Bell experiment would somehow prove non-locality and information FTL?

[heusdens]

Sure, then there is no difficulty. If you accept non-locality, then there is no problem with EPR settings. Only, then relativity is wrong. People want to stick to the principle of locality (except for the Bohmians) because it is the only natural way to get relativity going.

But remember that the EPR paradox works on physically distinct objects. As I said, as long as you restrict yourself to a single object, there is no problem, but it was not the problem at hand ! So this is then just discussing something else, and not the EPR-Bell situation - IOW, it is attacking a straw man.

General Relativity or Quantum Mechanics are neither wrong, it is just that we can not have a complete understanding of everything, cause we will always have to cope with a contradiction of some sort.

 

[heusdens]

Imagine that we send out an electron-positron pair in a singlet state, the electron to Alice, on mercury, and the positron on Bob, on Jupiter.

Does this then also count as one single object ?

Now, given that, quantum-mechanically, every interaction usually results in an entanglement, should we now say that all we observe, and others observe, during many years, is only "one single observation on one single object" ?

See, the problem with giving up locality is that science becomes extremely difficult to do. It would mean that anything that is done anywhere can change entirely the results of my experiments, and I have no way to shield them. Some influences might even come from a "submeasurement" that is, in my reference frame, still in the future !

But there's another difficulty to solve in the EPR problem. If, as you say, everything is just "one single object" and "observations can of course change the state and hence the outcome of a "subobservation", then how come that we cannot use this mechanism as a faster-than-light telephone ?

The "single object" reference is only valid when seen from the frame of reference of the object itself. Which in itself is neither good nor wrong, but just a different perspective on the situation.

We can not travel at the speed of light. If we could, we would not need faster-then-lightspeed travel, we would be everywhere instantaniously.
And since we can't we have the perspective which shows this Quantum paradox, but which doesn't involve faster then light speed travel.

When seen from the object itself, there is only one object and one observation of it.

 

[heusdens]

When seen from the perspective of a light beam, everything everywhere occurs at once. In fact there wouldn't be time. In that case, what is the need of faster then light travel, there is already everything everywhere at once.

We don't have that perspective. That's why in our reality things don't happen all at once (luckily!) and things are separate and occupy separate spatial positions.

 

[DrChinese]

And since, as in the dice experiment, we only have one observable in some state, if a measurement would alter that state, this would lead to disturbing both measurements in a related way.

The key word here is "disturbing". No one actually knows what is happening, whether there is a non-local causal influence or not. Wave function collapse itself - which does occur instantaneously and non-locally - may or may not be a physical phenomenon.

However, wave function collapse occurs with ALL measurements, not just with those involving entangled particles. So you may as well consider that ALL collapse is instantaneous and non-local. For example: when you find a photon a point A (i.e. probability of observation goes to 100%) then you have the probability go to zero everywhere else - even at points that are non-local to A.

 

[JesseM]

Wrong! The fact that opposite sides have an outcome that add up to 7 is INDEPENDEND of how we throw the dice!
It's a shame you don't see that!

Oh, I thought you meant that two dice were thrown, and if each person picked opposite sides of their own die, their results would add to seven. Sure, opposite sides of a single die will always add to 7--but this still isn't a proper analogy, because it is easy to explain in terms of local realism, there is no violation of Bell's inequality in your experiment.

The "local realism" aspect of this experiment is that observers can choose which side to inspect, which act is independend on of the "dice rolling" experiment.

And again, there is no violation of Bell's inequality here--the violation of Bell's inequality in my thought experiment is that when the experimenters picked the same box, they always got opposite results, yet when they picked different boxes, they found opposite results on less than 1/3 of the trials. You could recast this in terms of a dice if you want--it would be impossible to manufacture an ordinary classical die with pictures of cherries and lemons on each side, such that if I have a choice of 3 sides to inspect and you have a choice of 3 different sides to inspect, then if we choose to inspect opposite sides we'll always find different fruits, yet if we choose to inspect non-opposite sides, our chances of finding different fruits are smaller than 1/3.

By the way, it's spelled "independent".

First of all, I constructed this "experiment" that resembles some aspects of quantum nature.

Yes, but you completely ignored the issue which is central to any discussion of non-locality in QM--probabilities that violate Bell's inequality.

Furter: I did't state that measuring a spin status is equivalent to my roling dice experiment, of course not.

A spin status is not a fixed observable, since I guess that in some cases we disturb that status. And possible in other cases, this quantity does not get disturbed.

Sure, if you perform multiple measurements, you find that if you measure the spin along the same axis twice you get the same answer if there were no other measurements in between, but if you had measured along a different axis between these two measurements, then the results of these two measurements along the same axis may have changed. However, the issue of multiple measurements isn't really relevant here, since in entanglement experiments you only make a single measurement on each particle--the question is whether the answer to what you'd get on this measurement was already set at the time the particle was created, and you're just revealing a preexisting truth, or whether nature has to "improvise" an answer when you make the measurement. If nature is improvising, then the fact that two experimenters light-years apart always get opposite answers would suggest non-locality. In your dice example, I suppose the actual throwing of the dice represents a kind of "improvisation", but once the dice lands then there is a definite answer to what each side reads, so looking at a side is just reavealing a preexisting truth; moreover, the fact that opposite sides add to 7 can be explained causally, in terms of interactions between opposite sides moving through the atoms of the die at the speed of light or slower that insure the die always remains rigid as it moves so that any two given sides (the 6 and the 1, say) always remain opposite each other.

So the error in your logic is to assume that either the spin status is something fixed, or it is not fixed (independend of the measurement).
While a real world anology can already show that such an assumption is not always true, but depends on the set up of the experiment.

What real-world analogy shows that? Your dice analogy ignores the issue of probabilities which violate Bell's inequality, and if you're just talking about two people measuring sides of a single die, it also ignores the issue that the measurements can be made a large distance apart so there can't be a non-FTL causal connection between them (there is certainly a causal connection between the reading on one side of a die and the reading on its opposite side).

But still there is the anology. If A and B choose to observe the dice from the same position or opposite position, they get somehow correlated results (the result is either the same or adds up to 7), but in other cases not!

It's same remarkable, I think!
Now please explain me, when A looks from the top, but B chooses neither the top, nor the bottom, he gets uncorrelated results (in fact in this case, the outcomes can be a selection of 4 distinct values, for each side).
But what determines the outcome of the result that B observes?
a. The experiment itself, rolling the dice, or
b. The choice of which side to observe

Both, obviously. However, you seem to miss the point, the weird aspect of QM is not just that when people choose different axes to measure their results are uncorrelated, it's that the probabilities that they find opposite spins violates Bell's inequality. There would be no violation of Bell's inequality in your dice example.

Did you read over my scratch lotto card example? If so, did you understand why, under classical assumptions, if the Alice and Bob always found opposite fruits when scratching the same box, we should expect that when they scratched different boxes the probability of finding opposite fruits would be expected to be greater than or equal to 1/3?

 

[vanesch]

The "single object" reference is only valid when seen from the frame of reference of the object itself. Which in itself is neither good nor wrong, but just a different perspective on the situation.

Ok, then, what is the reference frame of our positron on Mercury and our electron on Jupiter ? Mind you that Bob, on Mercury, can decide to change the momentum of his positron (like he could change the path of his photon), independently of what happens to the electron on Jupiter, so even the CoG reference frame is ill defined. These momentum changes can (in principle) be done in such a way to maintain the entanglement of the spins.

When seen from the object itself, there is only one object and one observation of it.

What object ? The {electron - positron} system ? What qualifies as an observation, and what qualifies as an object for you ?

 

[JesseM]

When seen from the perspective of a light beam, everything everywhere occurs at once. In fact there wouldn't be time. In that case, what is the need of faster then light travel, there is already everything everywhere at once.

We don't have that perspective. That's why in our reality things don't happen all at once (luckily!) and things are separate and occupy separate spatial positions.

But "locality" and "non-locality" aren't defined from the perspective of a light beam in relativity (in fact, according to relativity your statement above is meaningless, since a light beam has no rest frame of its own to define a 'perspective'), they're defined in terms of the reference frames of inertial observers moving slower than light. If two events outside each other's light cones are correlated, and this correlation can't be explained in terms of both events having a common cause in some event that lies in both their past light cones, then this is a violation of locality. As I mentioned above, there is no violation of locality in your dice example, the fact that the side with the 6 and the side with the 1 always land opposite can be explained in terms of interactions moving through the center of the die slower than the speed of light which keep the die rigid (or at least semi-ridid, perfect rigidity is impossible in relativity) as it moves.

 

[vanesch]

Your dice analogy ignores the issue of probabilities which violate Bell's inequality, and if you're just talking about two people measuring sides of a single die, it also ignores the issue that the measurements can be made a large distance apart so there can't be a non-FTL causal connection between them (there is certainly a causal connection between the reading on one side of a die and the reading on its opposite side). Both, obviously. However, you seem to miss the point, the weird aspect of QM is not just that when people choose different axes to measure their results are uncorrelated, it's that the probabilities that they find opposite spins violates Bell's inequality. There would be no violation of Bell's inequality in your dice example.

Yes, that was also the point I tried to make: heusdens considers an "example" which is in no way a kind of EPR-Bell situation, and then explains it somehow realistically. But that's a straw man. As I tried to point out, EPR-Bell situations only occur with measurements FAR AWAY on DIFFERENT PHYSICAL OBJECTS (be it photons, "quantum dice", electrons or hairy mammoths), in such a way that different *possible* measurements can be made on these objects (by their remote observers), with different possible outcomes (one needs at least 3 different possibilities with at least 2 outcomes each). Talking about observations on a single object (remotely or not) doesn't qualify. There's never an EPR-Bell paradox there.

I could talk about the "twin paradox" of the age of a single person who remains at home, and it would also loose all its charm

 

[heusdens]

I understand that the simple dice throw can't qualify for an EPR experiment and that there is no EPR paradox there.
However, I'm not yet convinced that one could not design a more sophisticated example of a classical phenomena, that shows also the EPR paradox.
The constraints are:
- there is a single source
- there are two distantiated observers/observations (which can not influence each others outcome directly, although an observation may involve altering the observable)
- at least 3 different possibilities with at least 2 different outcomes

I will trie if I can come up with a better example then.

 

[heusdens]

But "locality" and "non-locality" aren't defined from the perspective of a light beam in relativity (in fact, according to relativity your statement above is meaningless, since a light beam has no rest frame of its own to define a 'perspective'), they're defined in terms of the reference frames of inertial observers moving slower than light. If two events outside each other's light cones are correlated, and this correlation can't be explained in terms of both events having a common cause in some event that lies in both their past light cones, then this is a violation of locality. As I mentioned above, there is no violation of locality in your dice example, the fact that the side with the 6 and the side with the 1 always land opposite can be explained in terms of interactions moving through the center of the die slower than the speed of light which keep the die rigid (or at least semi-ridid, perfect rigidity is impossible in relativity) as it moves.

Perhaps you are right about the perspective of a light beam. An object moving at light speed doesn't have a defined inertial frame of reference.
I made however the extrapolition that when nearing the speed of light, the clocks in the moving frame slow down (time dilatation) resp. to the inertial frame at rest, and that when taking the limit to light speed, the clock would in fact come to rest (with respect to the non-moving observer).
So I guessed that if one could think of the inertial frame of a particle moving at light speed, it would in fact not have time, the light would be every where instantanious.
Which might explain these kind of "spooky" instantanious-action-at-a-distance or non-locality in QM events.

 

[JesseM]

I understand that the simple dice throw can't qualify for an EPR experiment and that there is no EPR paradox there.
However, I'm not yet convinced that one could not design a more sophisticated example of a classical phenomena, that shows also the EPR paradox.
The constraints are:
- there is a single source
- there are two distantiated observers/observations (which can not influence each others outcome directly, although an observation may involve altering the observable)
- at least 3 different possibilities with at least 2 different outcomes

I will trie if I can come up with a better example then.

As long as causes can't propogate faster than the speed of light in your classical world, and the experimenter's choice of what to measure is independent of the state of the system being measured, then you won't be able to come up with an example where the Bell inequality is violated--Bell's theorem proves that definitively.

 

[heusdens]

Ok, then, what is the reference frame of our positron on Mercury and our electron on Jupiter ? Mind you that Bob, on Mercury, can decide to change the momentum of his positron (like he could change the path of his photon), independently of what happens to the electron on Jupiter, so even the CoG reference frame is ill defined. These momentum changes can (in principle) be done in such a way to maintain the entanglement of the spins.

What object ? The {electron - positron} system ? What qualifies as an observation, and what qualifies as an object for you ?

Yes, well that is the question, of course!
If we would maintain that the object is the entangled pair, this then eventually makes us conclude that it contains everything.

We have then the rather contradictionary concept of everything as one single object, which does not even have time or space, and in fact is equal to nothing at all...!

It is quite absurd to hold on to that concept.

Yet, if we do not, for obvious reasons, then we will end up with these kind of paradoxes or contradictions.

Which however then shows some ultimate property of nature, that we can not grasp it without such contradictions.

 

[heusdens]

As long as causes can't propogate faster than the speed of light in your classical world, and the experimenter's choice of what to measure is independent of the state of the system being measured, then you won't be able to come up with an example where the Bell inequality is violated--Bell's theorem proves that definitively.

The link you provided about Bells Theorem is great! Thanks.

 

[vanesch]

Yes, well that is the question, of course!
If we would maintain that the object is the entangled pair, this then eventually makes us conclude that it contains everything.

We have then the rather contradictionary concept of everything as one single object, which does not even have time or space, and in fact is equal to nothing at all...!

It is quite absurd to hold on to that concept.

In fact, not necessarily: the Copenhagen version of quantum theory does exactly that ! Or we can allow "explicit interactions at a distance", like in Bohmian mechanics (but these interactions are then for sure not relativistically invariant). But there are also resolutions to the EPR paradox which conserve a "localistic mechanism", but they require another weirdness: that the observers get copied (in the many-worlds view, which I find rather a natural view on quantum theory).

 

[gil7]

What is the path of information in the experimet; the information follow the path of the particles or goes "straight" betwee particles?

 

[heusdens]

In fact, not necessarily: the Copenhagen version of quantum theory does exactly that ! Or we can allow "explicit interactions at a distance", like in Bohmian mechanics (but these interactions are then for sure not relativistically invariant). But there are also resolutions to the EPR paradox which conserve a "localistic mechanism", but they require another weirdness: that the observers get copied (in the many-worlds view, which I find rather a natural view on quantum theory).

Or we can assume a higher dimension, in which the two observations are not spatially distantiated, but very close to each other.

 

[heusdens]

What to conclude from this QM paradox?

One of the points to look for in the intepretation of this seemingly paradoxical quantum nature is that ordinary (formal) logic does not perform very well on quantum events.

Sometimes this notions is established as a distinction between classical logic and "quantum mechanical" logic, a new logic that can deal with the nature of quantum mechanics.

It is however worthwhile noticing that philosophers/logicians smelled something "fishy" about formal logic long before these physical discoveries were made.

Most noticable philosophical progress was made by Hegel, who saw the contradictions of formal logic and sublated formal logic into a system of dialectics which both overcomes and maintaints formal logic.

Quantum mechanics has used this to their advantage.

See for example:
http://www.marx.org/reference/archive/hegel/help/mean05.htm

One of the logic rules that are not tennable in quantum mechanics is the law of excluded middle. The statement that an object either has property A or has not property A, is in quantum mechanics no longer tennable.

But also the law of identity, which merely says that an object/entity equals itself, has also problems when related to nature, since if it were to be assumed that the law of identity is applied always, it would mean no change whatsoever could take place in which something changes into something else. Everything would be motionless and without change.

If the strict rules of formal logic were to be applied, it could only be used in abstract and formal thought, not to the real world.

 

[CarlB]

Dear heusdens,

You might try the first half of this article, as it discusses a version of the problem that really illustrates well the problem:
http://arxiv.org/abs/quant-ph/9510002

Or we can assume a higher dimension, in which the two observations are not spatially distantiated, but very close to each other.

Every time I read papers like the one I just link in, I am reminded again just how weired "The World" is. It makes one want to explore alternatives to explain the quantum weirdness. There are various attempts. The one you've just mentioned seems to be brought up regularly by amateurs, but they can never get the equations to work with it, and so I doubt that it goes anywhere. But faith is what keeps people trying new (or old) ideas, in the face of odds that they are most certainly deluded, and it is faith that will someday solve these problems.

What these experiments do show is that QM is not joking around when they talk about the quantum states not being determined before you make the measurement. This is really the way it has to be.

Once you accept this by looking at stuff like the GHZ experiment, you have gained important insight. The insight is that in understanding a QM experiment, you simply cannot suppose that things are predetermined. And this insight is important because now you can go back and look at the experiment that Feynman said was the fundamental mystery of QM, the two slit experiment. And the two slit experiment is a lot simpler to understand than these other experiments.


When you take a class in QFT, you end up learning how to add up large numbers of things called Feynman diagrams. Intuitively, I always thought of each diagram as an alternative path for the experiment. I realize that other people think of it as just perturbation theory or whatever. But I like to imagine that there is a physical reality behind a calculation, a reason for why the calculation works, an ontology.

The most common ontological explanation for the weirdness is the MWI, which I find revolting. The idea is that the universe splits at each of the places where a measurement is made, and somehow only splits are allowed are ones that are consistent with the calculations, more or less.

The second most common is probably Bohmian mechanics, for which I find little motivation. The idea is that quantum objects are composed of a wave and a particle. The particle suffers a force that is determined by the wave. The wave can be calculated without knowing exactly where the particle. To know how to move, the particle only needs to know the shape of the wave in the region which it travels through.

In these experiments, the weird results come from interactions between the waves of the two (or three) moving quantum thingies. So the Bohmian mechanics say that the waves are just what you'd expect for interacting waves. And the particles just surf on the waves.

To me, the Bohmian interpretation implies that the wave must be present before the particle shows up. That is, the wave effects the path of the particle, but the particle does not effect the flow of the wave. To me this is very suggestive, and it calls into question the meaning of the word "event" in relativity.

In relativity, an "event" is something that happens at a particular point in space at a particular time. That would seem to be compatible with the "particle" definitions, but it is not compatible with the wave. The conclusion of a lot of physicists is therefore that the wave is not a part of reality, it's just the technique we use for calculating the interactions of particles.

I prefer to think of the wave as a part of reality, but to place it in the future (of the observer of the event), the future where the moving finger of fate has not yet written. As the finger moves, the particle advances. The wave is the stress that's present on spacetime before the finger of fate reaches that particular time.

Now the two slit experiment is fully understandable with light treated as a wave. It is only mysterious when it thought of as a particle experiment, how does the particle go through both slits? If you look at it from the "moving finger of fate" point of view, the little chunk of spacetime where the event takes place exists some minutes, hours and probably days before the actual experiment.

The event already exists, but its result is not yet determined. The particles, however, exist in the past and already their presence in the past influences the future, that chunk of spacetime is influenced by them, and it is deformed or stressed by the approaching presence of the particles. Engineers (and heavy equipment operators) know that the equations of stress and strain can be written as differential equations. Applied to a 4-D object like spacetime, the differential equations become wave equations, the same sort of things that define QM waves.

Before the particle actually shows up, it presumably induces stresses in all the places where it could go, and that is why we cannot assign a predetermined result to the experiments. It is only when the actual choice of the hand of fate is made that the experiment completes. At that time, fate makes the choice for the particle, and its stresses on the roads not taken fall to zero, while the stresses on the roads yet to take are subtly altered (which is sort of an issue with the Bohmian explanation).

This kind of ontology avoids the problem with spooky action at a distance, and the issues of a whole universe splitting up in unimaginably large numbers of measurements simultaneously. There's still only one universe, but at any given position of the finger of fate, the events of that universe are divided up into the things still to come (where stresses act like waves), and the things that have been written, (where the passages are written in particle tracks).

The weirdness of QM is sufficiently strong that you can start arguments among even people who know a great deal about it. I can't imagine a better hobby than trying to understand it.

 

[jtbell]

The weirdness of QM is sufficiently strong that you can start arguments among even people who know a great deal about it.

As evidence, observe the fact that the longest threads in this forum are invariably about the interpretation of quantum mechanics, not about the predictions that it makes for physical observables.

 

[heusdens]

This kind of inequality can not be performed with a dice machine and setup as I defined, since we have the rule, which is the normal macroscopic default, that a measurement does not influence the state of the object involved.

However, such constraints might not be the same for the quantum world.

That's the only way to produce these kind of inequalities.

And since, as in the dice experiment, we only have one observable in some state, if a measurement would alter that state, this would lead to disturbing both measurements in a related way.

It might still be doable if we break the law of "non disturbance" and would alter the experiment in such a way that the state of the dice changes - for instance, we let it roll in some direction - dependend on the state itself and on both the sides to observe.
What we must contain however is the symetry of the experiment. A and B observers can be interchanged without affecting the outcomes statistically.

I will try to work out an example of that.

I don't know if this will fit the descriptions, but let us assume we design the experiment in another way. We use the initial descriptions of the experiment, but now add to it that the "dice" we used is not in a fixed position, but instead it is rotating around it's axis (let's asume it is a vertical axis, from top to bottom).
That means, that some of the measurements get "blurred". It just means, the outcome is not settled, or unkown. Instead of a property of either it is (TRUE), or it isn't (FALSE), we then get the outcome that the property is unknown/undefined (NULL).

It is then rather easy to get outcomes which don't fit statistically the Bell inequality.

The property values are as follows:
True: 1,2,3
False: 4,5,6
Null: blurred


For example, let's describe the properties as follows:
A: Number we see from the top
B: Number we see from the side (which might be blurred)
C: Number we see from the bottom

It would then be relatively easy to have outcomes that violate the inequality:

N (A, ~B) + N (B, ~C) >= N (A, ~C)

 

[heusdens]

Imagine that we send out an electron-positron pair in a singlet state, the electron to Alice, on mercury, and the positron on Bob, on Jupiter.

Does this then also count as one single object ?

Now, given that, quantum-mechanically, every interaction usually results in an entanglement, should we now say that all we observe, and others observe, during many years, is only "one single observation on one single object" ?

That are good questions, and that is of course the problem. Since, realistically seen, there are not singular objects anywhere. Neither the electron for example is a singular object, there are always other particles involved. So, it is very difficult to extract singular objects.

 

[DrChinese]

I don't know if this will fit the descriptions, but let us assume we design the experiment in another way. We use the initial descriptions of the experiment, but now add to it that the "dice" we used is not in a fixed position, but instead it is rotating around it's axis (let's asume it is a vertical axis, from top to bottom).
That means, that some of the measurements get "blurred". It just means, the outcome is not settled, or unkown. Instead of a property of either it is (TRUE), or it isn't (FALSE), we then get the outcome that the property is unknown/undefined (NULL).

It is then rather easy to get outcomes which don't fit statistically the Bell inequality.

The property values are as follows:
True: 1,2,3
False: 4,5,6
Null: blurred


For example, let's describe the properties as follows:
A: Number we see from the top
B: Number we see from the side (which might be blurred)
C: Number we see from the bottom

It would then be relatively easy to have outcomes that violate the inequality:

N (A, ~B) + N (B, ~C) >= N (A, ~C)

Good try, but that does not fit the actual facts!

The reason is that there is NO "blurring" (regardless of how you define it) and there are apparently NO null values (regardless of how you define it).

Imagine the case where we measure the polarization of two entangled photons at angle settings of 0, 120 and 240, but the measurements are random on each side. We ALWAYS get agreement when the angle settings are the same, so how is there blurring or null values? On the other hand, when the settings are different we have a violation of Bell's Inequality as the values should be the same at least 1/3 of the time, but are actually the same only 1/4 of the time.

In other words: the violation of Bell's Inequality that you have above is not explainable when you also consider the perfect correlations.

 

[vanesch]

I don't know if this will fit the descriptions, but let us assume we design the experiment in another way. We use the initial descriptions of the experiment, but now add to it that the "dice" we used is not in a fixed position, but instead it is rotating around it's axis (let's asume it is a vertical axis, from top to bottom).
That means, that some of the measurements get "blurred". It just means, the outcome is not settled, or unkown. Instead of a property of either it is (TRUE), or it isn't (FALSE), we then get the outcome that the property is unknown/undefined (NULL).

It is then rather easy to get outcomes which don't fit statistically the Bell inequality.

The property values are as follows:
True: 1,2,3
False: 4,5,6
Null: blurred


For example, let's describe the properties as follows:
A: Number we see from the top
B: Number we see from the side (which might be blurred)
C: Number we see from the bottom

It would then be relatively easy to have outcomes that violate the inequality:

N (A, ~B) + N (B, ~C) >= N (A, ~C)

Again, you've found a setup which has nothing to do with the original setup, and moreover for which your "Bell inequality" is erroneously written down. Indeed, for a Bell inequality, we have to sum over a TOTAL PARTITION of the B-outcome. So, your B-outcome can now have 3 possible values:
"true", "false","blurred". You have to cut this set in two parts, and then apply the Bell inequality to that, because THAT is what happens in a true EPR experiment. Then you have:

N(A,B=~(true or false)) + N(B=(true or false),~C) >= N(A,~C) and that won't be violated (as are all the other inequalities resulting from other subdivisions of the outcomes at B).

So you didn't construct a system with a "Bell inequality violation" because the inequality you wrote down wasn't a Bell inequality.

 

[heusdens]

Yes, but the fact is if there is a separate measurement of all 3 properties A,B,C and only true or false values and I put that in a table, the bell inequality will hold no matter what the experiment is.
I could even create a table of any combination of A,B, C without an experiment, and always the inequality comes out.

The quantum variant of the measurement, holds to the fact that 'somehow' individual properties are being measured, while they are not. We only measure the constructs N (A, ~B), N (B, ~C) and N (A, ~C), and they may deviate from the inequality. That is why the inequality can be broken.
If we would rearrange that into:
A' = P (A, ~B)
B' = P (B, ~C)
C' = P (A, ~C)
Then the inequality will still hold.

 

[wm]

Clarifying realism and locality

True, you cannot logically stay with both realism and locality after Bell and Aspect.

Dear Doc: Given that there are differing ''brands'' of realism and locality (including Einstein realism, Bell locality; variously defined), would you mind defining the realism and the locality that you say we cannot logically stay with?

That is, could we have the definitions implicit in your reply above? Thus:

For DrC, realism is ...

For DrC, locality is ...

Thanks, wm

 

[heusdens]

So you didn't construct a system with a "Bell inequality violation" because the inequality you wrote down wasn't a Bell inequality.

http://www.upscale.utoronto.ca/GeneralInterest/Harrison/BellsTheorem/BellsTheorem.html

That page I got the equation from, and to my knowledge that is correct.
It says it doesn't matter what the population is, we just inspect three distinct properties A,B,C (which can be dependend properties) with at least two possible outcomes.

 

[DrChinese]

If we would rearrange that into:
A' = P (A, ~B)
B' = P (B, ~C)
C' = P (A, ~C)
Then the inequality will still hold.

The Inequality does NOT hold. That is the issue.

On the other hand, there are "prefect" correlations at ANY angle setting. That is the evidence that makes one suspect that there IS reality to the values at any angle setting. EPR created a definition of such "elements of reality", because the value of one entangled particle could be predicted without disturbing the other.

 

[DrChinese]

Dear Doc: Given that there are differing ''brands'' of realism and locality (including Einstein realism, Bell locality; variously defined), would you mind defining the realism and the locality that you say we cannot logically stay with?

That is, could we have the definitions implicit in your reply above? Thus:

For DrC, realism is ...

For DrC, locality is ...

Thanks, wm

I use the definitions generally associated with Einstein for both.

For DrC, Realism = "A particle must have a separate reality independent of the measurements. That is: an electron has spin, location and so forth even when it is not being measured." -Einstein. (In effect, that reality is observer independent.)

For DrC, Locality = Signals/information/causal influences/force carriers cannot propagate faster than c.

While some disagree, I believe these definitions map to the definitions Bell intended in his original paper, especially that of Reality. So to me, this is also Bell realism (i.e. they are equivalent). Bell realism is expressed mathematically as the idea that a particle has simultaneous definite spin or polarization values - independent of their actual measurement - at 3 or more angle settings; and that those values have probability of occurring that are in the range from 0 to 100%.

 

[ianbell]

Worth pointing out here that since in the standard EPR experiment the observations are considered as spacially separated rather than timelike sepertied events, it is meaningless to speak of Alice making her measurement "before" Bob makes his as there will be some observers who percieve Bob's measurement as occurring first.

 

[heusdens]

The Inequality does NOT hold. That is the issue.

Have you calculated that?
Can you give a numerical proof of it too?

On the other hand, there are "prefect" correlations at ANY angle setting. That is the evidence that makes one suspect that there IS reality to the values at any angle setting. EPR created a definition of such "elements of reality", because the value of one entangled particle could be predicted without disturbing the other.

Yes, of course there is reality to it, only we don't know what reality.

 

[vanesch]

Yes, but the fact is if there is a separate measurement of all 3 properties A,B,C and only true or false values and I put that in a table, the bell inequality will hold no matter what the experiment is.
I could even create a table of any combination of A,B, C without an experiment, and always the inequality comes out.

You've got it.

The quantum variant of the measurement, holds to the fact that 'somehow' individual properties are being measured, while they are not. We only measure the constructs N (A, ~B), N (B, ~C) and N (A, ~C), and they may deviate from the inequality. That is why the inequality can be broken.

YES. That's the whole point. So indeed, there is NO INDIVIDUAL QUANTITY that seems to correspond to each of the physical objects at the two remote experimenters. That's the whole point of the Bell inequalities. IF there were such a quantity (a "hidden variable") then there is only one possibility: that is that the hidden variable for the quantity to be measured is CHANGING at Bob's when Alice (very far away) is doing her measurement on an OTHER object (the famous action-at-a-distance).

So we are confronted with the puzzling point that:
1) Bob is doing a measurement on some object and Alice is doing some measurement on another object
2) What they measure is seemingly NOT a property of the object they measure (because if it were, you agree that the inequality should come out)
3) nevertheless, they find perfect anti-correlations !

BTW, that's why no "classical analogy" of such a violation can be set up. You cannot think of any classical system in which we:
1) measure the set of objects N(A,~B), ... and violate the inequalities
2) have perfect anti-correlations.

You can easily find setups where ONLY 1) or ONLY 2) is satisfied (that's what people often do and think they found the "solution"), but both together, doesn't work classically (unless you allow for long ropes between Alice and Bob...).

 

[vanesch]

Yes, of course there is reality to it, only we don't know what reality.

Even that is not true. We have a *theory* which gives us these predictions. It is not as if we found this empirically and had no clue how it happened. We HAVE a theory which predicts exactly this behaviour, and it is called quantum theory.

 

[heusdens]

YES. That's the whole point. So indeed, there is NO INDIVIDUAL QUANTITY that seems to correspond to each of the physical objects at the two remote experimenters. That's the whole point of the Bell inequalities. IF there were such a quantity (a "hidden variable") then there is only one possibility: that is that the hidden variable for the quantity to be measured is CHANGING at Bob's when Alice (very far away) is doing her measurement on an OTHER object (the famous action-at-a-distance).

So we are confronted with the puzzling point that:
1) Bob is doing a measurement on some object and Alice is doing some measurement on another object
2) What they measure is seemingly NOT a property of the object they measure (because if it were, you agree that the inequality should come out)
3) nevertheless, they find perfect anti-correlations !

BTW, that's why no "classical analogy" of such a violation can be set up. You cannot think of any classical system in which we:
1) measure the set of objects N(A,~B), ... and violate the inequalities
2) have perfect anti-correlations.

You can easily find setups where ONLY 1) or ONLY 2) is satisfied (that's what people often do and think they found the "solution"), but both together, doesn't work classically (unless you allow for long ropes between Alice and Bob...).

Yes, I thought that! We misassume something about propertyness in the quantum cases.

But then it could be claimed that - when redefining 'property' as follows:
A' = P(a, ~b)
B' = P(b, ~c)
C' = P(a, ~c)

the inequality:

P(A', ~B') + P(B', ~C') >= P(A', ~C')

still holds?

 

[DrChinese]

1. Have you calculated that?

2. Yes, of course there is reality to it, only we don't know what reality.

1. I see now that you were trying to create a new inequality with your "prime" designation. There is no purpose to following that further until your provide some meaning to what this is supposed to represent.

2. Well, you can say there is reality to it, but there may not be the simple Einsteinian reality that is commonly discussed. So when you say "reality", what do YOU mean? Are there simultaneous definite values at all angle settings regardless of the act of measurement? (If so, you must be a believer in the non-local branch of Bell's Theorem.)

 

[heusdens]

1. I see now that you were trying to create a new inequality with your "prime" designation. There is no purpose to following that further until your provide some meaning to what this is supposed to represent.

1.
The question was wether these *new properties* (derived from the old ones) conflict with the inequality or not. My guess is, they do not conflict, but I haven't calculated them.

2.
The question of meaning does not only apply to my new definition, but also to the already used old meaning. What in fact are Bob and Alice measuring in the first place? What is it in *that* definition that gives it meaning?

In fact, meaning, is a subjective term of some sort. What does it mean for a certain phenomena to have a certain property?
Is there intrinsic meaning in any of the phenomena of nature or any property we can define?
What does it mean for an object to have mass, speed, charge, spin, etc.?

In my point of view, both Alice and Bob just collect meaningless data. Only after they compare each others note, we can extract some meaning out if it.

[ note: compare this for example to a question like what is the value of a dollar. Some people tend to think that a dollar has some intrinsic property, we call value, although in fact we can only measure the value of a dollar or any other currency as an exchange value, that is the relative value of a dollar as compared to another currency. There is nothing in the dollar, or any other currency, that make it have some intrinsic property of value. ]

2. Well, you can say there is reality to it, but there may not be the simple Einsteinian reality that is commonly discussed. So when you say "reality", what do YOU mean? Are there simultaneous definite values at all angle settings regardless of the act of measurement? (If so, you must be a believer in the non-local branch of Bell's Theorem.)

In the perspective of relativity the term *simultanious* is a very observer dependend term. In what frame of reference and in what configuration of the set up are you asking this?