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de Broglie-Bohm theory (Bohmian mechanics) - Printable Version

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de Broglie-Bohm theory (Bohmian mechanics) - xelasnave - 05-07-2016

Would it be appropriate to offer a short run down on the theory here. 
de Broglie-Bohm theory (Bohmian mechanics)


RE: de Broglie-Bohm theory (Bohmian mechanics) - secur - 05-07-2016

de Broglie - Bohm (dBB) theory (a.k.a. Bohmian mechanics) was considered false by both de Broglie and Bohm! How's that for an attention-grabbing opening?

Louis de Broglie won the Nobel in 1929 for his major contribution to QM: the idea that matter has a wave aspect, often referred to as wave-particle duality. In 1920, when de Broglie began his studies, it was known that light - a wave, according to Maxwell - had also a particle nature (photons). de Broglie realized that perhaps electrons, which at that time were only known as particles, had also a wave aspect. In this way the two major types of "substance", light and matter, were brought into a unified picture. He was led to this by the quantization of electron energies in the atom. His idea directly inspired Schroedinger's famous equation.

But de Broglie had another, related great idea which brought him no success at all: de Broglie pilot wave theory, the genesis of dBB. At the famous Solvay conference of 1927 he presented it and was mercilessly shot down by Pauli and others. Indeed, there were some major holes in the theory, which were filled in much later (1950's) by Bohm. It was this humiliating experience which caused de Broglie to give up on the theory; he admitted, more or less, it was wrong.

Bohm picked up on it many years later, in the 1950's. He was motivated by realizing that von Neumann's famous "proof" that QM could not be explained by Hidden Variables, was wrong. So he developed the pilot wave idea basically just to demonstrate that, saying it probably wasn't right, was just a counterexample. He went through more than one name for it, "causal ontology", "ontological interpretation". I think the best name is "pilot wave theory", but generally dBB is preferred.

As time went on Bohm acquired collaborators, Vigier and Hiley, and an aging Louis de Broglie also got interested. dBB developed into a complete theory; all the holes were filled; and after an exhausting decades-long battle, has finally been accepted as an alternative by the physics establishment.

So much for history. Now for the theory itself.

But first - in case you don't know much about normal QM I must describe it a bit. A particle is accompanied by its wavefunction, described by Schroedinger's equation. (There are many related concepts, such as Dirac's equation, Quantum Field Theory, Multi World Interpretation ad infinitum which I shall completely ignore).

Now suppose we initially have a particle at a more-or-less known position, moving along at a more-or-less known velocity. Its wave function immediately starts spreading out, as waves do. Before long it will cover a large area. This wave defines position and velocity, but "uncertainly". It is composed of a number of "eigenfunctions" or "eigenwaves", separate components which develop independently (because the equation is linear). Each defines a different position / velocity. How they do that, you must take on faith.

Now when a scientist observes that particle he will find it in only one of the possible places given by the different eigenwaves. We say the wave "collapses" to just that one component.

A side note: he can observe the position or the velocity (technically, momentum) but not both, according to the famous Heisenberg Uncertainty Principle. But this detail, while very important, we can ignore here. Let's just say "the particle is observed", thinking of position, and don't worry about its momentum.

Anyway this is very strange according to classical thinking. Classically we can understand the particle's position (/ momentum) being uncertain, due to inability to measure accurately. But QM says no matter how well we measure they're still uncertain. Well, that's not so weird. But the really strange thing, we can know it must be in one of a few (possibly widely separated) positions, but it's not "really" in any of them (since the wave is spread throughout), until we look! Then it will be in one of those; the other possibilities have vanished forever - the wave function collapsed. This is so strange that 100 years later people are still arguing about it. (BTW the famous "2-slit experiment" illustrates this.)

The "Copenhagen interpretation" became the standard view of this situation. Today, from the point of view of dBB, all other interpretations basically follow this Copenhagen idea. It says that the particle simply does not exist until we measure it. (Alternatively, it exists in every possible place at once.) Only when we measure, does it "decide" where it will finally wind up.

That was roughly the situation when de Broglie turned his fertile imagination on the question. He came up with a way that the particle could be a regular physical entity: always in a definite place at any time, just as classical intuition demands. (Now we're finally getting to dBB theory.) In order to satisfy the "weird" experimental results he recast the wave function as a "pilot wave". The pilot wave travels in all the different superposed eigenwaves (called "channels") and relays information back to the real particle. It's as though the particle were a radio receiver and the pilot wave components, radio broadcasters (admittedly this is a bit weird also). One very important detail: the transmission of info must take place "non-locally" - faster than light.

Anyway the particle, before too long, actually enters one of the channels, and that's the one it will ultimately be found in. But following the information "broadcast" from the other channels it jerks around in such a way that the experimental results are still satisfied. (To explain this requires the concept of "interference" - let's skip it for now.) Thus, even though its motion is non-classical, at least it has a definite position at all times (that's the so-called "hidden variable") and moves continuously; never executes the "quantum jumps" required by Copenhagen.

de Broglie's idea failed on a few counts: it wasn't relativistic, more important it wouldn't work with multiple particles. Also interaction between electrons and photons were not described. For these reasons Pauli ripped him to shreds.

Many years later Bohm resuscitated the pilot wave, and with the help of Vigier and Hiley, managed to answer all the objections. Then he faced the much more difficult task of convincing the physics establishment ... finally succeeded in that too.

Well that's just an introduction. The details are endless, but I hope this gets you started.


RE: de Broglie-Bohm theory (Bohmian mechanics) - Schmelzer - 05-07-2016

(05-07-2016, 04:48 AM)secur Wrote: de Broglie - Bohm (dBB) theory (a.k.a. Bohmian mechanics) was considered false by both de Broglie and Bohm! How's that for an attention-grabbing opening?
Nice attention grabbing. But let's see:
(05-07-2016, 04:48 AM)secur Wrote: But de Broglie had another, related great idea which brought him no success at all: de Broglie pilot wave theory, the genesis of dBB. At the famous Solvay conference of 1927 he presented it and was mercilessly shot down by Pauli and others. Indeed, there were some major holes in the theory, which were filled in much later (1950's) by Bohm. It was this humiliating experience which caused de Broglie to give up on the theory; he admitted, more or less, it was wrong.
I think it is not a good idea to use such emotional "mercilessly" and "humilating" words in a scientific discussion. It may be attention grabbing, ok. But I would prefer to present here a positive example of educated scientific discussion.
The next point is that it does not matter at all what de Broglie thought at that time. At least not in this subforum, in the History subforum this would be appropriate. What matters here is if the problems raised by Pauli have been solved or not. They have been solved by Bohm.
(05-07-2016, 04:48 AM)secur Wrote: He went through more than one name for it, "causal ontology", "ontological interpretation". I think the best name is "pilot wave theory", but generally dBB is preferred.
Good point, an introductionary post has to contain all the names.
(05-07-2016, 04:48 AM)secur Wrote: Multi World Interpretation
Its name is "many worlds".


RE: de Broglie-Bohm theory (Bohmian mechanics) - Ioannis - 06-03-2016

secur Wrote:That was roughly the situation when de Broglie turned his fertile imagination on the question. He came up with a way that the particle could be a regular physical entity: always in a definite place at any time, just as classical intuition demands. (Now we're finally getting to dBB theory.) In order to satisfy the "weird" experimental results he recast the wave function as a "pilot wave". The pilot wave travels in all the different superposed eigenwaves (called "channels") and relays information back to the real particle. It's as though the particle were a radio receiver and the pilot wave components, radio broadcasters (admittedly this is a bit weird also). One very important detail: the transmission of info must take place "non-locally" - faster than light. 


a) Is the pilot wave a separate entity? IF it is then it is not an intrinsic property of the charged particle itself.
b) Does the pilot wave travels together with the charged particle?
c) Is the pilot wave in phase with the mass properties of charged particle or not?
d) IF the pilot wave travels together with the charged particle that means is a Wave-Particle instance at all moments then, the charged particle would be in a Quantum Tunneling state in its entire life after approaching the speed of light. It follows that under such circumstances the charged particle would be then undetectable in our world.
e) IF the pilot wave travels together with the charged particle what is the Relativistic Energy of the Wave-Particle entity? Einstein's Relativity predicts the Relativistic Energy for charged particles associated not to pilot waves. How dBB copes with this?


RE: de Broglie-Bohm theory (Bohmian mechanics) - secur - 06-03-2016

Thanks, interesting questions, which I'll attempt to answer before too long. Probably Schmelzer knows off the top of his head, it's his area.


RE: de Broglie-Bohm theory (Bohmian mechanics) - Ioannis - 06-03-2016

(06-03-2016, 08:29 PM)secur Wrote: Thanks, interesting questions, which I'll attempt to answer before too long. Probably Schmelzer knows off the top of his head, it's his area.

No worries.


RE: de Broglie-Bohm theory (Bohmian mechanics) - Schmelzer - 06-04-2016

(06-03-2016, 05:33 PM)Ioannis Wrote: a) Is the pilot wave a separate entity? IF it is then it is not an intrinsic property of the charged particle itself.
It is clearly a separate entity.

There is some more uncertainty about its status, but the basic dBB assumption is that it has some real existence. So, there is not only the trajectory, which is what we see around us, but also, additionally, some objectively existing wave function.

I tend to prefer another concept, namely that the wave function describes our knowledge. But this knowledge is, then, knowledge about the environment, in particular about the pointers of the measurement devices used in the preparation procedure. Thus, knowledge about some other, external objects, which are somehow correlated with the trajectory, but now the trajectory itself. So, in above variants is is not some intrinsic property of the particle itself, but something different, external.
(06-03-2016, 05:33 PM)Ioannis Wrote: b) Does the pilot wave travels together with the charged particle?
No, it is something completely different in nature, it is a function of all imaginable configurations.

The closest analogy is in classical theory the energy. It is a function of the trajectory - you can, for every trajectory, compute its energy, the energy of this particular trajectory. And, then, this energy "guides" the trajectory by energy conservation: The trajectory cannot be arbitrary, it has to continue in such a way that the energy remains unchanged in time. But the energy may not change at all, while the position of the particle changes in time. And the energy is defined also for all other configurations, not only the one which we see.
(06-03-2016, 05:33 PM)Ioannis Wrote: c) Is the pilot wave in phase with the mass properties of charged particle or not?
Hm. The pilot wave follows the Schrödinger equation. The mass is a parameter in the Schrödinger equation.
Schrödinger
d) IF the pilot wave travels together with the charged particle that means is a Wave-Particle instance at all moments then, the charged particle would be in a Quantum Tunneling state in its entire life after approaching the speed of light. It follows that under such circumstances the charged particle would be then undetectable in our world.
[/quote]
Sorry, I don't understand this text. Quantum theory, as well as dBB theory, are theories with an absolute but unmeasurable time. Every clock is, independent of any relativity, inaccurate, and even goes backward in time with some non-zero probability.
(06-03-2016, 05:33 PM)Ioannis Wrote: e) IF the pilot wave travels together with the charged particle what is the Relativistic Energy of the Wave-Particle entity? Einstein's Relativity predicts the Relativistic Energy for charged particles associated not to pilot waves. How dBB copes with this?
There is a variant of dBB theory for relativistic particles, but I don't like it. I prefer for relativistic theory the field theory. In this case, particles become quite irrelevant, quantum effects without any fundamental importance, like phonons in condensed matter theory (some "sound particles" which are simply quantum effects like the discrete energy levels in an atom).