Is action at a distance possible as envisaged by the EPR Paradox.

[unusualname]

BTW: Someone wrote about the need of mathematical physicists in order to solve any big problem. What have they brought to physics that is acknowledged by the rest of the physicists? I have great respect for them, some of the best ones are my friends, but their contributions are more considered as math. There is a funny story about Simon and Feynman where RF asked BS "who are you young man" to which "BS" answered "I am BS", to which it was replied: and "what is your field?". adn BS comments: can you imagine that F did not know about my work? i.e., for me: BS did not even understand that RF couldn't care less about the type of things he was doing.

I hope that mathematical Physicist will have some recognition as physicists some day. Some of them have deep physical intuition beside tremendous technical power, but so far, ...

Is that supposed to be funny? Modern theoretical physics is mainly mathematical physics, in fact it's been that way for a century or so, the last great achievements by non-mathematicians was probably back in Faraday's time.

The foundations of QM have been debated for nearly a century by many great thinkers, and the conclusion is that nothing will get resolved by "word" arguments about interpretations, there needs to be a model to back up the argument and that model has to be in the language of mathematics.

Of course we need experimental results from which to check our models, and in relation to the question of this thread we have Bell experiments of Aspect et al, GHZ and delayed choice erasure experiments all of which suggest non-locality unless you are a deluded person who thinks a classical explanation makes sense. (The other explanations in terms of reinterpreting reality may have their time, but let's give the physics a chance before opening the gates for the philosophical hordes)

The most promising current model that might account for non-locality seems to be the Holographic Principle, but to properly understand that you need to understand its origins in the work of Bekenstein and Hawking in the 70s on Black Hole Thermodynamics, then you need to understand how it works with current models in String Theory, LQG etc.

This is difficult stuff, with a heavy dose of mathematical formalism. It is the arena where the useful debate about understanding the universe is taking place, not the pseudo philosophical word-play that goes on in these forums.

If you ask the current great Physicists about QM interpretations they will probably admit we are no nearer a resolution, but they do at least know what they're talking about, here's what Joe Polchinski has to say about the fact that String Theory does not attempt to solve the interpretation problem:

This is an interesting question, to which there is no definite answer. On the one hand, since it was possible to quantize the other three interactions without changing the interpretation of QM, it is not obvious that one should not be able to do the same for gravity. If we restrict to `laboratory’ experiments with gravity (even building black holes in the lab), there is no sharp paradox that would require us to modify QM. QM makes us queasy, but if it gives consistent predictions for all processes we may just have to live with that. Things are much less clear when you get to cosmology. Chaotic inflation, for example, does seem to lead to paradoxes, which might be the clue to a deeper understanding of QM

Where in the last sentence he hints at MWI, but as you can see he's more interested in hard physics, not philosophical fluff, (quote taken from his comments in this blog entry replying to Smolin's The Trouble with Physics)

 

[billschnieder]

Nope, you won't be able to, ...

It took me 2 minutes to find this, and it looks worse than I had thought. Pay attention to how you characterized Bell's expectation value. Also pay attention to how you are factorizing ρ(λ), within the summation. There is no escape.

When scratched, any given box will reveal either a cherry or a lemon. Once Alice and Bob have both found the fruit behind the box they choose, they can adopt the convention that a cherry is represented by a +1 and a lemon is represented by a -1, and multiply their respective numbers together to produce a single number for each trial (and that single number will itself be +1 if they both got the same fruit, and -1 if they got different fruits). Then we are interested in the "expectation value" for a given choice of boxes--for example, E(a,b') means the average result Alice and Bob will get after multiplying their numbers together on the subset of trials where Alice chose to scratch box a and Bob chose to scratch box b'. The CHSH inequality then states that if we define the value S by S=E(a,b) - E(a,b') + E(a',b) + E(a',b'), then $$-2 \leq S \leq 2$$.

As for the hidden states, there are 16 different possibilities (and here I am replacing each fruit with the number they've chosen to represent it, so a=+1 means that the hidden fruit in box a on Alice's card is a cherry):

1: a=+1, a'=+1, b=+1, b'=+1
2: a=+1, a'=+1, b=+1, b'=-1
3: a=+1, a'=+1, b=-1, b'=+1
4: a=+1, a'=+1, b=-1, b'=-1
5: a=+1, a'=-1, b=+1, b'=+1
6: a=+1, a'=-1, b=+1, b'=-1
7: a=+1, a'=-1, b=-1, b'=+1
8: a=+1, a'=-1, b=-1, b'=-1
9: a=-1, a'=+1, b=+1, b'=+1
10: a=-1, a'=+1, b=+1, b'=-1
11: a=-1, a'=+1, b=-1, b'=+1
12: a=-1, a'=+1, b=-1, b'=-1
13: a=-1, a'=-1, b=+1, b'=+1
14: a=-1, a'=-1, b=+1, b'=-1
15: a=-1, a'=-1, b=-1, b'=+1
16: a=-1, a'=-1, b=-1, b'=-1

In this case, define something like A(a,12) to mean "the value Alice gets if she picks a and the hidden state of the two cards is 12", so going by the above we'd have A(a,12)=-1. Similarly B(b',7)=+1, and so forth. And we can assume that there must be well-defined probabilities for each of the possible hidden states, which can be represented with notation like p(8) and p(15) etc.

Since the expectation value E(a,b) is the average value Alice and Bob get when they multiply their results together in the subset of trials where Alice picks box a and Bob picks box b, we should have: $$E(a,b) = \sum_{N=1}^{16} A(a,N)*B(b,N)*p(N)$$. Likewise, we should also have $$E(a,b') = \sum_{N=1}^{16} A(a,N)*B(b',N)*p(N)$$. Combining these gives:

$$E(a,b) - E(a,b') = \sum_{N=1}^{16} [A(a,N)*B(b,N) - A(a,N)*B(b',N)]*p(N)$$

With a little creative algebra you can see the above can be rewritten as:

$$E(a,b) - E(a,b')$$
.
$$\ = \sum_{N=1}^{16} A(a,N)*B(b,N)*[1 \pm A(a',N)*B(b',N)]*p(N)$$
.
$$\ - \sum_{N=1}^{16} A(a,N)*B(b',N)*[1 \pm A(a',N)*B(b,N)]*p(N)$$

 

[RUTA]

If you ask the current great Physicists about QM interpretations they will probably admit we are no nearer a resolution, but they do at least know what they're talking about, here's what Joe Polchinski has to say about the fact that String Theory does not attempt to solve the interpretation problem:


Where in the last sentence he hints at MWI, but as you can see he's more interested in hard physics, not philosophical fluff, (quote taken from his comments in this blog entry replying to Smolin's The Trouble with Physics)

Typical response about QM from someone working in unification. I've received similar responses from Witten and Ashtekar (and Smolin in 2002, but his 2006 book shows he's given it more thought since). They're buried in the technical problems associated with the pursuit of a different beast -- unification of the forces and/or quantization of gravity. We need people working on all fronts, but the fronts are too big for anyone person to master them all. Likewise, you might ask the author of a particular interpretation of QM how it bears on unification and receive an equally vague answer. In general, both camps (unification and foundations) agree their problems have a common resolution, they're just working on that resolution from different directions.

 

[unusualname]

Typical response about QM from someone working in unification. I've received similar responses from Witten and Ashtekar (and Smolin in 2002, but his 2006 book shows he's given it more thought since). They're buried in the technical problems associated with the pursuit of a different beast -- unification of the forces and/or quantization of gravity. We need people working on all fronts, but the fronts are too big for anyone person to master them all. Likewise, you might ask the author of a particular interpretation of QM how it bears on unification and receive an equally vague answer. In general, both camps (unification and foundations) agree their problems have a common resolution, they're just working on that resolution from different directions.

I would think the resolution to QM interpretation will fall out rather easily once the "unification" people hit on the correct microscopic description of reality. I can't see how there could be much useful input the other way.

Of course, once it's all resolved someone will point to a passage in Kant which explained it all hundreds of years ago.

 

[JesseM]

According to you, the wikipedia article is wrong.

No, just that it was failing to adequately distinguish between two notions of the "mean" which could lead to certain readers (you) becoming confused. There weren't any statements that were clearly incorrect.

Why don't you correct it.

Your wish is my command. I have edited the opening section of the article to more clearly distinguish between the "sample mean" and the "population mean", and make clear that the expected value is equal to the population mean, not the sample mean:

For a data set, the mean is the sum of the values divided by the number of values. The mean of a set of numbers x1, x2, ..., xn is typically denoted by $$\bar{x}$$, pronounced "x bar". This mean is a type of arithmetic mean. If the data set was based on a series of observations obtained by sampling a statistical population, this mean is termed the "sample mean" to distinguish it from the "population mean". The mean is often quoted along with the standard deviation: the mean describes the central location of the data, and the standard deviation describes the spread. An alternative measure of dispersion is the mean deviation, equivalent to the average absolute deviation from the mean. It is less sensitive to outliers, but less mathematically tractable.

If a series of observations is sampled from a larger population (measuring the heights of a sample of adults drawn from the entire world population, for example), or from a probability distribution which gives the probabilities of each possible result, then the larger population or probability distribution can be used to construct a "population mean", which is also the expected value for a sample drawn from this population or probability distribution. For a finite population, this would simply be the arithmetic mean of the given property for every member of the population. For a probability distribution, this would be a sum or integral over every possible value weighted by the probability of that value. It is a universal convention to represent the population mean by the symbol μ.[1] In the case of a discrete probability distribution, the mean of a discrete random variable x is given by taking the product of each possible value of x and its probability P(x), and then adding all these products together, giving $$\mu = \sum x P(x)$$.[2]

The sample mean may be different than the population mean, especially for small samples, but the law of large numbers dictates that the larger the size of the sample, the more likely it is that the sample mean will be close to the population mean.[3]

As an experiment, let's now see if anyone edits it on the ground that it's incorrect (as opposed to edits for stylistic or other reasons). No fair editing it yourself!

It is obvious you are the one who is way off base and you know it.

So, you wish to completely ignore the quotes from various statistics texts I provided? You trust a user-edited site like wikipedia over published texts? Here they are again:

(edit: See for example this book which distinguishes the 'sample mean' $$\bar X$$ from the 'population mean' $$\mu$$, and says the sample mean 'may, or may not, be an accurate estimation of the true population mean $$\mu$$. Estimates from small samples are especially likely to be inaccurate, simply by chance.' You might also look at this book which says 'We use $$\mu$$, the symbol for the mean of a probability distribution, for the population mean', or this book which says 'The mean of a discrete probability distribution is simply a weighted average (discussed in Chapter 4) calculated using the following formula: $$\mu = \sum_{i=1}^n x_i P[x_i ]$$').

All the grandstanding is just a way to stay afloat, not a serious argument agains the well accepted meaning of expectation value.

Wikipedia: http://en.wikipedia.org/wiki/MeanWikipedia: http://en.wikipedia.org/wiki/Expected_value

Neither of these sources claim that the expected value is equal to the "sample mean" (i.e. the average of the results obtained on a series of trials), which is what I thought you were claiming when you said:

You are given a theoretical list of N pairs of real-valued numbers x and y. Write down the mathematical expression for the expectation value for the paired product.

...

Wow! The correct answer is <xy>

Of course if the "theoretical list" is supposed to represent a population rather than results from a series of trials, and we assume we are picking randomly from the population using a method that has an equal probability of returning any member from the list, in that case I would agree the answer is <xy>. But once again your statement of the problem didn't provide enough information, because the list could equally well be interpreted as a sample, and in that case the expectation value for the paired product would not necessarily be equal to <xy> since <xy> would just be the sample mean--do you disagree?

Again, you said nothing about "randomly picking" from a list, you just gave a list itself and asked for the probabilities of one entry on that list.

Yes, that is exactly what I did, and you answered that it was impossible to do because you wanted to use ONLY a probability approach that involved "trials".

No I didn't, I just said not enough information was provided. If you specify that the list is intended to be a population and we are picking randomly from the population, that's A-OK with me. I already told you this was fine with me at the end of post #1277.

You do the same thing for dice and coins and you have done the same thing in you famous scratch-lotto examples

In the scratch lotto example I explicitly specified that on each trial the experimenters were picking a box at random to scratch, and at some point I bet I even pedantically specified that "at random" means "equal probability of any of the three boxes". With coins and dice it's generally an implicit assumption that each result is equally probable unless the coin/die is specified to be weighted or something.

Well, excuse me for thinking your question was supposed to have some relation to the topic we were discussing, namely Bell's theorem.

While discussing Bell's INEQUALITIES, Not Bell's theorem which we haven't discussed at all

Bell's theorem is just that Bell's inequalities must be obeyed in any local hidden variables theory, and since QM theoretically predicts they will be violated in some circumstances, QM is theoretically incompatible with local hidden variables. Anyway, if you want to be pedantic we're discussing the entirety of Bell's derivation of the inequalities, and whether an analysis of the derivation implies that the inequality is only applicable under some limited circumstances (like it only being applicable to data where it is possible to "resort" in the manner you suggested). My claim is that the correct interpretation of the probabilities in Bell's derivation is that they were meant to be "limit frequentist" probabilities, and that if you look at the derivation with this interpretation in mind it all makes sense, and it shows the final inequalities do not have the sort of limited applicability you claim.

and continue to claim that Bell's equation (2) is not a standard mathematical definition for the expectation value of a paired product.

Nope, it's not. The standard mathematical definition for the expectation value of some variable x (whether it is obtained by taking a product of two other random variables A and B or in some other way) is just a sum or integral over all possible values of x weighted by their probabilities or probability densities, i.e. either $$\mu = \sum_{i=1}^N x_i P(x_i)$$ or $$\int x \rho(x) \, dx$$. You can see that this standard expression for the expectation value involves no variables besides x itself. Now depending on the nature of the specific situation we are considering, it may be that functions like P(x) or ρ(x) can themselves be shown to be equal to some functions of other variables, and this is exactly where Bell's equation (2) comes from. Here, I'll give a derivation:

If x is the product of the two measurement results A and B with detector settings a and b, then according to what I said above the "standard form" for the expectation value should be $$\mu = \sum_{i=1}^N x_i P(x_i)$$, and since we know that this is an expectation value for a certain pair of detector angles a and b, and that the two measurement results A and B are themselves always equal to +1 or -1, this can be rewritten as:

(+1)*P(x=+1|a,b) + (-1)*P(x=-1|a,b) = (+1)*[P(A=+1, B=+1|a,b) + P(A=-1, B=-1|a,b)] + (-1)*[P(A=+1, B=-1|a,b) + P(A=-1, B=+1|a,b)]

Then in that last expression, each term like P(A=+1, B=+1|a,b) can be rewritten as P(A=+1, B=+1, a, b)/P(a,b). So by marginalization (and assuming for convenience that λ is discrete rather than continuous), we have:

$$P(A=+1, B=+1|a,b) = \sum_{i=1}^N \frac{P(A=+1, B=+1, a, b, \lambda_i )}{P(a,b)}$$

And P(A=+1, B=+1, a, b, λi) = P(A=+1, B=+1|a, b, λi)*P(a, b, λi) = P(A=+1, B=+1|a, b, λi)*P(λi | a, b)*P(a,b), so substituting into the above sum gives:

$$P(A=+1, B=+1|a,b) = \sum_{i=1}^N P(A=+1, B=+1 | a, b, \lambda_i )*P(\lambda_i | a, b)$$

And if we make the physical assumption that P(λi | a, b) = P(λi) (the no-conspiracy assumption which says the probability of different values of hidden variables is independent of the detector settings), this reduces to

$$P(A=+1, B=+1|a,b) = \sum_{i=1}^N P(A=+1, B=+1 | a, b, \lambda_i )*P(\lambda_i )$$

Earlier I showed that the expectation value, written in its standard form, could be shown in this scenario to be equal to the expression

(+1)*[P(A=+1, B=+1|a,b) + P(A=-1, B=-1|a,b)] + (-1)*[P(A=+1, B=-1|a,b) + P(A=-1, B=+1|a,b)]

So, we can rewrite that as

$$(+1)*[ \sum_{i=1}^N P(A=+1, B=+1 | a, b, \lambda_i )*P(\lambda_i ) + \sum_{i=1}^N P(A=-1, B=-1 | a, b, \lambda_i )*P(\lambda_i )]$$$$+ (-1)*[ \sum_{i=1}^N P(A=+1, B=-1 | a, b, \lambda_i )*P(\lambda_i ) + \sum_{i=1}^N P(A=-1, B=+1 | a, b, \lambda_i )*P(\lambda_i )]$$

Or as a single sum:

$$\sum_{i=1}^N$$ P(λi) * [(+1*+1)*P(A=+1, B=+1|a,b,λi) + (-1*-1)*P(A=-1, B=-1|a,b,λi) + (+1*-1)*P(A=+1, B=-1|a,b,λi) + (-1*+1)*P(A=-1, B=+1|a,b,λi)]

And naturally if the value of a along with the specific choice of λi completely determine the value of A, and likewise the value of b along with the specific choice of λi completely determines the value of B (another physical assumption), then for any given i in the sum above, three of the conditional probabilities will be 0 and the other will be 1, so it's not hard to see (tell me if you want this step explained further) why the above can be reduced to:

$$\sum_{i=1}^N A(a,\lambda_i ) B(b, \lambda_i ) P(\lambda_i )$$

...which is just the discrete form of Bell's equation (2). So, hopefully you require no further proof that although Bell's equation (2) gives one form of the expectation value, it was not meant to contradict the idea that the expectation value can also be written in the standard form:

(+1)*P(product of A and B is +1) + (-1)*P(product of A and B is -1)

...which given the knowledge that both A and B are always either +1 or -1, and A is the result for the detector with setting a while B is the result for the detector with setting b, can be written as:

E(a,b) = (+1*+1)*P(detector with setting a gets result +1, detector with setting b gets result +1) + (+1*-1)*P(detector with setting a gets result +1, detector with setting b gets result -1) + (-1*+1)*P(detector with setting a gets result -1, detector with setting b gets result +1) + (-1*-1)*P(detector with setting a gets result -1, detector with setting b gets result -1)

...which is the equation I have been bringing up over and over. Last time I brought it up, you responded in post #1275 with:

False! The above equation does not appear in Bell's work and is not the expectation value he is calculating in equation (2).

Hopefully the above derivation shows you why Bell's equation (2) is entirely consistent with the above "standard form" of the expectation value, given the physical assumptions he was making. If you still don't agree, please show me the specific step in my derivation that you think is incorrect.

Oh so now you are saying if given a population from which you can easiliy calculate relative frequencies, you will still not be able to use your favorite "limit frequentist" approach to obtain estimates of true probabilities because the process used to sample the population might not be fair. Wow! You have really outdone yourself. If the "limit frequentist" approach is this useless, how come you stick to it, if not just for argumentation purposes?

It's useful in theoretical proofs involving probabilities, such as the derivation of the conclusion that Bell's inequality should apply to the "limit frequentist" expectation values in any local realist universe. And for experimental data, as long as the sample size is large we can use empirical frequencies to estimate a range for the limit frequentist probabilities with any desired degree of confidence, even though we can never be 100% confident the true limit frequentist probability lies in that range (but that's just science for you, you can never be 100% sure of any claim based on empirical evidence, even though you can be very very confident).

 

[JesseM]

It took me 2 minutes to find this, and it looks worse than I had thought. Pay attention to how you characterized Bell's expectation value. Also pay attention to how you are factorizing ρ(λ), within the summation. There is no escape.

So you had to look to a discussion with a different person from 2009 to find an example? Anyway, if you look closely you'll see that I did mention the assumption that Alice and Bob were picking which box to scratch at random:

The problem is that if this were true, it would force you to the conclusion that on those trials where Alice and Bob picked different boxes to scratch, they should find the same fruit on at least 1/3 of the trials. For example, if we imagine Bob and Alice's cards each have the hidden fruits A+,B-,C+, then we can look at each possible way that Alice and Bob can randomly choose different boxes to scratch, and what the results would be

Maybe I should have been more explicit about the fact that there was a probability of 1/3 that Alice would scratch a given box on any trial, and likewise for Bob, but that was certainly my implicit assumption. And I have spelled it out more explicitly in other posts, for example this one from a discussion with you in June:

That description is fine, though one thing I would add is that in order to derive the inequality that says they should get the same fruit 1/3 or more of the time, we are assuming each chooses randomly which box to scratch, so in the set of all trials the probability of any particular combination like 12 or 22 is 1/9, and in the subset of trials where they picked different boxes the probability of any combination is 1/6.

So yes, I have always assumed the limit frequentist notion of probability in any of my discussions of the lotto card example, and the post you quoted makes perfect sense with that interpretation if you keep in mind that there is a probability (in limit frequentist terms) of 1/9 that Alice and Bob will pick any given combination of boxes on each trial.

As an aside, can you please edit your post to remove the LaTex code after the words "With a little creative algebra you can see the above can be rewritten as"? The equation there is stretching the window badly, making this page hard to read.

 

[ThomasT]

When it exhibits wave-like behavior. Once it interacts with its environment, it acquires definite position (particle-like behavior) per decoherence.

I like to muse that reality is waves in a hierarchy of media, that the true god's eye view would just see a bunch of interacting waveforms, some bounded or particle-like, and some not, some more persistent than others, etc.

However, at the level of our experience, we see cars and computers and planets and ... moons. I don't think it makes much sense to say that the moon pops into and out of existence depending on whether we happen to be looking at it. The whole quantum-speak thing can get quite silly -- detectors, moons, cats in various 'superpositions' of existing and not existing, of being here and there.

RBW is not the only interpretation in which "non-interacting" means "non-existent." I got that idea from Bohr, Ulfbeck and Mottelson. Zeilinger has also been credited with that claim regarding photons.

It seems a bit silly to say that there's nothing moving from emitter to detector. Certainly the more sensible inference or hypothesis, and the one that practical quantum physics is based on, is that quantum experimental phenomena result from the instrumental probings of an underlying reality -- a reality which is presumably behaving according to some set of physical principles and which exists whether it's being probed or not.

Einstein's spooky action at a distance entails spacelike separated events determining, instantaneously, each other's existence. This is, prima facie, a nonsensical notion -- and Einstein was right to dismiss it.

Absolutely, RBW is an ontological interpretation of QM. What in particular strikes you as unreasonable about this ontology? The non-existence of non-interacting entities (manifested as nonseparability of the experimental equipment)? Or, blockworld?

It's not unreasonable. Especially if you're a GR person. I just find it conceptually unappealing. Anyway, is there any way to know to what extent some theoretical construction is a description of 'reality'?

 

[JesseM]

So can you please just answer the question: are you using (or are you willing to use for the sake of this discussion) the limit frequentist notion of probability, where "probability" is just the frequency in the limit as the number of trials goes to infinity?

No! I am not willing to pick and choose the definition of probability for argumentation purposes.

It's not "for argumentation purposes", it's for trying to understand what Bell actually meant, and how the probabilities in his derivation are interpreted by physicists. Your own argument which claims to show the derivation has very limited applicability is based on using a non-limit-frequentist interpretation of the probabilities in Bell's derivation. My claim is that this problem of limited applicability vanishes if we interpret the probabilities in his derivation in limit frequentist terms. Which is more likely a priori, that some guy posting on the internet is the first one to ever discover a major hole in Bell's derivation which never occurred to Bell or any other physicist, or that Bell and other physicists interpreted the probabilities in limit frequentist terms? (which again is a very common way to think about the meaning of probabilities, not some obscure notion I'm dragging up for the sake of being difficult) Are not even willing to consider that he might have been interpreting probabilities this way, to see if the problem of limited applicability would disappear in this case?

First you said it was ONLY the "frequentist" view you wanted. Now it is ONLY a particular variant of frequentism that you want

In post #1330 I linked back to an earlier discussion with you where I made clear that I was using "frequentist" probabilities to mean frequencies in the limit as the number of trials goes to infinity (what I am now calling 'limit frequentism' in hopes of avoiding exactly the sort of quibbling you're doing above), and an even earlier discussion with another poster from 2009 where I said the same thing, before you even started posting here. Hopefully this puts to rest the notion that I am somehow shifting my position, and if these posts don't convince you I again challenge you to find any posts by me discussing Bell inequalities where I haven't been talking in limit frequentist terms.

except when it involves coins and dice, you really use the "bayesian" view.

Nope, see the three paragraphs in post #1330 starting with "No. First of all, I'm not saying that the P(heads) is actually guaranteed..."

No, the "standard mathematical definition" of an expectation value involves only the variable whose value you want to find the expectation value for, in this case the product of the two measurement results.
...
In the standard definition would give us:
$$\sum_{i=1}^N R_i P(R_i )$$

Wikipedia: http://en.wikipedia.org/wiki/Expected_value

$$E(g(X))\int_{-\infty}^{\infty} g(X)f(X)$$

The wikipedia equation calculates an expectation value for a function of X rather than X itself, but the important thing is that the expectation value equations always can be reduced to a sum/integral over the product (possible value of variable in question)*P(variable takes that value), summed or integrated over all possible values. For example, if we define a new variable Y=g(X), then it can be shown that the above equation reduces to $$E(Y) = \int Y * P(Y)$$, which is the "basic form" I have been talking about. This is easier to see if we consider a discrete X and Y, so we want to show that this:

$$\sum_i g(x_i )f(x_i )$$

reduces to this:

$$\sum_j Y_j * P(Y_j )$$

First consider the case in which each x_i gives a unique Y_j when plugged into g(x). Then in that case, the probability of a given Y_j is naturally going to be the same as the probability of the corresponding x_i, and Y_j is equal to x_i, so the above will be satisfied. On the other hand, suppose there are multiple possible values of x_i which, when plugged into g(x), would give the same Y_j. Then for that value of j, it is true that P(Y_j) = (sum over all values of i for which g(x_i)=Y_j) f(x_i). So in that case, it must be true that for a specific value of j, Y_j*P(Y_j) = (sum over all values of i for which g(x_i)=Y_j) g(x_i)*f(x_i). So from this it's not hard to see why $$\sum_i g(x_i )f(x_i )$$ reduces to $$\sum_j Y_j * P(Y_j )$$...I don't feel like writing out a formal proof, but if you don't see why what I said above guarantees it, just imagine we have five possible values of x, namely x₁, x₂, x₃, x₄, x₅, and only two possible values of Y, Y₁ and Y₂, such that g(x₁) = g(x₃) = g(x₄) = Y₁, and g(x₂) = g(x₅) = Y₂. Then if we write out $$\sum_i g(x_i )f(x_i )$$ it would be:

g(x₁)*f(x₁) + g(x₂)*f(x₂) + g(x₃)*f(x₃) + g(x₄)*f(x₄) + g(x₅)*f(x₅)

And since g(x₁) = g(x₃) = g(x₄) and g(x₂) = g(x₅), we can gather together terms as follows:

g(x₁)*[f(x₁) + f(x₃) + f(x₄)] + g(x₂)*[f(x₂) + f(x₅)]

And since g(x₁)=Y₁ and g(x₂) = Y₂, and since P(Y₁) = [f(x₁) + f(x₃) + f(x₄)] and P(Y₂) = [f(x₂) + f(x₅)], the above reduces to:

Y₁*P(Y₁) + Y₂*P(Y₂)

...which is just $$\sum_j Y_j * P(Y_j )$$. Hopefully you can see how this would generalize to arbitrary sums $$\sum_i g(x_i )f(x_i )$$ and $$\sum_j Y_j * P(Y_j )$$, where every g(x_i) yields some Y_j.

You are way off base. Bell's equation two is the standard mathematical definition.The only difference between Bell's equation (2) and the last equation above, is that the symbols:
X = λ
g(X) = g(λ) = A(a,λ)*B(b,λ)
f(X) = ρ(λ)

The simplest mathematical definition deals not with the expectation value of a function of a random variable, but an expectation value of the random variable itself; i.e. not $$E(g(X)) = \int_{-\infty}^{\infty} g(X)f(X)$$ but rather $$E(Y) = \int Y*P(Y)$$. In any case, I don't really want to discuss the definition of "simple", my claim is just that all expectation values must reduce to that last form, and this is true of Bell's equation (2) as I showed in the derivation near the end of post #1335.

Bell is not trying to redefine anything. He is simply using the standard mathematical definition of expectation value for the paired product.

Any mathematician would understand that whatever form we choose to write an "expectation value", it can always be reduced to the form $$E(Y) = \int Y*P(Y)$$. Since Bell was ultimately computing the expectation value for the product of the two measurements, if we let Y equal the sum of the two measurements it must be true that his expression can be reduced to (sum over all possible values of Y) Y*P(Y). And I showed that such a reduction is in fact possible (given Bell's physical assumptions) in post #1335.

Note the dλ, at the end of the expression! There is no expression in Bell's paper as the following:

E(a,b) = (+1)*P(detector with setting a gets result +1, detector with setting b gets result +1) + (-1)*P(detector with setting a gets result +1, detector with setting b gets result -1) + (-1)*P(detector with setting a gets result -1, detector with setting b gets result +1) + (+1)*P(detector with setting a gets result -1, detector with setting b gets result -1)

Your claim that such an expression is missing, because Bell was simplifying for physicists is a cop-out.

No, it's just something that would be understood implicitly by anyone well-versed in probability theory, it isn't necessary to state the obvious. But since it's not obvious to you, again see the explicit derivation in post #1335.

Furthermore, there is no mention of "limit frequentist", let alone "frequentist" in Bell's paper. You are invoking those terms now only to escape humiliation.

I have already linked to posts dating way back where I explained that I interpreted Bell's probabilities in terms of the frequencies in the limit as number of trials goes to infinity, so the idea that I am changing my tune to "escape humiliation" is silly. And no, Bell doesn't mention limit frequentism, but he also doesn't mention any other notion of probability like finite frequentism or Bayesianism, so it's up to readers to interpret the meaning of "probability" in Bell's paper. Again, limit frequentism is pretty much the default assumption in theoretical proofs involving probabilities in science, but even if this weren't true, the mere fact that his derivation has some major holes when his probabilities interpreted in non-limit-frequentist terms, but these holes might disappear when we interpret his probabilities in limit frequentist terms (that is my assertion anyway), is good enough reason for you to at least consider that he might have meant the probabilities in this way before triumphantly proclaiming you have found a flaw in Bell's reasoning that has somehow escaped the notice of every physicist who studied it until now. At least, you should consider this possibility if you have any intellectual integrity and want to do your best to figure out what Bell meant, as opposed to just wanting to make a rhetorical case against him by picking an interpretation designed to make him look bad.

 

[RUTA]

I would think the resolution to QM interpretation will fall out rather easily once the "unification" people hit on the correct microscopic description of reality. I can't see how there could be much useful input the other way.

That's certainly the majority opinion. I think the best the foundations community can hope for is to find a new approach to unification, whereas a unified theory would certainly resolve all foundational issues.

As an example of how work in the foundations community might bear on the unification effort, our QM interpretation (Relational Blockworld) suggests a nonseparable Regge calculus approach to classical gravity (where nonseparable means "direct action" in the path integral approach). Obviously, changing classical gravity from Regge calculus (discrete, path integral version of GR) to nonseparable (direct action) Regge calculus, changes the quantum gravity program. It also changes what is meant by "unification," since the dynamical perspective, and therefore forces, are no longer part of a fundamental approach.

I didn't bring up unification per RBW to debate its merits, but merely to point out how the foundations community might contribute to the larger program of unification.

 

[RUTA]

However, at the level of our experience, we see cars and computers and planets and ... moons. I don't think it makes much sense to say that the moon pops into and out of existence depending on whether we happen to be looking at it. The whole quantum-speak thing can get quite silly -- detectors, moons, cats in various 'superpositions' of existing and not existing, of being here and there.

For most of us the phrase "not there when nobody looks" is simply a metaphor for the non-existence of non-interacting entities.

It seems a bit silly to say that there's nothing moving from emitter to detector. Certainly the more sensible inference or hypothesis, and the one that practical quantum physics is based on, is that quantum experimental phenomena result from the instrumental probings of an underlying reality -- a reality which is presumably behaving according to some set of physical principles and which exists whether it's being probed or not.

Einstein's spooky action at a distance entails spacelike separated events determining, instantaneously, each other's existence. This is, prima facie, a nonsensical notion -- and Einstein was right to dismiss it.

Well, if QM is right, one (or both) of these things has to go -- you can't have realism and locality. In our interpretation, we punt on realism, i.e., separability.

It's not unreasonable. Especially if you're a GR person. I just find it conceptually unappealing.

Most do

Anyway, is there any way to know to what extent some theoretical construction is a description of 'reality'?

That's a thorny epistemological question. Better leave that for another thread.

 

[JesseM]

There is no expression in Bell's paper as the following:

E(a,b) = (+1)*P(detector with setting a gets result +1, detector with setting b gets result +1) + (-1)*P(detector with setting a gets result +1, detector with setting b gets result -1) + (-1)*P(detector with setting a gets result -1, detector with setting b gets result +1) + (+1)*P(detector with setting a gets result -1, detector with setting b gets result -1)

Your claim that such an expression is missing, because Bell was simplifying for physicists is a cop-out.

Incidentally, in case Bill or anyone else has any further doubts on this point, note that on p. 14 of the paper http://cdsweb.cern.ch/record/142461/files/198009299.pdfpapers Bell does write the expectation value in a basically identical form in equation (13):

E(a,b) = P(yes, yes|a,b) + P(no, no|a,b) - P(yes, no|a,b) - P(no, yes|a,b)

 

[nismaratwork]

Incidentally, in case Bill or anyone else has any further doubts on this point, note that on p. 14 of the paper http://cdsweb.cern.ch/record/142461/files/198009299.pdfpapers Bell does write the expectation value in a basically identical form in equation (13):

E(a,b) = P(yes, yes|a,b) + P(no, no|a,b) - P(yes, no|a,b) - P(no, yes|a,b)

I think you need more, like killing a werewolf... take the heart, the head, and burn the body. Even then, I somehow doubt that billy will concede anything. I enjoyed reading the paper however.

ThomasT: Why does the appealing or unappealing nature of an ontology matter? The only thing that is relevant is matching with empirical evidence, the science, and the math. I find the inevitability of death quite unappealing, but I don't doubt it as a result.

 

[zonde]

What does Fair Sampling have to do with my comment? If I predict a -1 every time, and you predict +1 every time, and it always comes up -1... Then it doesn't really much matter how often that occurs.

In this experiment photons are created in H/V base but measurements are performed in +45/-45 base (measurement x) and L/R base (measurment y).
If you measure linearly polarized light in base that is rotated by 45° you get completely uncertain result - +1 and -1 have equal probabilities.
If you measure linearly polarized light in circular polarization base you get completely uncertain result as well - +1 and -1 have equal probabilities.
So without detection bias prediction for any measurement in this case is 0.5. That means that composed result from all involved measurements (mind you not output but calculation composed of many different outputs and provided you have algorithm for that) half of the time gives -1 and half of the time gives +1 without detection bias.

Because both involved measurements does not give definite result without detection bias GHZ is comparison of two different detection biases.
So this type of experiments is pure test of fair sampling without involvement of definite outcomes based on particle properties.

As I have said a million times all science involves the fair sampling assumption. There is nothing special about GHZ or Bell tests in that regard.

I can not claim that I have said this a million times but I have responded like this at least once already:

Yes, that's right. All the science rely on different approximations including fair sampling assumption. But all the science except QM does not blame reality, causality and whatever else when it discovers contradiction in it's conclusions. Instead it admits error and reexamines it's assumptions (including fair sampling assumption) one by one until it resolves contradiction.
So all the science involves the fair sampling assumption but all the science have quite strict rules when to give up fair sampling assumption.

And as I have also said too many times to count: if the GHZ result is due to some unknown weird bias... what is the dataset we are sampling that produces such a result? I would truly LOVE to see you present that one! Let's see:

LR=+1, +1, +1, ...
QM=-1, -1, -1, ...
Actual sample=Oops!

Actually, I had the predictions of LR and QM reversed in my little sample. It should be more like:

QM=+1, +1, +1, ...
LR=-1, -1, -1, ...

From the article you linked:
"First, one performs yyx, yxy, and xyy experiments. If the results obtained are in agreement with the predictions for a GHZ state, then the predictions for an xxx experiment for a local realist theory are exactly opposite to those for quantum mechanics."

So the dataset consists of outcomes for each of yyx, yxy, xyy and xxx experiments.
There are 8 possible different outcomes for each of those 4 experiments that are not even conducted at the same time. 16 of those possible different outcomes (8 outcomes * 4 experiments) are observed much more frequently than other 16. So please provide an algorithm how you get your "output" from 32 different outputs observed in experiment at different times for different setups.

See this article from Zeilinger and Pan:

Multi-Photon Entanglement and Quantum Non-Locality (2002)

"Comparing the results in Fig. 16.7, we therefore conclude that our experimental results verify the quantum prediction while they contradict the local-realism prediction by over 8standard deviations; there is no local hidden-variable model which is capable of describing our experimental results."

From the same article:
"If we assume the spurious events are just due to experimental errors, we can thus conclude within the experimental accuracy that for each photon, 1, 2 and 3, quantities corresponding to both x and y measurements are elements of reality. Consequently, a local realist, if he accepts that reasoning, would thus predict that for a xxx experiment only the combinations V'V'V',H'H'V',H'V'H', and V'H'H' will be observable (Fig. 16.6b)."

This type of reasoning is not only dispensable for ensemble interpretation but it is even contradicting ensemble interpretation. That's because it completely ignores the role of ensemble in determining outcome of measurement.

 

[DrChinese]

So this type of experiments is pure test of fair sampling without involvement of definite outcomes based on particle properties. So all the science involves the fair sampling assumption but all the science have quite strict rules when to give up fair sampling assumption.

From the article you linked:
"First, one performs yyx, yxy, and xyy experiments. If the results obtained are in agreement with the predictions for a GHZ state, then the predictions for an xxx experiment for a local realist theory are exactly opposite to those for quantum mechanics."
...

So I predict that every boy is male and you predict every boy is female. These are the kind of opposite predictions we make (it's an analogy ). I provide a random but potentially biased sample which consists of all male boys to 8 standard deviations. Now, exactly how is it that we always get male boys? For this to be science - your claim that is - you need to show me a reeeeeeeeeeeeeally big batch of female boys. Where are they?

This is the strict requirement you speak of. It applies to YOU, my friend. You can't claim it is science without showing something! Absence of evidence actually is evidence of absence when it comes to sampling.

 

[zonde]

In this experiment photons are created in H/V base but measurements are performed in +45/-45 base (measurement x) and L/R base (measurment y).
If you measure linearly polarized light in base that is rotated by 45° you get completely uncertain result - +1 and -1 have equal probabilities.
If you measure linearly polarized light in circular polarization base you get completely uncertain result as well - +1 and -1 have equal probabilities.
So without detection bias prediction for any measurement in this case is 0.5.

What about this you do not understand?

So I predict that every boy is male and you predict every boy is female. These are the kind of opposite predictions we make (it's an analogy ). I provide a random but potentially biased sample which consists of all male boys to 8 standard deviations. Now, exactly how is it that we always get male boys? For this to be science - your claim that is - you need to show me a reeeeeeeeeeeeeally big batch of female boys. Where are they?

This is the strict requirement you speak of. It applies to YOU, my friend. You can't claim it is science without showing something! Absence of evidence actually is evidence of absence when it comes to sampling.

Yes of course. You tell me what I predict and then easily refute my prediction.
You know how this is called?
A strawmen.

 

[DrChinese]

1. What about this you do not understand?

2. Yes of course. You tell me what I predict and then easily refute my prediction.
You know how this is called?
A strawmen.

1. Nothing. What's your point?

2. You are the local realist, what do YOU predict for the xxx case? Does it match QM or not?

 

[JesseM]

Max Jammer indeed, but the book is (in Amazon):

The Philosophy of Quantum Mechanics: The Interpretations of Quantum Mechanics in Historical Perspective by Max Jammer (Hardcover - June 1974)
5 used from $79.99

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Fines book is:
The Shaky Game (Science and Its Conceptual Foundations series) by Arthur Fine (Paperback - Dec. 15, 1996)
Buy new: $25.00 $22.28

12 new from $21.00
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Get it by Friday, Aug. 13 if you order in the next 22 hours and choose one-day shipping.
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There is from there an easy way to get to original writings by Einstein.

As for Einstein's realism, he did believe that the Moon did not even need apes I would bet.
But the real issue, I think, is realism at the microscopic level.

So you think that he would not have been a microscopic realist in the EPR sense? Specifically, if two entangled particles can each be measured on either of two or more noncommuting properties X and Y (like position and momentum), and measuring the value of property X for particle #1 allows us to determine with probability 1 what the value of property X would be for particle #2 if we measured property X for particle #2, then I understand the EPR paper to suggest this means there must be a local "element of reality" associated with particle #2 that predetermines the result it would give for a measurement of property X, even if we actually measure property Y for particle #2.

This quote by Einstein from p. 5 of Bell's paper http://cdsweb.cern.ch/record/142461/files/198009299.pdfpapers does suggest to me he favored microscopic realism in the EPR sense:

If one asks what, irrespective of quantum mechanics, is characteristic of the world of ideas of physics, one is first of all struck by the following: the concepts of physics relate to a real outside world ... It is further characteristic of these physical objects that they are thought of as arranged in a space time continuum. An essential aspect of this arrangement of things in physics is that they lay claim, at a certain time, to an existence independent of one another, provided these objects "are situated in different parts of space".

The following idea characterizes the relative independence of objects far apart in space (A and B): external influence on A has no direct influence on B ...

There seems to me no doubt that those physicists who regard the descriptive methods of quantum mechanics as definitive in principle would react to this line of thought in the following way: they would drop the requirement ... for the independent existence of the physical reality present in different parts of space; they would be justified in pointing out that the quantum theory nowhere makes explicit use of this requirement.

I admit this, but would point out: when I consider the physical phenomena known to me, and especially those which are being so successfully encompassed by quantum mechanics, I still cannot find any fact anywhere which would make it appear likely that (that) requirement will have to be abandoned.

I am therefore inclined to believe that the description of quantum mechanism ... has to be regarded as an incomplete and indirect description of reality, to be replaced at some later date by a more complete and direct one.

I am only bothered a lot by all lies and false info that have lead us to a situation where more physicist (in or close to QM) would relinquish locality and not realism at the miscroscopic level.

Do you really think it's true that "most physicists" would prefer to relinquish locality and not realism? If that were the case I would think Bohmian mechanics would be much more popular! Instead it seems to me that both the Copenhagen interpretation (which abandons 'realism') and the Many-worlds interpretation (whose 'realist' status depends somewhat on how you define 'realism', but it is an interpretation that many advocates say is a completely local one, see my post #8 on this thread for some references along with my own toy model illustrating how a local interpretation involving multiple copies of each experimenter can explain Bell inequality violations without being non-local) are a lot more popular, see some of the polls linked to here.

Also, I only add my physicist's sensitivity to real work done by Jammer and Fine (see also the conference where Fine (?), Jammer, Peirls and Rosen contributed for the 50th anniversary of EPR and other paper here and there, mostly the correspondence of Einstein (mainly with Born, but there are other gems), the Schlipp book, and one pocket book on AE's views on the world where there is more politics than physics but some good pieces anyway) and as much reading of Einstein as I could put my hands on. But as I do not read German, I loose lots of first hand material.

Any chance you could post some of Einstein's quotes that you think show he was not a "naive realist" or would not have agreed with the ideas in the EPR paper? If it would take too long to find them and type them up, I will understand of course.

 

[charlylebeaugosse]

So I predict that every boy is male and you predict every boy is female. These are the kind of opposite predictions we make (it's an analogy ). I provide a random but potentially biased sample which consists of all male boys to 8 standard deviations. Now, exactly how is it that we always get male boys? For this to be science - your claim that is - you need to show me a reeeeeeeeeeeeeally big batch of female boys. Where are they?

This is the strict requirement you speak of. It applies to YOU, my friend. You can't claim it is science without showing something! Absence of evidence actually is evidence of absence when it comes to sampling.

DrC is so right here: see the papers or books on GHZ. The contradiction occurs on every occurrence. Contrary to Bell's inequality- based Bell's Theorem, the GHZ sort, "Bell's Theorem without inequalities" does not use any statistical hypothesis as the story is:
Realism + Locality => An false equality (for each samplE, rather than for some ideal samplING).

No I had asked if anyone has seen a nice explanation of how locality is used. Any hint?

 

[charlylebeaugosse]

Is that supposed to be funny? Modern theoretical physics is mainly mathematical physics, in fact it's been that way for a century or so, the last great achievements by non-mathematicians was probably back in Faraday's time.

The foundations of QM have been debated for nearly a century by many great thinkers, and the conclusion is that nothing will get resolved by "word" arguments about interpretations, there needs to be a model to back up the argument and that model has to be in the language of mathematics.

Of course we need experimental results from which to check our models, and in relation to the question of this thread we have Bell experiments of Aspect et al, GHZ and delayed choice erasure experiments all of which suggest non-locality unless you are a deluded person who thinks a classical explanation makes sense. (The other explanations in terms of reinterpreting reality may have their time, but let's give the physics a chance before opening the gates for the philosophical hordes)

The most promising current model that might account for non-locality seems to be the Holographic Principle, but to properly understand that you need to understand its origins in the work of Bekenstein and Hawking in the 70s on Black Hole Thermodynamics, then you need to understand how it works with current models in String Theory, LQG etc.

This is difficult stuff, with a heavy dose of mathematical formalism. It is the arena where the useful debate about understanding the universe is taking place, not the pseudo philosophical word-play that goes on in these forums.

If you ask the current great Physicists about QM interpretations they will probably admit we are no nearer a resolution, but they do at least know what they're talking about, here's what Joe Polchinski has to say about the fact that String Theory does not attempt to solve the interpretation problem:


Where in the last sentence he hints at MWI, but as you can see he's more interested in hard physics, not philosophical fluff, (quote taken from his comments in this blog entry replying to Smolin's The Trouble with Physics)

I was a bit jocking, but how many Nobel prizes in physics cover papers whose main content was one or more theorems (in a sense accepted by mathematicians). And isn't it true that most mathematical physicists are homed in math dept (a bit less since super-string took control of the budgets in HEPhysics, but
1) what proportion of physicists consider superstring .
2) what proportion of physicists consider superstring as physics.
My main points was in fact that such statements and questions (including mine here) seem far from the subject, and far from physics. As I said, I have an immense consideratio for mathematical physicists.

 

[DevilsAvocado]

Let me give longer quote from Einstein essay:

But... this is an essay from 1949. How can this relate to Bell's Theorem?

So I think that Einstein would have discarded without regret any restrictions placed by orthodox QM on local realistic interpretation.

I don’t agree. As you state yourself:

Einstein was die hard empiricist.

I absolutely do not think Einstein would start looking for farfetched loopholes etc. He was way too smart for that. I think he would have accepted the situation, for the start of something new.

Restriction I am talking about is that the same measurement settings at both sites should give the same outcome with probability of 1.

Well, this is pretty obvious, isn’t it?? The completely "new thing" is when polarizers are nonparallel!? Einstein would of course immediately have realized that his own argument had boomeranged on him:

no action on a distance (polarisers parallel) ⇒ determinism
determinism (polarisers nonparallel) ⇒ action on a distance​

If we view Ensemble Interpretation as physically realistic interpretation and not as some other metaphysical interpretation we of course can not talk about some "Global RAM".
We can talk only about some "local RAM" that is justifiable by physical dynamics inside equipment used in experiments.

If we decide to have very long intervals between every entangled pair we should expect complete decoherence of entanglement.

Are you saying that if we run an EPR-Bell experiment as I proposed, we "should expect complete decoherence of entanglement" and the experiment would fail? No expected QM statistics??

 

[charlylebeaugosse]

A) So you think that he would not have been a microscopic realist in the EPR sense? Specifically, if two entangled particles can each be measured on either of two or more noncommuting properties X and Y (like position and momentum), and measuring the value of property X for particle #1 allows us to determine with probability 1 what the value of property X would be for particle #2 if we measured property X for particle #2, then I understand the EPR paper to suggest this means there must be a local "element of reality" associated with particle #2 that predetermines the result it would give for a measurement of property X, even if we actually measure property Y for particle #2.

B) This quote by Einstein from p. 5 of Bell's paper http://cdsweb.cern.ch/record/142461/files/198009299.pdfpapers does suggest to me he favored microscopic realism in the EPR sense:

(C) Do you really think it's true that "most physicists" would prefer to relinquish locality and not realism? If that were the case I would think Bohmian mechanics would be much more popular! Instead it seems to me that both the Copenhagen interpretation (which abandons 'realism') and the Many-worlds interpretation (whose 'realist' status depends somewhat on how you define 'realism', but it is an interpretation that many advocates say is a completely local one, see my post #8 on this thread for some references along with my own toy model illustrating how a local interpretation involving multiple copies of each experimenter can explain Bell inequality violations without being non-local) are a lot more popular, see some of the polls linked to here.

Any chance you could post some of Einstein's quotes that you think show he was not a "naive realist" or would not have agreed with the ideas in the EPR paper? If it would take too long to find them and type them up, I will understand of course.

The EPR paper, say "EPR" for short, was not written, and not even given imprimatur by Einstein, who considered the effect of choosing a measurement, not the outcome of measurements in his own analysis of the completeness of QM. Einstein never used the elements of reality as defined in "EPR". The way "EPR" uses the elements of reality would permit to deduce Bell's ineauality and Richard Friedberg did that as I said and cited in the book of Jammer you emntioned. Yet "EPR" say that elements of reality should be rooted in experiments. If one consider together only what can be measured on ONE pair, then one has at most 2 projections of the spin (in the Bohm-Bell setting), i.e., one measurement per particle, hence not enough data to have a Bell type inequality.

B) Now Einstein had some dose of realism, but so did Heisenberg, Bohr, etc... Einstein gave in 1931 a proof that microscopic realism is false when Bohr and Heisenberg believed in retrodictive compatibility of exact values for conjugate variables. It is about time to not attribute the mistakes of "EPR" to Einstein. See the book of Fine (the Shaky game) beside the book of Jammer. You may find one or two citations of Einstein where he violates microscopic realism in the sense of observables pre-existing measurement (something that happens to have been proven experimentally for EPR particles, but not for enough observables at once to get a Bell type story, of course). Why should I follow you in defining microscopic in the incomplete way used by Podolsky in "EPR"? (since I consider that "It is about time to not attribute the mistakes of "EPR" to Einstein." ) Perhaps I'd be happy with the element of reality if you accept that measurement must be made on one particle at least for any value to make sense as Podolsky hints at but does not do. Invoking a great name for a mistake once may be ok, and even valuable (e.g., to relaunch an issue mistreated by that person where that was not noticed by anyone ), but assuming Einstein was really wrong on realism, why associate his name to that? It would be better to work on science than on means for people to prove themselves smarter that Einstein (not implying you do that, but there is a bad collective behavior).

(C) The situation is a bit more complex than that as most people who declares themselves as "non-realist" have been over the years convinced that the villain that causes the contradiction between Bell's inequalities and nature is locality. Bell did not state his theorem as proving QM non-local: he knew well what he was doing, but, again, read the beginning of his 1964 paper, where he implies that that QM had been proven non-local by "EPR". Now there are many more Bohmian than I feel comfortable with and Bell is their hero (see the writtings of Sheldon Goldstein). No if you want to drag me to coocoo land, I would tell you that when I almost died (which lasted a month at least) I could not believe in god, but could not get satisfaction in many world either. I'll see later you post #8 as my navigation prowess is very limited (which is why I hopped DrC would open a vouple of new thread or tell me where to learn how to do that, and why I asked how to upload a file so that I can give reference to it, or post it in some other way).

 

[charlylebeaugosse]

But... this is an essay from 1949. How can this relate to Bell's Theorem?

One of the 2 main hypothesis of Bell theorem is that a form of microscopic realism holds trye (a strong form indeed, but let us not be too precise here). By 1931 already, most of the masters of QM, including Einstein, who was more than one of the founding fathers as he participated for a long time, and even his attacks where considered as precious bu Bohr) had been convinced that such microscopic realism did not exist in nature. This was still the main belief in 1949, and the fact that von Neumann (JVN) theorem had a false proof was irrelevant to most of these people (in fact the theories of de Broglie, later to be redone by Bohm, was implicit proof that the proof if not the statement of the non existence of HV by JVN was false). So no more that many great masters in 1964, but how did Feynman (e.g., ) react to that? The official story is that he through Clauser out of his office. Now even that second generation of masters is gone, or in part gone cucu with a few very lucid survivors and Clauser gets a Wolf Price with Aspect and Zeilinger. Thanks whoever, at least these are experimentalists (although not only for Zeilinger at least). But it seems to me that I repeat my posts over and over again.

 

[JesseM]

See the book of Fine (the Shaky game) beside the book of Jammer.

The book by Jammer is a bit expensive, but I found an https://www.amazon.com/dp/0226249476/?tag=pfamazon01-20 of the Fine book selling for just a little over three dollars, so I ordered that. Thanks for pointing me to this book, Einstein's life and thought have always interested me and this looks like an interesting reference.

You may find one or two citations of Einstein where he violates microscopic realism in the sense of observables pre-existing measurement (something that happens to have been proven experimentally for EPR particles, but not for enough observables at once to get a Bell type story, of course).

But what exactly do you mean by "observables pre-existing measurement"? For example, if we find that two entangled particles always have opposite spins when measured on the same axis A, one conclusion a local realist might make is that the particles already had a well-defined value for the property "spin on axis A" prior to measurement, and measurement simply revealed it. But a more general local realist conclusion would just be that the particles had properties prior to measurement which predetermined what result they would give if they were measured on axis A, without the assumption that the properties prior to measurement actually bear any resemblance to "spin". I don't necessarily think Einstein would have endorsed the first but I think the Einstein quote from Bell's paper that I posted suggests he would probably have endorsed the second.

No if you want to drag me to coocoo land, I would tell you that when I almost died (which lasted a month at least) I could not believe in god, but could not get satisfaction in many world either.

Well, regardless of whether many-worlds is "satisfying" on a philosophical or spiritual level (and in a certain way I think it could be, but that's probably a topic for the philosophy forum), it might at least offer hope for a local interpretation of QM that is "realist" in the sense of offering an objective picture of the world.

I'll see later you post #8 as my navigation prowess is very limited

To see the post you only need to click the link.

(which is why I hopped DrC would open a vouple of new thread or tell me where to learn how to do that, and why I asked how to upload a file so that I can give reference to it, or post it in some other way).

If you want to start a new thread, just press the "New Topic" button at the upper left of the list of thread titles on the main quantum physics forum page. For some instructions on how to include code in your posts that makes links to other pages, see http://www.themcfox.com/THE-NET/uBB-vBB-code.htm. If you want to link to a file you'll have to upload it to some internet page first, you could use a free file-hosting service like Easy Share to do this.

 

[DrChinese]

I'll see later you post #8 as my navigation prowess is very limited (which is why I hopped DrC would open a vouple of new thread or tell me where to learn how to do that, and why I asked how to upload a file so that I can give reference to it, or post it in some other way).

New thread started per your request!

 

[nismaratwork]

What about this you do not understand?


Yes of course. You tell me what I predict and then easily refute my prediction.
You know how this is called?
A strawmen.

That isn't a strawman, it's an analogy. There is a difference, and I'd like to hear your response to it. I've been reading about this "fair sampling bias" as it seems to be a major bone of contention in this thread for dozens of pages... I don't see how Dr. Chinese's question is a diversion, just an attempt to get a straight answer.

 

[charlylebeaugosse]

New thread started per your request!

Thanks a lot. What is the title of that thread (not meaning that people stick to the "subject".

 

[charlylebeaugosse]

But what exactly do you mean by "observables pre-existing measurement"? For example, if we find that two entangled particles always have opposite spins when measured on the same axis A, one conclusion a local realist might make is that the particles already had a well-defined value for the property "spin on axis A" prior to measurement, and measurement simply revealed it. But a more general local realist conclusion would just be that the particles had properties prior to measurement which predetermined what result they would give if they were measured on axis A, without the assumption that the properties prior to measurement actually bear any resemblance to "spin". I don't necessarily think Einstein would have endorsed the first but I think the Einstein quote from Bell's paper that I posted suggests he would probably have endorsed the second.

EPR particles are quite particular as there are conservation laws, but those manufest themselves only when a measurement is made. For instance, if Alice measures the normalized spin projection along axis a, Bob will for sure find the opposite value along the same axis. Since Bob can also make a measurement, say along b, one can infer (by a lengthy argument) that both particles had some definite spins, but only along these two axes, and retrodictively. Now Bohr, and in its trace, Heisenberg , admitted retrodictive coexistence of conjugate variables, not even mentioning that EPR particles was the context. To teh contrary, for particles that could hardly have been EPR particles, Einstein, Tolman and Podolsky proved in a Phys Rev Paper of 1931 that such retrodictive coexistence, and even pre-existence of a single observable to its measurement, could not be as otherwise the UP would be violated. They essentially proved a reverse time UP by showing that otherwise, an usual UP would be violated. So the confusion comes from
-a) forgetting the conservation principle, purposely, since
-b) otherwise all projections of the spin would make sense.
BUT, b) is a mistake as the pre-existence is only along directions along the observable make sense, which requires a measurement and when it comes to spin projections, for an EPR pair, at most two spin projections can be measured (one per particle).

This seems odd, but let us compare with Classical Mechanics (CM) and a better known part of QM. If a particle with total momentum zero separates in two in CM, the sum of the projections on the two particles will be zero for ALL directions (at once). In QM, the same zero sum is true for ANY direction, and any is not all. Now, thinl about measurements: in CM, if any measurement can be made, ALL measurements can be made, but by the UP, in QM, any measurement (among spin projection) but not ALL measurements of spin projevtion can be made. When it comes to QM, any is not all !.

This is only a piece of answer to your concerns, but perhaps enough for you to see the light.
I'd be delighted to explain any part that would be weak from the pedagogical point of view. But perhaps other who got that point can help making that clearer with different words. I might have though too much about that thes last years to measure what is clear and what is not, be it only because so many legends have taken control of the main pillar of physics.
(I have already told in one or more posts that in fact I came back to QM because I fell in the trap of non-locality and all the fairy tales that go with it and that only reading for months told me that I had indeed fallen in a trap. With that I disagree with Fine or at lest do not follow him , at least not yet, I must say that his book was the first trace of sanity I could find. His book then indicated others, Jammer and a series of things written by Einstein himself, instead of Podolsky, Bell, or others who played dangerous games with intentions and credos attributed to A.E. (of whom I am absolutely not an unconditional).

 

[JesseM]

Thanks a lot. What is the title of that thread (not meaning that people stick to the "subject".

That would be A Bell Theorem with no locality assumption?

 

[JesseM]

EPR particles are quite particular as there are conservation laws, but those manufest themselves only when a measurement is made. For instance, if Alice measures the normalized spin projection along axis a, Bob will for sure find the opposite value along the same axis. Since Bob can also make a measurement, say along b, one can infer (by a lengthy argument) that both particles had some definite spins, but only along these two axes, and retrodictively. Now Bohr, and in its trace, Heisenberg , admitted retrodictive coexistence of conjugate variables, not even mentioning that EPR particles was the context. To teh contrary, for particles that could hardly have been EPR particles, Einstein, Tolman and Podolsky proved in a Phys Rev Paper of 1931 that such retrodictive coexistence, and even pre-existence of a single observable to its measurement, could not be as otherwise the UP would be violated.

You mean this paper? But as far as I can tell the paper doesn't show that the particle couldn't have had hidden variables which predetermined what results it would give when its momentum was measured, just that the result of measuring its momentum would be different than its momentum before measurement (the act of measurement changes the momentum). But the concept "particle has hidden variables that predetermine what result it will give to each possible measurement" is logically different from the concept "measurement simply reveals the preexisting value for the variable being measured", my understanding is that Einstein would have endorsed the first but not the second. This is exactly the distinction I was making earlier when I said:

But what exactly do you mean by "observables pre-existing measurement"? For example, if we find that two entangled particles always have opposite spins when measured on the same axis A, one conclusion a local realist might make is that the particles already had a well-defined value for the property "spin on axis A" prior to measurement, and measurement simply revealed it. But a more general local realist conclusion would just be that the particles had properties prior to measurement which predetermined what result they would give if they were measured on axis A, without the assumption that the properties prior to measurement actually bear any resemblance to "spin". I don't necessarily think Einstein would have endorsed the first but I think the Einstein quote from Bell's paper that I posted suggests he would probably have endorsed the second.

 

[ThomasT]

For most of us the phrase "not there when nobody looks" is simply a metaphor for the non-existence of non-interacting entities.

Ok, but I still have a slight problem with that. It's either that we assume that there's an underlying reality affecting instrumental behavior, or we assume that there isn't. What do you think should be assumed?

It seems a bit silly to say that there's nothing moving from emitter to detector. Certainly the more sensible inference or hypothesis, and the one that practical quantum physics is based on, is that quantum experimental phenomena result from the instrumental probings of an underlying reality -- a reality which is presumably behaving according to some set of physical principles and which exists whether it's being probed or not.

Einstein's spooky action at a distance entails spacelike separated events determining, instantaneously, each other's existence. This is, prima facie, a nonsensical notion -- and Einstein was right to dismiss it.

Well, if QM is right, one (or both) of these things has to go -- you can't have realism and locality.

One or both of what things? EPR simply maintained that it's nonsensical to assume that the reality of one particle of an entangled pair is a function of the detection of the other particle. I don't think that the approximate correctness of qm entails that a local realistic description, or intuitive understanding, of entanglement is impossible. But then, a definitive local realistic model of entanglement hasn't been presented yet.

In our interpretation, we punt on realism, i.e., separability.

So, what, nonseparability (or inseparability) necessarily entails nonrealism? So, how would you characterize your theory/model/interpretation? As nonrealistic, but local? But this makes no sense. If it isn't, in some sense, realistic, then what does it mean to call it 'local'? Or, are you not calling it either realistic or local? Anyway, didn't you say that your model/interpretation is meant as a realistic description of the underlying ontology? This is the only problem I have with how you talk about it. If you just say that it's a simplification, perhaps even an oversimplification, of the underlying reality, which, given certain mathematical constructions and manipulations, can recover the statistical predictions of standard qm, then I have no problem with a charactarization of that sort.

(your RBW model is) not unreasonable. Especially if you're a GR person. I just find it conceptually unappealing.

Most do.

Well, given your obvious talents, are you working on anything that the rest of us might some day be able to actually understand?

Anyway, is there any way to know to what extent some theoretical construction is a description of 'reality'?

That's a thorny epistemological question. Better leave that for another thread.

But the main line of argumentation in this thread is about some people saying that Bell's stuff allows inferences about an underlying reality, and others saying that it doesn't. So, where exactly do you stand on this? Does it, or doesn't it? If Bell's stuff is just about models, and a certain class of models at that, then I can't argue with that. What's your opinion? Is it informing us about 'reality', or just informing us about what we can say about 'reality' in a certain form?

 

[ThomasT]

ThomasT: Why does the appealing or unappealing nature of an ontology matter?

By this I mean its understandability. And understanding has to do with visualizability. Why assume that the fundamental principles of our universe aren't visualizable? After all, we are part of reality. Why not assume that the principles that govern our physical universe pervade and permeate all scales of behavior and interaction? Whether you know it or not, qm is very much based on analogies from ordinary experience. A 'block' conception of reality, vis GR, contradicts our experience. Our universe appears to be evolving. Why not just assume that it 'is' evolving -- that 'change' or 'time' isn't just an illusion, but is real? Why not assume that the fundamental physical principles govern physical behavior at all scales?

Anyway, to get back to your question, if an ontological or epistemological description of 'reality' is at odds with our experience, then I think it should be seriously questioned. I think that this orientation accords with the best traditions of the scientific method. If you think otherwise, then I'm open to learning.

The only thing that is relevant is matching with empirical evidence, the science, and the math.

Wrt predicting the results of experiments, I agree. However, this isn't the only thing relevant to 'understanding' or really 'explaining' why things are as they are and why things behave as they do. Just because you can predict something doesn't mean that you understand how and why it happens. Standard qm is an example of this. The problem with the various interpretations of qm as they might relate to your question is that, ultimately, all of the various interpretations of standard qm revert or resort, in one way or another, to the statistical methods of standard qm in order to recover the predictions of standard qm. So, really, nothing is gained except a more or less acceptable, to whomever, 'realistic view', in a certain limited sense -- none of which is a definitive world view precisely because there are other 'world views' which predict exactly the same experimental results.

Wrt the OP of this thread, the question is, does the detection of a particle at detector A, spacelike separated from the 'possible' detection of a particle at detector B, determine the 'existence' of an underlying reality that, it might be assumed, determines the detection attribute registered by detector B? If you think that the answer to this must be, obviously, no, then you agree with EPR, and Einstein. Otherwise, you're a nonlocalist or spookyactionatadistanceist, in which case the onus is on you to demonstrate the physical existence of the spooky (or merely ftl?) propagations/interactions between A and B, or B and A, or whatever.

 

[charlylebeaugosse]

You mean this paper? But as far as I can tell the paper doesn't show that the particle couldn't have had hidden variables which predetermined what results it would give when its momentum was measured, just that the result of measuring its momentum would be different than its momentum before measurement (the act of measurement changes the momentum). But the concept "particle has hidden variables that predetermine what result it will give to each possible measurement" is logically different from the concept "measurement simply reveals the preexisting value for the variable being measured", my understanding is that Einstein would have endorsed the first but not the second. This is exactly the distinction I was making earlier when I said:

Non-existence of local realism means of course absence of HV a la Bell/Boh/de Broglie, since those HV are a strong form of microscopic realism (non only one has pre-existence of observable meaning and values to measurement but one also has predictability). Now, HV that are compatible with QM and such that not only what is measured but also whatever makes sense obeys he UP would be acceptable. Scrödinger and Einstein both thought that their contemporaries were too shy by sticky to the usual coordinates, and Fine explain how and why it could be legit to consider them more advanced about the next generation physics that the Copenhagen crowd, and not the contrary. Of course, they only had hopes and not a hint on how to get there, assuming that there is a there. Einstein would not have been long to dismiss the hypothesis of Bell's Theorem as not more physical than the theories of Bohm and de Broglie how which he made fun often. So Born is probably right in thinking that Einstein believed in HVs, but for sure not in the classical ones that Bell used but this is not sure as eh correspondance with Einstein shows that he did not understand anything of the EPR story. AND I cannot imagine Einstein not being saddened by someone putting words in his mouth as Bell does in the introduction of the 1964 paper and in many other places. I mean Bell did not even say "I think that Einstein believed this or that": he claims stuff as facts, a crime against basic scholarly acceptable attitudes and practices. The distinction naive-non-nave HV is for me absolutely crucial. Failing to do it lead simply to a false story and a false description of the physics models that people of importance in the field had in mind. Again, I am not a blind supporter of Einstein: I do not even consider it a big deal that a theory be not complete and I even expect that from any non-trivial theory supposed to cover a big chunk of physics. I also see good reasons to side with Bohr et al, except on the religious asp[ect of their credo and except for the fact that I consider that Schrödinger and Einstein were possibly right about the need to non-trivial new variable to get to some predictability, but a predictability that would not permit to predict nor even to give sense to conjugate variables in the generic case (EPR/ EPRB stories being special because of the conservation laws that provide an ephemeral quasi classic aspect to these particles, till first interactions (which is why such particles do not interfere as do the generic ones).

Hope that this gets clearer or that other may chip in as perhaps I am not clear enough in my English writing (you cross a border and you loose 30% on your IQ , have I been told... but what happens when you go back and forth?). All that is clear in my mind now, but I have doubt about being understood, or perhaps people do not read well enough (which is often my problem too).

PS: Thanks for the paper: I'll find the time to check, read, and answer about that. In fact, I may have to read more closely what you wrote too.
CleBG

 

[RUTA]

Ok, but I still have a slight problem with that. It's either that we assume that there's an underlying reality affecting instrumental behavior, or we assume that there isn't. What do you think should be assumed?

In our view, there is an "underlying reality" responsible for the experimental outcomes, but that "underlying reality" is not "screened off/non-interacting entities" propagating from the source to the detector. The outcomes reflect relations composing the experimental equipment, i.e., relations are fundamental, not "things" like the equipment (or trees or people, etc). In our ontology, there is a rule for the manner in which the experimental equipment ("things" in general) is constructed in the 4D "block." The RBW ontology can be depicted, see Figures 1-4 of arXiv 0908.4348, but it is non-dynamical, which I understand from a previous post you dislike. So, I wouldn't try to convince you that the RBW ontology is a powerful explanatory mechanism

One or both of what things? EPR simply maintained that it's nonsensical to assume that the reality of one particle of an entangled pair is a function of the detection of the other particle. I don't think that the approximate correctness of qm entails that a local realistic description, or intuitive understanding, of entanglement is impossible. But then, a definitive local realistic model of entanglement hasn't been presented yet.

It is largely agreed within the foundations community that the violation of Bell's inequality entails non-locality and/or non-separability (aka "realism"). The RBW philosopher of science tells me the use of "separability" rather than "realism" is nontrivial, i.e., there is much written about it. I'm not a philosopher, so I just use the terminology as he suggests.

So, what, nonseparability (or inseparability) necessarily entails nonrealism? So, how would you characterize your theory/model/interpretation? As nonrealistic, but local? But this makes no sense. If it isn't, in some sense, realistic, then what does it mean to call it 'local'? Or, are you not calling it either realistic or local? Anyway, didn't you say that your model/interpretation is meant as a realistic description of the underlying ontology? This is the only problem I have with how you talk about it. If you just say that it's a simplification, perhaps even an oversimplification, of the underlying reality, which, given certain mathematical constructions and manipulations, can recover the statistical predictions of standard qm, then I have no problem with a charactarization of that sort.

Yes, RBW is non-separable but causally local. Yes, "non-separable" means "not realism." You have to be careful here not to conflate causal locality with geometric locality, i.e., that used in differential geometry.

Well, given your obvious talents, are you working on anything that the rest of us might some day be able to actually understand?

RBW is counterintuitive but not conceptually challenging. Formally, it's a nightmare (have you ever tried to do Regge calculus?), but its ontology can be depicted -- again, see Fig 1-4 of arXiv 0908.4348. While only an arXiv paper, it has been accepted for presentation at the 2010 PSA meeting (they only take about 10% of all submissions) and it's in the "revise and resubmit" phase at Foundations of Physics, so it has received a couple favorable reviews anyway

But the main line of argumentation in this thread is about some people saying that Bell's stuff allows inferences about an underlying reality, and others saying that it doesn't. So, where exactly do you stand on this? Does it, or doesn't it? If Bell's stuff is just about models, and a certain class of models at that, then I can't argue with that. What's your opinion? Is it informing us about 'reality', or just informing us about what we can say about 'reality' in a certain form?

I use physics to make ontological inferences. In fact, that's why I do physics. Can I argue that it's reasonable to do so? I wouldn't even try.

 

[charlylebeaugosse]

One funny aspect of all that is that it is the absence of realism that permits strong correlations. Assume the observable values correlated to each other on each particles, as when one assumes locality. Then if three spin projections make sense at once, on eget another form of Bell Theorem. I one has one projection per particles (alone or in a pair), no Bell inequality but at most trivial and true ones. If one has at most two projections for a pair, still no Bell inequality but trivial and true ones.

Other funny thing, that makes me rather sad indeed: if one abandon realism, no good reason to have non-locality. So one has to violate, without any experimental baking,
- realism that intuitively should come with the superposition principle and the uncertainty principle,
- and locality that is natural with relativity

where just abandoning local realism would do. The general practice of physics should have eradicated the realism and non-locality for a long time. It was eradicated till Bell, except for a few isolated examples. Now, we have to work hard to come back to non-realism (always in the microscopic -and classical-sense -where "and classical" is to not dismiss, at least not now, the people from CQT who follow Griffith, Omnes, Hartle, Gell-Mann and now Hohenberg) and locality. One good thing is that non-realism should be taken much more seriously than ever before, as a discussion of "Interferences (the usual ones), Wheeler's delayed choice and related delayed choice issues" would reveal, I am sure.

 

[RUTA]

Other funny thing, that makes me rather sad indeed: if one abandon realism, no good reason to have non-locality. So one has to violate, without any experimental baking,
- realism that intuitively should come with the superposition principle and the uncertainty principle,
- and locality that is natural with relativity

where just abandoning local realism would do.

I assume you mean to say "if one abandons realism, there is no good reason to have locality." Then you conclude "one has to violate ... locality that is natural in relativity."

In Relational Blockworld we have locality and separability in the classical (statistical) limit of an underlying graphical spacetime structure. There is non-separability at the level of individual relations (graphical level), but Poincare invariance (which includes Lorentz invariance) holds at the graphical level.

So, the point is, you can create a model that is non-separable ("not realism") and local at the quantum level while becoming separable in a statistical limit (classical limit).