Boole vs. Bell - the latest paper of De Raedt et al

[harrylin]

JesseM wrote:

The very idea that the probability distribution for lambda would be different depending on which two settings were actually used in measurements would, by definition, be a violation of the no-conspiracy condition.

To which I replied:

I immediately agree with that and I suppose De Raedt et al too.

Upon reading the other discussions I'm not so sure anymore: it depends on what you mean with "the probability distribution for lambda".

I understood you to mean the general possibilities for any unknown variables before any measurement is attempted; and it certainly would be a conspiracy if random processes would be different in a convenient way for different settings.

However if you meant the probability of actual unknown values of unknown variables under the condition of actual settings, obviously some of those values may be functions of the actual settings. As I think De Raedt et al argue, such unknown variables may be different for different settings, so that the assumption that they will be the same would be erroneous. This relates to my doubt about Bell's mixing of the probability distribution with the expectation values.

 

[billschnieder]

Replying to "Bell defines lambda to only deal with hidden variables from a time prior to the choice of detector settings":


To get this thread back on track: Although I still don't fully understand this topic, from reading the paper I guess that it's important for the mathematical arguments of De Raedt et al that hidden variables exist everywhere - thus not only in the photons but also in the instruments. Is my understanding correct?

Thus I wonder (and this is a shot in the dark), if hidden variables could only exist in either the photons or in the instruments, would then Bell's theorem perhaps be correct?

Thanks,
Harald

You are right that the thread was getting off track. Sorry for my role in that. Even if hidden variables could exist only in either the photons or instruments, Bell's theorem will still not be correct. Simply because it is based on simultaneous use of incompatible expectation values from QM and experiments in an inequality based on compatible expectation values.

Admitting the presence of hidden variables in the instruments, only makes it more apparent what the error is but does not eliminate the error which is elsewhere.

 

[DrChinese]

You still haven't answered the questions clarifying what you mean by dataset. See my previous response to you and address the points raised. Specifically:

1) Do you want me to give you a dataset in which each point is a triple of angles, or a triple of outcomes? From your last post it appears you are suggesting a triple of outcomes like (++-) is that correct, just so I do not proceed on a faulty assumption.

2) If you want a triple of outcomes, those must correspond to *outcomes* from an experiment, but your description of the experiment only includes *two* stations, so where is the third outcome coming from? Unless they are not really outcomes from an experiment but something else. Please describe this "something else" so that it us three values.

3) What method are you going to use to select pairs from these triples, in a manner that is similar to what is actually done in Bell-test experiments? This question is very important and simply saying you will do it arbitrarily does not cut it. We are trying to discuss here the issues that are important for understanding the reason experiments violate Bell inequalities.

Once you address those issues, it will then be clear what you mean by "realistic dataset" and you then I will present one, if you haven't withdrawn your request by then.

1) Yes, a triple of outcomes.

2) The outcomes are for observations that may or may not be performed. All I specify is that the outcome could be predicted in advance with certainty for any ONE of the three. I do not assert that I could predict all three in advance (it should be obvious that I don't believe more than ONE could be predicted in advance). On the other hand, if you say that realism holds, you are saying that Alice's reality does NOT depend on Bob's choice of measurement.

3) If it makes you feel better, I will use a random number generator. I don't see how that matters to you - other than I won't cherry pick the sample to make my point (scout's honor). Of course, you must give me enough data to distinguish one result from another. I would expect that would be about 15 to 20 items. You are allowed to cherry pick the dataset.

Fair enough?

 

[billschnieder]

1) Yes, a triple of outcomes.

2) The outcomes are for observations that may or may not be performed.

As I hope you now realize from the other thread too, you are asking for a dataset from an impossible experiment, as evidenced from the fact that you are unable to describe to me the experiment that is supposed to produce this dataset. Yet you do not want to admit that such a dataset is impossible simply because the experiment is impossible, you rather want to ascribe some mystical reason.

All I specify is that the outcome could be predicted in advance with certainty for any ONE of the three. I do not assert that I could predict all three in advance (it should be obvious that I don't believe more than ONE could be predicted in advance). On the other hand, if you say that realism holds, you are saying that Alice's reality does NOT depend on Bob's choice of measurement.

You are asking for a dataset in which the triple therefore correspond to possibilities. But you explicitly specify that you do not require them to be simultaneously actual, which you must do, if you are trying to accurately reflect realism. Realism requires that the three entitities are simultaneously actual. The results of experiments (outcomes) are actualities, not possibilities. So either your dataset is not the result of an experiment, contrary to your claim, or it is the result of an impossible experiment. Either way, the dataset request is inconsistent and unreasonable. If you think there is a third option, please explain it.

3) If it makes you feel better, I will use a random number generator. I don't see how that matters to you - other than I won't cherry pick the sample to make my point (scout's honor). Of course, you must give me enough data to distinguish one result from another. I would expect that would be about 15 to 20 items. You are allowed to cherry pick the dataset.

The shortcomings of points (1) and (2) are enough to sink your request. But the reason (3) is important is that it must correspond to what is done in Bell test experiments. In that respect, your (3) still falls severely short. Just saying "random number generator" is not enough. You need to spell out clearly so that anyone else following along should be able to repeat and verify. For example: something like

- Given 90 triples (a,b,c), for the first 30, I will consider only (a,b) to calculate P(a,b), for the next 30, I will calculate P(b,c) and for the last 30, I will calculate P(a,c).

OR

- Given 90 triples (a,b,c), I will randomly select without replacement 30 triples from which I will consider only (a,b) to calculate P(a,b), I will repeat the procedure except consider only (b,c) to obtain P(b,c) and the same for P(a,c).

The above two will be consistent with what is done in Bell test experiments. This is how clear I want your method to be expressed, I'm not saying you should use only one of the above. Those are just examples to show you the level of clarity and transparency I'm after.

However, your description of the dataset and the experiment that is supposed to have produced it is still dubious, and even after you resolve the issue of the selection method, it is even more important that you address the issues raised in (1) and (2) above.

Fair enough?

No. See above.

 

[DrChinese]

As I hope you now realize from the other thread too, you are asking for a dataset from an impossible experiment, ...

You are the one saying that photons have simultaneous well-defined values for observables, not me. So no, there is no experiment implied here (impossible or otherwise). Just asking you to tell me what possibilities there are for the triples. Obviously, we both know you were never going to produce them.

 

[billschnieder]

You are the one saying that photons have simultaneous well-defined values for observables, not me.

And where did I make that claim? According to realists, Photons do have simultaneous well-define properties at all times whether they have been measured or not. Do you understand the difference between a particle property and an observable?

So no, there is no experiment implied here (impossible or otherwise). Just asking you to tell me what possibilities there are for the triples.

So now you have done a 180 and you are no longer referring to a dataset of actual outcomes from an experiment but a dataset ofpossible outcomes. This is fine with me so long as you are absolutely sure this is what you want.

To those following, let it be clear that DrC has requested not a dataset containing simultaneously actual(existing) particle properties (which would be a realistic dataset), but a dataset of possible outcomes of an experiment, impossible or otherwise (which has nothing to do with realism). In other words, contrary to the initial claim that a "realistic dataset" was being requested, this new demand is NOT a "realistic" dataset.

Remember that realism is the idea that particles have well defined properties at all times even when they are not being measured. And non-realism is the idea that particles only have well defined properties when measured.

Now that we have point (1) and (2) cleared up, please address point (3).

Obviously, we both know you were never going to produce them.

You will be surprised.

-------
Truth can never be told so as to be understood, and not be believed. -William Blake

 

[harrylin]

Memo for myself and perhaps new ones dropping in:
In a parallel thread I asked what this dataset discussion has to do with Boole.
Billschnieder replied:

"
Yes it has to do with Boole because Boole derived Bell-like inequalities and called them "conditions of possible experience". ie, according to Boole, Bell-like inequalities can never be violated if the variables involved can be *simultaneously experienced* (cf. actualities, simultaneous existence, realism); But if the "dataset" being requested is not from an experiment and can not be simultaneously experienced (cf. DrC's dataset request), a violation should be expected.
"

Thanks Bill, I'm not yet convinced one way or the other but I agree that this is relevant.

 

[billschnieder]

Memo for myself and perhaps new ones dropping in:
In a parallel thread I asked what this dataset discussion has to do with Boole.
Billschnieder replied:

"
Yes it has to do with Boole because Boole derived Bell-like inequalities and called them "conditions of possible experience". ie, according to Boole, Bell-like inequalities can never be violated if the variables involved can be *simultaneously experienced* (cf. actualities, simultaneous existence, realism); But if the "dataset" being requested is not from an experiment and can not be simultaneously experienced (cf. DrC's dataset request), a violation should be expected.
"

Thanks Bill, I'm not yet convinced one way or the other but I agree that this is relevant.

If I may ask, what aspects are not clear yet or what aspects of the other side's explanation do you have difficulty letting go?

 

[JesseM]

I now found it back, indeed on p.18 of Tim Maudlin's "Quantum non-locality and relativity":

real laboratory conditions at best allow some approximation of perfect agreement or disagreement

So, that appears to be a non-starter - except if QM predicts a perfect correlation of observations, contrary to the facts.

Harald

That's an odd use of "contrary to facts"--normally a scientist would only say that a theoretical prediction is contrary to facts if there were experiments that clearly rejected it within the limits of experimental prediction, not just when experiments aren't precise enough to provide perfect confirmation. For example, classical physics and relativity and quantum physics all predict that total energy should be conserved in a collision, but it's impossible in practice to measure kinetic energy of random thermal motions with total precision--so would you say that the theoretical prediction of energy conservation is "contrary to facts"? If not, I see no reason to say that about the QM prediction of perfect correlations with identical detector settings, Maudlin wasn't claiming above that the lack of total agreement was due to anything other than the imprecision of our detectors (which don't always manage to detect both members of an entangled pair, and may pick up stray particles that aren't members of the pair, for example).

 

[harrylin]

That's an odd use of "contrary to facts"--normally a scientist would only say that a theoretical prediction is contrary to facts if there were experiments that clearly rejected it within the limits of experimental prediction, not just when experiments aren't precise enough to provide perfect confirmation. For example, classical physics and relativity and quantum physics all predict that total energy should be conserved in a collision, but it's impossible in practice to measure kinetic energy of random thermal motions with total precision--so would you say that the theoretical prediction of energy conservation is "contrary to facts"? If not, I see no reason to say that about the QM prediction of perfect correlations with identical detector settings, Maudlin wasn't claiming above that the lack of total agreement was due to anything other than the imprecision of our detectors (which don't always manage to detect both members of an entangled pair, and may pick up stray particles that aren't members of the pair, for example).

Classical physics predicts that our measurements on thermal motions will have a certain spread; the prediction is that if we do many measurements, the measurement results will generally not have a perfect correspondence with each other, even for the hypothetical case that we could perfectly measure the variables for the prediction. I understand from Tim Maudlin's precision that it is similar or even more so (HUP?) for the correlations between the quantum measurements under consideration.

By the way, please explain how your example fits with Boole's inequalities.

 

[harrylin]

If I may ask, what aspects are not clear yet or what aspects of the other side's explanation do you have difficulty letting go?

There is not so much something "to let go" as things that still need to "sink in".

Unless I see a more appropriate example than Boole's patients (in which case the doctors could be bewildered due to a non-random distribution of unknown variables), I may not be able to discern if the perceived flaw in Bell's derivation is insignificant, or if it really leads to an erroneous result. Sometimes a flaw in a derivation is entirely without consequences, in which case it's just nitpicking.

 

[billschnieder]

There is not so much something "to let go" as things that still need to "sink in".

Unless I see a more appropriate example than Boole's patients (in which case the doctors could be bewildered due to a non-random distribution of unknown variables), I may not be able to discern if the perceived flaw in Bell's derivation is insignificant, or if it really leads to an erroneous result. Sometimes a flaw in a derivation is entirely without consequences, in which case it's just nitpicking.

There is no flaw in Bell's derivation. The issue is that the expectation values from QM or experiments are not compatible with those in Bell's inequality, as explained in the "Violation of Bell's inequality" thread.

The summary of the De Raedt argument is the following:
Bell's inequality

1 + <bc> >= |<ab> - <ac>|

is derived in a way that requires that the following factorization MUST be possible

1 + <bc> >= |<a(b - c)>|

Such a factorization is possible if all three observables are results of a single experiment, such as (a1, b1, c1). If you are in doubt about this factorizability requirement, see this post and the next one, where I go through Bell's derivation in detail to show where this requirement comes in (https://www.physicsforums.com/showpost.php?p=2830780&postcount=1211, https://www.physicsforums.com/showpost.php?p=2830781&postcount=1212)

However the expectation values from QM and Experiments, correspond to three different experiments (a1,b1), (b2,c2), (a3,c3). So that substituting these into Bell's inequality, you get

1 + <b2c2> >= | <a1b1> - <a3c3> |

Note that it is not possible to do the factorization as Bell assumed because a1 is different from a3. However, if you naively think a1 is equivalent to a3, then you might be tempted to drop the indices and say

1 + <b2c2> >= | <a(b1 - c3)> |

By dropping all the indices, Bell proponents naively think the variables from QM and experiments should be compatible. De Raedt et al show using the doctors example that such operations are wrong. But you do not need the doctors example to see the error in the above.

From the above, ai,bi,ci correspond to three list of values (+1, -1) which correspond to the outcome at when the angle is a,b,c. Take for example a1 corresponds to the list of outcomes when Alice set her detector to angle a, and b1 corresponds to the list of outcomes when Bob set his detector to angle b, during experiment (1).

Same for b2,c2 and same for a3,c3.

 

[DrChinese]

1. According to realists, Photons do have simultaneous well-define properties at all times whether they have been measured or not. Do you understand the difference between a particle property and an observable?

2. So now you have done a 180 and you are no longer referring to a dataset of actual outcomes from an experiment but a dataset of possible outcomes. This is fine with me so long as you are absolutely sure this is what you want.

3. To those following, let it be clear that DrC has requested not a dataset containing simultaneously actual(existing) particle properties (which would be a realistic dataset), but a dataset of possible outcomes of an experiment, impossible or otherwise (which has nothing to do with realism). In other words, contrary to the initial claim that a "realistic dataset" was being requested, this new demand is NOT a "realistic" dataset.[/B]

Remember that realism is the idea that particles have well defined properties at all times even when they are not being measured. And non-realism is the idea that particles only have well defined properties when measured.

4. You will be surprised.

1. You will recall that there is a correspondence between the underlying property(properties) - which are presumed not to be directly observable - and what we can see upon measurement, which we call the observable. So yes, I thought this was clear enough that I didn't need to point out the obvious every time. Since in every case, EVERY SINGLE OBSERVABLE corresponds to an EPR element of reality, the real question is whether these elements of reality are simultaneously well defined. I say that the realist says YES. Can you answer a simple question? Yes or no, elements of reality corresponding to observables are simultaneously real with well defined values independent of the act of observation?

2. I never discussed any actual feasible experiment. I am simply asking, for ONE entangled photon, what are the values a set of these might have for the 3 specified angle settings. Does 1 photon have these or not? If you are a realist, you are saying it has these 3 plus (infinitely?) many more.

3. Realistic does not mean a realistic experiment. If there are real values for observables associated with properties of a photon, what are they?

4. You have spent countless posts doing everything but surprising me. How much longer am I going to wait? As I have said: 1 photon, 3 angle settings, about 15 or 20 data points.

zzzzzzzzzzzzzzzzzzzzzzzzzzz.

As I said, I think we both know where things will end up. You will continue to bob and weave. Maybe you can help my Mavs win tonight against the Heat.

 

[billschnieder]

1. You will recall that there is a correspondence between the underlying property(properties) - which are presumed not to be directly observable - and what we can see upon measurement, which we call the observable.

Recall from where?

You are confused about the meaning of realism. Once more:

Realism is the idea that particles have well defined properties at all times whether or not those properties are measurable or not.

realism does not mean

Observables must be simultaneously actual (exist simultaneously)

Do you deny this? If not why the insistence on defining realism to mean simultaneous existence of observables?

Since in every case, EVERY SINGLE OBSERVABLE corresponds to an EPR element of reality, the real question is whether these elements of reality are simultaneously well defined.

And in your mind, for an element of reality to be simultaneously well defined means all observables corresponding to it must be simultaneously measurable? This is so naive I don't even believe I'm still trying to make you understand this.

The fact that every observable corresponds to an element of reality and all elements of reality are simultaneously well defined does not mean all observables are simultaneously measurable. Is this so difficult that you can not understand such basic logic? Let me put it another way:

We have a tablet with two well defined chemicals X and Y (aka elements of reality). In addition we have two glasses of different liquids A and B. In addition we have a theory which predicts with certainty the following *observables*:

a) if you place the tablet into liquid A, and drink it, it will taste sweet (X interacts with A to produce the sweetness).
b) if you place the tablet into liquid B, and drink it, it will taste bitter (Y interacts with B to produce the bitterness).

It is obvious that each observable (a) or (b) above *corresponds* to an element of reality. The two elements of reality (X,Y) in the particle are simultaneously well defined even before any experiment is performed. The prediction of the *observables* are certain. This is exactly what EPR were talking about.

YET! And please pay particular attention here: The *observables* (a) and (b) are not, and can NEVER be simultaneously actual, simply because you can only place your tablet into one of the two liquids. Once you place you tablet, you destroy the tablet. Therefore, the fact that a realist says elements of reality are well defined even when experiments are not performed, does not mean the results of all possible *observables* which can correspond to those observables are also simultaneously actual. This is the part that you either do not understand, or do understand yet refuse to acknowledge.

I say that the realist says YES. Can you answer a simple question? Yes or no, elements of reality corresponding to observables are simultaneously real with well defined values independent of the act of observation?

So then the answer is:

YES - elements of reality *corresponding to* observables are simultaneously real (actual) with well defined values independent of the act of observation.

but

NO - this does not mean the *observables* are simultaneously real (actual) with well defined values!

2. I never discussed any actual feasible experiment. I am simply asking, for ONE entangled photon, what are the values a set of these might have for the 3 specified angle settings. Does 1 photon have these or not? If you are a realist, you are saying it has these 3 plus (infinitely?) many more.

Without an actual measurement/experiment you do not have an *observable* which can be said to exist. An *observable* which can not be *observed* is a contradiction. So if you want to change your mind yet again to say you are asking me for a list of triples of observables, you MUST specify the experiment which is supposed to have provided these observables. If you are asking for three observables corresponding to the three angle settings, then you are not asking for a realistic dataset since it is impossible to measure all three angles simultaneously. So any violation of Bell's inequality by such a dataset will not mean elements of reality which correspond to these *observables* do not exist, since as I have demonstrated, it is possible to have well defined *elements of reality*, and not have simultaneously actual *observables*.

Also note, if an experiment is not performed, you do not have any angles, since the angles come into the picture only in an experiment. Particle hidden elements of reality will not be something like (+,-,+) which are observables, but will be some other hidden property such as a vector in 3D space which when transformed through the instrument angles (a,b,c), will then yield an observable such as (+,-,+). As explained in the previous point, realism requires that the hidden elements of reality have well defined values apart from measurement, but realism does not require that the *observables* be simultaneously actual. This is not rocket science.

3. Realistic does not mean a realistic experiment. If there are real values for observables associated with properties of a photon, what are they?

I hope my explanation makes it crystal clear to anyone following and to you why your dataset request is nonsensical. It is based on a misunderstanding of the EPR paper and the meaning of realism.

4. You have spent countless posts doing everything but surprising me. How much longer am I going to wait? As I have said: 1 photon, 3 angle settings, about 15 or 20 data points.

Your request is equivalent to "Show me a square circle". And I have spent countless posts trying to get you to define what you mean by a "square circle". Once you do that, I will provide you the dataset consistent with your request. Unless and until you define clearly in an unambiguous way what this elusive "realistic dataset" is, there is no point for me to provide anything. So the ball is in your court.

As I said, I think we both know where things will end up. You will continue to bob and weave. Maybe you can help my Mavs win tonight against the Heat.

I think it is you who is bobbing and weaving. You have been unable to unambiguously describe what you mean by a "realistic dataset".

 

[DrChinese]

...
We have a tablet with two well defined chemicals X and Y (aka elements of reality). In addition we have two glasses of different liquids A and B. In addition we have a theory which predicts with certainty the following *observables*:

a) if you place the tablet into liquid A, and drink it, it will taste sweet (X interacts with A to produce the sweetness).
b) if you place the tablet into liquid B, and drink it, it will taste bitter (Y interacts with B to produce the bitterness).

It is obvious that each observable (a) or (b) above *corresponds* to an element of reality. The two elements of reality (X,Y) in the particle are simultaneously well defined even before any experiment is performed. The prediction of the *observables* are certain. This is exactly what EPR were talking about.

YET! And please pay particular attention here: The *observables* (a) and (b) are not, and can NEVER be simultaneously actual, simply because you can only place your tablet into one of the two liquids. Once you place you tablet, you destroy the tablet. Therefore, the fact that a realist says elements of reality are well defined even when experiments are not performed, does not mean the results of all possible *observables* which can correspond to those observables are also simultaneously actual. This is the part that you either do not understand, but do understand yet refuse to acknowledge.


So then the answer is:

YES - elements of reality *corresponding to* observables are simultaneously real (actual) with well defined values independent of the act of observation.

but

NO - this does not mean the *observables* are simultaneously real (actual) with well defined values!
...

Great example! Let's use that one. Now using your above as a template, but with extra tablets so we have 3: what are the values (certain outcomes) for a set of X or Y glasses where the outcomes vary by tablet? Clearly you present me something analogous to the following, where we don't know if the liquid is X or Y (as that is the property which cannot be simultaneously measured):

Liquid Tab A Tab B Tab C
-------------------------
X B B S
Y S S B
X B B S
X B B S
Y S S B
X B B S
Y S S B
Y S S B
Y S S B
etc

Which of course transforms to my example perfectly. So give me your version of the above, or just label as I will:

Tab A = 0 degrees
Tab B = 120 degrees
Tab C = 240 degrees

Or maybe you will weave and bob some more.

 

[billschnieder]

Great example! Let's use that one. Now using your above as a template, but with extra tablets so we have 3: what are the values (certain outcomes) for a set of X or Y glasses where the outcomes vary by tablet? Clearly you present me something analogous to the following, where we don't know if the liquid is X or Y (as that is the property which cannot be simultaneously measured):

Liquid Tab A Tab B Tab C
-------------------------
X B B S
Y S S B
X B B S
X B B S
Y S S B
X B B S
Y S S B
Y S S B
Y S S B
etc

Which of course transforms to my example perfectly. So give me your version of the above, or just label as I will:

Tab A = 0 degrees
Tab B = 120 degrees
Tab C = 240 degrees

Or maybe you will weave and bob some more.

First of all, the example is meant to show you that you do not understand the meaning of "realism", a point you have conceded by failing to respond to it. Secondly, if we had to modify the example to be similar to Bell's case, it will not be what you are suggesting above. It will be the following:

- The two photons will correspond to two tablets of a given kind produced at a time, one given to Alice and the other to Bob, each of whom has three different liquids (a,b,c). The experiment at each station will involve a random choice of one of the liquids, an aliquot of which they then mix with the given tablet and drink to obtain either the "sweet" (+) outcome or the "bitter"(-) outcome.
- The tablet properties (chemicals), being hidden are not specified. We do not know how many of them there are, but we can say each particle pair has a well defined "chemical composition" (elements of reality) which interacts with the liquids (a,b,c) (detector settings) to produce the observables ("sweet", "bitter").

- The above 2 points clearly represent a realistic situation. Do you deny this?

Now make your dataset request in the context of the above remembering that realism does not mean "observables" must exist simultaneously but that elements of reality exists simultaneously.

 

[JesseM]

Classical physics predicts that our measurements on thermal motions will have a certain spread; the prediction is that if we do many measurements, the measurement results will generally not have a perfect correspondence with each other, even for the hypothetical case that we could perfectly measure the variables for the prediction.

I'm talking about the correspondence between the energy before and after each collision, not comparing the energies of different collisions. Do you agree that for each specific collision, classical physics (and relativity and quantum physics) predict that the total energy of an isolated system prior to two parts colliding should be exactly equal to the total energy of the system after the two parts collide? And do you agree that due to measurement error, it's impossible to show experimentally that energy is perfectly conserved in this way, but that doesn't mean the prediction is falsified by experiment, just that measurements aren't precise enough to exactly confirm it (and given the experimental error, the experiments fit with what we'd expect if energy were indeed perfectly conserved as predicted)?

By the way, please explain how your example fits with Boole's inequalities.

Nothing specifically, I was just addressing your comment that the quantum prediction of perfect correlations for entangled particles is "contrary to evidence". Just as with energy conservation, I would say that although we can't exactly confirm the prediction due to experimental error, the evidence is consistent with what we'd expect if QM correctly described nature.

 

[DrChinese]

First of all, the example is meant to show you that you do not understand the meaning of "realism", a point you have conceded by failing to respond to it. Secondly, if we had to modify the example to be similar to Bell's case, it will not be what you are suggesting above. It will be the following:

- The two photons will correspond to two tablets of a given kind produced at a time, one given to Alice and the other to Bob, each of whom has three different liquids (a,b,c). The experiment at each station will involve a random choice of one of the liquids, an aliquot of which they then mix with the given tablet and drink to obtain either the "sweet" (+) outcome or the "bitter"(-) outcome.
- The tablet properties (chemicals), being hidden are not specified. We do not know how many of them there are, but we can say each particle pair has a well defined "chemical composition" (elements of reality) which interacts with the liquids (a,b,c) (detector settings) to produce the observables ("sweet", "bitter").

- The above 2 points clearly represent a realistic situation. Do you deny this?

Now make your dataset request in the context of the above remembering that realism does not mean "observables" must exist simultaneously but that elements of reality exists simultaneously.

Sounds realistic to me, and already requested, Mr. Bob N. Weaver. But I keep asking for ONE and ONLY ONE glass to be tested at each data point, for 3 tablets. I have never said anything about 2. Just one. Does ONE photon (glass) have 3 simultaneous possibilities or not? I realize in your perverse world, there is some enormous difference between a possibility and an actuality but this is just bob & weave semantics to me. But I am following your lead on your analogy, so in the wise words of the late Marvin Gaye: let's get it on.

 

[billschnieder]

Sounds realistic to me, and already requested, Mr. Bob N. Weaver. But I keep asking for ONE and ONLY ONE glass to be tested at each data point, for 3 tablets. I have never said anything about 2. Just one. Does ONE photon (glass) have 3 simultaneous possibilities or not?

Do you even bother to read what I write? If you did, you will realize that according to the analogy, the photons correspond to the tablets, the glasses correspond to the angles. Now for the last time, could you please phrase your dataset request in accordance with the scenario presented in my previous post, making sure you state explicitly the following:

1) What does each data point of triples represent that is supposed to be realistic. And please don't tell me observables because I have already explained (and you conceded by virtue of non-response) that just because hidden elements of reality are real, does not imply that all observables corresponding to them are/can be simultaneously real.
2) How are you going to select pairs from these triples in a way that is consistent with the way pairs are selected in Bell test experiments. I have given you two examples of the level of clarity needed.

These are not onerous requests. If you can not provide even the very basic information required by the above, it shows that your request is just hot air. If you can not be serious enough to address these basic points which I have been requesting from you for a very long time now, then it will be clear that you do not even know what you are talking about.

So please, please, please, clearly specify your dataset request in a well-formed manner. Unless you do not really want me to provide a dataset but would rather prefer that I get fed-up with you and abandon the issue. Sorry, I won't, you will have to either clarify your request this time, or withdraw it.

I realize in your perverse world, there is some enormous difference between a possibility and an actuality but this is just bob & weave semantics to me. But I am following your lead on your analogy, so in the wise words of the late Marvin Gaye: let's get it on.

Actual
1. used to emphasize something that is real or exists in fact.

"Everything that exists is possible but not everything that is possible, exists"
"Everything that is actual is possible but not everything that is possible, is actual"

This is philosophy 101. If you want to object to the above, say so clearly and state clearly what alternative you are proposing. You are making yourself look foolish by contesting the above.

 

[DrChinese]

Do you even bother to read what I write?

Ditto, ace. We are using your analogy my way.

3 tabs = 3 angles
X/Y/and whatever else you want, unknown liquids
Bitter=+, Sweet=-

ONE PHOTON PER DATA ITEM, NOT TWO.

Now really Bill, how hard can you make this? I even gave you some to get started. Sheeesh.

Liquid Tab A Tab B Tab C
-------------------------
X B B S
Y S S B
X B B S
X B B S
Y S S B
X B B S
Y S S B
Y S S B
Y S S B
etc and you can add any Z's, W's and so on you like.

But if you can't grasp that, I will switch it this way if you think that makes a difference.

Tab X Y Z
-------------------------
A: B B S
B: S S B
A: B B S
A: B B S
B: S S B
A: B B S
B: S S B
B: S S B
B: S S B
etc and you can add any C's, D's and so on you like.

Now there WILL be a reference to the entangled partners at some point, but for now we are only discussing possibilities for ONE of the pair, as I keep saying. For a realist, this really should not be so difficult. Because you say these possibilities exist INDEPENDENT of an actual experiment.

 

[DrChinese]

... just because hidden elements of reality are real, does not imply that all observables corresponding to them are/can be simultaneously real...

That is the OPPOSITE of the EPR argument, which was: that individual elements of reality exist simultaneously, and that the possibility of specifying same proves QM is incomplete.

op·po·site/ˈäpəzit/
Adverb: In a position facing a specified or implied subject: "she was sitting opposite".
Adjective: Having a position on the other or further side of something.

 

[DrChinese]

Bill, for our example:

We need something that is analogous to a series of photons of unknown polarization characteristic (each one being labeled type of Tab A, B, and additional if that helps you is fine with me). (The A and B are NOT Alice and Bob though. We are not to that yet.)

These being tested at least 3 different ways (using Liquids X, Y and Z, similar to my angles 0/120/240). There should be a binary outcome (Bitter or Sweet, similar to + or -) which is the same for each Tab/Liquid combo. You can specify that any way you like as long as we have some approximately equal set of Bitter/Sweet outcomes. We will agree that one a Tab is mixed with a Liquid, it cannot be retested with another Liquid.

Does that work?

 

[harrylin]

I'm talking about the correspondence between the energy before and after each collision, not comparing the energies of different collisions. [..]

In contrast, Bell's theorem is about the correspondence between sets of measurement results from the interactions - not between idealised input and output values. A good theory ("local realistic" or not) must be able to predict the real correlations between experimental outputs.

Nothing specifically, I was just addressing your comment that the quantum prediction of perfect correlations for entangled particles is "contrary to evidence". Just as with energy conservation, I would say that although we can't exactly confirm the prediction due to experimental error, the evidence is consistent with what we'd expect if QM correctly described nature.

Again: my point was that as Tim Maudlin indicated, QM does in fact predict imperfect correlations between realistic measurement results; and Bell's Theorem is that no local hidden variable theory can reproduce those predictions.

 

[harrylin]

That is the OPPOSITE of the EPR argument, which was: that individual elements of reality exist simultaneously, and that the possibility of specifying same proves QM is incomplete. [...]

Dear DrChinese, the EPR argument is not the topic of this thread; even if it were that EPR made a wrong argument, that could certainly not affect the possibility to invent a local model of QM.

Note that IMHO Bill's statement about observables is quite independent of EPR's statements about unobservable "elements of reality".

 

[harrylin]

Bill, for our example:

We need something that is analogous to a series of photons of unknown polarization characteristic (each one being labeled type of Tab A, B, and additional if that helps you is fine with me). (The A and B are NOT Alice and Bob though. We are not to that yet.)

These being tested at least 3 different ways (using Liquids X, Y and Z, similar to my angles 0/120/240). There should be a binary outcome (Bitter or Sweet, similar to + or -) which is the same for each Tab/Liquid combo. You can specify that any way you like as long as we have some approximately equal set of Bitter/Sweet outcomes. We will agree that one a Tab is mixed with a Liquid, it cannot be retested with another Liquid.

Does that work?

That's better for me: as an onlooker I do prefer the example in which the tablets stand for photons and the glasses for detectors (please do not present flying glasses with liquids that fall on tablets, that just causes confusion ).

 

[harrylin]

There is no flaw in Bell's derivation. The issue is that the expectation values from QM or experiments are not compatible with those in Bell's inequality, as explained in the "Violation of Bell's inequality" thread.
[..] Note that it is not possible to do the factorization as Bell assumed [..]

Bill,

Thanks for your nice summary in post #47.

Regretfully I did not yet find the time to work through it; when I do I'll come back to it.

Just a comment on your appraisal: in my book an invalid mathematical operation is an error, or, to be less severe, a flaw.

 

[JesseM]

In contrast, Bell's theorem is about the correspondence between sets of measurement results from the interactions - not between idealised input and output values.

No, the simplest form of Bell's theorem deals with contradictions between local realism and the theoretical predictions of QM in ideal experiments with perfect detection (which is certainly allowed by the laws of physics even if it's not practical to do with present technology), not real experiments with realistic detectors. Of course there are also modified versions of Bell's theorem that deal with imperfect detectors, and these are the ones that are used in actual experiments, but the original point of the theorem was simply to show a theoretical conflict between local realism and the fundamental equations of quantum mechanics (if two theories have predictions which are at odds in idealized experiments that would be possible in principle but are realistically impractical, that is sufficient for a theoretical proof that the two theories are incompatible; for example, we know general relativity and QM are incompatible based on different predictions about things going on at the Planck scale which are far outside of the energy ranges we can actually test in practice).

Again: my point was that as Tim Maudlin indicated, QM does in fact predict imperfect correlations between realistic measurement results; and Bell's Theorem is that no local hidden variable theory can reproduce those predictions.

No, you've quite misunderstood what Bell's theorem is about here. All of Bell's papers that I've read deal with idealized experiments with perfect detection rates, and they are intended as theoretical proofs that the laws of QM are incompatible with local realism, not guides to experiment. Again you can find modified Bell inequalities that do take into account limits on detector efficiency, but Bell's original arguments were not concerned with such practical issues.

 

[harrylin]

No, the simplest form of Bell's theorem deals with contradictions between local realism and the theoretical predictions of QM in ideal experiments with perfect detection (which is certainly allowed by the laws of physics even if it's not practical to do with present technology), not real experiments with realistic detectors. [..]
you've quite misunderstood what Bell's theorem is about here. All of Bell's papers that I've read deal with idealized experiments with perfect detection rates [..].

Jesse thanks for the clarification to my question if QM actually predicts a perfect correlation in principle (that is, zero theoretical precision limit). I was not thinking about detection limits (for which I suppose that there is no relevant theoretical limit) but about such things as Heisenberg's uncertainty principle and detection time windows.

QM doesn't make claims about flying photons (that is a semi-realistic interpretation based on one out of several models); instead it predicts photon observations at detectors. I was under the impression that in QM no certain and precise correlation between two photons is possible in principle, and the mention in De Raedt's paper of the timing events of stochastic processes suggested to me that this may be relevant.

Thus, can someone clarify if indeed, and how, QM predicts no theoretical precision limit for the correlation between two photon detection events?

 

[harrylin]

In post #47:

[...] The issue is that the expectation values from QM or experiments are not compatible with those in Bell's inequality, as explained in the "Violation of Bell's inequality" thread.

The summary of the De Raedt argument is the following:
Bell's inequality

1 + <bc> >= |<ab> - <ac>|

is derived in a way that requires that the following factorization MUST be possible

1 + <bc> >= |<a(b - c)>|

Such a factorization is possible if all three observables are results of a single experiment, such as (a1, b1, c1). If you are in doubt about this factorizability requirement, see this post and the next one, where I go through Bell's derivation in detail to show where this requirement comes in (https://www.physicsforums.com/showpost.php?p=2830780&postcount=1211, https://www.physicsforums.com/showpost.php?p=2830781&postcount=1212)

However the expectation values from QM and Experiments, correspond to three different experiments (a1,b1), (b2,c2), (a3,c3). So that substituting these into Bell's inequality, you get

1 + <b2c2> >= | <a1b1> - <a3c3> |

Note that it is not possible to do the factorization as Bell assumed because a1 is different from a3. However, if you naively think a1 is equivalent to a3, then you might be tempted to drop the indices and say

1 + <b2c2> >= | <a(b1 - c3)> |

By dropping all the indices, Bell proponents naively think the variables from QM and experiments should be compatible. De Raedt et al show using the doctors example that such operations are wrong. But you do not need the doctors example to see the error in the above.

From the above, ai,bi,ci correspond to three list of values (+1, -1) which correspond to the outcome at when the angle is a,b,c. Take for example a1 corresponds to the list of outcomes when Alice set her detector to angle a, and b1 corresponds to the list of outcomes when Bob set his detector to angle b, during experiment (1).

Same for b2,c2 and same for a3,c3.

Bill, thanks for the link to that one year old thread which elaborates on eq.2 in Bell's paper, as well as the derivation of eq.15. This summary was really helpful for me.

Now if I correctly understand it, it is argued that the unknown lambda in Bell's derivation must be of the same value (or of the same average value, this certainly is an issue!):

1. between each photon pair
and also
2. between consecutive measurements with different angle settings.

Correct? Thanks for the improved understanding. :-)

Meanwhile I found back the paper of Bell on Bertlmann's socks:
http://cdsweb.cern.ch/record/142461?ln=en

There he seems to be aware of that kind of issues - even with mention of patients in Lyon and Lille. He argues near the end of his paper that common influences should average out. And he claims without hesitation that a similar inequality must be valid for the socks, based on the fair sampling hypothesis.

Comments on his sock washing inequality are welcome.

 

[billschnieder]

That's better for me: as an onlooker I do prefer the example in which the tablets stand for photons and the glasses for detectors (please do not present flying glasses with liquids that fall on tablets, that just causes confusion ).

I agree,

- Three liquids correspond to three angles, two tablets correspond to two photons which for our case are identical. Bitter = +, sweet = -.

It is very important not to confuse this simple analogy by changing the glasses to now be photons as DrC wants to do. If I accept this, we by the time we are done, we will not have any clarity. We want clarity not obfuscation and I am baffled why DrC is resisting it. We have a clear correspondence between the EPR experiment and the analogy that should be enough so I continue to ask the same question I have been asking and getting no response from DrC.

 

[billschnieder]

Ditto, ace. We are using your analogy my way.

3 tabs = 3 angles
X/Y/and whatever else you want, unknown liquids
Bitter=+, Sweet=-

ONE PHOTON PER DATA ITEM, NOT TWO.

NO! The analogy as I phrased it is clearly similar to the EPR case. If you want to give a different analogy, you will have to explain it in a similar manner as I've done below so that it is clear to anyone that it corresponds to the EPR case. What you have suggested is a joke.

- The two photons will correspond to two tablets of a given kind produced at a time, one given to Alice and the other to Bob, each of whom has three different liquids (a,b,c). The experiment at each station will involve a random choice of one of the liquids, an aliquot of which they then mix with the given tablet and drink to obtain either the "sweet" (+) outcome or the "bitter"(-) outcome.
- The tablet properties (chemicals), being hidden are not specified. We do not know how many of them there are, but we can say each particle pair has a well defined "chemical composition" (elements of reality) which interacts with the liquids (a,b,c) (detector settings) to produce the observables ("sweet", "bitter").


1) What does each data point of triples represent that is supposed to be realistic?
2) How are you going to select pairs from these triples in a way that is consistent with the way pairs are selected in Bell test experiments?

This is not Hard at all, the fact that you keep bobbing and weaving tells alot.
Now phrase your dataset according to the above description which you have already agreed is a good analogy. Or explain why you can not do it unless you switch glasses with tablets.

 

[JesseM]

Jesse thanks for the clarification to my question if QM actually predicts a perfect correlation in principle (that is, zero theoretical precision limit). I was not thinking about detection limits (for which I suppose that there is no relevant theoretical limit) but about such things as Heisenberg's uncertainty principle and detection time windows.

The uncertainty principle only applies when you have non-commuting operators. If you measure both particles at the same detector angle, the two measurement operators should commute, so there should be no uncertainty.

QM doesn't make claims about flying photons (that is a semi-realistic interpretation based on one out of several models); instead it predicts photon observations at detectors. I was under the impression that in QM no certain and precise correlation between two photons is possible in principle

No, that's incorrect. If both polarizers are set to the same angle, and there are no issues with detector efficiency, then QM predicts they will either both pass through the polarizers or both be reflected by them, with probability 1. In general, if one polarizer is set to angle a while the other is set to angle b, then the probability they will both pass through (the probability that both are "vertically polarized" relative to the polarizer) is given by the equation P_VV = (1/2)*cos²(a-b) -- see the top of p. 3 of this intro to entanglement and Bell's inequalities for example. That paper also notes that the probability that both are "horizontally polarized" is given by P_HH = (1/2)*cos²(a-b), while the probability that one photon is horizontally polarized while the other is vertically polarized is given by P_HV = P_VH = (1/2)*sin²(a-b). So if a=b, since cos²(0) = 1 the probability both are vertically polarized or both are horizontally polarized is 1/2 + 1/2 = 1, and since sin²(0)=0 the probability that one is vertically polarized while the other is horizontally polarized is 0.

 

[harrylin]

The uncertainty principle only applies when you have non-commuting operators. If you measure both particles at the same detector angle, the two measurement operators should commute, so there should be no uncertainty. [..] If both polarizers are set to the same angle, and there are no issues with detector efficiency, then QM predicts they will either both pass through the polarizers or both be reflected by them, with probability 1.

Do those measurement operators include the detector atoms and the timing precision for identifying entangled photons? I still think that they don't...

[..] So if a=b, since cos²(0) = 1 the probability both are vertically polarized or both are horizontally polarized is 1/2 + 1/2 = 1, and since sin²(0)=0 the probability that one is vertically polarized while the other is horizontally polarized is 0.

Your interpretation implies that there is in principle no limit to the accuracy of such things as detection angle, timing accuracy, etc...
I keep thinking that this is at odds with Maudlin's "at best allow some approximation"; and although Bell thought along the lines that you sketched, he did not want to rely on that argument in "Bertlemann's socks". There he admitted that Bohm's example is "idealized" and he stressed that his general argument does not rely on such unattainable perfection.

Harald

 

[DrChinese]

NO! The analogy as I phrased it is clearly similar to the EPR case. If you want to give a different analogy, you will have to explain it in a similar manner as I've done below so that it is clear to anyone that it corresponds to the EPR case. What you have suggested is a joke.


This is not Hard at all, the fact that you keep bobbing and weaving tells alot.
Now phrase your dataset according to the above description which you have already agreed is a good analogy. Or explain why you can not do it unless you switch glasses with tablets.

It's my challenge, ace. And you STILL refuse to take it. One photon, 3 angles. Not 2. One less than 2. That's ONE. How many ways can I say it? So you can represent a set of photons with a set of tabs. 3 glasses correspond to 3 angles. Outcomes are binary, bitter or sweet or red or green, I don't care. Lemme know when you can come up with a dataset.

I have a nap to take now, while you bob some more. Can you please help my Mavs? They need a little extra something right now, and you appear to be doing a good job.

 

[billschnieder]

It's my challenge, ace. And you STILL refuse to take it.

Sure it is your challenge, which does not make sense and I've been trying to extract a coherent description of the challenge from you. Apparently it is harder than a root-canal extraction. If you want someone else to actually respond to the challenge, then you will have to put aside your pride and make an effort to actually explain the challenge in detail.

So you can represent a set of photons with a set of tabs. 3 glasses correspond to 3 angles. Outcomes are binary, bitter or sweet or red or green, I don't care. Lemme know when you can come up with a dataset.

So you finally agree with my description but do not specify what the dataset means. From the discussion so far (summarized below), I will have to infer what you mean by "dataset"

Do you want me to give you a dataset in which each point is a triple of angles, or a triple of outcomes?

Yes, a triple of outcomes...The outcomes are for observations that may or may not be performed.

you are asking for a dataset from an impossible experiment, as evidenced from the fact that you are unable to describe to me the experiment that is supposed to produce this dataset.

no, there is no experiment implied here (impossible or otherwise). Just asking you to tell me what possibilities there are for the triples.

Given the above, I can infer that your "dataset" is a list of triples of *possible outcomes* of the experiment as described in the analogy which you now agree to. In other words, you want a list containing something like (+,-,+) for each identical pair of tablets (photons) corresponding to the *possible outcomes* when mixed with three different liquids (a,b,c) (angles).

Here is the dataset you are requesting. I am providing it despite the fact that you have refused to specify how you will derive terms involving pairs from this dataset to substitute in Bell's inequality 1 + <bc> >= |<ab> - <ac>|, in a manner that is similar to what is done in Bell test experiments.

a, b, c
-----------
-1, +1, -1
+1, -1, -1
+1, +1, -1
-1, -1, -1
-1, -1, -1
-1, +1, +1
-1, +1, -1
+1, +1, -1
+1, +1, -1
+1, -1, -1
+1, -1, +1
+1, -1, +1
-1, +1, +1
+1, +1, +1
-1, +1, -1
+1, +1, +1
+1, +1, +1
-1, +1, -1
-1, -1, -1
-1, -1, +1