Prior interaction as an unwarranted assumption of EPR

[glengarry]

"Prior interaction" as an unwarranted assumption of EPR

I think it should be understood that the concept of "entanglement" is not native to the mathematical formalism of QM, but only comes to us with Einstein's assumption (in the EPR paper) that there is an initial, composite wavefunction that can somehow later split into two simple wavefunctions, and that an observed result of one of these simple wavefunctions will dictate the exact state of the other wavefunction.

But the idea that there was a prior "interaction" that had occurred that led to a composite wavefunction is already a classical, spacetime picture that was never warranted by the formalism of QM itself. That is, the formalism offers no explanation as to how certain theoretical entities (i.e. "particles") may possibly relate to one another. In other words, a single "observable" yields only a single quantity; at no point is there ever any mention of multiplicity.

But for some reason, Einstein was able to get away with making this assumption, because if not, then QM would have been exposed as an exercise in tautological thought. That is, the notion that a simple system (as represented by a wavefunction) can be observed in order to yield a particular result does not offer much in the way of compelling physics. So, the idea of complexity had to be allowed into the picture in order to elevate QM into the pantheon of theories that are understood to be dynamically interactive (i.e. "physical").

Furthermore, the very idea that wavefunctions are capable of joining and splitting relies upon a kind of mathematical metaphysics that is simply not permitted from within the canonical understanding of QM as a mere predictive formalism that can only relate to classical spacetime descriptions by way of the principle of complementarity.

From where I stand, it makes sense to assert that Bell's theorem (and the associated question of particulate "entanglement") is only meaningful when this unwarranted assumption is allowed to remain in effect. That is, the only time that we can even start to speak rigorously about "relations" between "systems" is when we delve into quantum field theory, and when we do this, the mathematical simplicity of pure, formal QM begins to degenerate into complexities that are anything but pleasant to contemplate. In other words, what had previously been a "clean" formalism that is completely described by the application of linear operators on a field of values now becomes an exercise in mathematical "sloppiness" that is known as perturbation theory.

 

[DrChinese]

I think it should be understood that the concept of "entanglement" is not native to the mathematical formalism of QM, but only comes to us with Einstein's assumption (in the EPR paper) that there is an initial, composite wavefunction that can somehow later split into two simple wavefunctions, and that an observed result of one of these simple wavefunctions will dictate the exact state of the other wavefunction.

But the idea that there was a prior "interaction" that had occurred that led to a composite wavefunction is already a classical, spacetime picture that was never warranted by the formalism of QM itself. That is, the formalism offers no explanation as to how certain theoretical entities (i.e. "particles") may possibly relate to one another. In other words, a single "observable" yields only a single quantity; at no point is there ever any mention of multiplicity.

But for some reason, Einstein was able to get away with making this assumption, because if not, then QM would have been exposed as an exercise in tautological thought. That is, the notion that a simple system (as represented by a wavefunction) can be observed in order to yield a particular result does not offer much in the way of compelling physics. So, the idea of complexity had to be allowed into the picture in order to elevate QM into the pantheon of theories that are understood to be dynamically interactive (i.e. "physical").

Furthermore, the very idea that wavefunctions are capable of joining and splitting relies upon a kind of mathematical metaphysics that is simply not permitted from within the canonical understanding of QM as a mere predictive formalism that can only relate to classical spacetime descriptions by way of the principle of complementarity.

From where I stand, it makes sense to assert that Bell's theorem (and the associated question of particulate "entanglement") is only meaningful when this unwarranted assumption is allowed to remain in effect. That is, the only time that we can even start to speak rigorously about "relations" between "systems" is when we delve into quantum field theory, and when we do this, the mathematical simplicity of pure, formal QM begins to degenerate into complexities that are anything but pleasant to contemplate. In other words, what had previously been a "clean" formalism that is completely described by the application of linear operators on a field of values now becomes an exercise in mathematical "sloppiness" that is known as perturbation theory.

Besides this being wrong, it is also flat wrong. 2 particles can be entangled that share no common source. In fact, yesterday I read where 3 independently created photons were entangled. There is no requirement that they EVER existed at the same time in any reference frame. In other words, their wave functions (if they are separate particles that is) were never overlapping. So that pretty well blows you idea that this is part of the Bell reasoning out the window, wouldn't you agree? Of course, QM DOES predict the observed behavior and it reflects non-separable entangled particle behavior, not that of clasiccal particles in classical spacetime. (These are quantum particles in quantum spacetime - whatever that may be.)

 

[glengarry]

I feel that it is absolutely urgent that we disabuse ourselves of the notion that "quantum mechanics"--as a mere formalism which applies linear operators to a field of values an infinite number of times so as to "realize" a "prediction" that is given by the inner product of vectors in state space--has any kind of relevance to the world of empirical phenomena.

I have said this before and I will repeat it here: the mental picture that speaks of "particles" is nothing other than a pedagogical tool that allows novice minds to come to grips with a fairly imposing mathematical edifice. This idea is akin to the thought that we typically learn to count by way of quantifying "real" objects like apples. But the apples are not any part of the theory of counting.

My point here is not to make some kind of positive statement about the nature of reality-as-experienced. My point, rather, is to show that theoretical physics, finally, is about our ability to develop self-consistent lines of reasoning that are manifestly compelling. There should not be any "sacred cows" (e.g. Bell's theorem) whose assumptions that we are afraid to question.

Finally, if QM truly does "predict" entangled particle behavior, I would expect that this would have been a major point of interest in the decade before the EPR paper when the formalism was being hashed out. My point is that without the contributions of someone (i.e. Einstein) who was viscerally opposed to the idea that physical reality can possibly be "described" by probabilistic wavefunctions, then there would be no such thing as Bell's theorem.

 

[DrChinese]

I feel that it is absolutely urgent that we disabuse ourselves of the notion that "quantum mechanics"--as a mere formalism which applies linear operators to a field of values an infinite number of times so as to "realize" a "prediction" that is given by the inner product of vectors in state space--has any kind of relevance to the world of empirical phenomena.

...

My point, rather, is to show that theoretical physics, finally, is about our ability to develop self-consistent lines of reasoning that are manifestly compelling. There should not be any "sacred cows" (e.g. Bell's theorem) whose assumptions that we are afraid to question.

Finally, if QM truly does "predict" entangled particle behavior, I would expect that this would have been a major point of interest in the decade before the EPR paper when the formalism was being hashed out. My point is that without the contributions of someone (i.e. Einstein) who was viscerally opposed to the idea that physical reality can possibly the "described" by probabilistic wavefunctions, then there would be no such thing as Bell's theorem.

Well, I think 1935 was a reasonable time for folks (EPR) to have discovered this. And I think EPR's contribution is in fact enormous. Obviously, it took years for the full implications of QM to be discovered and I have no idea how you expected it to be fully understood in 1927. Bell was 1965, almost 40 years later. Maybe you would have discovered it earlier, but it took other great minds longer to consider and conceive the implications of entanglement.

As to QM's relevance to empirical phenomena: what exactly is it that you think it doesn't do? I mean, assuming you are criticizing it as a "mere formalism". Doesn't look too bad from here to me.

 

[glengarry]

It isn't meant to be a criticism. The term "mere" is meant to emphasize that QM is only a mathematical system of thought, and that to think of it as anything "more" is to confuse matters and to therefore do it injustice, and to do injustice to the rest of us, who have a stake in whether or not the concepts of theoretical physics are "believable."

If you want to know my honest opinion of what QM is all about, here it is. I think that the general notion of "quantum theory" is nothing but an inflection point in our evolution as a species that is slowly but surely discovering its own rationality. That is, there has always been a split between the notions of reality-as-experienced and reality-as-such. The problem, however, is that the subtle arguments that give philosophers reason to make such distinctions are severely "levelled down" when it comes to discussions in public forums like these. So, the problem with QM is that it is the first "generally accepted" logical construction that includes bits-and-pieces of both kinds of reality.

We can understand the wave theories of de Broglie and Schrodinger as attempts to flesh out a way of conceptually approaching the idea of reality-as-such. But this paradigm was radically different from the "classical" paradigm wherein the sole topic under discussion is the prediction of the various phenomena within reality-as-experienced.

So now, it almost becomes a necessary reaction on the part of the establishment (represented by Max Born) to "interpret" the wavefunction as manifesting a field of probabilities rather than an independently subsisting "something" whose future behavior is anything but certain. But I don't think that it does any of us any good to ignore the original inspiration behind contemporary QM: that there is something fundamentally "oscillatory" about the natural order. And furthermore, I think that all of the talk about what canonical QM is "really" supposed to represent only serves to distract us from coming to terms with an immediately intuitive "picture" of physical reality that necessarily includes the notions of continuity and harmonic oscillation.

Theoretical physics currently finds itself in the midst of a century long struggle to decide whether it wants to finally take the mathematical leap (i.e. becoming Platonic idealism) so that our creative impulses can finally be directed towards questions of physical reality; or whether it wants to remain mired within the mode of philosophical empiricism, which always sees "theory" as a handmaiden to brute, unthinking material sensibility.

On a personal note, about a year-and-a-half ago, I experienced a month-long meditation on the nature of physical reality that finally allowed me to rid myself of the "cult of Aristotle" that the modern physics establishment always pays homage to. I came up with an idea of physical reality that is at once immediately intuitive (it deals in independently subsisting geometric forms), and that raises interesting mathematical questions.

But seeing as I am homeless and mentally unstable, I am really in no position to seek after official recognition for my ideas. I have no patience for writing books/articles, but I do enjoy the wide-openness of public discussion forums. The only thing that I can do is to try to get people to open themselves up to the possibility of taking the "Platonic turn", so that we can start discussing things that, in my opinion, will turn out to be much more fruitful when our lives are said and done.

I have nothing against the founders of probabilistic QM, Bell, or anyone else. In fact, I feel that I am operating within the spirit of these people because they would not have been able to push the intellectual envelope of physical thought without stepping on the toes of those who preceded them.