A Bell Test Violates Local Realism w/ Loophole-Free Electron Spins 1.3km Apart

[simplex1]

It appears that Bell's inequality is just a mathematical theorem not directly connected with Quantum Mechanics.

Bell's inequality: "For any collection of objects with three different parameters, A, B and C, the number of objects which have parameter A but not parameter B plus the number of objects which have parameter B but not parameter C is greater than or equal to the number of objects which have parameter A but not parameter C."
Source: http://www.upscale.utoronto.ca/PVB/Harrison/BellsTheorem/BellsTheorem.html

For example:
The number of objects which have parameter A but not parameter B = 2 (AC and CA)
The number of objects which have parameter B but not parameter C = 2 (BA and AB)
The number of objects which have parameter A but not parameter C = 2 (AB and BA)
In conclusion: 2+2>=2, 2>=0 which is a true relation.

Now, just because a math theorem is true, this does not mean it can apply to QM as long as in Quantum Mechanics a particle can be in two different places at the same time while a math function of t can have only one value. In mathematics we can have x(1 sec) = 4 m but not x(1 sec) = 4 m and x(1 sec) = 12 m. In QM what appears to be a function with two values (forbidden in mathematics) is something possible.

How do we know that Bells's inequality holds if applied to QM?

 

[bhobba]

It appears that Bell's inequality is just a mathematical theorem not directly connected with Quantum Mechanics.

It says if QM is true certain classical inequalities based on properties existing independent of observation and locality are violated. Obviously it relates to QM.

Thanks
Bill

 

[stevendaryl]

It appears that Bell's inequality is just a mathematical theorem not directly connected with Quantum Mechanics.

Bell describes a very broad class of possible theories of physics, and proves a fact that holds of every theory in that class, but does not hold of Quantum Mechanics. So QM is not a theory in that class (and more importantly, can't be "implemented" using any theory in that class).

It's about QM in a negative sense--it shows that there can't be a classical-type theory explaining the results of quantum mechanics, as Einstein had hoped.

As I said, the class of theories that Bell considered is extremely broad. A locally realistic theory in Bell's sense includes any theory described by particles and fields that propagate at or slower than light speed, where particles have definite properties at all times and fields have definite values at every point in space and time. Of course, because of the uncertainty principle, QM isn't a theory of this type, but Einstein had hoped that the uncertainties were due to our ignorance about the true state of the particles and fields, and that if we knew the true state.

 

[DrChinese]

It appears that Bell's inequality is just a mathematical theorem not directly connected with Quantum Mechanics.

Bell's inequality: "For any collection of objects with three different parameters, A, B and C, the number of objects which have parameter A but not parameter B plus the number of objects which have parameter B but not parameter C is greater than or equal to the number of objects which have parameter A but not parameter C."

... Now, just because a math theorem is true, this does not mean it can apply to QM ...

How do we know that Bells's inequality holds if applied to QM?

Here is a simple test. It's called the DrChinese challenge.

1. You have a series of trials. Perhaps 10 or so. You will specify the value + or - for 2 Type I entangled photons being polarization tested at 3 angles: 0, 120 and 240 degrees. So you will provide 6 values per trial, 3 for each photon.

2. Because they are Type I entangled, we know that the measurements for any SAME angle on the photons will give the same results, both + or both -. They will MATCH (in fact they are as close to clones as it gets). Outside that, you can put + or - to your heart's content and arrange things as you like.

3. Whenever any pair is measured at DIFFERENT angles, the difference is always 120 degrees or 240 degrees. Quantum mechanics predicts that measurements on Type I photons will MATCH 25% of the time in either case. The QM general prediction for Type I entanglement is Match%=cos^2(theta) where theta is the angle difference.

4. After you hand pick your trial values, we will calc the average MATCH % for the cases where there is a difference of 120 or 240 degrees. You cannot help but provide trials in which the lower limit is 1/3, thus proving that there is no "hidden variable" data set in which the predictions of QM match a classical example. This is Bell's Theorem as applied to QM, answering your question above.

Alice Bob
0 / 120 / 240 0 / 120 / 240
+ + - + + -

The above is a starter trial. Add your own. As it happens, even in 1 trial, the average is 2 matches in 6 permutations. That's 1/3. You can't write down any set of trials that cumulatively will drop the average below this value of 1/3 and bring it any closer to the actual experimental value of 1/4 (25%).

The conclusion is that Alice's outcome is "somehow" influenced by Bob's choice of measurement angle, or vice versa. Or more generally, Bell says: "No physical theory of local Hidden Variables can ever reproduce all of the predictions of Quantum Mechanics." I have provided a prediction of QM that cannot be reproduced in classical fashion, please try as you like until you are convinced.

 

[stevendaryl]

No, that is absolutely not true. Whatever nonlocality there is in QM can't be use to transmit signals.

There might be (I don't know for sure) a sense in which it is possible to transport random messages faster-than-light. I haven't thought about it, but you can think of the results of a spin measurement as being a random number. Using an entangled pair of particles, it's possible to get the same random number to Alice and Bob instantaneously.

 

[Mentz114]

Sticking my neck out somewhat, it seems to me

1. The difference between the expected correlations in the entangled case and the unentangled case is that interference is present in the entangled case.
( I think it is possible to derive interfernce formulae by starting with entangled states )
2. Adding a hidden variable is equivalent to adding which-path information which will suppress the interference
3. Therefore no HV can simulate the effects of entanglement.

This came to me while I was thinking about the EPR in terms of entropy and density matrices but it looks a bit glib.

 

[bhobba]

Logic is the study of valid reasoning, so that's not possible.

This was sorted out by Von Neumann:
https://en.wikipedia.org/wiki/Quantum_logic

It purely formal - nothing to do with reasoning about the implications QM.

Its useful in very mathematical treatments of QM:
https://www.amazon.com/dp/0387493859/?tag=pfamazon01-20

Thanks
Bill

 

[ddd123]

Logic is the study of valid reasoning, so that's not possible.

Petitio principii! Lol.

 

[stevendaryl]

Petitio principii! Lol.

No, it's not. If we define logic to be the study of those forms of reasoning that are generally valid, then it's not possible for logic to be invalid. Talking about logic being invalid is like talking about red roses that are yellow. By definition, if it's yellow, it's not a red rose.

 

[stevendaryl]

This was sorted out by Von Neumann:
https://en.wikipedia.org/wiki/Quantum_logic

It purely formal - nothing to do with reasoning about the implications QM.

Its useful in very mathematical treatments of QM:
https://www.amazon.com/dp/0387493859/?tag=pfamazon01-20

Quantum logic doesn't imply the invalidity of classical logic. People certainly use classical logic in reasoning about quantum mechanics.

 

[bhobba]

Quantum logic doesn't imply the invalidity of classical logic. People certainly use classical logic in reasoning about quantum mechanics.

That's right. Its a purely formal part of certain axiomatic treatments. Its better to look on it as a boolean algebra.

Thanks
Bill

 

[Simon Phoenix]

The credibility of this article: http://www.drchinese.com/Bells_Theorem.htm written by the user DrChinese and talking about Bell's Theorem is quite low.

Wow - well I've been reading these forums for quite a while (but participating only recently). Not that he needs a vote of confidence, but Dr Chinese has been posting excellent stuff, particularly on entanglement, ever since I started reading this forum - and probably for a good while before then.

And you base your estimation of his 'credibility' on a historical sketch which puts things in context? Even if he got a few bits of this wrong (and I'm not saying he did) who gives a flying thingamabob? Sheesh.

Anyway - the history of that period is endlessly fascinating - and one can only imagine the confusion and sheer incredulity as bit by bit the classical world-view was found to be seriously wanting. I like to think it was Einstein who first really saw the storm brewing. There was a paper of his written around 1909 (not 100% sure of the date to be honest - it might be later, even around 1917) in which he showed that for black body radiation some of the fluctuations could be attributed to a particle-like behaviour and some to a wave-like behaviour. I suspect he thought "holy crap" at about that point, or the equivalent in German, but I could be wrong :-)

Entanglement is about much more than just correlation - Bell's original paper is an absolutely brilliant piece of work that gives us an experimental way of deciding this issue by examining correlations between observables, but the implications go much further, as Bell was only too well aware.

 

[bhobba]

What do you mean by "logic"? As I understand it there are different kinds of logics in mathematics - depends on your starting rules (eg do you want to hold the law of the excluded middle as valid? Again as I understand it, it's perfectly possible to construct mathematically sound logics in which this principle is not deemed to hold).

That's correct. Its simply a formal system and forms what's called a Boolean Algebra:
https://en.wikipedia.org/wiki/Boolean_algebra

It turns out in QM the usual Boolen Algabra of standard logic is not what its based on. A technical discussion of logics in general can be found in Chapter 1 of Varadarajan - Geometry of Quantum theory. Its relation to QM an be found in Chapter 4 - Logics Associated With Hilbert Space. This is tied up with a famous theorem called Pirons Theorem:
http://stanford.library.usyd.edu.au/archives/sum2008/entries/qt-quantlog/#5

Its all part of a very mathematical treatment of QM. It is often said that when mathematicians get a hold of a physical theory they change it to something unrecognisable

It certainly is a LOT harder. My background is math not physics and that book by Varadarajan stretchers me to my limit. I can follow it with time (a lot of it) and effort (again a lot of it) - but just.

Thanks
Bill

 

[Dale]

A bunch of off topic and inflammatory posts have been deleted and this thread is closed.