Validity of Relativity

ttn

They better "materialize" some way, or they will have no dynamical consequences. Nobody thinks that the irreducible randomness at some point brings into existence a new (physical) scalar field, or a big set of polished bronze numerals reading "0.732752" (or whatever the random number was). But if what's being explained by the underlying stochastic theory is some kind of measurement outcome, then obviously the generated random numbers have to have a real physical effect on *something* which then in turn physically influences the macroscopic measurement devices (which *nobody*, except crazy MWI-people, denies are beables).

All of the points in the last few posts have been pointless semantic distractions. It's clear that any random numbers generated by a stochastic theory have to manifest themselves in some physical way -- otherwise they would be irrelevant to empirical observations and there's be no point at all in hypothesizing the theory in question. The only question can be: where (at what spacetime event) do such numbers arise?

To answer this question is to admit non-locality (in the kind of examples we've been discussing). If Bob makes the "first" measurement and there is something random that controls his outcome, then the subsequent effect of that number (or its various causal effects near Bob) constitutes nonlocality.

And to *not* answer this question is to admit non-locality. If Bob makes the "first" measurement and this new random number comes into existence *not* at some spacetime event near Bob, but (say) simultaneously along some spacelike surface through Bob's measurement event, said popping into existence constitutes nonlocality.

ttn

You've got to be kidding!?! First off, the unitary evolution is deterministic. Second, it *doesn't* "explain the correlation just fine" since it predicts that Alice's box never ever reads definitely "H" or definitely "T" -- in direct contradiction with what Alice (by assumption in *your* example) sees.

I will grant, however, that if you are going to begin by throwing out the empirical data that was supposed to define this situation (Alice and Bob each see H or T w/ 50/50 probability, but the two outcomes are always paired HH or TT) then, yeah, sure unitary-only QM can explain the correlations. Just like Ptolemy's theory of the solar system can explain the last 100 days of data for the price of tea in china...




Are you still talking about unitary-only QM?

I don't know what to say. If you think the above, you simply haven't understood Bell Locality at all. The whole point of this condition is to ask: are the beables of a theory sufficient to explain certain observed facts in a local way? For your example of the irreducibly-random theory which purports to explain the HH/TT correlation, Bell Locality is violated: a complete specification of beables along some spacelike surface prior to both measurement events does *not* screen off the correlation.


The version of Bell Locality that actually gets *used* in the derivation is actually equivalent to this weaker condition. The probability of one event is conditionalized not just on a complete specification of beables in the past light cone of that event, but across a spacelike hypersurface that crosses also the past light cone of the *other* event. That is, we do not presuppose what is nowadays sometimes called "separability".




I'm sorry, but every time you start analyzing probabilities and such, you turn into a mathematician -- i.e., you completely forget about the physical situation that we're talking about here. The whole question of locality is whether goings on near Alice are *alone* sufficient to account for all that there is to account for near Alice (her outcomes). What you have now lapsed into calling the "statistical independence hypothesis" is the *physical* requirement that a *local physics theory* shouldn't have its probabilities for one event, *depend* on happenings at spacelike separation, when a *complete specification of beables* in the past light cone of the first event is already given.

Yes, one can *deduce* from this "statistical independence" -- a complete specification of beables in the past of the two events should screen off any correlations between the outcomes. But this is not an arbitrary hypothesis; it is a *consequence* of the basic requirement, which is *locality*.

Let me ask you a serious question: have you ever read Bell's papers on this stuff?

ttn

I don't agree; this is not deterministic. There could be irreducible stochasticity in the initial assignment of a value to the "scalar field."

I see no reason to postulate the existence of any physical scalar fields. The point is too simple to deserve such fanciness: you could have a theory in which there is irreducible randomness (the production of some random number from some kind of probability distribution), but in which that number (whatever it turns out to be) is then "available" at other spacetime events to affect beables. And my point is simple: if it is only available at spacetime points in the future light cone, the theory is local; if it's available also outside the future light cone, the theory is nonlocal.


I don't understand this attitude at all. Beables are beables. I'm happy to permit, under the banner of "irreducibly stochastic theories", theories in which the evolution of beables is non-deterministic. But as I said before, what would be the *point* of the randomness if it didn't affect the beables??? It would then have no effect on *anything* because there *is* (by definition) nothing but the beables! You seem to want to parse "irreducibly stochastic theories" as something in which, in addition to the beables, there are these other "things" that "exist", except that they are "random" in the sense that they don't exist in any particular measure/degree/value/whatever. But "random" isn't the same as "indefinite".

You say that as soon as one assigns physical existence to the random quantities, the theory becomes deterministic. I could not disagree more strongly. First, if you *don't* assign physical existence to the random quantities, what the heck is the point? They then play absolutely no role in the dynamics. And second, whether you do or don't assign physical existence to the random quantities, has no bearing whatever on whether the theory is deterministic. A theory in which there is randomness which affects things, is *not deterministic*. For example: orthodox QM (with the collapse postulate) is *not* a deterministic theory, even though there is irreducible randomness (which of the eigenstates the initial state collapses to) and the "outcome" of this "random choice" manifests itself immediately in the beables (the wave function is now that eigenstate).


But then there'd be no need to talk about their locality or anything, since they would play no role whatsoever in the evolution of beables (and hence no role whatsoever in the explanation of empirical observations).

ttn

Please don't tell me I've spent all this time trying to explain things to you, only to have *this* appear as your considered view.

Sure, you can explain EPR/Bell data with a theory in which the causes of certain events come from the future. Do you seriously think such a theory would be "locally causal"?

Hurkyl

Pointless semantic distractions?!?! Does that mean you no longer care to assert that what I put forth as an alternative to "locality" is actually Bell-locality?


The random numbers that are "generated" are the manifestation -- they are not any sort of dynamical entities, and they do not have any sort of effect on anything. They are nothing more than the result when you insist that a stochastic theory produce an actual outcome.

(A stochastic theory, of course, doesn't like to produce outcomes... it prefers to simply stick with a probability distribution on the outcome space)

ttn

I don't know what you're referring to. What did you put forth as an alternative to "locality"? And I think I'm just confused about what you're asking here: I'm the one who thinks Bell Locality is a perfectly good definition of locality; so if your proposed alternative "is actually Bell Locality" wouldn't that make it not really an alternative at all?



The outcomes appear in some physical form -- like, in your example, the positions of a bunch of electrons that make a phosphor screen light up a big glowing green "H" or something. Perhaps this just takes us back to our earlier argument about what constitutes a "theory". I'm taking it for granted that there exist physical things like video screens and electrons, and asking about theories which might explain the underlying dynamics of whatever is at the next-level-down. You (still) seem to think it's ok to assert as a theory some mathematical/probabilistic statement like "P(HH)=.5, P(TT)=.5, P(HT)=P(TH)=0". That may be a correct description of the observed outcomes, but (the way I am thinking about this, as a physicist) it is *not* a *theory*.

If we accept as a given that the observed result is (say) produced by electrons landing "here" instead of "there" on the screen, then your proposed stochastic theoretical explanation of the observations better include some way for the random numbers to affect electrons. If they "do not have any sort of effect on anything" then you are just spinning your wheels, failing in principle to propose the kind of thing that could ever possibly address the issue at hand.

Really, this comes down to the old objection that one could just take the quantum mechanical formalism as a blind algorithm, which makes no claims about any beables... and hence make correct predictions without ever asserting anything that could possibly construed as violating local causality. Of *course* one can do this. One can avoid making nonlocal claims by refusing to claim anything about anything. Duh. But we *know* that big macroscopic things exist, and we *know* they're made of littler things. The question is: is it possible that the dynamics of the little stuff (or the sub-little stuff, or whatever) respects local causality? Bell gave a theorem that the answer is no: no locally causal (bell local) theory can account for what's observed.

Putting tape over your mouth and refusing to assert a theory does not constitute a counterexample to this theorem.

Hurkyl

Unitary evolution provides us with a state:

(|HH> + |TT>) / sqrt(2)

from which it's easy to derive the correlation. Furthermore, if we actually conduct an experiment to test if there's a correlation, unitary evolution provides us with the resulting state

(|HH> + |TT>)|correlated> / sqrt(2)

As opposed to the state we'd get when there wasn't any entanglement at all:

((|HH> + |TT>)|correlated> + (|HT> + |TH>)|uncorrelated>) / 2



I'm talking about any sort of statistical theory.


Before I respond to the next part, allow me to remind you of your post #133 that launched this particular arc:
Yes -- it's Bell Locality that is violated: in particular, it's statistical independence hypothesis. But other forms of locality, such as what I stated here, are not violated.

First off, notice that your first question is very circular. Filling in the implicit stuff (as I understand it), you say:

"The whole point of the Bell locality condition is to ask: are the beables of a theory sufficient to explain certain observed facts in a Bell local way?"

But you did not ask for a toy theory that was Bell local: you asked for a theory that was consistent with Lorentz invariance: with special relativity. (In fact, isn't the whole point of this thread to ask the question of consistence with special relativity?)

Bell locality is, indeed, violated, because one of its underlying assumptions is that there is no statistical dependence. By looking at all of the responses through the filter of Bell locality, you are, in fact, asking:

"Is there any theory consistent with special relativity that is capable of predicting statistical dependence, under the condition that there is no statistical dependence?"


I am a mathematician, incidentally.

You try to make it sound important by calling it a "physical requirement" -- but that amounts to nothing more than saying that it's an axiom that you wish to require your mathematical models of the physical universe to satisfy.

Try me.

I've read a few papers, including stuff you have linked in the past. I never bothered to pay attention to who the author is.

Hurkyl

Of course the random variables have an effect on electrons.

But this has absolutely nothing to do with the idea of a random number generator you seem to be using in post #171.


You seem to have in your mind that a stochastic universe would be analogous to how a computer program will use a pseudorandom number generator to spit out a sequence of numbers, and then use those numbers to control how things dance across its screen.

But that's not how statistics works! A random variable is nothing more than a measure on a space of outcomes. In fact, it is a very difficult problem to try and give any sort of precise meaning to the word "random number generator".


(In a classical theory)
E.G. one random variable could be on the space of possible positions and momentums of an electron. Another random variable could be on the configurations of the electromagetic field. The dynamics of the theory would allow us to compute a new random variable on the space of possible positions, momentums, and accelerations of the electron.

(Of course, this is just marginalized from the joint distribution over the electron position, momentum and acceleration and the electromagnetic field configuration)

ttn

"easy to derive" is irrelevant. The state is already *empirically wrong*. What exists is not a superposition of HH and TT; what exists is *either* HH *or* TT.

You seem to be using/assuming the MWI without being willing to admit the well-known weirdness of such a view. Sure, unitary evolution can get you that superposition, and you can twist and turn and eventually connect this up with what we do experience (by denying that what we see in front of our face is the truth, i.e., by postulating that we're all deluded about what the outcomes of the experiments actually were). But normally when a physicist asks if some theory or other "explains the data" he or she is not looking for a metaphysical-conspiracy-theory about how, really, the data we got directly from looking at an apparatus is a delusion.



I'm sorry, I don't follow you. The alternative you proposed (as near as I can tell) was:

"Are all the beables here sufficient to describe what's going to happen?"

But as I pointed out, this just *is* the Bell Locality condition. Maybe we're not on the same page about what the phrase "sufficient to describe what's going to happen" means. I told you what that phrase means for Bell Locality, but I don't understand what, if anything, you're proposing as an alternative. You seemed to simply reject my proposal for the meaning of that phrase on the grounds that it presupposed the statistical independence hypothesis, but that simply is not true.



I asked for a theory that was consistent with SR. You just postulated some joint probabilities without ever providing a theory.


I'm sorry, but saying this over and over again doesn't make it so. What you are calling "no statistical dependence" is equivalent to the factorization of the joint probability, yes? Here's what Bell says about this: "Very often such factorizability is taken as the starting point of the analysis. Here we have preferred to see it not as the *formulation* of 'local causality', but as a consequence thereof." [from La Nouvelle Cuisine, page 243 of Speakable and Unspeakable, 2nd edition] I've tried and tried to explain this, without success, so I'll just have to refer you to that paper where Bell explains very clearly what the local causality condition is, and how factorization ("statistical independence") follows as a logical consequence. Factorization is *not* simply assumed; it is a consequence of a *physical* assumption -- namely, that there be no superluminal causation.



Obviously I don't agree. I'd say: by thinking (erroneously) that Bell Locality means nothing but statistical independence, you are missing the whole point. Incidentally, I find it interesting that you cannot apparently resist converting Bell Locality (which is a *physical* condition) into factorizability (which is a purely mathematical condition).



Not that I think there's anything wrong with that, but I'm not surprised.


Precisely right. I take as an axiom that physical theories should respect relativistically local causation. And then it is proved that no theory consistent with that axiom can agree with the data. So I say "oops!" I guess that axiom is *false*. No locally causal theory can explain the data.



I don't think I've ever linked to Bell's papers, because I don't know of any of them being online. Anyway, take it as a friendly recommendation. Bell is a brilliant physicist and a brilliant writer, and if you want to understand where I am coming from you would probably be better off just reading Bell in the original than listening to me. (I am far less brilliant.) Because everything I'm saying here, Bell already said, and said better. Plus, the reason I get so hot under the collar about this stuff is that, despite the incredible clarity of Bell's writings, he has been almost universally misunderstood by the "experts" on these topics. (I quoted Bell himself pointing that out yesterday.) So I find it extremely frustrating that people have such strong opinions on what Bell did or didn't prove, when they haven't even bothered to read Bell's papers. You are obviously a smart guy who has enough background knowledge to get completely clear on these issues; so I say, if you *want* to get clear on these issues, if these are issues you are *interested* in, then it would be a shame if you didn't read Bell's papers.

DrChinese

No, I am not actually saying this is my opinion since I drift towards oQM most of the time. I am merely pointing out one possibility. Does it really seem so weird that the future might influence the past? And, yes, I definitely consider such a theory to be local in every sense of the word. But it is not realistic. So it would be local non-realistic, and therefore consistent with Bell's Theorem.

And to counter your assertion ("no Bell local theory can agree with experiment"), I instead state that "no Bell realistic theory can agree with experiment". Bell realistic meaning: any theory in which there is a more complete specification of the system than the HUP allows. You cannot beat the HUP!

And please, do not bother with BM as a candidate. I am talking about a theory in which the HUP is beaten. EPR thought they had it, but experiment showed otherwise. If you can't beat the HUP, even in principle, then you are acknowledging that there are no hidden variables in the first place.

ttn

Sigh. I count at least 6 major confusions here. (1. reverse-temporal causation certainly is *not* "local in every sense of the word". 2. A theory with reverse-temporal causation, assuming such a thing could even be made well-defined, could be 100% "realistic". 3. A "local non-realistic" theory is not consistent with Bell's theorem anyway, if what you mean is what Bell meant: the full, two-part argument that no local theory, realistic or not, can agree with the empirical predictions of QM. 4. What you call my "assertion" is actually something that has been proved rigorously, unlike the vague and arbitrary statement you seem to want to "counter" me with. 5. The meaning of "You cannot beat the HUP" depends crucially on the meaning of "HUP" -- if one takes HUP as a restriction on the simultaneous *reality* of certain variables, then you are, like Bohr, just rejecting the conclusion of EPR without demonstrating any error in the argument; and if one takes HUP as merely a restriction on simultaneous *knowledge* of certain variables, then something like BM *does* count as a "candidate" since it makes the same empirical predictions as quantum theory and yet has particles following definite trajectories. 6. No experiment ever "showed otherwise", i.e., refuted the EPR argument; with the help of Bell's theorem we now know that the kind of theory EPR lobbied for is not empirically viable; but this does *not* mean that experiment has refuted the argument they used to arrive at that belief; the argument might be valid, but the *premises* false.)

This last is the most crucial. EPR believed in locality. EPR also constructed an argument for the proposition that "Locality --> Hidden Variables". Putting these together, they proposed that a local hidden variables theory should be sought to replace orthodox QM.

We now know from Bell that such a theory cannot work. Does this mean that EPR were wrong? Yes, in the sense that the kind of theory they said they thought should be sought turns out to be impossible. But does this mean that their *argument* for the statement "Locality --> Hidden Variables" was flawed? No!!!! It means only that *either* that argument was flawed, or the *other premise* ("Locality") is false.

Nobody has ever pointed out a flaw in the EPR argument (widespread opinion to the contrary notwithstanding). Indeed, the argument has been re-formulated in rigorous terms several times recently. So that leaves no choice but to blame the empirical violation of Bell's inequalities on that first premise, "Locality".

Here it is again in slow motion:

EPR: Locality --> HV's

Bell: Locality + HV's --> X

Experiment: X is false

Conclusion: Locality is false.

Of course, as this thread has certainly made clear, this conclusion is only *interesting* for those who believe that the sense of "locality" needed to make the argument go through, is something that we ought to believe in the first place based on relativity theory. There are some people who deny that (for reasons that don't make any sense to me, but whatever). My point here is just that saying "experiment refuted EPR" represents, as Bell once said about the critics of Einstein, "misunderstanding [that] could hardly be more complete."

vanesch

Well, that's still "deterministic" in my book, in that there are quantities out there, which were there "from the beginning", but of which we simply DIDN'T KNOW things. These are exactly the "hidden variables", the hidden beables, hidden because of some or other principle (or practical situation) which makes it impossible for us to know anything more about it than a probability distribution.


But this "being available" is exactly the notion of a beable, no ? It then is a part of the description of the "physics" (hidden or not). In that, you suppose the quantity to HAVE a value, but you simply DON'T KNOW WHICH. So IF you would know the value, then the theory would be deterministic, right ?
I mean, you're thinking of one or other phenomenon which is "making the detector click" or not, and if only we knew its value, then we would KNOW in advance whether the detector would click or not. But as such, the stochasticity is still reducible. It can be "irreducible" for us if it is *in principle* unknowable, but it can still be "hidden determinisitic", in that one COULD think up a constant field over spacetime with a random value, which is then going to determine the outcomes.
And when this is potentially possible, you have Bell's condition.
But let us now take quantum theory in an extremist Copenhagen view: there are only macroscopic bodies, which follow strictly classical physics, except that in the equations of motion, we have to introduce random events. In order to know the statistical distribution of these random events, we use quantum mechanics, which is however, not supposed to even describe a microscopic world. Electrons and atoms don't exist. Just macroscopic bodies. But we "pretend" there to be microscopic objects, and wavefunctions and all that, but this is nothing but a big game, which has only one purpose: calculate the statistical distribution of the random actions on the classical dynamics of macroscopic bodies.
Well, that statistical distribution, deemed to be irreducibly stochastic (that means, "it just happens that way" and there's no underlying mechanism which causes it ; all the QM formalism is just a trick to calculate it but doesn't represent anything) is what it is.
And how do we check whether it is compatible with the geometry of spacetime ? Well, we calculate a set of probabilities of outcomes from the point of view of one observer. And then we do the same for another observer, which suffers a lorentz boost. And guess what ? They come to the same statistical predictions. It is not possible to derive a "preferred reference frame" from these statistical predictions. THIS is the one and only condition that is necessary for this theory to be COMPATIBLE with the spacetime geometry.
Whether this is to be called "local" or not is your business. "Local" really has only a strict meaning in the case of deterministic theories, where THE outcome (not the *probability* of an outcome, because probability is an epistemological concept) at an event E is DETERMINED by what's in the past lightcone of E ; and this locality is even only needed to what "we can really influence and know in the lab".
In a deterministic theory, locality is needed to avoid the "I can change the future so as not to produce what I learned about the future" paradox.
In a purely stochastic theory, what remains of this requirement to avoid a paradox is "information locality", for the same reason.
And "Bell locality" is an EXTRA REQUIREMENT one can postulate, for one's own liking, and which comes in fact down to requiring that statistical effects in a theory are derivable from an underlying deterministic, local, theory.



Ok, but then you cannot require anything a priori about THESE random elements, and you seem to do so! Why cannot these elements of randomness have correlations ?

Exactly ! Irreducible randomness, to me, is something akin of "the will of the gods". This, as compared to "randomness induced by lack of knowledge".

In orthodox QM, the wavefunction is not a beable. It's a trick to do calculations of a probability distribution. A way to quantify the will of the gods, if you want to.

I will agree with you that I have difficulties with such a view too (hence my preference for MWI, where at least there IS something underlying). And of course in the more von Neuman approach, where the wavefunction is a beable, you're perfectly right that it is non-local.

But (though it is not my view) if you simply see QM as a "trick to calculate irreducible stochastical influences on a classical dynamics of macroscopic bodies" and hence deny the existence of a microscopic world, I think you have no clash per se with the Minkowski geometry of spacetime (in which only these macroscopic bodies live of course, not the non-existing microworld). The calculated probabilities do not allow you to find a specific reference frame and they also do not allow you to create a paradox (thanks to information locality).
I simply think that in such a case, "locality" has not much meaning beyond these statements.
It is only when you want to deny the irreducible stochastical character of the probabilities calculated thanks to the formalism of quantum theory, and when you try to think of a MECHANISM (involving microscopic beables) that you run into problems. And when you consider the "projection of the wavefunction" as something physically happening, you have a bluntly non-local process of course.

DrChinese

*Sigh* (that's a joke, by the way)...

EPR did NOT make the above argument in their paper, they said: If QM is complete, then there cannot be simultaneous reality to non-commuting observables. And I agree with this conclusion.

What they did not know, but would have been surprised to learn, is that Aspect-like experiments would NOT yield more information on the separated particles than would be allowed by the HUP. They believed, but did not prove, that the HUP could be beaten. So far, the HUP still stands. Ultimately, that is the heart and soul of the debate.

ttn

That's not a conclusion, it's a definition/elaboration of "completeness". The actual argument was for the conclusion that there *is* simultaneous reality to non-commuting observables -- and hence that QM is *not* complete. And the argument was based crucially on locality, a fact you don't seem to appreciate at all.

I guess, since even Einstein thought that Podolsky's text buried the main point under pointless "erudition", Podolsky, and not you, should be blamed for your confusion over the point and content of the EPR argument.



My disagreement could not be more complete.

If you think the point of *either* EPR or Bell's Theorem (or Aspect's experiments) was to actually, in practice, "yield more information ... than would be allowed by the HUP" you have completely and totally missed the whole point of this entire debate.

Sigh. (not a joke)

Hurkyl

Yes -- when there is no statistical dependence between A and B, we have P(A and B) = P(A) P(B) and we have P(A|B) = P(A).

I don't think Bell Locality means nothing but statistical independence -- but it's that aspect of Bell Locality from which this whole debate stems. (At least the part in which I'm involved)

I'm willing to grant the other aspects of Bell Locality, just not the assumption of statistical independence...
... or whatever Bell happened to be assuming that is equivalent to assuming statistical independence.

In one of the papers you linked before, Bell Locality was formulated in terms of three postulates: parameter independence, statistical independence (I believe it was called "observation independence"), and something else I can't remember.


Wait a minute, I thought it was proved no Bell Local hidden variable theory could agree with the data.


I'm going to rewind back to the original theory I posted, where I simply posited the existence of a pair of coins that were governed by a joint probability distribution. Upon reflection, I realize that there is a problem with this, but for reasons entirely different than what you've said. So let me make a slight modification before we continue.

Let us start with special relativity, but also add in some additional postulates:
(1) There exist objects called "magic coins", and they come in pairs.
(2) Magic coins can be in one of three states (in addition to whatever SR says): U, H, or T.
(3) Any two pairs of magic coins are otherwise identical.
(4) There is some sort of interaction called "flipping" that can be triggered in a laboratory setting that causes a magic coin in the U state to nondeterministically transition into the H or T state.
(5) Otherwise, magic coins do not change their state.
(6) The flipping interaction for each pair of magic coins is governed by the joint probability distribution P(HH) = P(TT) = 1/2, P(HT) = P(TH) = 0. (And the distribution over all pairs of coins factors into those of the individual pairs)


The important things to note are:

(A) The theory is nondeterministic. There is nothing to determine whether the coin undergoes U-->T or U-->H.

(B) The probabilities are understood in the frequentist interpretation: we say the probability of an event E is p when the ratio of the number of times event E occurs over the number of (identical) experiments approaches p as the number of experiments goes to infinity.

In particular, this means probabilities represent nothing more than asymptotic behavior: it is entirely nonsensical to try and use them to describe an individual experiment.


It follows from the axioms of the theory that:

For the experiment where we take a magic coin and flip it, we have P(H)=1/2.

For an experiment where Alice and Bob take a pair of magic coins and flip them, we have

P(Bob sees H | Alice sees H) = 1.

and

P(Bob sees H | Alice sees T) = 0.


It does not follow from the axioms of the theory that it is impossible for Bob to see H and Alice to see T. (But the probability of it happening is zero)


This theory claims to be complete and local in the respect that everything that can be determined can be entirely determined with the local beables.


The important thing this is trying to convey relates to the usage of probabilities. Normally, (as far as I can tell) the usage of statistics in physics is either entirely aphysical, or it is based upon a very shaky logical foundation.

For example, the frequentist definition of probability requires examining a hypothetical infinite sequence of similar experiments. But we have problems such as:
(1) The limiting ratio may not be well defined.
(2) The sequence of events is hypothetical, and cannot be physical.
(3) We don't know how to classify experiments as similar! (Well, we do know one way, but then we'd never see probabilities other than 0% or 100%)

But, at least in the above theory, we can put the frequentist definition on a rigorous footing -- since there are no factors that affect the outcome of a coin flip, it's clear that we can consider any two coin flipping experiments as similar. (And experiments involving multiple coins are similarly easy) We don't have to worry if we can define a hypothetical sequence of experiments and if the limiting ratio will be defined, because one of the axioms of the theory is that we can do so without any worries.



I do prefer a view that's MWI-like, although I do not know if it leads to MWI. I don't like a nondeterministic theory -- I would prefer to make a statistical theory, and take statistics seriously.

In this interpretation, when we say something is a random variable, we do not mean that it is something that can acquire an outcome! That means that it is something that assigns nonnegative real numbers to the possibles outcomes that add up to one.

Other interpretations suffer from two very difficult philosophical problems:
(1) They are nondeterminsitic. They assert that there is no reason the measurement turns out the way it did... it just did. But at least we have this probability distribution that describes the results!

(2) It is mysterious why and how the frequentist definition of probability manages to describe anything!


But my interpretation solves both problems.

(1) It is a deterministic theory of random variables.
(2) Probabilities are fundamental elements of reality -- so we don't have to use the frequentist definition to talk about probabilities.

It does raise the philosophical issue about why it looks like we see outcomes, but that question does have an answer.



But, if you insist that it's too radical of an approach, we can stick with nondeterminism, and assert that quantum mechanics without the collapse postulate is capable of describing everything that can be described -- it has a unitarily evolving "state of the universe", and the only other things that can possibly be described are the probabilities involving the outcomes of measurements. But, as you remember, the classical usage of probabilities are statements about asymptotic behavior, and not statements about individual events.

ttn

I think we're talking past one another. I wasn't saying that the quantities out there had values "from the beginning." I think my use of the word "initial" was confusing. I meant only: from the moment at which the stochastic part of the dynamics does its thing. Before that moment, this value didn't exist. At that moment, it was randomly produced (and then "exists" in the same way that anything else real exists).




Yes, sure. I would assume that the random numbers that an irreducibly stochastic dynamics generates, are beables (or are somehow or other "encoded" in the beables). I mean, seriously, the beables are (by definition) all that exists. This is what I was saying before: if your stochastic dynamics doesn't (randomly) affect the beables, then it doesn't affect *anything* and you might as well just get rid of that part of the dynamics.


We should forget about knowledge here. It's causing unnecessary confusion. Just imagine that we're god; we're omniscient about all the beables. I'm perfectly happy to accept as a logical possibility that the evolution equations for the beables (i.e., the dynamics of the theory) aren't deterministic. That means: even god, in his omniscience, can't predict in advance how certain things will go. There's just no present fact that uniquely determines the future. This is all just what we mean when we say a theory is irreducibly stochastic. Yes?


No, I'm not assuming or requiring that going in. My argument (well, Bell's... well, EPR's!) is that a *local* stochastic theory cannot explain the perfect correlation which is observed (and which QM predicts) when Alice and Bob measure along the same axis. This can be made rigorous if "local" means "Bell Local" (though I understand you for some reason think that would be circular since Bell Locality already tacitly assumes determinism.



I'm not sure such a thing is sufficiently well-defined for purposes of assessing its locality. Remember, to apply the criterion of Bell Locality, one needs some candidate for what a "complete description of beables" consists of. And then one also needs sufficient formal dynamical laws to map the evolution of beables onto experimental results somehow. And there seems to be a disconnect there -- which amounts basically to the measurement problem -- for this "extremist Copenhagen" view. For there exists something (the wave function) which is both essential to the calculation of probabilities for measurement outcomes, and specifically claimed *not* to be a beable. Oh and this mysterious entity evolves according to dynamical laws which are manifestly not lorentz invariant.

As I see it, there are simply two possibilities: the wave function is, or is not, a beable. If it is, then it's quite clear that the theory is nonlocal (but in agreement with experiment). If it isn't a beable, then we are obliged to calculate probabilities for empirical outcomes based on whatever *are* the beables (which I guess would have to be something else macroscopic) in which case I think it is obvious that we cannot make the correct predictions anymore (since basically there is nothing left of the theory)... in which case the question of whether the thing is local or not is completely moot.

not in a stochastic theory, it isn't!!!

No. I don't know how better to say it. I am perfectly willing to allow a stochastic theory. Stochastic vs deterministic, and local vs nonlocal, just aren't the same issue. Maybe you're right that it is simplest to understand the meaning of "locality" for deterministic theories, where THE outcome is DETERMINED by what's in the past lightcone of E (for a local theory) but, say, is not determined by what's in the past lightcone of E (but is instead determined by stuff happening at spacelike separation) for a nonlocal theory.

But... and here is the fundamental thing we don't seem to be able to get on the same page about... isn't the *obvious* way to generalize this to say: for stochastic theories, it makes no sense to talk about THE outcome that is DETERMINED. The whole *meaning* of a stochastic theory is that many outcomes are in principle possible, and all the theory can do is state the PROBABILITIES for the VARIOUS POSSIBLE outcomes (based on the state of the beables in the past light cone). But then the definition of locality that works fine for deterministic theories, simply goes over in the obvious way: the PROBABILITIES for the VARIOUS POSSIBLE outcomes should be "fixed" (not the OUTCOMES should be fixed, but the PROBABILITIES for different possible outcomes should be fixed) by a complete specification of beables in the past light cone. That's it. It's perfectly OK for something irreducibly random to happen that brings about the particular event E -- but still, even in an irreducibly stochastic non-deterministic theory, we can ask: does the theory predict that the probabilities for these different possible happenings depends on stuff going on at spacelike separation? If so, the theory (though still genuinely, irreducibly stochastic) is nevertheless nonlocal.

It's like this. Take one of Hurkyl's U/H/T magic coin flipping boxes (but forget about pairs of them; there's just the one). And suppose you have some theory according to which:

* If the box is in the U state and the button is pushed and the price of tea in china is above one dollar, then H or T will appear with probability 50/50

but

* If the box is in the U state and the button is pushed and the price of tea in china is less than one dollar, then H or T will appear with probability 90/10

(and suppose that the event to which "the price of tea in china" refers is spacelike separated from the pushing of the button)

Now, I don't think anybody can deny that this theory is irreducibly stochastic. I am *specifically denying* that there is any hidden variable which "really determines" whether H or T appears. It's just random. Irreducibly random. Yet this *theory* says that the *probabilities* governing the randomness (which is just the kind of dynamics this theory has, since it isn't deterministic) *depend on spacelike-separated goings-on*. I say that makes it a non-local stochastic theory.

Do you disagree with that???


I have no problem with irreducible randomness. I swear, I really don't. I'm not trying to swindle you. I *get* what it means. I get that there's a difference between a *really* stochastic theory (like OQM) and a theory in which we speak of probabilities for purely epistemological reasons (though the theory itself is completely determinstic... as happens in classical stat mech). So, sure, "the will of the gods". Fine. My only point is: it still makes sense to ask whether the gods take into consideration space-like-separated information when the exert their arbitrary/inexplicable/random/stochastic will at some event.



I think you are blurring two different issues. Merely positing a mechanism involving microscopic beables does not in any way settle the question of determinism. It's possible to posit a mechanism involving micro-beables which is deterministic, sure. It's also possible to posit a mechanism involving micro-beables which *isn't* deterministic, i.e., which is irreducibly stochastic.

Here's how I want to slice it up. First issue: are you positing a theory, or not? A theory is simply some postulated mechanism for something. For all the kinds of examples we care about in this thread, I assume such a thing would involve microscopic beables, but whatever. The point is, if your "thing" doesn't posit any beables (micro or otherwise) and/or any mechanism for something, then your "thing" isn't a theory. Indeed, it's not even *about* anything.

Now once you've got a theory, you can ask: are its dynamical equations deterministic, or not? This is a perfectly distinct question -- though of course you will get yourself very confused if you try to ask this question when you haven't yet got a theory.

Finally: is the theory *local*? This is also a perfectly distinct question from the above two, though, again, you'll get yourself awfully confused if you take something that isn't a theory (say, your preference for vanilla over chocolate) and start asking questions like "is it local"? Such questions of course have no answer.

Hmmmm. Having written all this, I guess I hope you'll just ignore all of it except the bit about the H/T box and the price of tea in china. I think, if we really disagree about something (and aren't just talking past one another) it will emerge clearly from consideration of that example.

ttn

All right. Be sure to let me know when you figure out exactly what that was.


Sounds like you're really on top of it after all.



In regard to (6), what if only one (or neither) of the boxes has its button pushed? You seem to be assuming that they both get pushed when you say P(HH) = P(TT) = 1/2, etc. But won't you allow that whether the buttons get pushed is a free choice that (say) two separated humans get to make?


I don't have (and never had) any problem with that.


This contradicts what you said just above. If *all you mean* by the statements about probability is that about half of a large collection of results will be H (the other half T), then on what grounds do you claim the theory is not deterministic? A deterministic theory (with "hidden variables") could be equally well consistent with (B). Maybe your point is that you are just *stipulating* (A). Like I said, I have no problem with that. But then (B) really makes no sense. (A) *commits* you do a stronger meaning for the probabilities ("propensities" or whatever).


But this is *precisely* what a non-deterministic theory *does do*. It says: even at the level of a single individual experiment, there is an irreducible 50/50 chance (or whatever) for the two outcomes. Of course it can't tell you which outcome will appear in any particular case -- that's just the whole point of it being stochastic. But to say that one has genuine non-determinism *is* to say something about an individual event -- namely, it is to deny that there exist any "hidden variables" which determine the outcome of that event.



Huh? What is the meaning of "impossible" other than "the probability of it happening is zero"?



Do the "local beables" for Alice's experiment include (a) whether Bob chose to push his button and (b) the outcome of Bob's experiment?

Please also see the example (from my other earlier post today) about the H/T box in which the probabilities depend on the price of tea in china. That's really what's at issue here.



This is all completely irrelevant. It's possible to have a physics theory that is deterministic, and it's also possible to have one that includes irreducible randomness. If one is worried about it, one can prove that in the latter case the probabilities (or if you prefer, call them propensities) asisgned by the theory map correctly onto frequentist probabilities. But who cares about any of that? We are all perfectly happy to just accept the possibility of stochastic theories.

The *real* question at issue here is: what does it mean for such a theory to be *local*?

Worrying about relative frequencies for lots of repeated trials is never going to address this.



I have no idea what you mean by "a statistical theory" if this is supposed to be neither nondeterministic nor deterministic. If "statistical" means deterministic, then we have been seriously talking past one another lately, which I guess would be good to realize later than never.


Yes, I understand all this. But you seem to be missing some crucial aspects of the *physics* problem. For example, experiments actually *do* (just as a sheer matter of empirical fact) have particular outcomes. So then either that particular outcome was determined from prior beables, or there was some element of irreducible randomness. It's 100% either-or. You can't just float "statistical" as an alternative by being vague about whether the underlying dynamics are or aren't deterministic.




"we have this probability distribution"... FROM WHERE? If from experiment, sure, no problem, but don't mistake that kind of empirical data for a *theory*. And if you are getting the probabilty distribution from some proposed underlying theory, then it should be possible to ask things like: is the theory deterministic? is the theory local?

You seem to just want to make an end run around all of this by (as I've thought all along) never positing a theory, and just talking about statistics. I don't object to your doing that. But I do object to your claiming to be doing something other than that, while simply doing that.



What!!??? Your theory is *deterministic*? What in bloody %&@# have we been arguing about then?



What happened to your theory being (merely 2 seconds ago) deterministic???

You have completely lost me.



OK, now I'm starting to think you're drunk or something. QM without the collapse postulate is *deterministic*, so why the heck do you describe this as a way of "sticking with nondeterminism"??? And here's an important fact that QM w/o the collapse postulate is (contrary to your statement) completely *incapable* of describing: that needles on measuring apparatuses in labs always point in particular directions (that cats are always definitely alive or dead, etc...). You talk about "the probabilities involving the outcomes of measurements"... but the whole crazy thing about QM w/o collapse is that measurements *don't have outcomes anymore*!!! That's what MWI is all about!

Ugh. I thought we were just disagreeing about some one little thing, but now it seems (not surprisingly, in retrospect) that there are huge major gulfs of confusion (about the meaning of "determinism", etc....) between us. Maybe it's not even worth pursuing. Tell me what you think of the H/T-price-of-tea-in-china example; I'd like to hear your thoughts on whether my example theory is or isn't local. But I don't have the energy (or time) to start over from scratch and figure out what "determinism" means, etc...