# Fun question RE: Bell's Theorem

1. Jul 14, 2006

### 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" [Broken]

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.

Last edited by a moderator: May 2, 2017
2. Jul 14, 2006

### 3trQN

Does ¬(1)->¬(2)?

3. Jul 14, 2006

### roundedge

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

4. Jul 14, 2006

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

5. Jul 15, 2006

### roundedge

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

6. Jul 15, 2006

### JesseM

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.

7. Jul 15, 2006

### Staff: Mentor

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".)

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.

Last edited by a moderator: May 2, 2017
8. Jul 15, 2006

### Hurkyl

Staff Emeritus
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.

9. Jul 15, 2006

### 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.

10. Jul 16, 2006

### Staff: Mentor

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.

11. Jul 17, 2006

### 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. **

:rofl:

Last edited: Jul 17, 2006
12. Jul 17, 2006

### vanesch

Staff Emeritus
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...

13. Jul 17, 2006

### Careful

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 truely 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 :rofl:

14. Jul 25, 2006

### 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.

15. Jul 25, 2006

### Jimmy Snyder

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

Last edited: Jul 25, 2006
16. Jul 25, 2006

### 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.)

17. Jul 25, 2006

18. Jul 25, 2006

### Staff: Mentor

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

19. Jul 26, 2006

### Careful

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

Last edited: Jul 26, 2006
20. Jul 28, 2006