New work by Tim Palmer and Sabine Hossenfelder

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

Re: New work by Tim Palmer and Sabine Hossenfelder

Postby Jarek » Tue Feb 18, 2020 2:48 am

Richard,
this discussion is not only about QM, but also classical field theories like electromagnetism or general relativity: if physics solves them using Euler-Lagrange, then current state of the field is local realistic "hidden variable" - satisfies Bell's assumptions leading to inequalities violated by physics - contradiction.
While QM might have dozens of philosophical interpretations (due to collapses caused by not including environment), Lagrangian formalism is pure math - doesn't leave so much freedom, wanting to solve a model we can use Euler-Lagrange or the least action principle ... what other options are there? Which one is used by physics?
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Re: New work by Tim Palmer and Sabine Hossenfelder

Postby Guest » Tue Feb 18, 2020 3:18 am

gill1109 wrote:By the way, I do believe myself that quantum correlations are probably consequences of the spinorial properties of spacetime.


Can you elaborate a little bit?
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Re: New work by Tim Palmer and Sabine Hossenfelder

Postby gill1109 » Tue Feb 18, 2020 4:11 am

Jarek wrote:Richard,
this discussion is not only about QM, but also classical field theories like electromagnetism or general relativity: if physics solves them using Euler-Lagrange, then current state of the field is local realistic "hidden variable" - satisfies Bell's assumptions leading to inequalities violated by physics - contradiction.
While QM might have dozens of philosophical interpretations (due to collapses caused by not including environment), Lagrangian formalism is pure math - doesn't leave so much freedom, wanting to solve a model we can use Euler-Lagrange or the least action principle ... what other options are there? Which one is used by physics?

I don't see the contradiction. Bell's theorem is also pure math (or can be seen as pure math). Bell made *three* assumptions in order to derive his inequalities, not two. You forget the "no-conspiracy" assumption. So Euler-Lagrange is fine, and we must assume that "no-conspiracy" is false. And that is exactly confirmed by your proposal to use the "time symmetric" approach. Hidden variables in past and future.
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Re: New work by Tim Palmer and Sabine Hossenfelder

Postby Jarek » Tue Feb 18, 2020 4:51 am

So how does physics solve its equations? - can we try to answer this question from time symmetry perspective:

Does it use asymmetric Euler-Lagrange, Schrodinger - leading to inequalities violated by experiments?
Or maybe it rather uses symmetric: least action, path ensembles - which you also agree don't lead to these problematic inequalities.

Is there a third option?
If not, why can't we just imply that physics objectively uses the latter?
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Re: New work by Tim Palmer and Sabine Hossenfelder

Postby FrediFizzx » Tue Feb 18, 2020 6:18 am

gill1109 wrote:I don't see the contradiction. Bell's theorem is also pure math (or can be seen as pure math). ...

Bell's "theorem" is NOT pure math. The inequalities are pure math which it is based on but the "theorem" itself is a pure word theorem. And..., guess what? It is physically impossible for anything to violate the inequalities. That should be your first clue that something is wrong with the "theorem". Does quantum mechanics exceed the bounds of the inequalities? Sure. So how could that be? Simple. QM shifts to an inequality with a higher bound and NEVER violates any of the Bell inequalities.
.
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Re: New work by Tim Palmer and Sabine Hossenfelder

Postby Jarek » Tue Feb 18, 2020 7:05 am

FrediFizzx wrote:Bell's "theorem" is NOT pure math.

So maybe let's focus on simpler Mermin's:
Pr(A=B) + Pr(A=C) + Pr(B=C) >= 1
which is nearly "tossing 3 coins, at least 2 are equal".
Its derivation doesn't need any ambiguous "locality", "realism", just that "there exists Pr(ABC) probability distribution" assumption:
Pr(A=B) = P(000) + P(001) + P(110) + P(111)
Pr(A=B) + Pr(A=C) + Pr(B=C) = 2P(000) + 2P(111) +sum_ABC P(ABC) = 2P(000) + 2P(111) + 1 >= 1

Isn't it just a simple pure math?

It is physically impossible for anything to violate the inequalities.

Here in page 4 is its violation with QM formalism: https://arxiv.org/pdf/1212.5214

That should be your first clue that something is wrong with the "theorem".

Indeed, somehow the assumptions used to derive this inequality are nonphysical.

Here the only used assumptions is just: there exists P(ABC) probability distribution.

But how such obvious assumption could not be true???

So Ising model is an example of situation where this assumption is not true - instead of single probability distribution P(ABC), from symmetry we have two amplitudes psi(ABC) as in QM - to be added over unmeasured variables, then multiplied to get the probabilities, as in Born rule: https://physics.stackexchange.com/quest ... mble-ising

Image
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Re: New work by Tim Palmer and Sabine Hossenfelder

Postby minkwe » Tue Feb 18, 2020 7:49 am

Heinera wrote:
minkwe wrote:I've been saying something similar here for years. Counterfactual outcomes are not statistically independent of actual outcomes.

There is nothing in the proof of Bell's theorem that requires that counterfactual outcomes must be statistically independent of actual outcomes.

There absolutely is. You say that because you do not understand Bell's theorem. Perhaps you should make a bit more of an effort to understand the point being made. We've had this discussion before. You can review the old threads from 2014 to see that I was saying exactly what Tim Palmer is now saying.

See for example this thread: viewtopic.php?f=6&t=44
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Re: New work by Tim Palmer and Sabine Hossenfelder

Postby minkwe » Tue Feb 18, 2020 8:10 am

Jarek wrote:
FrediFizzx wrote:Bell's "theorem" is NOT pure math.

So maybe let's focus on simpler Mermin's:
Pr(A=B) + Pr(A=C) + Pr(B=C) >= 1
which is nearly "tossing 3 coins, at least 2 are equal".
Its derivation doesn't need any ambiguous "locality", "realism", just that "there exists Pr(ABC) probability distribution" assumption:
Pr(A=B) = P(000) + P(001) + P(110) + P(111)
Pr(A=B) + Pr(A=C) + Pr(B=C) = 2P(000) + 2P(111) +sum_ABC P(ABC) = 2P(000) + 2P(111) + 1 >= 1

Isn't it just a simple pure math?

Hi Jarek,
You are both right. The above is pure math, but the above is Bell's "Inequalities" not Bell's Theorem.

It is physically impossible for anything to violate the inequalities.

Here in page 4 is its violation with QM formalism: https://arxiv.org/pdf/1212.5214

Again, you are talking past each other. I have read your posts carefully, and I think you have been treated unfairly by "Dave (aka DrChinese)" on Sabine's blog and I think you actually agree with Fred more than you think. But I don't think you understand what Fred is saying. Fred is right that nothing can violate Bell's inequalities. But you think QM does. What we have is Fred saying 1 orange + 1 orange = 1 fruit, and you are saying 1 orange + 1 orange = 2 fruits. By fruit Fred means types of fruit but you mean items of fruit. The same games are played all the time to claim violation of Bell's inequalities -- use one definition to derive it, and then switch the definition to claim violation. Fred is being more consistent that you are in that case.

That should be your first clue that something is wrong with the "theorem".

Indeed, somehow the assumptions used to derive this inequality are nonphysical.

As you've shown yourself, the inequalities do not need physical assumptions to derive and is pure math, therefore it is impossible to violate if the maths of the claimed "violation" is correct. The physical assumptions come in when applying the inequalities and that is the area where Bell's theorem also comes in.

Here the only used assumptions is just: there exists P(ABC) probability distribution.

Exactly. So that is the only assumption that fails.

But how such obvious assumption could not be true???

See viewtopic.php?f=6&t=44. The assumption is obviously false for the experiment that is the subject for these types of inequalities.

So Ising model is an example of situation where this assumption is not true - instead of single probability distribution P(ABC), from symmetry we have two amplitudes psi(ABC) as in QM - to be added over unmeasured variables, then multiplied to get the probabilities, as in Born rule: https://physics.stackexchange.com/quest ... mble-ising

I won't claim to understand the Ising model, but I don't think you need to go that far to understand why such an assumption must be false for these types of experiments.
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Re: New work by Tim Palmer and Sabine Hossenfelder

Postby minkwe » Tue Feb 18, 2020 8:17 am

Here is the relevant part from that thread from 2014:
In a recent thread, I tried to show the error in Bell/CHSH type inequalities and their alleged violation by QM and experiments. Some have been unable to understand the argument. I will attempt again to illustrate the issue. We will use an analogy of coin-tossing which maintain all the key features of the Bell-CHSH discussion. To my knowledge, nobody has presented the argument in this manner before. I will present the argument in two parts.

Feel free to ask clarifying questions as we go along. If there is interest, I may even discuss exactly how all the loopholes fit into this analogy, and why they are irrelevant, including super-determinism, and show exactly the flaw in Gill's most recent paper.

Part 1: The Bell argument

Assumptions:
1. Coins are local realistic
2. Coins have only two possible outcomes H = +1, T=-1

Derivation of the equality (cf inequality):
- Let A be the outcome we get when we toss a single coin.
- We assume that the other outcome we could have gotten also exists, even though we did not get it, call it B.
- Tossing a single coin produces either H or T and not both. Possible outcomes for AB are (HT, TH)
- Therefore A + B = 0, and E(A) + E(B) = 0 for all local realistic coins.

QM predictions:
- QM predicts E(A) = E(B) = 0.25.

Bell's theorem:
- Since from QM E(A) + E(B) = 0.5 =/= 0, it means QM is not local realistic.

Aspect-type experiments:
- We need to test experimentally whether QM or local realism is correct. Unfortunately we can only read one outcome at a time from a single coin. However, if we toss two coins, we can still obtain accurate estimates of E(A) and E(B) in the form of <A> and <B>, where A is the outcome we get from the first coin, and <B> is the outcome we get from the second coin. We should get similar results because the two coins are drawn from the same population.
- After the experiment we observe <A> = <B> = 0.25, <A> + <B> = 0.5, exactly what QM predicted.
- Therefore QM is correct and local realism is wrong.

Part 2: The unraveling
--------------------------
The argument I have made many times is that the reason for the violation is due to an erroneous substitution of actual results from two separate systems, into an expression derived using actual & counter-factual results from a single system. It sounds so simple but why has this been difficult to understand so far? This discussion between Heinera and Richard in a related thread illustrates why:

Heinera wrote:
So if the original correlations (all computed on the whole set) didn't violate the CHSH inequality (CHSH<2), and the correlations computed on four disjoint random subset would not change much, we can now conclude that the four latter correlations would still not significantly violate the CHSH inequality, since term by term, they are approximately equal to the original correlations?


gill1109 wrote:
Yes Heinera, you are home. They might violate it a little, but in all probability they won't violate it by much



Let us translate these innocent looking argument to our coin toss system:

If we measure <A> on a fair sample, of the population, we should get almost the same result as the population.
If we measure <B> on a fair sample, of the population, we should get almost the same result as the population.
Just because we measured <A> on one fair sample, and <B> on a different fair sample, does not change the fact that E(A) + E(B) = 0 for the population. You might violate it a little due to experimental error, but it shouldn't matter whether we use a single population or two disjoint fair samples of the population. Then the expectation values from the two coins should still not significantly violate the expression we obtained from the single coin



So what is wrong with this argument:
-------------------------------------------
First, let us present a counter-example which shows that the QM prediction is fully consistent with local-realism:

- We have a local realistic coin with a (H,T) probability distribution of [0.625,0.375]. E(A) = E(B) = 0.625(1)+0.375(-1) = 0.25, E(A) + E(B) = 0.5, fully agreeing with the experiments and QM.
- What about our local-realistic relationship E(A) + E(B) = 0 which we derived. Is it still valid for our local-realistic coins? Yes of course, provided we throw only single coins. Let us throw the coins on a glass table and read A from above, and B from below, and create a spreadsheet. Each row of the spreadsheet will necessarily sum to 0, and therefore <A> + <B> = 0. Agreeing with E(A) + E(B) = 0.
- How can the same local-realistic coins produce <A> + <B> = 0 in one experiment and <A> + <B> = 0.5, in another experiment? Because values calculated on two coins are not the same as values calculated on a single coin.

- Further illustration of the problem:
-------------------------------------------
Most people do not understand that counter-factual results do not have the same correlations as actual results. Take my coins for example, if the probability of H is 0.625, then the counter-factual probability for H can not also be 0.625. To illustrate even further, the actual result is what we get, the counter-factual result is what we did not get but could have gotten. If the likelihood of getting H is 0.625, then of course the likelihood of not getting H is 1-0.625 = 0.375. So the counter-factual probability is (1 - actual probability).

Failure to understand this elementary point is at the root of Bells theorem.

In the CHSH expression, S = E(a, b) − E(a, b′) + E(a′, b) + E(a′ b′), only [two] of the expectation values is actual, and the others are counterfactual. Bell assumed erroneously that each of those correlations should get the same functional form as the actual ones, not realizing that because they are counterfactual, we must flip the probability distributions.

If the actual E(a,b) = -cos(a-b)**2, then the counterfactual E(a,b) must be flipped to 1 - cos(a-b)**2.
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Re: New work by Tim Palmer and Sabine Hossenfelder

Postby Joy Christian » Tue Feb 18, 2020 8:32 am

minkwe wrote:
In the CHSH expression, S = E(a, b) − E(a, b′) + E(a′, b) + E(a′ b′), only [two] of the expectation values is actual, and the others are counterfactual. Bell assumed erroneously that each of those correlations should get the same functional form as the actual ones, not realizing that because they are counterfactual, we must flip the probability distributions.

If the actual E(a,b) = -cos(a-b)**2, then the counterfactual E(a,b) must be flipped to 1 - cos(a-b)**2.

That is it. If you do this in the standard derivation of the bounds on CHSH, you get the bounds -4 and +4, not -2 and +2. And those bounds are of course never "violated" in the experiments.

***
Last edited by Joy Christian on Tue Feb 18, 2020 9:20 am, edited 1 time in total.
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Re: New work by Tim Palmer and Sabine Hossenfelder

Postby Jarek » Tue Feb 18, 2020 8:44 am

minkwe,
great, so we agree that "there exists P(ABC) probability distribution" can be seen as the only used assumption, hence Bell theorem shows that this assumption is non-physical. Also Richard agrees:
gill1109 wrote:Exactly! A. Fine long ago showed the mathematical equivalence of the satisfaction of all Bell inequalities with the existence of a joint probability distribution reproducing all observable marginal distributions.

This is a basic assumption of (Kolmogorov) probability theory ( https://en.wikipedia.org/wiki/Probability_axioms ): that there exists a probability distribution on Omega (= {ABC: A,B,C in {0,1}} here).
QM defines state with amplitudes on Omega instead of probabilities - to be added over unmeasured variables, then multiplied to get probabilities.

So the question is to understand how this assumption might not be true in physics.
Tossing 3 coins, this assumption is true.

I don't understand what do you propose not to satisfy this assumption?
Could you maybe give a simple model for which we cannot assume it?

Regarding the use of Ising model for that, just find formula for probability distribution of values inside such Boltzmann sequence ensemble (Wick-rotated Feynman path ensembles) - it is a simple math exercise, its sketch is in diagram I have attached before, we get states defined by amplitudes on Omega instead of probabilities.
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Re: New work by Tim Palmer and Sabine Hossenfelder

Postby Heinera » Tue Feb 18, 2020 10:37 am

minkwe wrote:
Heinera wrote:
minkwe wrote:I've been saying something similar here for years. Counterfactual outcomes are not statistically independent of actual outcomes.

There is nothing in the proof of Bell's theorem that requires that counterfactual outcomes must be statistically independent of actual outcomes.

There absolutely is.


Well, why don't you put your effort where your mouth is and come up with a local HV model where counterfactual outcomes are dependent on actual outcomes, and reproduces the quantum correlations? I understand GitHub is a great place to post it.
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Re: New work by Tim Palmer and Sabine Hossenfelder

Postby gill1109 » Tue Feb 18, 2020 11:42 am

One of my favourite short proofs of Bell's theorem goes as follows. Sorry, it is a bit long.

Imagine a huge apparatus (1500 meters long) with at each end of it a toggle switch which is either in a neutral position "off", or which can be flipped up to "1" or flipped down to "2" (these are "on" positions).

When you toggle the switch to one of the "on" positions, something goes on inside the apparatus, and inside it, a piece of paper gets printed, and then ejected, with either "+1" or "-1" written on it.
Suppose that the whole system, as far as the causes of what gets printed out, can be described by some classical deterministic many particles system. The whole thing starts in some initial state omega. The two toggle switches are switched to "on" positions. And after some brief deterministic evolution, out come the two outputs. Of course, every time you perform this trial again, omega is different. So, for omega in some huge set Omega, and a, b in the set of inputs {1, 2}, we have functions f and g, defined om Omega x {0, 1} x {0, 1} such that *if* the inputs are a, b and *if* the initial state is omega, *then* the outputs will be f(omega, a, b) and g(omega, a, b).

Classical physics gives us models of counterfactuals: what would happen, if ... !

So far, I have assumed a rather strong form of *realism*.

Now we make two more important assumptions.

1) Locality: the length of time between inputs and outputs is so short that f(omega, a, b) doesn't depend on b and g(omega, a, b) doesn't depend on a (4 microseconds could do)

2) No-conspiracy: in the actual trial, omega will be picked (outside our control) by chance. We suppose that outside of the box, we can generate effectively random settings A and B and we will input their outcomes "1" or "2" into the toggle switches.

Now we define functions of omega as follows X_ab(omega) = f(omega, a, b); Y_ab(omega) = g(omega, a, b)

We think of them as eight *counterfactual* random variables: what the outcomes would have been, at both ends of the apparatus,dependent on what the inputs could have been.

The locality assumption tells us that X_a1 = X_a2, so we just call it X_a, for a = 1, 2; and Y_1b = Y_2b, so we just call it Y_b, for b = 1,2

Now we have four counterfactual random variables X_1, X_2, Y_1, Y_2

But our model assumption is that when we insert *random* settings A and B, the *factual* outcomes are the ones picked out by the setting. So defining X = X_A and Y = Y_B, the pair X, Y are the two outcomes which are observed as outputs; the pair A, B are the two settings which were chosen by some random mechanism and factually inserted into the apparatus, one at each end.

[Mathematically, we are replacing Omega with a much bigger space which also contains the "causes" of the outcomes of the coin tosses]

[Moreover, I am not saying that all these things really exist: I'm just saying that my understanding of physics tells me that a mathematical model of this type could closely describe the statistics of the experiments that we could actually do]

Now, the assumption of no-conspiracy + locality + realism tells us that

E(XY | A=a, B = b) = E(X_a Y_b | A=a, B=b) = E(X_a Y_b) (***)

Notice that I have used every single one of the assumptions made so far !!!

Trivially, we have the CHSH inequality for the four random variables X_1, X_2, Y_1, Y_2, all defined on the same probability space, ie with a joint probability distribution.
But by the key equality (***) we now also have the CHSH inequality for the four *experimentally measurable correlations* E(XY | A=a, B = b)
Each of the four is determined using a disjoint set of trials.

In practice, one should take account of sampling error: an observed average over a finite number of trials is not the same as a theoretical expectation value. Any applied statistician who has been given the most rudimentary statistical training will be able to tell you how close they are likely to be. Experimental physicists are indeed forced to learn something about error bars and all that.
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Re: New work by Tim Palmer and Sabine Hossenfelder

Postby minkwe » Tue Feb 18, 2020 10:17 pm

Heinera wrote:Well, why don't you put your effort where your mouth is and come up with a local HV model?

Huh? You serious? Do you have anything useful to contribute to the discussion rather than perpetual trolling?
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Re: New work by Tim Palmer and Sabine Hossenfelder

Postby gill1109 » Wed Feb 19, 2020 12:29 am

minkwe wrote:
Heinera wrote:Well, why don't you put your effort where your mouth is and come up with a local HV model?

Huh? You serious? Do you have anything useful to contribute to the discussion rather than perpetual trolling?

Seriously, guys ... Heinera asked for "a local HV model where counterfactual outcomes are dependent on actual outcomes, and reproduces the quantum correlations". Well, that's very easy if you violate "no-conspiracy". Start by creating a data set following the standard QM rules. (You do that on *one* classical computer ). Now you fill in the "not observed" (i.e., missing) counterfactual outcomes, just how you like. And Bob's your uncle!
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Re: New work by Tim Palmer and Sabine Hossenfelder

Postby Jarek » Wed Feb 19, 2020 12:56 am

Even simpler - you just need to dissatisfy this single assumption: "there exists joint probability distribution on Omega".
It is really easy with Ising model thanks to using nearly the same math (Feynman -> Boltzmann path ensemble) - instead of probability on Omega, as in QM states are defined by amplitudes on Omega, which have to be added for unmeasured variables, then multiplied to get probabilities.
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Re: New work by Tim Palmer and Sabine Hossenfelder

Postby minkwe » Thu Feb 20, 2020 8:49 am

Jarek wrote:Even simpler - you just need to dissatisfy this single assumption: "there exists joint probability distribution on Omega".
It is really easy with Ising model thanks to using nearly the same math (Feynman -> Boltzmann path ensemble) - instead of probability on Omega, as in QM states are defined by amplitudes on Omega, which have to be added for unmeasured variables, then multiplied to get probabilities.

Hi Jarek,
See this post from a few years ago, for an explanation why there is no joint probability distribution (ABC) in the EPR experiment viewtopic.php?f=6&t=181. Again, I'm not familiar with the Ising model but the very nature of the EPR experiment makes the existence of a joint probability distribution an exception rather than the rule.

Also, these article goes into a lot more detail about why the lack of such a distribution should be expected:
https://arxiv.org/abs/0907.0767
http://www.panix.com/~jays/vorob.pdf

There is however a subtlety that we should never lose sight of, and that a lot of people miss repeatedly. Although the lack of such a probability distribution can invalidate the applicability of such inequalities there are situations in which the probability distribution could be imagined to exist but the distribution used in the derivation is different than the one measured in actual experiments. The coin toss example I gave above illustrates this succinctly, how a mathematical relation can be derived using one distribution, and an experiment sampling a different distribution would appear to violate it. I also recently posted an illustration from category theory to show why this is the case in experiments like the EPR. You can find it here viewtopic.php?f=6&t=373&p=8529p8529#p8529

There are a few undeniable facts:

* The CHSH expression E(AB) − E(AB') + E(A'B) + E(A'B') <= 2, contains a mixture of two actual expectation values and two counter-factual expectation values. This is simply what the derivation demands by considering what might be imagined.
* For set of particle pairs, it is impossible measure all the particle pairs at angles (a,b,a',b') simultaneously. Thus, in the experimental data, there is no joint measurement of of outcomes (A, A', B, B'). In practice, 4 disjoint paired distributions (A, B), (A, B'), (A', B), (A', B') are sampled.
* As Vorob proved, it is not always possible to reconstruct a joint distribution for (A, A', B, B') from such separate disjoint distributions, even one could be imagined to exist. See my post viewtopic.php?f=6&t=181 for an explanation why. Also note that when calculating E(AB) − E(AB') + E(A'B) + E(A'B') from an experiment, what matters is ONLY the fact that such a distribution exists in the experimental data not whether the distribution can be imagined to exist. In short, imaginary experimental data does not exist.
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Re: New work by Tim Palmer and Sabine Hossenfelder

Postby Joy Christian » Thu Feb 20, 2020 9:02 am

minkwe wrote:* The CHSH expression E(AB) − E(AB') + E(A'B) + E(A'B') <= 2, contains a mixture of two actual expectation values and two counter-factual expectation values.

I don't undersatnd this. There can be only one actual expectaion value among the four, and three conuterfactual expectaion values.

***
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Re: New work by Tim Palmer and Sabine Hossenfelder

Postby minkwe » Thu Feb 20, 2020 10:47 am

gill1109 wrote:One of my favourite short proofs of Bell's theorem goes as follows. Sorry, it is a bit long.

Says everything. What you showed is not a proof of Bell's theorem but of Bell's inequalities. But I don't think these days anyone is interested in proofs of Bell's inequalities because there is little doubt that the inequalities are valid. The question is about the meaning of the inequalities and whether they are applicable to EPR-type experiments, and what they mean for physics.

So sorry, contrary to the claim, you haven't proved Bell's theorem.
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Re: New work by Tim Palmer and Sabine Hossenfelder

Postby minkwe » Thu Feb 20, 2020 10:55 am

Joy Christian wrote:
minkwe wrote:* The CHSH expression E(AB) − E(AB') + E(A'B) + E(A'B') <= 2, contains a mixture of two actual expectation values and two counter-factual expectation values.

I don't undersatnd this. There can be only one actual expectation value among the four, and three conuterfactual expectaion values.

***


Hi Joy, because E(AB), E(A'B') do not share any terms. But you are right, the derivation actually implies only a single actual and 3 counterfactual expectation values.
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