What puzzles me about this problem is what is meant by choice. If we apply the principles of physical science to psychology then 'choice' has no coherent meaning. Either we live in a deterministic world, with no choice, or it is a bit wobbly random at fine grain, which is not choice either. Choice seems to be a naive concept based on our intuitive conflation of tokens and types of events (instances and ensembles). So choice has to be taken out of the discussion. There then arises a question of what makes an event 'random' if, as we know, causality fans out exponentially into the past and so the cause of any event will have some randomness in its history; but where does this randomness have to be in the history?

And if there is no choice is there really any nonlocality over and above the distributed nature of the causal relation of a superposed quantum system in all cases?

I ask as someone rather ignorant of these matters but interested to know.

Jonathan,

I think you know what I mean by choice. You switch on the random number generator and it makes "choices".

There is nothing "distributed". Distance plays no role in entanglement.

Random actually means "relatively random", and for the definition.... Well, there is none, yet, but will be. In many, many years from now :)

Yes, you indeed seem ignorant of these matters :)

This puzzles me more Mario. When I said distributed I meant in both space and time. If space and time play no role here what is meant by non-locality?

It seems that you abandon the vernacular meaning of choice and replace it with 'what happens'. That seems fine but Bohr's conception of QM invoked choice and that seems to be relevant to the concept of non-locality. The implication is that it is the choice of an act of measurement that can 'alter' the state of the other entangled 'particle'. But if there is no choice there is no 'altering' to be done, so there seems to be no reason to attribute the state of the other particle to the measurement interaction of the first. As far as I can see we have a situation that is much the same as that for a quantum system of a single particle, except that there is a dynamically indivisible connection from one point to two points rather than from one to one.

Relatively random sounds a bit vague. If bases were selected according to a code based on the intervals between notes in the prelude of Bach's first cello suite, (which are not random) unbeknown to the physicists doing the experiment, would the results fail to violate Bell's inequality? I suspect not. Is randomness really necessary or is it lack of possible epistemic connection that matters?

The hypothesis of the Bell inequality is locality. Therefore to violate it, there should be nonlocality.  But nonlocality without randomness would violate causality, therefore randomness is necessary too.

In a Bell type experiment, a random choice is not necessary, it is used to close a loophole, for if the basis is chosen before the pair is emitted, it could influence the initial state.  The randomness is the one of the quantum law.

@John: "If space and time play no role here what is meant by non-locality?"

Exactly. The whole thing is wrong and Newton is to blame :) 

Do you know a bit of programming in a higher language, say C ? In C you can calculate with numbers, you can print out letters and words.You can even create images on the computer screen. But none of these exist in the computer - it is all our imagination. In computer only high and low exist and operators AND, NOT and flip-flop. Newton's mechanical parameters : space-time, mass, charge, particles, etc. are,  similarly, only our imagination. When you look at skies your eyes get excited and your brain receive information that it, fantastically, interprets as planets and stars. But that is of course nonsense. A different brain could imagine little green monsters playing in your backyard out of the same data. The true theory of space fabric does not know about spatio-mechanical parameters nor any other crazy things we can imagine in our brains. The only thing, I'd say, that for sure exist in Space is quantum information. Quantum theory is an attempt of theory of space fabric - pretty well done but with serious flaws. It namely combines fantasy (kilogram, meter, second, Coulomb...) and true variables (qubit, ..?), and that is why it is so anti-intuitive. It has a funny name too: quantum mechanics. It is like saying "white black" or "reddish blue".

In the existing quantum theory a lot of things are hard to describe with such a clarity as entanglement.

If you know a bit of QM, write down whatever you think is a description of a maximally entangled two particle state. (I am using usual QM slang so that we understand each other.) Then, write down whatever you think is an operator that describes a single instance of measurement of Bell inequality. Now act with the operator on the state to calculate what measurement(s) will give you and you will see that during the calculation you never have to refer to space and time!    

I will have to leave answering to other points for a later time.

@Claude.

I agree with all. But I am sure that statement that randomness is a law of quantum physics holds true. Please explain.

There's no need that the bases are chosen randomly. All that's needed is that the bases are chosen independently. That is, it has to be sure there's no correlation between the chosen basis and the supposed underlying state determining the results. It is completely sufficient if the result was predetermined by something which cannot be influenced by, nor is correlated with, anything (including hidden variables) inside the past light cone of the pair creation.

That was my initial impression, Christopher, and clearly Claude's point about there needing to be the randomness of the quantum law to avoid transmitting information supraluminally.

I still think that non-locality must entail things being distributed in space and time since otherwise you would be making the two measurements at the same point in spacetime. The correlation equations do not involve reference to space and time because this is not a quantitative issue but presumably the set up of the experiment dictates what differences, at least in space, are involved and there has to be a measurable difference either in space or time for there to be two measurements?

Of course if your measurements are not spatially separated, what you're measuring is not nonlocality, but only noncontextuality.

Cristopher, regarding your statement on requirement for independence please explain how exactly would you define (base) A being independent of (base) B without using  term "random" ? What you want to say is that B should be chosen relative random to A. But to accomplish that either A or B (or both) should be random with respect to the whole Universe, meaning random. I do not see any other way. Or is there? 

@Johnatan's "there has to be a measurable difference either in space or time for there to be two measurements?"

This is an interesting point. I submit that in measuring perfectly entangled state there is always in fact only one measurement, no matter how many times you measure the system. Once you made the first measurement your quantum system is destroyed, converted to a classical system containing one bit of information that you can measure once (as usually done), never or 1000  times - none of these matters anymore. Non-locality does  not mean that something is happening over a distance but simply that distance does not matter. 

Dear Mario,

You can split spacetime into four regions:

Now the last category clearly is uninteresting for our purposes, since under the assumption of locality they cannot influence the experiment. Now events in category 1 cannot influence measurement B in any way, and events in category 2 cannot influence measurement A in any way. Also note that those regions reach infinitely into the past. Now there could be information in region 1 which exists since the beginning of time, was never influenced by anything coming from region 3, and completely determined the setting of measurement A, and the same in region 2 for B. Then clearly the settings in A and B would be causally independent.

But actually, I think true causal independence is not even needed; it's statistical independence that's needed (the difficulty being that the statistical independence must also hold for any possible hidden variables which we cannot just check); causal independence is just a way to get statistical independence. Indeed, I'd say you could use good (cryptographically secure) pseudo random number generators, as long as you use different generators with independently selected seeds. While formally, the selection of the PRNG could have influenced the particle creation if done earlier, practically it would need an intelligent being to figure out how to prepare states to "cheat" on the Bell inequality. So unless you believe in an intelligence intentionally fooling us, I'd say using a PRNG would be more convincing than a truly random process, since with a PRNG we know exactly where the decision comes from. But probably an even better experiment would be to combine a PRNG with a quantum random number generator: Then any mechanism would have to both take into account the PRNG algorithms and influence the quantum randomness generators accordingly to generate fake nonlocality.

Well, I guess you cannot ever completely rule out "intelligent deceptive local hidden variables with total determinism". But that interpretation doesn't seem quite attractive anyway.

I realised after writing non-locality in my last post I meant to write 'demonstration of entanglement' and tried to edit this in straight away but the RG system crashed on me, so we may have got into a crossed wire issue. People seem to use 'non-locality' in different ways depending on whether they think it has to be invoked or whether you retain a local interpretation, as maybe Christopher does?

Cristopher,

If we do not assume that in the time period starting by an  EPR being generated and ending when Alice and Bob measure it it is possible to

1) invent a new, never-heard-of PRNG

2) generate a random sed for seeding it (which by the way is much longer string than required to generate a random basis)

then it does not take ANY intelligence to calculate what basis one is goiung to use. You see, the problem is that both PRNG formula and the seed existed long time before the measurements.  

Claude,

You still owe me an explanation why do you think that "randomness is one of quantum laws". Maybe I was reading all the wrong books but I hve never found a formulation of quantum theory that has a postulate "Randomess exists" or that existence pof randomness is mathematically deduced from postulates of quantum theory.

Regarding special theory, light cones and world lines. Let us imagine that EPR pair is generated at one point in time and space (epicentre) and is left to expand.Let us imagine that Alice and Bob measure the pair at equal, large distance and at the same time as perceived from from the epicentre. Whoever measures first destroys entanglement and converts the system to a classical one. However, for an observer  moving fast parallel to the line connecting Alice and Bob depending on the sense of movement it may seem that either Alice or Bob do the collapse.  Can we say that non-locality invalidates causality?

I would guess NO. Because neither Alice nor Bob , at least in this experiment, have no way of discerning whether they are collapsing the virgin quantum system  or are measuring notorious classical  one.