [quant-ph] 25 Dec 2014
Operational formulation of time reversal in quantum theory: reconsidering Wigner's theorem http://arxiv.org/abs/1507.07745

 

[georgir]

But if you allow backwards causality you automatically lose locality, you can not keep it. Because anything "now" can affect you even if not "nearby" by using a proxy in your common past/future. So to what sense can you say you keep locality? I don't see it.

 

[the_pulp]

But if you allow backwards causality you automatically lose locality, you can not keep it. Because anything "now" can affect you even if not "nearby" by using a proxy in your common past/future. So to what sense can you say you keep locality? I don't see it.

I can't explain it in rigorous terms. I would say that there is a continuous path of "events" that goes from the spacetime point "particle B being measured here and now" to the spacetime point "particle A being measured 100 kilometres and now" and correlates them.

Not every separate pair of spacetime points, not causaly locally connected, are locally connected. In fact most of them are not. The only spacetime points that are not classicaly localy connected, but are locally conected are the spacetime points where there are entangled particles.

I insist I am explaining it with my amateur words what I understood from those papers just to state, in short terms, what should be said in longer sentences. Any of the pros here are welcomed to state precisely (or correct) what I am trying to say.

Ps: As I usually do from time to time, thanks to all the teachers here that make this forum so enlightening!

 

[DrChinese]

But if you allow backwards causality you automatically lose locality, you can not keep it. Because anything "now" can affect you even if not "nearby" by using a proxy in your common past/future. So to what sense can you say you keep locality? I don't see it.

In the scenario described, locality is maintained.

Locality is the idea that influences cannot propagate at a rate faster than c. In either time direction, it defines boundaries. All existing nonlocal experiments can be described in these terms (if causality is dropped).

There are no known nonlocal correlations outside of these parameters.

 

[georgir]

But then any non-local "influence" can be explained out in the same way. You can approximate any space-like line with a series of null-like zig-zags. So even if you your model is full of rampant time-travel and teleportation and stuff, you can still say "it is local". This seems nonsense to me.

Just call it what it is, non-local interaction.

 

[DrChinese]

But then any non-local "influence" can be explained out in the same way. You can approximate any space-like line with a series of null-like zig-zags. So even if you your model is full of rampant time-travel and teleportation and stuff, you can still say "it is local". This seems nonsense to me.

Just call it what it is, non-local interaction.

Ah, that is not it at all! In such experiments (eg entanglement swapping and others), the setup clearly includes the zig-zag points as part of the context. This is the appeal of the interpretation, actually.

On the other hand, non-local interpretations suffer from exactly the opposite issue. Namely, why do the non-local effects ONLY occur between entangled systems and nothing else. And why does the future appear to affect the past?

Again, a matter of preference.

 

[ddd123]

Ok, so it is hidden variable theory. Why is a non local hidden variable theory not plausible?

After a long search I've found reading this paper is the quickest way to understand why, for a layperson: http://www.quantum3000.narod.ru/papers/edu/cakes.pdf . The authors basically found a very specific setup that makes nonlocality easy to convey in words: Bell's theorem is much more general and its logic may elude a layperson. But, since a single counter-example to locality is sufficient to break it, even if you haven't understood Bell's theorem you still will understand why locality breaks with this example, so you can let it go.

 

[ZapperZ]

Hi, I was just wondering if the following can be viewed as an explanation for randomness in quantum events. My knowledge of quantum physics is not all that good. I've got a bit of philosophical bent, which is the source of my interest. Anyways...

Assume that when particles interact, what determines what will happen is based on the information available to the particles that interact. It's hard not to write this in anthropomorphic terms, so I'll just give up and write it with words like "decide", "sense", and so on. Another way to put this assumption is that particles "sense" their environment (presumably through their wavefunction) and, based on what environment they "sense", they mutually "decide" what to do next (or you could say nature "decides" what to do next). So the outcome of quantum particle interactions is determined by the information available to the particles.

Now assuming this to be true, it seems to me, as ignorant as I am, that this could explain why quantum interactions are unpredictable. Let me explain why.

If the above assumption is true, then it seems to follow that each particle "senses" a different environment from every other particle, that is, the set of information for every particle is different from every other particle. This would be because (1) every particle is in a different location from every other one, so they all "see" a different field than each other. (2) Each has different light cones, so they all have different information from each other. Therefore no particle can "sense" what another particle can "sense". You cannot duplicate the exact field that one particle "senses", even if you painstakingly build an environment to be the same, as there are just too many particles out there.

Now, further supposing that what the particle(s) will "decide" to do depends sensitively on the environment they can "sense", it would seem that there would be no way to predict what it will do, simply because we will always have incomplete information. Hence, in this view, what will happen is determined by the information the particles have, but is not determinable by us, because we don't have that information, and can't have it.

So, in this view, it seems to me that you cannot expect to be able to predict what a particle will do, because you will never have the requisite information. So then you would expect to find what will happen next to be undeterminable, and a particle "choosing" a random outcome out of a set of possibilities would seem intuitive. At least it does to me, and I hope I have made no logical error here. :)

When you put an instrument near a particle, the instrument (which is just another collection of particles) cannot measure the same enviromnment that the other particle, as it is not in the same place and does not have the same light cone.

So I hope that my idea is clear, and I'm interested to know what people think. I have not seen this idea before and argument before, so I thought I'd ask those who know more than I do. I don't know what this would mean for other weird aspects of quantum mechanics, but it seems to fit this aspect. One thing I just thought of that might defeat this idea is if you put two particles on opposite sides of a third, then maybe this would be enough information to know what the third is "sensing". So maybe that defeats this idea, Idunno. :)

The problem I have with this premise, and with this as a starting point, is that you are trying to explain what is essentially a very mathematical theory using zero mathematics, and instead, using a very hand-waving argument. You don't try to explain something that has unbelievable accuracy using something that is extremely vague. That is like trying to explain physics using tarot cards!

Also note that "size" isn't an issue. Superconductivity is the clearest evidence of quantum mechanics, and it involves a gazillion electrons having a single, coherent description/wavefunction. No matter how large a superconductor is, the entire supercurrent has long-range coherence over the superconducting regime of the solid, meaning it is describe by one coherent wavefunction. So your understanding of "macroscopic object" is already invalidated by this.

Zz.

 

[gill1109]

After a long search I've found reading this paper is the quickest way to understand why, for a layperson: http://www.quantum3000.narod.ru/papers/edu/cakes.pdf . The authors basically found a very specific setup that makes nonlocality easy to convey in words: Bell's theorem is much more general and its logic may elude a layperson. But, since a single counter-example to locality is sufficient to break it, even if you haven't understood Bell's theorem you still will understand why locality breaks with this example, so you can let it go.

Yes this is a nice example but actually it is just another example of CHSH. And experimentally it is not directly useful: the event which is supposed to have probability zero will actually occur sometimes. Your experiment will prove that one of your assumptions of the argument is not correct. More precisely: when you put this to experiment, you will effectively be testing an inequality, and your conclusion will be statistical.

 

[ddd123]

Yes this is a nice example but actually it is just another example of CHSH. And experimentally it is not directly useful: the event which is supposed to have probability zero will actually occur sometimes. Your experiment will prove that one of your assumptions of the argument is not correct. More precisely: when you put this to experiment, you will effectively be testing an inequality, and your conclusion will be statistical.

Why is that? That ket cannot be realized exactly for 100% of events?

 

[gill1109]

Why is that? That ket cannot be realized exactly for 100% of events?

Of course, nothing is perfect when we do experiments. The quantum state is not realized perfectly, the measurements are not realized perfectly. Hence you do not get experimental *proof* that some probability is zero. Or that some correlation is 100%. You just get statistical evidence. So finally your experiment needs to be accompanied by a statistical calculation (error bars, p-values).

The experiment corresponding to the Hardy-Kwiat paper is "just another" CHSH type experiment with two parties (Alice and Bob) choosing between two settings a and b = 1, 2 and observing binary outcomes A and B = +/- 1. The experiment delivers us a set of 16 relative frequencies P(A, B| a, b) where A and B are binary outcomes and a and b are binary settings. According to local realism, the corresponding vector of 16 probabilities lies inside a polytope whose vertices are given by the deterministic local models corresponding to all possible 16 deterministic local "instruction sets" (Alice's particle goes to Alice's detector with definite instruction for a particular outcome for each of the two possible settings, and Bob's similarly). According to quantum mechanics the vector of 16 probabilities can lie outside this polytope. The Hardy state and measurements generate one particular point (vector of 16 probabilities) outside of the polytope. You do the experiment and then you give the *statistical* evidence that what you have observed is close to what Hardy predicted, and therefore (because its close enough) outside of the local realist polytope.

Actually you should envisage all this going on in an 8 dimensional affine subspace of R^16 since whatever else, we certainly believe in "no-signalling", according to which P(A | a, b) does not depend on b and P(B | a, b) does not depend on a. That turns out to deliver 4 linearly independent linear constraints on the 16 probabilities. Moreover, in sets of 4, they have to add up to 1; another 4 linearly independent linear constraints. Then there are the 16 linear inequalities: each probability has to be greater than or equal to 0.

There are 8 interesting "faces" to this "local realism" polytope. They are all the 8 variations of CHSH corresponding to the various symmetries of the experiment. So in the end, doing the Hardy-Kwiat experiment comes down to verifying, statistically, that CHSH has been violated.

 

[stevendaryl]

For those who think of retrocausality as a lunatic idea, I recommend this lecture by Huw Price, who argues for retrocausality using a tiny number of relatively uncontroversial assumptions from quantum mechanics.

 

[LaserMind]

Retro-causality yes. Then transitions then become 'steps' in 'zero time' - perfect!.

We think of a quantum energy exchange between, say, atoms of hydrogen in a gas without considering the separation of the atoms. Why? Oh, because its 'too small' so let's neglect that awkward complication. We can fix that omission using retro-causality - giving us step transitions again. What we want to retain logical integrity!

So in spatially separated examples, retro causality reduces the *effective* separation to zero and we have, indeed steps again.