Is action at a distance possible as envisaged by the EPR Paradox.

[charlylebeaugosse]

A) So you think that he would not have been a microscopic realist in the EPR sense? Specifically, if two entangled particles can each be measured on either of two or more noncommuting properties X and Y (like position and momentum), and measuring the value of property X for particle #1 allows us to determine with probability 1 what the value of property X would be for particle #2 if we measured property X for particle #2, then I understand the EPR paper to suggest this means there must be a local "element of reality" associated with particle #2 that predetermines the result it would give for a measurement of property X, even if we actually measure property Y for particle #2.

B) This quote by Einstein from p. 5 of Bell's paper http://cdsweb.cern.ch/record/142461/files/198009299.pdfpapers does suggest to me he favored microscopic realism in the EPR sense:

(C) Do you really think it's true that "most physicists" would prefer to relinquish locality and not realism? If that were the case I would think Bohmian mechanics would be much more popular! Instead it seems to me that both the Copenhagen interpretation (which abandons 'realism') and the Many-worlds interpretation (whose 'realist' status depends somewhat on how you define 'realism', but it is an interpretation that many advocates say is a completely local one, see my post #8 on this thread for some references along with my own toy model illustrating how a local interpretation involving multiple copies of each experimenter can explain Bell inequality violations without being non-local) are a lot more popular, see some of the polls linked to here.

Any chance you could post some of Einstein's quotes that you think show he was not a "naive realist" or would not have agreed with the ideas in the EPR paper? If it would take too long to find them and type them up, I will understand of course.

The EPR paper, say "EPR" for short, was not written, and not even given imprimatur by Einstein, who considered the effect of choosing a measurement, not the outcome of measurements in his own analysis of the completeness of QM. Einstein never used the elements of reality as defined in "EPR". The way "EPR" uses the elements of reality would permit to deduce Bell's ineauality and Richard Friedberg did that as I said and cited in the book of Jammer you emntioned. Yet "EPR" say that elements of reality should be rooted in experiments. If one consider together only what can be measured on ONE pair, then one has at most 2 projections of the spin (in the Bohm-Bell setting), i.e., one measurement per particle, hence not enough data to have a Bell type inequality.

B) Now Einstein had some dose of realism, but so did Heisenberg, Bohr, etc... Einstein gave in 1931 a proof that microscopic realism is false when Bohr and Heisenberg believed in retrodictive compatibility of exact values for conjugate variables. It is about time to not attribute the mistakes of "EPR" to Einstein. See the book of Fine (the Shaky game) beside the book of Jammer. You may find one or two citations of Einstein where he violates microscopic realism in the sense of observables pre-existing measurement (something that happens to have been proven experimentally for EPR particles, but not for enough observables at once to get a Bell type story, of course). Why should I follow you in defining microscopic in the incomplete way used by Podolsky in "EPR"? (since I consider that "It is about time to not attribute the mistakes of "EPR" to Einstein." ) Perhaps I'd be happy with the element of reality if you accept that measurement must be made on one particle at least for any value to make sense as Podolsky hints at but does not do. Invoking a great name for a mistake once may be ok, and even valuable (e.g., to relaunch an issue mistreated by that person where that was not noticed by anyone ), but assuming Einstein was really wrong on realism, why associate his name to that? It would be better to work on science than on means for people to prove themselves smarter that Einstein (not implying you do that, but there is a bad collective behavior).

(C) The situation is a bit more complex than that as most people who declares themselves as "non-realist" have been over the years convinced that the villain that causes the contradiction between Bell's inequalities and nature is locality. Bell did not state his theorem as proving QM non-local: he knew well what he was doing, but, again, read the beginning of his 1964 paper, where he implies that that QM had been proven non-local by "EPR". Now there are many more Bohmian than I feel comfortable with and Bell is their hero (see the writtings of Sheldon Goldstein). No if you want to drag me to coocoo land, I would tell you that when I almost died (which lasted a month at least) I could not believe in god, but could not get satisfaction in many world either. I'll see later you post #8 as my navigation prowess is very limited (which is why I hopped DrC would open a vouple of new thread or tell me where to learn how to do that, and why I asked how to upload a file so that I can give reference to it, or post it in some other way).

 

[charlylebeaugosse]

But... this is an essay from 1949. How can this relate to Bell's Theorem?

One of the 2 main hypothesis of Bell theorem is that a form of microscopic realism holds trye (a strong form indeed, but let us not be too precise here). By 1931 already, most of the masters of QM, including Einstein, who was more than one of the founding fathers as he participated for a long time, and even his attacks where considered as precious bu Bohr) had been convinced that such microscopic realism did not exist in nature. This was still the main belief in 1949, and the fact that von Neumann (JVN) theorem had a false proof was irrelevant to most of these people (in fact the theories of de Broglie, later to be redone by Bohm, was implicit proof that the proof if not the statement of the non existence of HV by JVN was false). So no more that many great masters in 1964, but how did Feynman (e.g., ) react to that? The official story is that he through Clauser out of his office. Now even that second generation of masters is gone, or in part gone cucu with a few very lucid survivors and Clauser gets a Wolf Price with Aspect and Zeilinger. Thanks whoever, at least these are experimentalists (although not only for Zeilinger at least). But it seems to me that I repeat my posts over and over again.

 

[JesseM]

See the book of Fine (the Shaky game) beside the book of Jammer.

The book by Jammer is a bit expensive, but I found an https://www.amazon.com/dp/0226249476/?tag=pfamazon01-20 of the Fine book selling for just a little over three dollars, so I ordered that. Thanks for pointing me to this book, Einstein's life and thought have always interested me and this looks like an interesting reference.

You may find one or two citations of Einstein where he violates microscopic realism in the sense of observables pre-existing measurement (something that happens to have been proven experimentally for EPR particles, but not for enough observables at once to get a Bell type story, of course).

But what exactly do you mean by "observables pre-existing measurement"? For example, if we find that two entangled particles always have opposite spins when measured on the same axis A, one conclusion a local realist might make is that the particles already had a well-defined value for the property "spin on axis A" prior to measurement, and measurement simply revealed it. But a more general local realist conclusion would just be that the particles had properties prior to measurement which predetermined what result they would give if they were measured on axis A, without the assumption that the properties prior to measurement actually bear any resemblance to "spin". I don't necessarily think Einstein would have endorsed the first but I think the Einstein quote from Bell's paper that I posted suggests he would probably have endorsed the second.

No if you want to drag me to coocoo land, I would tell you that when I almost died (which lasted a month at least) I could not believe in god, but could not get satisfaction in many world either.

Well, regardless of whether many-worlds is "satisfying" on a philosophical or spiritual level (and in a certain way I think it could be, but that's probably a topic for the philosophy forum), it might at least offer hope for a local interpretation of QM that is "realist" in the sense of offering an objective picture of the world.

I'll see later you post #8 as my navigation prowess is very limited

To see the post you only need to click the link.

(which is why I hopped DrC would open a vouple of new thread or tell me where to learn how to do that, and why I asked how to upload a file so that I can give reference to it, or post it in some other way).

If you want to start a new thread, just press the "New Topic" button at the upper left of the list of thread titles on the main quantum physics forum page. For some instructions on how to include code in your posts that makes links to other pages, see http://www.themcfox.com/THE-NET/uBB-vBB-code.htm. If you want to link to a file you'll have to upload it to some internet page first, you could use a free file-hosting service like Easy Share to do this.

 

[DrChinese]

I'll see later you post #8 as my navigation prowess is very limited (which is why I hopped DrC would open a vouple of new thread or tell me where to learn how to do that, and why I asked how to upload a file so that I can give reference to it, or post it in some other way).

New thread started per your request!

 

[nismaratwork]

What about this you do not understand?


Yes of course. You tell me what I predict and then easily refute my prediction.
You know how this is called?
A strawmen.

That isn't a strawman, it's an analogy. There is a difference, and I'd like to hear your response to it. I've been reading about this "fair sampling bias" as it seems to be a major bone of contention in this thread for dozens of pages... I don't see how Dr. Chinese's question is a diversion, just an attempt to get a straight answer.

 

[charlylebeaugosse]

New thread started per your request!

Thanks a lot. What is the title of that thread (not meaning that people stick to the "subject".

 

[charlylebeaugosse]

But what exactly do you mean by "observables pre-existing measurement"? For example, if we find that two entangled particles always have opposite spins when measured on the same axis A, one conclusion a local realist might make is that the particles already had a well-defined value for the property "spin on axis A" prior to measurement, and measurement simply revealed it. But a more general local realist conclusion would just be that the particles had properties prior to measurement which predetermined what result they would give if they were measured on axis A, without the assumption that the properties prior to measurement actually bear any resemblance to "spin". I don't necessarily think Einstein would have endorsed the first but I think the Einstein quote from Bell's paper that I posted suggests he would probably have endorsed the second.

EPR particles are quite particular as there are conservation laws, but those manufest themselves only when a measurement is made. For instance, if Alice measures the normalized spin projection along axis a, Bob will for sure find the opposite value along the same axis. Since Bob can also make a measurement, say along b, one can infer (by a lengthy argument) that both particles had some definite spins, but only along these two axes, and retrodictively. Now Bohr, and in its trace, Heisenberg , admitted retrodictive coexistence of conjugate variables, not even mentioning that EPR particles was the context. To teh contrary, for particles that could hardly have been EPR particles, Einstein, Tolman and Podolsky proved in a Phys Rev Paper of 1931 that such retrodictive coexistence, and even pre-existence of a single observable to its measurement, could not be as otherwise the UP would be violated. They essentially proved a reverse time UP by showing that otherwise, an usual UP would be violated. So the confusion comes from
-a) forgetting the conservation principle, purposely, since
-b) otherwise all projections of the spin would make sense.
BUT, b) is a mistake as the pre-existence is only along directions along the observable make sense, which requires a measurement and when it comes to spin projections, for an EPR pair, at most two spin projections can be measured (one per particle).

This seems odd, but let us compare with Classical Mechanics (CM) and a better known part of QM. If a particle with total momentum zero separates in two in CM, the sum of the projections on the two particles will be zero for ALL directions (at once). In QM, the same zero sum is true for ANY direction, and any is not all. Now, thinl about measurements: in CM, if any measurement can be made, ALL measurements can be made, but by the UP, in QM, any measurement (among spin projection) but not ALL measurements of spin projevtion can be made. When it comes to QM, any is not all !.

This is only a piece of answer to your concerns, but perhaps enough for you to see the light.
I'd be delighted to explain any part that would be weak from the pedagogical point of view. But perhaps other who got that point can help making that clearer with different words. I might have though too much about that thes last years to measure what is clear and what is not, be it only because so many legends have taken control of the main pillar of physics.
(I have already told in one or more posts that in fact I came back to QM because I fell in the trap of non-locality and all the fairy tales that go with it and that only reading for months told me that I had indeed fallen in a trap. With that I disagree with Fine or at lest do not follow him , at least not yet, I must say that his book was the first trace of sanity I could find. His book then indicated others, Jammer and a series of things written by Einstein himself, instead of Podolsky, Bell, or others who played dangerous games with intentions and credos attributed to A.E. (of whom I am absolutely not an unconditional).

 

[JesseM]

Thanks a lot. What is the title of that thread (not meaning that people stick to the "subject".

That would be A Bell Theorem with no locality assumption?

 

[JesseM]

EPR particles are quite particular as there are conservation laws, but those manufest themselves only when a measurement is made. For instance, if Alice measures the normalized spin projection along axis a, Bob will for sure find the opposite value along the same axis. Since Bob can also make a measurement, say along b, one can infer (by a lengthy argument) that both particles had some definite spins, but only along these two axes, and retrodictively. Now Bohr, and in its trace, Heisenberg , admitted retrodictive coexistence of conjugate variables, not even mentioning that EPR particles was the context. To teh contrary, for particles that could hardly have been EPR particles, Einstein, Tolman and Podolsky proved in a Phys Rev Paper of 1931 that such retrodictive coexistence, and even pre-existence of a single observable to its measurement, could not be as otherwise the UP would be violated.

You mean this paper? But as far as I can tell the paper doesn't show that the particle couldn't have had hidden variables which predetermined what results it would give when its momentum was measured, just that the result of measuring its momentum would be different than its momentum before measurement (the act of measurement changes the momentum). But the concept "particle has hidden variables that predetermine what result it will give to each possible measurement" is logically different from the concept "measurement simply reveals the preexisting value for the variable being measured", my understanding is that Einstein would have endorsed the first but not the second. This is exactly the distinction I was making earlier when I said:

But what exactly do you mean by "observables pre-existing measurement"? For example, if we find that two entangled particles always have opposite spins when measured on the same axis A, one conclusion a local realist might make is that the particles already had a well-defined value for the property "spin on axis A" prior to measurement, and measurement simply revealed it. But a more general local realist conclusion would just be that the particles had properties prior to measurement which predetermined what result they would give if they were measured on axis A, without the assumption that the properties prior to measurement actually bear any resemblance to "spin". I don't necessarily think Einstein would have endorsed the first but I think the Einstein quote from Bell's paper that I posted suggests he would probably have endorsed the second.

 

[ThomasT]

For most of us the phrase "not there when nobody looks" is simply a metaphor for the non-existence of non-interacting entities.

Ok, but I still have a slight problem with that. It's either that we assume that there's an underlying reality affecting instrumental behavior, or we assume that there isn't. What do you think should be assumed?

It seems a bit silly to say that there's nothing moving from emitter to detector. Certainly the more sensible inference or hypothesis, and the one that practical quantum physics is based on, is that quantum experimental phenomena result from the instrumental probings of an underlying reality -- a reality which is presumably behaving according to some set of physical principles and which exists whether it's being probed or not.

Einstein's spooky action at a distance entails spacelike separated events determining, instantaneously, each other's existence. This is, prima facie, a nonsensical notion -- and Einstein was right to dismiss it.

Well, if QM is right, one (or both) of these things has to go -- you can't have realism and locality.

One or both of what things? EPR simply maintained that it's nonsensical to assume that the reality of one particle of an entangled pair is a function of the detection of the other particle. I don't think that the approximate correctness of qm entails that a local realistic description, or intuitive understanding, of entanglement is impossible. But then, a definitive local realistic model of entanglement hasn't been presented yet.

In our interpretation, we punt on realism, i.e., separability.

So, what, nonseparability (or inseparability) necessarily entails nonrealism? So, how would you characterize your theory/model/interpretation? As nonrealistic, but local? But this makes no sense. If it isn't, in some sense, realistic, then what does it mean to call it 'local'? Or, are you not calling it either realistic or local? Anyway, didn't you say that your model/interpretation is meant as a realistic description of the underlying ontology? This is the only problem I have with how you talk about it. If you just say that it's a simplification, perhaps even an oversimplification, of the underlying reality, which, given certain mathematical constructions and manipulations, can recover the statistical predictions of standard qm, then I have no problem with a charactarization of that sort.

(your RBW model is) not unreasonable. Especially if you're a GR person. I just find it conceptually unappealing.

Most do.

Well, given your obvious talents, are you working on anything that the rest of us might some day be able to actually understand?

Anyway, is there any way to know to what extent some theoretical construction is a description of 'reality'?

That's a thorny epistemological question. Better leave that for another thread.

But the main line of argumentation in this thread is about some people saying that Bell's stuff allows inferences about an underlying reality, and others saying that it doesn't. So, where exactly do you stand on this? Does it, or doesn't it? If Bell's stuff is just about models, and a certain class of models at that, then I can't argue with that. What's your opinion? Is it informing us about 'reality', or just informing us about what we can say about 'reality' in a certain form?

 

[ThomasT]

ThomasT: Why does the appealing or unappealing nature of an ontology matter?

By this I mean its understandability. And understanding has to do with visualizability. Why assume that the fundamental principles of our universe aren't visualizable? After all, we are part of reality. Why not assume that the principles that govern our physical universe pervade and permeate all scales of behavior and interaction? Whether you know it or not, qm is very much based on analogies from ordinary experience. A 'block' conception of reality, vis GR, contradicts our experience. Our universe appears to be evolving. Why not just assume that it 'is' evolving -- that 'change' or 'time' isn't just an illusion, but is real? Why not assume that the fundamental physical principles govern physical behavior at all scales?

Anyway, to get back to your question, if an ontological or epistemological description of 'reality' is at odds with our experience, then I think it should be seriously questioned. I think that this orientation accords with the best traditions of the scientific method. If you think otherwise, then I'm open to learning.

The only thing that is relevant is matching with empirical evidence, the science, and the math.

Wrt predicting the results of experiments, I agree. However, this isn't the only thing relevant to 'understanding' or really 'explaining' why things are as they are and why things behave as they do. Just because you can predict something doesn't mean that you understand how and why it happens. Standard qm is an example of this. The problem with the various interpretations of qm as they might relate to your question is that, ultimately, all of the various interpretations of standard qm revert or resort, in one way or another, to the statistical methods of standard qm in order to recover the predictions of standard qm. So, really, nothing is gained except a more or less acceptable, to whomever, 'realistic view', in a certain limited sense -- none of which is a definitive world view precisely because there are other 'world views' which predict exactly the same experimental results.

Wrt the OP of this thread, the question is, does the detection of a particle at detector A, spacelike separated from the 'possible' detection of a particle at detector B, determine the 'existence' of an underlying reality that, it might be assumed, determines the detection attribute registered by detector B? If you think that the answer to this must be, obviously, no, then you agree with EPR, and Einstein. Otherwise, you're a nonlocalist or spookyactionatadistanceist, in which case the onus is on you to demonstrate the physical existence of the spooky (or merely ftl?) propagations/interactions between A and B, or B and A, or whatever.

 

[charlylebeaugosse]

You mean this paper? But as far as I can tell the paper doesn't show that the particle couldn't have had hidden variables which predetermined what results it would give when its momentum was measured, just that the result of measuring its momentum would be different than its momentum before measurement (the act of measurement changes the momentum). But the concept "particle has hidden variables that predetermine what result it will give to each possible measurement" is logically different from the concept "measurement simply reveals the preexisting value for the variable being measured", my understanding is that Einstein would have endorsed the first but not the second. This is exactly the distinction I was making earlier when I said:

Non-existence of local realism means of course absence of HV a la Bell/Boh/de Broglie, since those HV are a strong form of microscopic realism (non only one has pre-existence of observable meaning and values to measurement but one also has predictability). Now, HV that are compatible with QM and such that not only what is measured but also whatever makes sense obeys he UP would be acceptable. Scrödinger and Einstein both thought that their contemporaries were too shy by sticky to the usual coordinates, and Fine explain how and why it could be legit to consider them more advanced about the next generation physics that the Copenhagen crowd, and not the contrary. Of course, they only had hopes and not a hint on how to get there, assuming that there is a there. Einstein would not have been long to dismiss the hypothesis of Bell's Theorem as not more physical than the theories of Bohm and de Broglie how which he made fun often. So Born is probably right in thinking that Einstein believed in HVs, but for sure not in the classical ones that Bell used but this is not sure as eh correspondance with Einstein shows that he did not understand anything of the EPR story. AND I cannot imagine Einstein not being saddened by someone putting words in his mouth as Bell does in the introduction of the 1964 paper and in many other places. I mean Bell did not even say "I think that Einstein believed this or that": he claims stuff as facts, a crime against basic scholarly acceptable attitudes and practices. The distinction naive-non-nave HV is for me absolutely crucial. Failing to do it lead simply to a false story and a false description of the physics models that people of importance in the field had in mind. Again, I am not a blind supporter of Einstein: I do not even consider it a big deal that a theory be not complete and I even expect that from any non-trivial theory supposed to cover a big chunk of physics. I also see good reasons to side with Bohr et al, except on the religious asp[ect of their credo and except for the fact that I consider that Schrödinger and Einstein were possibly right about the need to non-trivial new variable to get to some predictability, but a predictability that would not permit to predict nor even to give sense to conjugate variables in the generic case (EPR/ EPRB stories being special because of the conservation laws that provide an ephemeral quasi classic aspect to these particles, till first interactions (which is why such particles do not interfere as do the generic ones).

Hope that this gets clearer or that other may chip in as perhaps I am not clear enough in my English writing (you cross a border and you loose 30% on your IQ , have I been told... but what happens when you go back and forth?). All that is clear in my mind now, but I have doubt about being understood, or perhaps people do not read well enough (which is often my problem too).

PS: Thanks for the paper: I'll find the time to check, read, and answer about that. In fact, I may have to read more closely what you wrote too.
CleBG

 

[RUTA]

Ok, but I still have a slight problem with that. It's either that we assume that there's an underlying reality affecting instrumental behavior, or we assume that there isn't. What do you think should be assumed?

In our view, there is an "underlying reality" responsible for the experimental outcomes, but that "underlying reality" is not "screened off/non-interacting entities" propagating from the source to the detector. The outcomes reflect relations composing the experimental equipment, i.e., relations are fundamental, not "things" like the equipment (or trees or people, etc). In our ontology, there is a rule for the manner in which the experimental equipment ("things" in general) is constructed in the 4D "block." The RBW ontology can be depicted, see Figures 1-4 of arXiv 0908.4348, but it is non-dynamical, which I understand from a previous post you dislike. So, I wouldn't try to convince you that the RBW ontology is a powerful explanatory mechanism

One or both of what things? EPR simply maintained that it's nonsensical to assume that the reality of one particle of an entangled pair is a function of the detection of the other particle. I don't think that the approximate correctness of qm entails that a local realistic description, or intuitive understanding, of entanglement is impossible. But then, a definitive local realistic model of entanglement hasn't been presented yet.

It is largely agreed within the foundations community that the violation of Bell's inequality entails non-locality and/or non-separability (aka "realism"). The RBW philosopher of science tells me the use of "separability" rather than "realism" is nontrivial, i.e., there is much written about it. I'm not a philosopher, so I just use the terminology as he suggests.

So, what, nonseparability (or inseparability) necessarily entails nonrealism? So, how would you characterize your theory/model/interpretation? As nonrealistic, but local? But this makes no sense. If it isn't, in some sense, realistic, then what does it mean to call it 'local'? Or, are you not calling it either realistic or local? Anyway, didn't you say that your model/interpretation is meant as a realistic description of the underlying ontology? This is the only problem I have with how you talk about it. If you just say that it's a simplification, perhaps even an oversimplification, of the underlying reality, which, given certain mathematical constructions and manipulations, can recover the statistical predictions of standard qm, then I have no problem with a charactarization of that sort.

Yes, RBW is non-separable but causally local. Yes, "non-separable" means "not realism." You have to be careful here not to conflate causal locality with geometric locality, i.e., that used in differential geometry.

Well, given your obvious talents, are you working on anything that the rest of us might some day be able to actually understand?

RBW is counterintuitive but not conceptually challenging. Formally, it's a nightmare (have you ever tried to do Regge calculus?), but its ontology can be depicted -- again, see Fig 1-4 of arXiv 0908.4348. While only an arXiv paper, it has been accepted for presentation at the 2010 PSA meeting (they only take about 10% of all submissions) and it's in the "revise and resubmit" phase at Foundations of Physics, so it has received a couple favorable reviews anyway

But the main line of argumentation in this thread is about some people saying that Bell's stuff allows inferences about an underlying reality, and others saying that it doesn't. So, where exactly do you stand on this? Does it, or doesn't it? If Bell's stuff is just about models, and a certain class of models at that, then I can't argue with that. What's your opinion? Is it informing us about 'reality', or just informing us about what we can say about 'reality' in a certain form?

I use physics to make ontological inferences. In fact, that's why I do physics. Can I argue that it's reasonable to do so? I wouldn't even try.

 

[charlylebeaugosse]

One funny aspect of all that is that it is the absence of realism that permits strong correlations. Assume the observable values correlated to each other on each particles, as when one assumes locality. Then if three spin projections make sense at once, on eget another form of Bell Theorem. I one has one projection per particles (alone or in a pair), no Bell inequality but at most trivial and true ones. If one has at most two projections for a pair, still no Bell inequality but trivial and true ones.

Other funny thing, that makes me rather sad indeed: if one abandon realism, no good reason to have non-locality. So one has to violate, without any experimental baking,
- realism that intuitively should come with the superposition principle and the uncertainty principle,
- and locality that is natural with relativity

where just abandoning local realism would do. The general practice of physics should have eradicated the realism and non-locality for a long time. It was eradicated till Bell, except for a few isolated examples. Now, we have to work hard to come back to non-realism (always in the microscopic -and classical-sense -where "and classical" is to not dismiss, at least not now, the people from CQT who follow Griffith, Omnes, Hartle, Gell-Mann and now Hohenberg) and locality. One good thing is that non-realism should be taken much more seriously than ever before, as a discussion of "Interferences (the usual ones), Wheeler's delayed choice and related delayed choice issues" would reveal, I am sure.

 

[RUTA]

Other funny thing, that makes me rather sad indeed: if one abandon realism, no good reason to have non-locality. So one has to violate, without any experimental baking,
- realism that intuitively should come with the superposition principle and the uncertainty principle,
- and locality that is natural with relativity

where just abandoning local realism would do.

I assume you mean to say "if one abandons realism, there is no good reason to have locality." Then you conclude "one has to violate ... locality that is natural in relativity."

In Relational Blockworld we have locality and separability in the classical (statistical) limit of an underlying graphical spacetime structure. There is non-separability at the level of individual relations (graphical level), but Poincare invariance (which includes Lorentz invariance) holds at the graphical level.

So, the point is, you can create a model that is non-separable ("not realism") and local at the quantum level while becoming separable in a statistical limit (classical limit).

 

[DevilsAvocado]

By this I mean its understandability. And understanding has to do with visualizability. Why assume that the fundamental principles of our universe aren't visualizable? After all, we are part of reality. Why not assume that the principles that govern our physical universe pervade and permeate all scales of behavior and interaction? Whether you know it or not, qm is very much based on analogies from ordinary experience. A 'block' conception of reality, vis GR, contradicts our experience. Our universe appears to be evolving. Why not just assume that it 'is' evolving -- that 'change' or 'time' isn't just an illusion, but is real? Why not assume that the fundamental physical principles govern physical behavior at all scales?

Very nice post TT.

I agree; we all want the world to be logical and understandable. No one wants it to be horrible, incomprehensible or 'magical'. We want to know that it all works the way we 'perceive' it. We also want nature to be 'homogeneous' on all scales. It’s very logical and natural, and I agree.

But I think it could be a mistake... or at least lead to mistakes.

A classical mistake is when one of the brightest minds in history, Albert Einstein, did not like what his own field equations for theory of general relativity revealed – the universe cannot be static.

Albert Einstein was very dissatisfied, and made a modification of his original theory and included the cosmological constant (lambda: Λ) to make the universe static. Einstein abandoned the concept after the observation of the Hubble Redshift, and called it the '"biggest blunder" of his life.

(However, the discovery of cosmic acceleration in the 1990s has renewed interest in a cosmological constant, but today we all know that the universe is expanding, even if that was not Albert Einstein’s logical hypothesis.)

Another classical example is Isaac Newton, who found his own law of gravity and the notion of "action at a distance" deeply uncomfortable, so uncomfortable that he made a strong reservation in 1692.

We must learn from this.

I think that humans have a big "ontological weakness" – we think that the human mind is "default" and the "scientific center" of everything in the universe, and there are even some who are convinced that their own brain is greatest of all . But there is no evidence at all that this is the case (please note: I’m not talking about "God").

One extremely simple example is "human colors". Do they exist? The answer is No. Colors only exist inside our heads. In the "real world" there is only electromagnetic radiation of different frequency and wavelength. A scientist trying to visualize "logical colors" in nature will not go far.

Anyway, to get back to your question, if an ontological or epistemological description of 'reality' is at odds with our experience, then I think it should be seriously questioned. I think that this orientation accords with the best traditions of the scientific method. If you think otherwise, then I'm open to learning.

Have you ever tried to visualize a four-dimensional space-time? Or visualize the bending and curving of that 4D space-time?? To my understanding, not even the brightest minds can do this?? Yes, it works perfectly in the mathematical equations, but to imagine an "ontological description" that fits "our experience"... is this even possible?? Yet, we know it’s there, and we can take pictures of it in the form of gravitational lensing on the large cosmological scale:

Abell 1689 is a galaxy cluster in the constellation Virgo

Does this fits your picture of a "logical reality"...?

– What’s the weather today honey?
– I don’t know... it looks BENT??​

Wrt predicting the results of experiments, I agree. However, this isn't the only thing relevant to 'understanding' or really 'explaining' why things are as they are and why things behave as they do. Just because you can predict something doesn't mean that you understand how and why it happens.

I don’t think mainstream science claims the full understanding of EPR-Bell experiments, it’s still a paradox. What is a fact though is that either locality and/or realism have to go if QM is correct (and QM is the most precise theory we got so far):

Bell's Theorem proves that QM violates Local Realism.​

Wrt the OP of this thread, the question is, does the detection of a particle at detector A, spacelike separated from the 'possible' detection of a particle at detector B, determine the 'existence' of an underlying reality that, it might be assumed, determines the detection attribute registered by detector B? If you think that the answer to this must be, obviously, no, then you agree with EPR, and Einstein. Otherwise, you're a nonlocalist or spookyactionatadistanceist, in which case the onus is on you to demonstrate the physical existence of the spooky (or merely ftl?) propagations/interactions between A and B, or B and A, or whatever.

This is spot on the problem, in several "dimensions". There seems to be some in this thread that for real thinks that Einstein would have stuck to his original interpretation of the EPR paradox, despite the work of John Bell and the many experimentalists who are verifying QM predictions and Bell's Theorem, time after time. I’m pretty sure that this would not have been the case. Just look at the cosmological constant and Hubble Redshift. Einstein changed his mind immediately. He did not start looking for "loopholes" in Hubble's telescope or any other farfetched 'escape' – he was a diehard empiricist.

We already know that there are problems in getting full compatibility between QM and GR when it comes to gravity in extreme situations, and EPR-Bell is just another verification of this incompatibility. If we try to solve the EPR-Bell situation as a "spookyactionatadistanceist" we get problems with SR and http://en.wikipedia.org/wiki/Relativity_of_simultaneity" . If we try to solve it as a "surrealist" (non-separable/non-realism) we get the problems RUTA is struggling with.

So this question is definitely NOT solved, and it’s definitely NOT easy.

But, let’s not make it too easy by saying the problem doesn’t exist at all, because there’s still QM-incompatible gravity dragging us down, and it will never go away...

 

[charlylebeaugosse]

I assume you mean to say "if one abandons realism, there is no good reason to have locality." Then you conclude "one has to violate ... locality that is natural in relativity."

In Relational Blockworld we have locality and separability in the classical (statistical) limit of an underlying graphical spacetime structure. There is non-separability at the level of individual relations (graphical level), but Poincare invariance (which includes Lorentz invariance) holds at the graphical level.

So, the point is, you can create a model that is non-separable ("not realism") and local at the quantum level while becoming separable in a statistical limit (classical limit).

No I conclude that the Occam Razor would tell us to abandon realism so that there would not be any reason to invoke non-locality to escape the contradiction that results from Bell's inequalities. Abandoning realism would not let one have GHZ either. Hot having realism brings us back to what people thought till 1963. Now of course, the opinion of the masters (who created QM and its origins, except for de Broglie who remained realist) on realism is no more enough and to get rid of the weak statements about local realism, we have to show that microscopic realism is indeed false as the Copenhagen school though and as Einstein partly proved already in 1931 with Tolman and Podolky (then all statements against local realism would be obsolete: if there is no realism, of course there is no "local realsim", no " blue realism'; adjectives beside realism become moot , and this is what I want to prove, as a few others. But physics is not math and one often needs several "proofs" to cover as many philosophical points of view as one can: one proof of non existence of realism will convince some but not other. Decisive proofs belong to the realm of mathematics (including logic) and in physics , one has more or less decisive arguments, usually resting on experiments some of which being possibly thought experiments.

Sometimes, for very weak statements such as "local realism is false" where one would like "realism is false" (very weak because from 1927 to 1963 the admitted status was" local (naive) realism is not what one has in nature"), one can get a contradiction with experiment so obvious that one does not need many "proofs" to convince enough people. The problem here is that so many legends, misquotations etc have spoiled the subject that many people got confused, to the points that many leading experts of the next generations after the founding fathers have said and written very false statements about non-locality, e.g., that non-locality follows from the type of experiments that Clauser, Aspect, Gisin, Zeilinger, their teams and other teams have done on the Bphm-Bell version of EPR pairs.

I have realized only recently that the strength of the arguments against local realism indicate by itself that the result is probably too weak (which I claim for many reasons). This being said, when one says "proof" one should recall that one deals with proofs in the sense of Physics. For instance fair sampling is not proven, et there are better known issues.
What is clear is that the description of history that accompany Bell's theory is very much lacking precision and accuracy and this has caused many misconceptions and false statements.

This is about the very beginning of the quote. I cannot make sense of the rest as there are other things that should also be the contrary of what is written: for instance, separability relates to locality and not to realism. This being said, getting macroscopic realism out of microscopic realism is something that I believe happens but that I would be happy to see a proof of, even if a very simple model if the discussion os precise and rigorous enough: does a reference exist?

 

[charlylebeaugosse]

Any chance you could post some of Einstein's quotes that you think show he was not a "naive realist" or would not have agreed with the ideas in the EPR paper? If it would take too long to find them and type them up, I will understand of course.

The book of Fine, the Shaky Game, that you have bought contains examples and references to more. I have cited many times the ETP paper of 1931 which has been uploaded by someone these last days (perhaps you(?) after the post that I quote now). In teh Born Einstein correspondence, one see Einstein making fun twice of the theories of de Brolie and Bohm, which EXACTLY means that he considered the type of microscopic realism used by Bell for his 1964 theorem way too naive to correspond to the laws of nature. AND Einstein gave several versions of the main point of the EPR paper (or "EPR"), that he mostly formulated as "either there is non-locality (something unacceptable to Bohr according to Popper who discussed with Bohr, many times I think (?) or QM is incomplete. he considered the version of Podolsky, i.e., "EPR" too obscure and missing the main point(s). In all these proofs/arguments that Einstein wrote on QM non complete (in letters or published) he NEVER used elements of reality. As proofs belong to math including logic, you do not expect that I will prove my views on Einstein's opinion, but see Fine's book on that matter and Einstein's writing including the 1931 ETP paper and
the report of the state of the EPR subject as described by Einstein in 1933 (2 years before "EPR") given by Rosenfeld, Bohr's close collaborator where you will learn that Einstein used himself the word "paradox" in the context of the problem covered by "EPR", while many contemporary "masters" state that the word "paradox" got eventually attacked to that matter by the community of physicists who understood that something was wrong with the argument, or other nonsenses of the same kind. Some of these new "masters" got me excited with non-locality and it took me a few weeks if not a few months of intensive reading originals and books such as Fine's and some by Jammer for instance (but also other sources) to see how deeply and widely polluted the subject was. Many disciplines would collapse with that level of non-professionalism by the masters. I cannot imagine something of that kind happening in math (and this is not directly because of the difference of nature between math and physics). Well, I prefer to write about physics issues as I am not an historian anyway.

 

[RUTA]

This is about the very beginning of the quote. I cannot make sense of the rest as there are other things that should also be the contrary of what is written: for instance, separability relates to locality and not to realism.

Separability relates to realism, not causal locality. Are you thinking "locality" in the sense of a differentiable manifold being locally homeomorphic to the reals? That's constitutive locality, not causal locality.

This being said, getting macroscopic realism out of microscopic realism is something that I believe happens but that I would be happy to see a proof of, even if a very simple model if the discussion os precise and rigorous enough: does a reference exist?

We get macroscopic separability from microscopic nonseparability in arXiv 0908.4348. We can't discuss that paper here, it's still under review (revise & resubmit stage). I only made reference to it as an example of nonseparable and local going to separable and local in a statistical sense. I have trouble following your posts and (mistakenly?) thought you were claiming that one couldn't have a nonseparable and local underlying theory.

 

[zonde]

1. Nothing. What's your point?

I was explaining what is prediction for full sample from LR perspective.

2. You are the local realist, what do YOU predict for the xxx case? Does it match QM or not?

In case of full sample LR prediction is that all possible outcomes happen with equal probabilities:
P(H'H'H')=1/8
P(H'H'V')=1/8
P(H'V'H')=1/8
P(H'V'V')=1/8
P(V'H'H')=1/8
P(V'H'V')=1/8
P(V'V'H')=1/8
P(V'V'V')=1/8
It matches QM with complete decoherence.

QM prediction for ideal case (no decoherence at all) was:
P(H'H'H')=1/4
P(H'H'V')=0
P(H'V'H')=0
P(H'V'V')=1/4
P(V'H'H')=0
P(V'H'V')=1/4
P(V'V'H')=1/4
P(V'V'V')=0

Observed result was roughly:
P(H'H'H')=7/32
P(H'H'V')=1/32
P(H'V'H')=1/32
P(H'V'V')=7/32
P(V'H'H')=1/32
P(V'H'V')=7/32
P(V'V'H')=7/32
P(V'V'V')=1/32

 

[DevilsAvocado]

zonde, it would be interesting if you could reply to the last question in https://www.physicsforums.com/showpost.php?p=2837946&postcount=1350".

 

[DevilsAvocado]

In Relational Blockworld, if the entity "isn't there," i.e., is "screened off," it doesn't exist at all. So, the answer to your question is that there is no Moon to wonder

RUTA, I have been thinking (for once ).

If everything that is "screened off" does not exist, I guess that photons emitted in an earlier "process", "traveling" thru vacuum without any interaction, do not exist, right?

But if the photons in the http://en.wikipedia.org/wiki/CMB" (CMB) that have been traveling thru the space since the "last scattering", 400 000 years after the Big Bang, did not exist until they bumped into one of humans apparatus – How can the CMB be stretched out (redshifted) during billions of years if it DID NOT EXIST...??

We do have pretty good data of the CMB from http://en.wikipedia.org/wiki/Cosmic_Background_Explorer" :

[PLAIN]http://upload.wikimedia.org/wikipedia/commons/thumb/6/6c/PLANCK_FSM_03_Black.jpg/800px-PLANCK_FSM_03_Black.jpg

How do you explain this?

 

[zonde]

But... this is an essay from 1949. How can this relate to Bell's Theorem?

I don’t agree. As you state yourself:

I absolutely do not think Einstein would start looking for farfetched loopholes etc. He was way too smart for that. I think he would have accepted the situation, for the start of something new.

Well, you was asking about hypothetical "what if" situation.
There are no solid arguments to defend either position so I think that we can safely leave it at that - we disagree.

Well, this is pretty obvious, isn’t it?? The completely "new thing" is when polarizers are nonparallel!? Einstein would of course immediately have realized that his own argument had boomeranged on him:

no action on a distance (polarisers parallel) ⇒ determinism
determinism (polarisers nonparallel) ⇒ action on a distance​

Here I would not agree that this ("polarisers nonparallel") is completely new thing because it is essentially HUP.

You are trying to ascribe to Einstein non-contextual determinism a la Bell. But that was not position of Einstein. His position was Ensemble Interpretation and it's essence is contextuality. Ensemble is a factor in determining measurement outcome for individual photon so it is related to context of individual measurement.

Are you saying that if we run an EPR-Bell experiment as I proposed, we "should expect complete decoherence of entanglement" and the experiment would fail? No expected QM statistics??

Yes, experiment would fail.
When you take theoretical QM predictions you disregard experimental imperfections. That is so more or less everywhere in theory.
But when you come to experimental verification you substitute idealized theoretical prediction with something like: theoretical prediction + experimental imperfections, with the aim to minimize these experimental imperfections.
For QM one of possible experimental imperfections has a name "decoherence" except if you specifically explore decoherence.
So when the effect from "experimental imperfections" is too high experiment is a failure. But it does not falsify theory. It is simply not useful in this case.

So the answer to your question: "No expected QM statistics?" is that result of experiment would not allow to determine QM statistics as decoherence would be too high.

 

[JesseM]

Non-existence of local realism means of course absence of HV a la Bell/Boh/de Broglie,

But is there any reason to think Einstein believed in the "non-existence of local realism"?

since those HV are a strong form of microscopic realism (non only one has pre-existence of observable meaning and values to measurement but one also has predictability). Now, HV that are compatible with QM and such that not only what is measured but also whatever makes sense obeys he UP would be acceptable.

But what does it even mean for hidden variables to obey the uncertainty principle? For example, suppose we believe that measurement invariably alters the momentum of a particle, so that the momentum you measure at time T is always different from the momentum immediately before measurement. But suppose that before measurement, there were already hidden variables associated with the particle that predetermined what momentum would be measured if the particle's momentum was measured at time T. Would Einstein have said that such a theory was impossible? What if it was impossible to measure all the hidden variables simultaneously, so it was impossible to use them to determine both the position and momentum at a single time?

Anyway, did Einstein consider the uncertainty principle to be "sacred", not to be overturned even in future theories? Some of his thought-experiments with Bohr tried to find ways to violate it, though perhaps Bohr's answers convinced him that it was a basic principle of nature.

Einstein would not have been long to dismiss the hypothesis of Bell's Theorem as not more physical than the theories of Bohm and de Broglie how which he made fun often.

Bohm and de Broglie was a speculative idea about non-local hidden variables, but Bell gave a general proof that a wide class of local hidden variables theories were incompatible with QM--do you think Einstein would have denied this conclusion?

So Born is probably right in thinking that Einstein believed in HVs, but for sure not in the classical ones that Bell used but this is not sure as eh correspondance with Einstein shows that he did not understand anything of the EPR story.

What do you mean by "classical ones"? What would a non-classical hidden variables theory look like?

 

[DevilsAvocado]

Here I would not agree that this ("polarisers nonparallel") is completely new thing because it is essentially HUP.

Is this really correct?? According to Wikipedia:

In quantum mechanics, the Heisenberg uncertainty principle states by precise inequalities that certain pairs of physical properties, like position and momentum, cannot simultaneously be known to arbitrary precision. That is, the more precisely one property is measured, the less precisely the other can be measured. In other words, the more you know the position of a particle, the less you can know about its velocity, and the more you know about the velocity of a particle, the less you can know about its instantaneous position.

And the statistics of nonparallel polarizers is all about the QM version of Malus' law: cos^2(a-b)

I don’t get it? Are saying that Einstein had already discovered the "things" Bell did later?

Yes, experiment would fail.

Unless you are saying that every EPR-Bell experiment will fail every time no matter what the "interval" and setup – according to you – this is very strange.

If you are not saying this I can, even as a layman, guarantee you that the QM statistics will be the same regardless if the intervals between the entangled pairs is 100 microseconds, 100 seconds, 100 minutes, 100 days, or 100 months. Expecting anything else is not very bright. It’s like expecting different probabilities from throwing dice with 1 min intervals, or 1 hour intervals...

If you are saying that every EPR-Bell experiment will fail every time no matter what, I can only conclude that this is not the opinion in mainstream science:

http://plato.stanford.edu/entries/bell-theorem/"
...
In the face of the spectacular experimental achievement of Weihs et al. and the anticipated result of the experiment of Fry and Walther there is little that a determined advocate of local realistic theories can say except that, despite the spacelike separation of the analysis-detection events involving particles 1 and 2, the backward light-cones of these two events overlap, and it is conceivable that some controlling factor in the overlap region is responsible for a conspiracy affecting their outcomes. There is so little physical detail in this supposition that a discussion of it is best delayed until a methodological discussion in Section 7.

But let’s put like this, to get by this little "problem", suppose sometime in the future there will be 100% detection efficiency in EPR-Bell experiments.

How would the Ensemble Interpretation handle EPR-Bell experiments with very long intervals between the entangled pairs, where is the "memory" located that handle the QM statistics correct?

Or even worse: If a very advanced civilization in the future decided to setup 1000 individual EPR-Bell experiments, separated by 1 lightyear, and fire one entangled pair at relative angle 22.5º, in the same moment, and then gather the 1000 individual results to check the collective QM statistics (they will of course get cos^2(22.5) = 85%).

The obvious question: How do you handle this scenario in the Ensemble Interpretation??

 

[RUTA]

RUTA, I have been thinking (for once ).

If everything that is "screened off" does not exist, I guess that photons emitted in an earlier "process", "traveling" thru vacuum without any interaction, do not exist, right?

But if the photons in the http://en.wikipedia.org/wiki/CMB" (CMB) that have been traveling thru the space since the "last scattering", 400 000 years after the Big Bang, did not exist until they bumped into one of humans apparatus – How can the CMB be stretched out (redshifted) during billions of years if it DID NOT EXIST...??

We do have pretty good data of the CMB from COBE. How do you explain this?

Very good question! I understand that Wheeler and Feynman gave up on direct action for cosmological reasons, i.e., the universe is so empty that most photons will never hit anything and therefore will never contribute to the action. I saw a talk on direct action at Imperial College last month where the speaker was trying to resolve this "problem" via horizons. After my talk, that speaker was very interested to know how we handled this problem. He was surprised when I told him we don't have photons, so we don't have to account for "non-interacting entities." The CMB represents relations between "here and now" and "there and then." That's all there is to it.

Now of course, we have to change GR accordingly and that's nontrivial. We're using direct action Regge calculus (which is NOT how it was intended to be used) and that approach is nasty. We're only now working on the 2-body freefall problem. We'll study that solution to obtain a direct action explanation for redshift (which also gives us time difference). Once we have that, we'll do the 2-body orbital problem to see what we have to say about dark matter.

Our nonseparable approach to classical gravity will be empirically distinct from GR. Exactly how it differs is what we're working on now. If it passes existing empirical data, then we'll propose an experiment where it differs. If it passes that test, then perhaps we'll understand why GR thwarted quantization. You realize how unlikely these things are? We have a much better chance of winning the mega lottery

 

[zonde]

Is this really correct?? According to Wikipedia:

And the statistics of nonparallel polarizers is all about the QM version of Malus' law: cos^2(a-b)

I don’t get it? Are saying that Einstein had already discovered the "things" Bell did later?

No, I don't think Einstein had discovered contradictions that Bell discovered. But it might be that he didn't considered anything like naive model of Bell as anything plausible.

Unless you are saying that every EPR-Bell experiment will fail every time no matter what the "interval" and setup – according to you – this is very strange.

No, I am not saying this.

If you are not saying this I can, even as a layman, guarantee you that the QM statistics will be the same regardless if the intervals between the entangled pairs is 100 microseconds, 100 seconds, 100 minutes, 100 days, or 100 months. Expecting anything else is not very bright. It’s like expecting different probabilities from throwing dice with 1 min intervals, or 1 hour intervals...

Dice throwing does not suffer from decoherence where observing QM statistics does.

If you are saying that every EPR-Bell experiment will fail every time no matter what, I can only conclude that this is not the opinion in mainstream science:

But let’s put like this, to get by this little "problem", suppose sometime in the future there will be 100% detection efficiency in EPR-Bell experiments.

How would the Ensemble Interpretation handle EPR-Bell experiments with very long intervals between the entangled pairs, where is the "memory" located that handle the QM statistics correct?

Or even worse: If a very advanced civilization in the future decided to setup 1000 individual EPR-Bell experiments, separated by 1 lightyear, and fire one entangled pair at relative angle 22.5º, in the same moment, and then gather the 1000 individual results to check the collective QM statistics (they will of course get cos^2(22.5) = 85%).

The obvious question: How do you handle this scenario in the Ensemble Interpretation??

You are mixing in 100% detection efficiency but I don't understand what role it plays in you argument. In case of 100% detection efficiency you will observe complete decoherence between H and V modes. So QM statistics will reduce to product state statistics (they are QM statistics as well).

About "global RAM" I explained that there is no such thing so if some of the pairs are not within each other's coherence interval inside common measurement equipment you can not observe entanglement but only QM statistics that describe product state.

 

[DevilsAvocado]

You are mixing in 100% detection efficiency but I don't understand what role it plays in you argument. In case of 100% detection efficiency you will observe complete decoherence between H and V modes. So QM statistics will reduce to product state statistics (they are QM statistics as well).

About "global RAM" I explained that there is no such thing so if some of the pairs are not within each other's coherence interval inside common measurement equipment you can not observe entanglement but only QM statistics that describe product state.

Okay, we probably misunderstand each other. Could you in simple English briefly describe how the Ensemble Interpretation explains what happens in an EPR-Bell experiment (let’s pretend it’s 100% perfect to avoid the logjam about loopholes etc)? And what is included in the "Ensemble"?

 

[DevilsAvocado]

Very good question!

Thanks RUTA! It’s the first time a Professor of Physics gave me credit! I’m buying champagne for tonight!

I understand that Wheeler and Feynman gave up on direct action for cosmological reasons, i.e., the universe is so empty that most photons will never hit anything and therefore will never contribute to the action.

Wow!! Wheeler and Feynman did struggle with this!? (now I have to buy two bottles ) Pardon a layman, but what is "direct action"? Is it a part of the time-symmetric http://en.wikipedia.org/wiki/Wheeler%E2%80%93Feynman_absorber_theory" ?

I saw a talk on direct action at Imperial College last month where the speaker was trying to resolve this "problem" via horizons. After my talk, that speaker was very interested to know how we handled this problem. He was surprised when I told him we don't have photons,

Hehe, kinda understand the speaker ... "we don't have photons" ... huh??

Now of course, we have to change GR accordingly and that's nontrivial. We're using direct action Regge calculus (which is NOT how it was intended to be used) and that approach is nasty. We're only now working on the 2-body freefall problem. We'll study that solution to obtain a direct action explanation for redshift (which also gives us time difference). Once we have that, we'll do the 2-body orbital problem to see what we have to say about dark matter.

This is very interesting. I can see that you have a lot of work to do. Modifying GR is probably not an easy task. Is this the http://en.wikipedia.org/wiki/Two-body_problem" you are working on? (Edit: Below is of course the 2-body orbital problem, sorry... )

[URL]http://upload.wikimedia.org/wikipedia/commons/0/0e/Orbit5.gif[/URL]

then perhaps we'll understand why GR thwarted quantization

Great! Amazing! Exciting! I admire you guys!

You realize how unlikely these things are? We have a much better chance of winning the mega lottery

Well, people win a lot of money on the lottery every day. It’s just a matter of probability (and bet).

 

[Loren Booda]

Can Planck black holes be shown to violate the Bell inequality?