Fun question RE: Bell's Theorem

[roundedge]

If you're not familiar with Bell's inequality, and the subsequent experiment, I suggest perusing over http://www.upscale.utoronto.ca/GeneralInterest/Harrison/BellsTheorem/BellsTheorem.html"

But essentially, an experiment is done with counting the number of electrons with certain spins, and applying that number to bells inequality, which dictates that the number of things with quality A and not B plus the number with B and not C will be greater than the number with B and not C. It is expected that the number of electrons with specific spins, and not spins, should corroborate with the innequality, assuming the following:

1. the validity of logic

2. objective reality

3. locality

however the results of the experiment contradict the inequality.

Thus, by reducto ad absurdum, one or more of those three assumptions must be wrong.

Personally, I'd prefer to believe that we've somehow misconceptualized what spin is, or we've made a mistake in assuming that spin can be considered a quality, or that an electron can be considered an individual with individual qualities, than concede one of those three assumptions. However, if forced to bite the bullet, what assumption do you think would be the first to go.

 

[3trQN]

Does ¬(1)->¬(2)?

 

[roundedge]

No, I don't think so. The two are mutually exclusive.

 

[Rade]

I vote for the statement that Bell's Inequality leads to the conclusion that: "it is logically valid that hidden variables are non-local"

 

[roundedge]

does anybody know if there's been any follow up on this experiment. It is pretty significant.

 

[JesseM]

But essentially, an experiment is done with counting the number of electrons with certain spins, and applying that number to bells inequality, which dictates that the number of things with quality A and not B plus the number with B and not C will be greater than the number with B and not C. It is expected that the number of electrons with specific spins, and not spins, should corroborate with the innequality, assuming the following:

1. the validity of logic

2. objective reality

3. locality

A many-worlds type interpretation could in principle also be compatible with the violation of Bell's inequality, without needing to violate logic or locality--I guess it depends what you mean by "objective reality", the many-worlds interpretation does try to give an objective description of the reality, but the reality it describes is a multiverse with multiple versions of the same system existing side-by-side.

 

[Doc Al]

If you're not familiar with Bell's inequality, and the subsequent experiment, I suggest perusing over http://www.upscale.utoronto.ca/GeneralInterest/Harrison/BellsTheorem/BellsTheorem.html"

The theorem described on this page is often referred to as Bell's first theorem. Note that the assumption "Parameters exist whether they are measured or not" describes what can be called a non-contextual hidden variable model. Bell's first theorem shows that such a model is inconsistent with the experimentally-confirmed facts of quantum mechanics. (Rejecting such a model does not reject "objective reality".)

But essentially, an experiment is done with counting the number of electrons with certain spins, and applying that number to bells inequality, which dictates that the number of things with quality A and not B plus the number with B and not C will be greater than the number with B and not C. It is expected that the number of electrons with specific spins, and not spins, should corroborate with the innequality, assuming the following:

1. the validity of logic

2. objective reality

3. locality

Some comments:

1.) Lots of luck rejecting the validity of logic, whatever that might mean. Kind of cuts you off at the knees.

2.) "Objective reality" is not synonymous with the non-contextual hidden variable models that are rejected by Bell's first theorem. That's a red herring.

3.) Locality is where the real action is. Bell's second theorem, which makes no such assumption as "Parameters exist whether they are measured or not", shows (at least as I have come to understand it) that locality itself is contradicted by some of the experimentally-confirmed facts of quantum mechanics.

As JesseM states, the MWI interpretation does claim to preserve locality in some sense, but it comes with too high a "price tag" in my opinion.

 

[Hurkyl]

As JesseM states, the MWI interpretation does claim to preserve locality in some sense, but it comes with too high a "price tag" in my opinion.

Which simply means that you wish the universe to truly be classicalish, rather than having it appear as an emergent property.



There are other roads too. For example, relational QM treats the use of a wavefunction collapse as a gauge freedom -- an analysis done without collapse (where everything is manifestly local!) and one where a collapse happens at some point are (correctly!) studying the same physical system.



Another one is definitions of locality -- Bell's theorem uses a very particular definition that, IMHO, is not completely general.

For example, whatever happens in a spatial region is completely described by the restriction of the state to that region, or anything causally determining it. (where I'm using "complete" in the sense that it can correctly compute all frequentist probabilities -- we're lucky we can even get that much information about a nondeterminstic theory!)

IMHO, that should be enough to call the universe "local" in the most general sense -- I don't think it's a warranted assumption that you can analyze what happens in a region by independently analyzing its subregions. But even if it's a warranted assumption, I don't think it's essential to the notion of locality.

 

[Careful]

** Which simply means that you wish the universe to truly be classicalish, rather than having it appear as an emergent property. **

Why would our measurement of the universe not be an emergent property, even if the latter satisfies classical laws ? There is nothing quantum about that.

 

[Doc Al]

Which simply means that you wish the universe to truly be classicalish, rather than having it appear as an emergent property.

Not sure what you mean by "emergent" in this context or why you think MWI is more or less "emergent" than other models. Certainly the non-contextual hidden variable models refuted by Bell's first theorem are as non-emergent as can be.

Nor do I understand what you mean by "classicalish"--quantum behavior seems pretty nonclassical to me.

 

[Careful]

** Certainly the non-contextual hidden variable models refuted by Bell's first theorem are as non-emergent as can be. **

Non-contextual hidden variables (an overpriced way of saying : properties exist even if they are not measured) - as they were used (for example a definite spin vector) first *might* not the smartest models to play with. And if you can come up with an experiment which refutes them, please go ahead you will get a Nobel prize for that one. Moreover, if you choose your hidden variables carefully, that what we call spin, momentum, position etc. are as *emergent* as it can be.

**
Nor do I understand what you mean by "classicalish"--quantum behavior seems pretty nonclassical to me. **

 

[vanesch]

A many-worlds type interpretation could in principle also be compatible with the violation of Bell's inequality, without needing to violate logic or locality--I guess it depends what you mean by "objective reality", the many-worlds interpretation does try to give an objective description of the reality, but the reality it describes is a multiverse with multiple versions of the same system existing side-by-side.

Indeed. In point (2), instead of "objective reality" one should write "naive reality" (what we observe, is there, and only what we observe, is there).

Much ink has flown over the Bell inequalities. If you do a search on them here, you'll find at least 50 threads dealing with them. I'm kinda tired to discuss all that again...

 

[Careful]

... I'm kinda tired to discuss all that again...

Me too ... it all boils down to what you ``believe'' or not. If you are smart enough you can shortcut them and who knows, perhaps they might even turn out to be irrelevant for physics ! All you can say, is that they are putting two major challenges : (a) one for experiment, to truly violate them (the inequalities violated in experiment are not the real ones) (b) an intellectual challenge for ``local'' realists to redefine reality such that Bell inequality violation occurs naturally. It could be that (b) is unnecessary, but we have to play around with something

 

[BoTemp]

Personally, I'd take a look at another assumption which was made but not stated:

4. Spin is always conserved

Definitely always is classically, and as such the expectation values should be quantum mechanically, but that doesn't show that it will be in each and every case. I guess it should still average out over billions of trials, but if I were going to do serious investigation into this matter I'd check that out as well.

 

[Jimmy Snyder]

2. objective reality

Since the publication of Sokol's "Transgressing the Boundaries: Towards a Transformative Hermeneutics of Quantum Gravity", I thought no one believed in objective reality anymore.

http://www.physics.nyu.edu/faculty/sokal/transgress_v2/transgress_v2_singlefile.html

There are many natural scientists, and especially physicists, who continue to reject the notion that the disciplines concerned with social and cultural criticism can have anything to contribute, except perhaps peripherally, to their research. Still less are they receptive to the idea that the very foundations of their worldview must be revised or rebuilt in the light of such criticism. Rather, they cling to the dogma imposed by the long post-Enlightenment hegemony over the Western intellectual outlook, which can be summarized briefly as follows: that there exists an external world, whose properties are independent of any individual human being and indeed of humanity as a whole; that these properties are encoded in ``eternal'' physical laws; and that human beings can obtain reliable, albeit imperfect and tentative, knowledge of these laws by hewing to the ``objective'' procedures and epistemological strictures prescribed by the (so-called) scientific method.

 

[NateTG]

Actually, there are other assumptions that are perhaps more subtle.

For example:
It's assumed that the measurement orientation can be chosen in a nondeterministic fashion.
(Is the experiment valid if the random orientation generator always picks the same orientations?)

It's assumed that the two particles are not local to each other. (What happens if there is a very small wormhole between the two particles that are being measured, which is just big enough to transfer spin-state information?)

It's assumed that real processes can be modeled using the mathematically standard notion of probability.
(If we can say that the (simultaneous) probability of a particle's spin measurment in orientation A being 1 and the particles spin measurement in orientation B being 1 is undefined, then Bell's theorem is no longer valid.)

 

[Rade]

Since the publication of Sokol's "Transgressing the Boundaries: Towards a Transformative Hermeneutics of Quantum Gravity", I thought no one believed in objective reality anymore.http://www.physics.nyu.edu/faculty/sokal/transgress_v2/transgress_v2_singlefile.html

Scientists do not "believe" in objective reality, they "know" objective reality--we can call this Sokol's lapse.

 

[Doc Al]

Since the publication of Sokol's "Transgressing the Boundaries: Towards a Transformative Hermeneutics of Quantum Gravity", I thought no one believed in objective reality anymore.

I hope you realize that the Sokal paper was a hoax! (A brilliant one.)

 

[Careful]

Personally, I'd take a look at another assumption which was made but not stated:

4. Spin is always conserved

Definitely always is classically, and as such the expectation values should be quantum mechanically, but that doesn't show that it will be in each and every case. I guess it should still average out over billions of trials, but if I were going to do serious investigation into this matter I'd check that out as well.

Sssht, hidden variable models with variable spin length are known for long time and do reproduce perfect two point correlation functions but again involve a different point of view on measurement theory (so these fall under the class of models where you give up dichotomic variables) - at least the naive ones which immediately come to my mind. You probably know that the quantized electron (which has constant spin length) is easier than the classical counterpart where spin length is variable due to classical zitterbewegung - hence a better correspondence arises through averaging (see Barut and Unal).

Careful

 

[Bubble99]

Here is a paper that proposes a possible loophole in Bell's Theorem...
http://www.pnas.org/cgi/content/full/98/25/14224

 

[wm]

Bell's theorem and Bell's error?

Here is a paper that proposes a possible loophole in Bell's Theorem...
http://www.pnas.org/cgi/content/full/98/25/14224

It is good to read papers such as this. For it is good to add names to that growing band of thinkers who question the validity of Bell's * theorem. However (in my view), this paper (like so many others on Bell's theorem), muddies the waters: in that it misses Bell's error.

In my view: Bell's theorem, claimed by many to be ''the most profound discovery of science'', is nothing but an exercise in defective logic. That is (to be clear): It is Bell's logic that is defective.

So we modify roundedge's question [adding ''BELL'S'' (with some whistles)] and answer it:

If you're not familiar with Bell's inequality, and the subsequent experiment, I suggest perusing over http://www.upscale.utoronto.ca/GeneralInterest/Harrison/BellsTheorem/BellsTheorem.html"

<SNIP> assuming the following:

1. the validity of [BELL'S] logic

2. objective reality

3. locality

however the results of the experiment contradict the inequality.

Thus, by reducto ad absurdum, one or more of those three assumptions must be wrong. <SNIP>

Thus: Bell's logic is wrong! To establish this fact, I encourage students to study Bell's papers and note the Bellian assumptions that cannot be confirmed by experiment. It is then no mystery anymore (to students) that Bell's theorem is not confirmed by experiment - the results of which are independent of any ''theorem'' ... and therefore most certainly independent of invalid or silly theorems.

* Dare I add, in the language of my mentors (and acknowledging my debt to them): Bell's silly theorem?

 

[xiankai]

i was perusing the first mathematical assumption in the summary that;

Number(A, not B) + Number(B, not C) greater than or equal to Number(A, not C)

however i am not able to complete understand it. the reasons is as follows:

Assume that,

Number(A, not B) = Number (A, not B, C) + Number (A, not B, not C)
Number(B, not C) = Number (A, B, not C) + Number (not A, B, not C)
Number(A, not C) = Number (A, B, not C) + Number (A, not B, not C)

and

Number(A, not B) + Number(B, not C) ≥ Number(A, not C)

subtituting

Number (A, not B, C) + Number (A, not B, not C) + Number (A, B, not C) + Number (not A, B, not C) ≥ Number (A, B, not C) + Number (A, not B, not C)

Cancelling out Number (A, not B, not C) and Number (A, B, not C), we are left with

Number (A, not B, C) + Number (not A, B, not C) ≥ 0

which is pretty much saying that the sum of 2 sets can be zero or more, but that can be applied to any 2 sets

can someone guide me through this mathematical block

 

[RandallB]

<SNIP> assuming the following:

1. the validity of [BELL'S] logic

2. objective reality

3. locality

however the results of the experiment contradict the inequality.
- - one or more of those three assumptions must be wrong. <SNIP>


Thus: Bell's logic is wrong!

The paper referenced by Bubble99 address an explanation requiring a extra dimension that pulls a part of the future test observation into the solution variable; meaning a Non-Local solution so that at least option #3 Locality (as in Einstein Classical Local) must not to be true.
I have no problem with that – declaring non-locality in the Einstein Classical Sense of local is the foundation of QM (And other similar expatiations like BM, String, MWI, etc.).

But mw what remains a mystery to me is what logical steps you are using to define the Bell Theorem as wrong? And I assume you mean to say it is as silly as Von Newman’s proof. You seem to go from <SNIP> to THUS with no stated reasons or supporting logic.

Even if you have some reasonable logic here; are you claiming that it might exclude #3 Classical Locality from being false, thus invalidating the foundation of QM and others?
Or just that we can never know what we hope to know.

 

[Doc Al]

i was perusing the first mathematical assumption in the summary that;

Number(A, not B) + Number(B, not C) greater than or equal to Number(A, not C)

This is not an assumption, it is the thing which is to be proven.

however i am not able to complete understand it. the reasons is as follows:

Assume that,

Number(A, not B) = Number (A, not B, C) + Number (A, not B, not C)
Number(B, not C) = Number (A, B, not C) + Number (not A, B, not C)
Number(A, not C) = Number (A, B, not C) + Number (A, not B, not C)

OK.

and

Number(A, not B) + Number(B, not C) ≥ Number(A, not C)

Again, this expression is what is being proven; this is Bell's first theorem. (Call it expression #1.)

subtituting

Number (A, not B, C) + Number (A, not B, not C) + Number (A, B, not C) + Number (not A, B, not C) ≥ Number (A, B, not C) + Number (A, not B, not C)

Cancelling out Number (A, not B, not C) and Number (A, B, not C), we are left with

Number (A, not B, C) + Number (not A, B, not C) ≥ 0

For some reason, you are approaching the proof of Bell's first theorem backwards, but no problem. You have just shown that Expression #1 is equivalent to this last expression, which is obviously true. (Given the assumption that every member of the set is definitely A or not-A, B or not-B, C or not-C.) Thus if you started with this last expression, you could just work backwards and show that Expression #1--Bell's theorem--is true.

which is pretty much saying that the sum of 2 sets can be zero or more, but that can be applied to any 2 sets

That's correct. But by cleverly applying that truism to these particular two sets, you are able to derive something of interest.

 

[Doc Al]

But wm what remains a mystery to me is what logical steps you are using to define the Bell Theorem as wrong? And I assume you mean to say it is as silly as Von Newman’s proof. You seem to go from <SNIP> to THUS with no stated reasons or supporting logic.

Indeed. wm's empty tirade moves me to quote the bard (Macbeth, Act V, Scene V):

"It is a tale... full of sound and fury, signifying nothing."​

 

[DrChinese]

i was perusing the first mathematical assumption in the summary that;

[1] Number(A, not B) + Number(B, not C) greater than or equal to Number(A, not C)

however i am not able to complete understand it. the reasons is as follows:

Assume that,

Number(A, not B) = Number (A, not B, C) + Number (A, not B, not C)
Number(B, not C) = Number (A, B, not C) + Number (not A, B, not C)
Number(A, not C) = Number (A, B, not C) + Number (A, not B, not C)

and

Number(A, not B) + Number(B, not C) ≥ Number(A, not C)

subtituting

Number (A, not B, C) + Number (A, not B, not C) + Number (A, B, not C) + Number (not A, B, not C) ≥ Number (A, B, not C) + Number (A, not B, not C)

Cancelling out Number (A, not B, not C) and Number (A, B, not C), we are left with

[2] Number (A, not B, C) + Number (not A, B, not C) ≥ 0

which is pretty much saying that the sum of 2 sets can be zero or more, but that can be applied to any 2 sets

can someone guide me through this mathematical block

You have it exactly right so far. The next step is to re-cast your [1] so you have something like:

[3] Number(A, not B) + Number(B, not C) - Number(A, not C) >= 0

The Quantum Mechanical prediction for [3] at certain angles is actually less than zero. You can see this argument in its entirety at my page:

Bell's Theorem and Negative Probabilities

 

[wm]

Bell challenge

Indeed. wm's empty tirade moves me to quote the bard (Macbeth, Act V, Scene V):

"It is a tale... full of sound and fury, signifying nothing."​

''Doc Al doth protest too much, methinks. Teach not thy lip such scorn ...'' after William Shakespeare.

''Let us hope these analyses also may one day be illuminated, perhaps harshly, by some simple constructive model. However that may be, long may Louis de Broglie continue to inspire those who suspect that what is proved by impossibility proofs is lack of imagination'' per John Bell (1982: 997).


Doc, how about a positive contribution? Why not list and number your favourite* ''Bell theorems'' (in descending order, citing sources)?

I'll match it with a numbered list of significations from my post.

* That is: List only those that you've personally analysed and will vouch for. Not silly ones that can be refuted by classical experiments or logic.

Good luck, wm

 

[Doc Al]

The burden of proof is on you, wm, to provide an argument, not just a rant. Why not give us a citation of your peer-reviewed, published work decimating Bell's theorem? Certainly by now you must have published something?

At the very least it should be an easy matter for you to point out Bell's errors in logic. If it's not too much trouble.

 

[RandallB]

Why not list and number your favourite* ''Bell theorems'' (in descending order, citing sources)?

I'll match it with a numbered list of significations from my post.

* That is: List only those that you've personally analysed and will vouch for. Not silly ones that can be refuted by classical experiments or logic.

Good luck, wm

How about you starting off with what must be one of your favourite conclusions:

"Thus: Bell's logic is wrong! "

Just fill us in on the missing significant parts that come just before "Thus:"

 

[wm]

The ''Bell challenge'' remains!

The burden of proof is on you, wm, to provide an argument, not just a rant. Why not give us a citation of your peer-reviewed, published work decimating Bell's theorem? Certainly by now you must have published something?

At the very least it should be an easy matter for you to point out Bell's errors in logic. If it's not too much trouble.

Dear Doc Al, What's this burden that you conjure? Please expand on your logic: Who asked me to provide an argument? But while you're at it, please note:

I responded, as I thought best in the circumstance, to an interesting thread-opener -- encouraging the interested questioner to probe a liitle deeper -- at the same time clarifying the fact that I did not support a cited paper; adding that (in my view) there is a difference between logic (in general terms) and the logic used by Bell.

As far as I'm aware, I responded appropriately to that first post -- ever interested in encouraging students (and others) to master a subject for themselves. (I take it that you're now running from your scornful claim of ''no signicance'' in my first post to this thread?)

As for citing my published work: I'd like to maintain my anonymity a little longer.

So dear Doc Al, if you have faith (Oh ye of little faith) in your mastery of this topic: Why not PLACE YOUR QUESTION and its context on the forum; just as the courageous originator of this thread did!?

To make it easy for you: Why not simply provide one version of Bell's theorem that you personally endorse, then ask your question in relation to it?

Good luck, once more, wm

PS: I'll soon be away from my computer for several days, so take your time and make it good. HOWEVER: For now, could you cite all of your own published work on Bell's theorem? I could then maybe study it while I'm away