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

[DrChinese]

"No physical theory of local Hidden Variables can ever reproduce all of the predictions of Quantum Mechanics.

The significance of this statement is as follows: Quantum Mechanics is the "strange" theory introduced in 1927 by Niels Bohr and Werner Heisenberg to describe the fundamental nature of basic particles: the atomic nucleus, electrons and light (photons, or electromagnetic waves). This theory was a tremendous improvement upon pre-existing theory, and yielded immediate successes. In fact, the same theory exists today as Quantum Mechanics with virtually no change (although it has been extended to explain more phenomena). The 1927 version introduced such novel concepts as: the Heisenberg Uncertainty Principle; Max Born's statistical interpretation of the wave function, including superposition; and Bohr's complementarity (wave-particle duality). In addition, it included important recent advances such as the Schoedinger wave function (1925); the Pauli exclusion principle (1923); Bohr's semi-classical model of the atom (1913); additional contributions from Louis de Broglie and Paul Dirac; and of course the early seminal work of Max Planck (1900) and Albert Einstein (1905)."

1) Louis de Broigle formulated the wave-particle duality principle, not Bohr (see: https://en.wikipedia.org/wiki/Louis_de_Broglie).
2) The basis of Quantum Mechanics appeared in September 1925 due to Werner Heisenberg, not in 1927. Schrodinger published his paper regarding the wave function in January 1926. DrChinese puts Schrodinger in 1925 before Heisenberg (1927) which is incorrect.

Wow, 1925 instead of 1927. That changes everything. As most around here know well, there is no one date or one creator of QM. Sorry if my 5 sentence historical summary fails for you. I will thank you for commenting on this though, as I did not realize I had placed Niels Bohr's next to Heisenberg's name. Another name would be an improvement, perhaps Dirac or Schroedinger or de Broglie. I'll get on that right away.

As best I can tell, the purpose of you quoting one of my web pages is... to discredit me? Please, don't waste your time, I'm not worth it.

But since you quoted: "No physical theory of local Hidden Variables can ever reproduce all of the predictions of Quantum Mechanics." Got anything to say that relates to the science? Anything to say about Bell proofs or more importantly, the subject of this thread: entanglement?

 

[DrChinese]

That doesn't seem like much of a limitation. For any two events $A$ and $B$, you can get from $A$ to $B$ through slower-than-light signals, if you allow signals to propagate back in time. You just go back in time from $A$ to an event $C$ in the intersection of the backwards light cones of $A$ and $B$, and then go forward in time to $B$.

I agree. But then you immediately run into the problem of why you use the absolute value of delta(time). I.e. you are using backwards in time propagation of a quantum effect (or component of an effect). Why should that be necessary if there is instantaneous FTL influences over distances without limit? You'd think, at first blush, that nothing like that would enter into it.

Yet for a basic Alice and Bob, as I showed, there is a very strict limit on that maximum distance: 2 * c * average(|delta(time)|) and for 1 entanglement swap added: 4 * c * average(|delta(time)|).

 

[bhobba]

Wow, 1925 instead of 1927. That changes everything. As most around here know well, there is no one date or one creator of QM.

That's true. But it's modern form, using mathematics acceptable to physicists, is generally attributed to Dirac when he published his transformation theory in December 1926. A mathematically correct approach didn't occur until Von Neumann published his book in 1932, although I have read he basically had the key idea the state was an element of a Hilbert space in 1926.

1) Louis de Broigle formulated the wave-particle duality principle, not Bohr (see: https://en.wikipedia.org/wiki/Louis_de_Broglie).
2) The basis of Quantum Mechanics appeared in September 1925 due to Werner Heisenberg, not in 1927. Schrodinger published his paper regarding the wave function in January 1926. DrChinese puts Schrodinger in 1925 before Heisenberg (1927) which is incorrect.

The history is more complex than that eg it ignores Dirac's q numbers. All the different approaches were shown to be equivalent by Dirac in 1926 with his transformation theory - although since it was published in December 1926 it may not have been available until 1927 so that's when some accounts may put the year as. Earlier attempts had issues:
http://www.lajpe.org/may08/09_Carlos_Madrid.pdf

I read what Dr Chinese wrote and its pretty much OK. Always remember regarding years of discovery, similar to Von Neumann, the year it was published and the year it was discovered may differ. For Schroedinger's equation it was actually formulated in 1925, but published 1926.

Thanks
Bill

 

[DrChinese]

I read what Dr Chinese wrote and its pretty much OK.

Well, I am the forum's "OKest" science advisor.

And I used to be miles ahead of you in posts too. But apparently I have been lagging lately while you have been eating Wheaties.

 

[bhobba]

Well, I am the forum's "OKest" science advisor.

Good one.

On a serious note, and Feynman has commented on this, historical accounts as told by physicists sort of percolate through the physics community as a kind of folk lore. They get published in physics books etc. But a strict analysis by a historian may show it has issues. Its generally nothing to worry about - except for the pedantic.

Thanks
Bill

 

[simplex1]

The aim of this paper is to give a brief account of the development of the mathematical equivalence of quantum mechanics. In order to deal with atomic systems, Heisenberg developed matrix mechanics in 1925. Some time later, in the winter of 1926, Schrödinger established his wave mechanics. In the spring of 1926, quantum physicists had two theoretical models that allowed them to predict the same behaviour of the quantum systems, but both of them were very different. Schrödinger thought that the empirical equivalence could be explained by means of a proof of mathematical equivalence. Source: http://www.lajpe.org/may08/09_Carlos_Madrid.pdf

Heisenberg is the creator of Quantum Mechanics and nobody else. The other people that followed like Schrodinger just found a more elegant form for this theory or improved it a bit in a way or another, but what they did was not something crucial.
QM was about finding a mathematical expression that gives the spectrum of any kind of atom, molecule, chemical compound, etc. Heisenberg was the first to discover such a general formula. Up to him it was not known if such a mathematical expression exists, excepting for the particular case of Hydrogen.
Schrodinger started to work on his theory after reading the September 1925 paper of Heisenberg.

 

[DrChinese]

On a serious note, and Feynman has commented on this, historical accounts as told by physicists sort of percolate through the physics community as a kind of folk lore. They get published in physics books etc. But a strict analysis by a historian may show it has issues. Its generally nothing to worry about - except for the pedantic.

Thanks
Bill

Good point. I don't pedant too often so that works for me.

I remember when I wrote that paragraph, been a few years. I wrestled with whether to compress it to X sentences, or X+1, etc trying to get it right. Every version either did an injustice to someone, or it went on longer and longer, or it presupposed deeper knowledge of physics. Finally I said to myself: "For the audience I am writing for, this is the best I can do. Although I'll probably get skewered for it some day by a pedantic QM historian. Then my reputation will be shot for good, my page rank will plunge; and next readers may even start to question Bell's Theorem itself."

Well friends, I guess this is the beginning of the end. If only I had made Dirac more prominent... P.A.M., I'm so sorry!

 

[bhobba]

Heisenberg is the creator of Quantum Mechanics and nobody else.

I think you need to read a proper history on the subject. As I said its modern form is attributed to Dirac. The people that contributed to that achievement were quite a few - Heisenberg, Schroedinger, Bohr, Summerfeld and Dirac himself with his q numbers (look it up if you don't know about q numbers).

And, as I said, dates are quite fungible because of when something was discovered and when it was published.

Heisenberg used ideas from the Bohr-Summerfeld old quantum theory:
https://en.wikipedia.org/wiki/Old_quantum_theory

QM is one of those interesting developments that really can't be attributed to anyone.

The metamorphoses of the old quantum theory to its modern form started with Heisenberg - that would be a reasonable statement. But Schroedinger, for example, didn't make any use of Heisenberg's ideas in developing his equation - it grew out of a question someone asked him about De-Brogle's hypothesis - if particles are waves then it should be governed by a wave equation. Here is that history:
http://arxiv.org/pdf/1204.0653.pdf

And, interestingly, he even made an error in its derivation - but what an error.

Dirac with his q numbers is different to either Heisenberg or Schroedinger - but it was influenced by a pre-print he saw of Heisenberg's original paper. When Heisenberg saw Dirac's paper he said it was a much better effort than what he did.

BTW none of this is meant to belittle the accomplishments of any of the people involved or to elevate anyone - they all played an important role.

Thanks
Bill

 

[DrChinese]

...Heisenberg is the creator of Quantum Mechanics and nobody else. ...

Thank god I mentioned Heisenberg prominently.

I'll just erase the names of all those other Physics Nobel laureates, they're just pretenders.

 

[bhobba]

Well friends, I guess this is the beginning of the end. If only I had made Dirac more prominent... P.A.M., I'm so sorry!

His ghost will haunt you for the rest of your life

Seriously though here is an interesting article on the history of his contributions:
http://arxiv.org/pdf/1006.4610.pdf

Thanks
Bill

 

[DrChinese]

His ghost will haunt you for the rest of your life

Seriously though here is an interesting article on the history of his contributions:
http://arxiv.org/pdf/1006.4610.pdf

Thanks
Bill

"The Principles of Quantum Mechanics belongs to the great literature of the 20th Century"... I couldn't agree more. I have it on my shelf.

 

[simplex1]

I will reformulate the example with the two computers to exclude the correlation between the two functions that generate random numbers.

This time somebody runs on two computers two different random number generators with different seeds. To simplify the example we assume that only 1 and 0 are generated.
If one looks at computer A or B he sees two strings of random numbers, totally uncorrelated. However, if the observer counts how many 1 are in a string of 1000 bits he will notice that there are about 500 on both computers. So if the property "number of 1 in a string of 1000 is measured" on both computers the same value ~500 is obtained and it appears that the two computers communicate to each other or are entangled when in reality they are not.

In conclusion this entanglement can be just an impression an illusion.

 

[DrChinese]

I will reformulate the example with the two computers to exclude the correlation between the two functions that generate random numbers.

This time somebody runs on two computers two different random number generators with different seeds. To simplify the example we assume that only 1 and 0 are generated.
If one looks at computer A or B he sees two strings of random numbers, totally uncorrelated. However, if the observer counts how many 1 are in a string of 1000 bits he will notice that there are about 500 on both computers. So if the property "number of 1 in a string of 1000 is measured" on both computers the same value ~500 is obtained and it appears that the two computers communicate to each other or are entangled when in reality they are not.

In conclusion this entanglement can be just an impression an illusion.

Why didn't I think of that?

The short version, as I told you before, is that EPR made the same "mistake" as you. They had the good excuse that Bell didn't come until 20 years later. And I also told you earlier that you would return to conclusions such as the above as long as you evade Bell's Theorem. If you don't like my Bell's Theorem with Easy Math
then try something like https://www.physicsforums.com/threads/bells-theorem-easy-explained.562942/

Regardless, until you see that (local) hidden variables are not feasible as a way to explain entangled state statistics, it won't make sense to you. Your thinking works great when trying to explain correlations that show up as certain - 100% match or 0% match. But they will NOT match QM in virtually any other case. That is what was overlooked. Bell discovered that in a system that tracks QM, you cannot have a classical mechanism. You example cannot be mapped to a quantum system and mimic it.

The Mermin example is the easiest to follow, and that's what one page of mine is based on. It's not that hard. I learned it, so how hard could it be?

 

[bhobba]

"The Principles of Quantum Mechanics belongs to the great literature of the 20th Century"... I couldn't agree more. I have it on my shelf.

Interestingly that was Einstein's view as well. He kept a copy by his bed, apparently mumbling ‘Where’s my Dirac?’ when he came upon a particularly knotty problem.

Einstein had issues with QM - but he understood the theory very well.

Thanks
Bill

 

[ddd123]

On a serious note, and Feynman has commented on this, historical accounts as told by physicists sort of percolate through the physics community as a kind of folk lore.

Like that Bhabha scattering is cursed, and those who studied it first all died under mysterious circumstances. Spooky!

 

[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.