Bohmian Mechanics

Originally posted by KazetNagorra
It's a bit more subtle than that. Take for instance the Heisenberg uncertainty principle, which basically is just a statement that wave functions exist in the L^2 Hilbert space. For many simple cases, we know that the wave function evolves deterministically in time. But the description as wave functions means that a particle really doesn't have such a t ...[text shortened]... oes show that the "classical" picture of particles having fixed position and momentum does fail.

Ah ha, yes, I almost edited my earlier post to say something about the Heisenberg uncertainty principle, because I do understand that quantum particles are not simply miniature billiard balls with definitive locations. As I recall they are typically treated as "probability clouds" and all that good stuff, and that certainly is a sound approach given what we know. So, at a given point in time, there's a nonzero probability that a given electron in an apple seed on Earth could flit over to the Andromeda galaxy and then flit back. I guess all I'm saying is that there may be a good reason for an electron to do that, and it isn't something that happens on a whim -- without causation.

Originally posted by black beetle
OK, it 's very close now at my local time zone.
MXmas to you all and yours,
May You Always Be Happy
😵

Don't get too plastered. That's what New Years Eve is for. 😉

Originally posted by Soothfast
Ah ha, yes, I almost edited my earlier post to say something about the Heisenberg uncertainty principle, because I do understand that quantum particles are not simply miniature billiard balls with definitive locations. As I recall they are typically treated as "probability clouds" and all that good stuff, and that certainly is a sound approach given what ...[text shortened]... for an electron to do that, and it isn't something that happens on a whim -- without causation.

If you consider a particle scattering from some potential well, such that it would reflect in the classical case (a barrier higher than the kinetic energy of the particle), some part of the wave packet will tunnel through. The whole process is described completely deterministically. The "problems" (probalistic stuff) really only arise when we consider "measurement" of particles (tunneled or not).

Originally posted by Soothfast
I wasn't aware that David Bohm was involved in writings about philosophy of mind and neuropsychology. I reckon I ought to get a book of his, or two!

But I agree with others who say quantum mechanics, as a formal construct, is logically consistent. It is "merely" the interpretation of its consequences, and the consequences of quantum physics in general ...[text shortened]... mechanics for mathematicians, using the notation and logical constructs that I'm accustomed to.

Edit: "But I agree with others who say quantum mechanics, as a formal construct, is logically consistent. It is "merely" the interpretation of its consequences, and the consequences of quantum physics in general, that I have qualms with."

Of course it is logically consistent.
As regards the interpretation of the consequences, Bohm's interpretation is perfectly good to me, for I see Kosmos as a single nexus of conditions in which everything simultaneously depends on, and is depended on by, everything else😵

The post that was quoted here has been removed

I read Lee Smolin's "The Trouble With Physics" earlier this year, where he makes a similar case. In essence, at least in the area of physics concerned with Grand Unified Theories, if you're not working on string theory you're very unlikely to get grants, tenure, or your papers published. It's verging on becoming a religion.

In the introduction to the book "Quantum Theory: A Mathematical Approach" (a book I'm weighing against the text by Brian Hall I linked to earlier) Peter Bongaarts notes that in the past mathematics and physics in many regards formed an integrated subject, with people such as Newton, Gauss, Riemann, Hilbert, von Neumann, Weyl, and others working in both fields. He goes on to say:

All this is a thing of the past. From the 1950s onward physics and mathematics parted company, or rather mathematics underwent a drastic change in the way is was formulated, largely due to the Bourbaki movement. It became more abstract, more "formal".... Another cause was the growing specialization in all of science and, more recently, the increasing publication pressure leading to much narrowly focused short-term research. The language of mathematics is now very different from that of physics.

I can see the hurdles presented to a mathematician by training who takes a fancy to quantum theory or general relativity. It's not simply something so "trivial" as notation. The way physicists "do" mathematics is just odd, "loose," and fraught with questionable leaps of logic and "hand-waving." It's reflected in physics textbooks right down to the introductory level. In this way physicists have erected an enormous barrier around their subject, so that stands alone on an island. Mathematics has evolved and modernized, but physicists are still working with antiquated notions and notation fraught with "infinitesimals" and other oddities that sweep a lot of dirt under the carpet. Physicists may have moved beyond "classical physics" to "modern physics," but they have not adopted modern mathematics across the board. Their textbooks still use "classical mathematics," especially at the introductory level. Put another way, physicists do mathematics today the way mathematicians did mathematics in the 19th century.

I know I'm not characterizing this quite right, because the barrier is a subtle one that is hard to nail down. So, doubtless physicists will pounce on me here. I hasten to acknowledge that underlying their antiquated notation and weird mathematical dialects, they are still doing serious mathematics that ultimately rests on a sound foundation. General relativity and quantum theory certainly have solid, logical foundations. But none of it is reflected in the literature. If you're not steeped in the "culture" starting at the freshman level, it is very difficult for an outsider to get in. Physics needs to clean up and modernize its mathematics, desperately. The essence of string theory, quantum theory, and relativity theory is all purely mathematical. More communication between mathematicians and physicists, as existed a century ago, would probably reinvigorate and revolutionize physics in a way that hasn't happened in, well, about a century.

Could pilot-wave theory make a comeback?

http://www.wired.com/2014/06/the-new-quantum-reality

Erratum: "silicon oil" likely should be spelled "silicone oil."

Originally posted by Paul Dirac II
Could pilot-wave theory make a comeback?

http://www.wired.com/2014/06/the-new-quantum-reality

Erratum: "silicon oil" likely should be spelled "silicone oil."

This article is saying some things I've been thinking for a long time. And this is interesting:

At the Solvay conference, Einstein objected to a probabilistic universe, quipping, “God does not play dice,” but he seemed ambivalent about de Broglie’s alternative. Bohr told Einstein to “stop telling God what to do,” and (for reasons that remain in dispute) he won the day. By 1932, when the Hungarian-American mathematician John von Neumann claimed to have proven that the probabilistic wave equation in quantum mechanics could have no “hidden variables” (that is, missing components, such as de Broglie’s particle with its well-defined trajectory), pilot-wave theory was so poorly regarded that most physicists believed von Neumann’s proof without even reading a translation.

More than 30 years would pass before von Neumann’s proof was shown to be false, but by then the damage was done. The physicist David Bohm resurrected pilot-wave theory in a modified form in 1952, with Einstein’s encouragement, and made clear that it did work, but it never caught on. (The theory is also known as de Broglie-Bohm theory, or Bohmian mechanics.)

So a bloomin' mathematician may have been the railroad switch that shunted much of 20th-century physicist groupthink onto the "quantum physics is magic" track. Even Richard Feynman has said that the double-slit experiment "is impossible, absolutely impossible, to explain in any classical way" -- which Bohmian mechanics just might demonstrate to be hogwash.

I think Sheldon Goldstein hits the nail on the head:

The neglect [of Bohmian mechanics] continues. A century down the line, the standard, probabilistic formulation of quantum mechanics has been combined with Einstein’s theory of special relativity and developed into the Standard Model, an elaborate and precise description of most of the particles and forces in the universe. Acclimating to the weirdness of quantum mechanics has become a physicists’ rite of passage. The old, deterministic alternative is not mentioned in most textbooks; most people in the field haven’t heard of it. Sheldon Goldstein, a professor of mathematics, physics and philosophy at Rutgers University and a supporter of pilot-wave theory, blames the “preposterous” neglect of the theory on “decades of indoctrination.” At this stage, Goldstein and several others noted, researchers risk their careers by questioning quantum orthodoxy.

Originally posted by Soothfast
This article is saying some things I've been thinking for a long time. And this is interesting:

At the Solvay conference, Einstein objected to a probabilistic universe, quipping, “God does not play dice,” but he seemed ambivalent about de Broglie’s alternative. Bohr told Einstein to “stop telling God what to do,” and (for reasons that remain in di ...[text shortened]... d several others noted, researchers risk their careers by questioning quantum orthodoxy.

The problem with the de Broglie-Bohm theory is that if it makes the same predictions as traditional quantum mechanics then it has this pointless extra metaphysical entity in it and if it does make different predictions then it's ruled out by experiment (but see below). As I understand dBB theory the pilot wave is identical to the wavefunction in QM but instead of a probabilistic interpretation they have a classical particle guided by the pilot wave. But in order for it to reproduce the results of the Standard Model the pilot waves have to interact - and importantly self-interact - in the same way, otherwise the couplings and masses won't run. So what determines all the interactions is the pilot wave and I'm left wondering about what exactly the particle in dBB does.

If it is the dBB particle is allowed to interact the problems become worse. You then have one momentum connected with the pilot wave and one momentum associated with the particle. Why does the motion of the particle not affect what the pilot wave is doing?

Worse still I think it is very hard to make it compatible with Quantum Field Theory as the number of particles isn't conserved so there has to be some way for a photon to split into an electron and a positron - not a problem for a Quantum Field but I think it is for the cannon ball like particle as it's number has to change. If the particles are pointlike and classical their cross-section for collision is zero and it is difficult to see how interactions such as matter anti-matter annihilation can happen. If the uncertainty is produced by our lack of knowledge of the initial state of the particle then it is a hidden variable theory and Bell's theorem applies. I think dBB is just awkward.

There is an excellent book (a collection of papers) called Speakable and Unspeakable in Quantum Mechanics by John Bell where he states that he thinks that dBB is identical to Everett's many worlds hypothesis. He was a fan of local realism but his inequality was found to be violated in nature so he accepted that dBB wasn't viable and became a fan of Many Worlds instead.

The many worlds interpretation has the benefit of exactly reproducing all the predictions of Quantum Mechanics in a realist way. My objection is that the universes come with weightings and it's not clear to me what a weighting for a universe is. If the probability is 3:1 for an event does that mean there are three universes where it happened and one where it didn't? What if the observation is of time to decay for a single nucleus, are there then a continuous infinity of universes?

I think that it is very difficult to make a deterministic theory reproduce all the results of Quantum Theory. I think that it is virtually impossible to hold onto the concept of a particle. My feeling is an interpretation should keep the wave aspect, but explain the particle aspect in terms of the size of the wave-packet.

The bad thing about the Copenhagen interpretation is that it isn't an interpretation, it just makes some statements about what the theory predicts and puts a dividing line between classical apparatus and quantum particles. Bohr and Heisenberg were really strongly influenced by logical positivism and so they were careful not to add metaphysical entities to the extent of denying the reality of the wavefunction. So it's entirely unsatisfying. This is also the good thing as there's little metaphysical baggage to block new interpretations.

Originally posted by DeepThought
The problem with the de Broglie-Bohm theory is that if it makes the same predictions as traditional quantum mechanics then it has this pointless extra metaphysical entity in it and if it does make different predictions then it's ruled out by experiment (but see below). As I understand dBB theory the pilot wave is identical to the wavefunction in QM but ...[text shortened]... This is also the good thing as there's little metaphysical baggage to block new interpretations.

Well, time will tell, perhaps. It will, that is, if physicists* haven't painted themselves so far into a corner in their mode of thinking that they will never again make another breakthrough that corresponds to reality. I somehow get the feeling that some of the problem, as mentioned in the article, is that dBB is "under-researched." The mathematics of quantum physics has been optimized for one viewpoint, and very few seem keen on entertaining another viewpoint. The young won't, otherwise they'll be denied positions and promotions; and the old won't either, for they're set in their ways and have built their reputations on conventional interpretations of reality. All of your objections are based on the framework of conventional interpretations.

Accepting a theory because it counts your beans accurately is not necessarily what science is about. Anyone can weave a crazy quilt such as the Standard Model to explain things already known and proximate to what is known, but the problem is that the quilt won't necessarily extend to cover truly radical aspects of reality. What the Standard Model is, I think, is a tangent plane to one point on a "surface" that is anything but a plane. It meshes well with reality near the point of tangency, but that is all. I wouldn't go so far as to say dBB is the winning hypothesis, but it is under-researched, and for no good reason other than silly prejudice. Too many big egos are at stake, much as with string theory.




* Physicists involved in GUT research and related fields.

Originally posted by Soothfast
Well, time will tell, perhaps. It will, that is, if physicists* haven't painted themselves so far into a corner in their mode of thinking that they will never again make another breakthrough that corresponds to reality. I somehow get the feeling that some of the problem, as mentioned in the article, is that dBB is "under-researched." The mathematics of ...[text shortened]... , much as with string theory.




* Physicists involved in GUT research and related fields.

By the Standard Model I mean the standard model of particle physics, I don't mean the Copenhagen Interpretation, the standard model should be independent of any given interpretation of quantum theory. Given the level of evidence for the Standard Model any interpretation not consistent with it (at least at energy scales accessible to accelerators) can be ruled out out of hand. The Standard Model is the most heavily tested theory in science, it's not expected to be the end of the road, but at energy scales below ~10TeV it's to all intents and purposes rigorously true. Fundamentally dBB is a hidden variable theory and if the experiments by Aspect et al are to be believed it's ruled out empirically.

With String Theory I agree, it's become a paradigm but there isn't any actual experimental evidence for it. The initial reason for its popularity is that it automatically has a spin 2 particle so it's a candidate quantum theory of gravity which avoids most of the problems a naive approach to quantizing gravity entails. It shouldn't be squeezing out alternative theories given the absence of any experimental corroboration. Also the huge effort on what is basically a speculative theory is strange.

Originally posted by DeepThought
By the Standard Model I mean the standard model of particle physics, I don't mean the Copenhagen Interpretation, the standard model should be independent of any given interpretation of quantum theory. Given the level of evidence for the Standard Model any interpretation not consistent with it (at least at energy scales accessible to accelerators) can be ...[text shortened]... ble theory and if the experiments by Aspect et al are to be believed it's ruled out empirically.

The Standard Model, quantum theory, relativity theory -- as I understand it, all are essentially mathematical constructs independent of any particular interpretation. That is, they all largely speak to "how," and not to "why." At least, not "why" at too deep a level. So, all these theories work within their appointed spheres of influence, with the Standard Model in particular being something of a hodgepodge of theories cobbled together into that crazy quilt I mentioned -- correct me if I'm wrong, though!

But the theories don't exactly work well with one another, with quantum physics and general relativity being the foremost example. To someday unify all the disparate pieces we need a Big Picture that makes sense -- a coherent conception of reality free of manifest nonsense such as "nothing exists until it's measured" and the like. That's where interpretation comes in, and the "why" of it all becomes critically important. So as I said, a theory that counts the beans correctly is not necessarily what science is about. Right now the Copenhagen Interpretation is tolerated because, well, it doesn't get in the way of doing physics and making accurate calculations. Yet it may be that the breakthrough we need to go beyond the Standard Model will require a radically altered interpretation of the current body of theory. That's pretty much my point, I guess.

Originally posted by DeepThought
The problem with the de Broglie-Bohm theory is that if it makes the same predictions as traditional quantum mechanics then it has this pointless extra metaphysical entity in it and if it does make different predictions then it's ruled out by experiment (but see below). As I understand dBB theory the pilot wave is identical to the wavefunction in QM but ...[text shortened]... This is also the good thing as there's little metaphysical baggage to block new interpretations.

Edit: The problem with the de Broglie-Bohm theory is that if it makes the same predictions as traditional quantum mechanics then it has this pointless extra metaphysical entity in it and if it does make different predictions then it's ruled out by experiment (but see below). As I understand dBB theory the pilot wave is identical to the wavefunction in QM but instead of a probabilistic interpretation they have a classical particle guided by the pilot wave. But in order for it to reproduce the results of the Standard Model the pilot waves have to interact - and importantly self-interact - in the same way, otherwise the couplings and masses won't run. So what determines all the interactions is the pilot wave and I'm left wondering about what exactly the particle in dBB does."


No metaphysical entities in the dBB theory;

In Bohmian Mechanics the particles are primitive and the w/f secondary, for the behavior of the particles is described by their positions; and the w/f does not give a complete description of a quantum system, but it simply governs the positions of the particles. Well, nothing but the positions of the particles are the so called “hidden variables” and surely Bell was fully aware of the fact that this term is unfortunate. In 1987 he stated that the image of the visible world is not contained in the w/f but in the microscopic aspect of the complementary variables; according to him, and of course to Bohm too, the most hidden (but surely not metaphysical) of all variables in the pilot-wave picture is the w/f, which manifest itself to us solely by means of its influence on the complementary variables.

So, what the particle is doing?
The state of an N-particle system is described by its w/f, a spinor-valued function on the space of possible configurations of the system and its actual configuration defined by the actual positions of its particles; then, as the theory is defined by Schrödinger's Equation and the Guiding Equation together with the specification of the Hamiltonean, including all interactions that contribute to the total energy, we have a deterministic second-order theory of particles in constant motion, describing particles moving under the influence of differ forces, hence accounting for all the phenomena of non-relativistic quantum mechanics. The particle, guided by a wave, is simply doing its thing whilst the guiding wave propagates in a multidimensional-configuration instead of a 3D space (an action which by the way is the origin of the non-locality of QM). And its thing is, for example in the case of the Two-Slit experiment, that the motion of a particle passing through just one of the two holes in screen, is influenced by waves propagating through both holes. However, when We determine the slit through which the particle passes, the above mentioned interference pattern will be destroyed, and this effect of Our observation is a simple consequence of Bohmian Mechanics. How? By means of the collapse of the w/f.

Bohm was aware of a specific dynamism. He believed that observation implies interaction, and he was rejecting the hypothesis that a system under observation could be a closed system. On the contrary, he suggested that a system under observation is just a subsystem of a larger closed system, which could even be the whole Kosmos, or any smaller closed system that contains the subsystem under observation; the configuration of this larger system splits into the configuration of the subsystem and the configuration of the environment of the subsystem. The larger system is completely described by the w/f evolving according to Schrödinger's Equation, together with the configurations of the subsystem and the configuration of the environment of the subsystem. The w/f of the subsystem is obtained by the plugging of the configuration of the environment into the w/f of the larger system, whilst the configuration of the subsystem obeys the Guiding Equation with the conditional w/f on its right-hand side; and the conditional w/f obeys Schrödinger's Equation for the subsystem when that system is suitably decoupled from its environment, whilst it collapses randomly according to the quantum equilibrium hypothesis.
Of course, since QM cannot define the conditional w/f, in other words the Actual Configuration of the Environment, whatever is meant from an orthodox point of view as “w/f of a subsystem” obscure it remains
😵

Happy New Year to Everybody😵