Pilot Wave Theory: Mechanics Explained

[NJV]

What, physically, does a pilot wave in itself consist of? Every source I've found wasted my time with pages upon pages of circumlocution, but none ever got to the point. So please don't cite any other sources. I just want the basic idea of it. I'm referring to the mechanics of the pilot wave, not its mathematics.

 

[Fredrik]

The only way to answer that would be to present a new theory from which the pilot wave theory can be derived. What makes you think there is such a theory? And what makes you think that you can distinguish between the mechanics and the mathematics?

 

[NJV]

I meant that I didn't want people to come up with formulae as an explanation. Formulae describe the behavior of a system. They do not explain it.

 

[JK423]

With a quick googling i found this: http://www.uncletaz.com/library/scimath/pilotwave.html
Its quite simple

 

[Demystifier]

What, physically, does a pilot wave in itself consist of? ... I just want the basic idea of it.

The basic idea is that the pilot wave does NOT consist of something more fundamental. The idea is that pilot wave is a fundamental entity by itself.

You may not like this idea, but that's what the idea is.

 

[NJV]

Still, that leaves the question what form this fundamental entity has. Is it the actual cause of the movement of the particles, or rather, is it the movement of the particles itself? I've found out very little about what to imagine this pilot wave to be. Heck, I don't even know if it's longitudinal or transversal. Is it comparable to an air sound wave? A phonon in metal? The fluctuating movement of electrons in an AC? Does the pilot wave have any discrete existence of itself, or it is akin to a quasiparticle?

I'm sorry if I sound stupid. It's just that I can't find a source anywhere which seems to say the first thing about what a pilot wave in itself really is.

Thanks for the article, but it, neither, taught me anything new.

 

[Fredrik]

I meant that I didn't want people to come up with formulae as an explanation. Formulae describe the behavior of a system. They do not explain it.

People often say things like that, and I blame the schools for teaching the philosophy of science badly, but maybe I should blame the philosophers for not doing a better job explaining these things to the scientists who teach science teachers. What we consider an explanation depends on the context. For example, general relativity explains the "action at a distance" in Newton's theory of gravity. If your immediate concern is only that action at a distance seems impossible, then the mathematics of GR is a satisfactory explanation. If you're also wondering why GR does such a great job of predicting the results of experiments, then it's not.

In those cases when a mathematical model that's a part of a very accurate theory of physics can't give you an answer that you would consider an explanation, nothing else can. The best possible answer you could hope for in this case would be another (and better) theory of physics from which Bohm's theory can be derived.

 

[FayeKane]

What we consider an explanation depends on the context.

True!

when a mathematical model can't give you an answer that you would consider an explanation, nothing else can.

False!

My hobby is explaining complex stuff in a way that normal (i.e. stupid) people can understand, because I love the way Feynman did that so well.

My readers would gain nothing from GR equations, but "spacetime is denser near mass" is something they DO understand. That is, for them, the mathematical model doesn't provide an explanation, but an alternative model does.

--flk

 

[Mentz114]

FayeKane:

but "spacetime is denser near mass" is something they DO understand. That is, for them, the mathematical model doesn't provide an explanation, but an alternative model does.

Unfortunately it's a bad analogy giving the impression that spacetime is stuff. Spacetime is an abstraction - it does not have density but a defect called curvature that varies.

 

[dx]

"spacetime is denser near mass" is something they DO understand

Your readers may 'understand' when you tell them that, but unfortunately it has no content, and is technically wrong unless you say what it means for spacetime to be 'dense'. All it does is use some technical words in a non-technical way so that it generates some kind of vague mental image. This, btw, is not at all what Feynman does.

 

[Dmitry67]

FayeKane:

Unfortunately it's a bad analogy giving the impression that spacetime is stuff. Spacetime is an abstraction - it does not have density but a defect called curvature that varies.

Then they come here and ask "Where is a center of the Universe?" :)

Normal (i.e. stupid people) read about black holes, singularities, big bang, extra dimensions and stuff, put it in their heads, shake it, and here is an example of the result:
https://www.physicsforums.com/showthread.php?t=340518

 

[Dmitry67]

The question have been answered, you just did not like the answer.

Fundamental entities (contrary to atoms, molecules, iphones) are not made of something, because they are fundamental.

 

[Dmitry67]

EDIT:
The truth is that question can't be answered. At LEAST yet, but likely never as pilot wave is probably wrong and even if it was right that's far from a guarantee that the wave itself is composed of something individual that we can speak of separately. Why in the heck do you think it is? You need to learn allot more about physics before you start dipping into the philosophies of QM as you obviously have no idea to what extent these ideas are to be carried and how they apply.

Yes, I believe that BM is wrong and personally I prefer MWI, but it does not change the fundamental thing: fundametal entities do not consist of something - otherwise they would not be FUNDAMENTAL (personal insult ignored)

 

[James Leighe]

Yes, I believe that BM is wrong and personally I prefer MWI, but it does not change the fundamental thing: fundametal entities do not consist of something - otherwise they would not be FUNDAMENTAL (personal insult ignored)

Not to drag on but I said that it was unlikely that it was made of anything in my post. (and what insult?)

 

[zenith8]

What, physically, does a pilot wave in itself consist of? Every source I've found wasted my time with pages upon pages of circumlocution, but none ever got to the point. So please don't cite any other sources. I just want the basic idea of it. I'm referring to the mechanics of the pilot wave, not its mathematics.

Hello NJV,

Shall I try?

In non-relativistic quantum mechanics the pilot wave, or wave field, is a real field objectively existing in 3d space that is represented mathematically by the 3N-dimensional wave function of Schroedinger theory. It is a time-dependent distribution of energy (or more strictly energy-momentum) in space.

So now you tell me that you don't know what energy is. Well, it doesn't seem to bother most physicists, but let's just say that energy is something which:

(1) is conserved.

(2) exists in different forms

(3) can be stored

(4) can be transferred through space or from one material body to another

(5) can be transformed into other forms of energy

Now in the de Broglie-Bohm interpretation of QM or pilot-wave theory - which is what you're referring to - electrons (say) exist as particles in addition to the pilot wave. Because the wave field is a repository of energy it can exert a force on the particles (the so-called 'quantum force'). Like all such a fields it has a potential energy function (Bohm's 'quantum potential' Q) and the force is given simply by $$-\nabla Q$$.

Remember that in general, potential energy is a property of fields, and the potential function Q represents the potential energy available to the particle at a specific position in the wave field.

Depending on the prevailing circumstances, some (or all) of a particle's energy-momentum can be transferred and temporarily stored in its wave field. Once stored in the field, energy-momentum can be returned to the particle if circumstances change, and its kinetic energy will then increase (it will accelerate). This has the interesting consequence that the motion of a quantum particle need not be in a straight line even if there no external field present.

For example, if the pilot-wave passes an obstacle (such as a couple of slits) then its form will change (it will develop an interference pattern in this case) and energy will be transferred to and from the particle traveling through it according to the usual equations; the electron trajectory will then deviate from its classical (Newtonian path). It will end up getting guided into places where there is constructive interference in the pilot wave, and so after multiple experiments we see an 'interference pattern' developing in the positions of particle detections on a screen placed on the other side of the slits.

Even though Feynman (and God knows how many textbook writers) said no-one knew how to do this in terms of electrons following trajectories. He was just wrong.

So to summarize the properties of the pilot wave and the quantum potential:

(1) the pilot wave exhibits the usual wave properties (e.g. reflection, transmission, diffraction, interference etc.) and obeys the principle of linear superposition. The whole experimental field of 'matter wave optics' depends on this being the case, thus indicating unequivocally that the wave field objectively exists (in order for it to act in such a manner, and be acted upon).

(2) Since the Schroedinger equation is homogeneous, the pilot wave is not a radiated field and there is no source term for the field.

(3) The environment surrounding a quantum particle (in part) determines the shape of the pilot wave..

(4) The pilot wave is the repository of potential energy in a quantum system.

(5) The pilot wave acts on the quantum particle similar to an external field and receives or imparts energy and momentum to the particle.

(6) The quantum potential represents a portion of the energy contained in the pilot wave and is the amount of potential energy available to the particle at its specific position in the pilot wave field.

(7) The magnitude of the quantum potential is independent of the intensity of the pilot wave.

(8) Non-local connections between particles in a many-particle quantum system are facilitated through the operation of the quantum potential.

If you want to know what it is at a deeper level than that, then the answer is that nobody knows. But that doesn't stop you from asking or trying to find out (though don't tell ZapperZ - it'll be our little secret..).

 

[zenith8]

Hi NJV - any comment?

 

[ArjenDijksman]

What, physically, does a pilot wave in itself consist of? Every source I've found wasted my time with pages upon pages of circumlocution, but none ever got to the point. So please don't cite any other sources. I just want the basic idea of it. I'm referring to the mechanics of the pilot wave, not its mathematics.

I think the best way to understand pilot waves is to look how they behave: http://www.physorg.com/news78650511.html

There's an essay at the current FQXi contest that discusses ordinary pilot waves.

 

[Dmitry67]

Another question to Bohmians.

As in BM initial conditions are infinitely complex (as they pre-code properties of the future history of all matter in the Universe at the moment of BB) then as I understand, in BM the "Fine tuning" problem does not exist.

Because, if initial conditions is the so long list of numbers without any apparent sense, why not add another 30 parameters of the Standard Model to that list, without giving any explanation why they have any specific values?

What a nice way to "explain" everything :)

 

[Demystifier]

Another question to Bohmians.

As in BM initial conditions are infinitely complex (as they pre-code properties of the future history of all matter in the Universe at the moment of BB) then as I understand, in BM the "Fine tuning" problem does not exist.

Because, if initial conditions is the so long list of numbers without any apparent sense, why not add another 30 parameters of the Standard Model to that list, without giving any explanation why they have any specific values?

What a nice way to "explain" everything :)

BM is not attempting to be a theory of "everything". It only attempts to explain how in measurements physical quantities attain definite values.

You could address your objection above to classical mechanics as well, but nobody else would agree with you that THIS is the reason why classical mechanics is not satisfying.

 

[Dmitry67]

On the emotional side:
Correct me if I am wrong, but isn’t BM an attempt to recover some sort of ‘objective reality’ behind the QM weirdness? Even that level of reality is unachievable experimentally, it gives a hope (to Bohmians) that somewhere deep inside there are good old billiard balls? And now you renounce it by claiming that ‘it is just an attempt to fit the measured data’?

On the technical side:
Yes, BM is not a TOE. But there are 2 options:
* Future TOE also contains these zillions and zillions of numbers as initial conditions at the BB, even the equations were different from BM. In that case, my claim is still valid.
* Future TOE has much simpler initial conditions. Then how we get these zillions numbers when BM emerges from TOE? Where the information comes from? In a sequence of random events, like in CI? But it is a denial of the very idea of BM – determinism.

 

[Demystifier]

And now you renounce it by claiming that ‘it is just an attempt to fit the measured data’?

Don't twist my words! I never said that.

* Future TOE also contains these zillions and zillions of numbers as initial conditions at the BB, even the equations were different from BM. In that case, my claim is still valid.

Yes, your claim is valid. However, by TOE one usually means generally valid equations of motion. Not a principle that determines the initial conditions.
Of course, you may also wish to have a principle that determines the initial conditions, but that's simply not what most physicists interested in the fundamental question of physics are searching for.

 

[Dmitry67]

For me TOE *must* include the initial conditions. Otherwise it is not a Theory of EVERYTHING.

Probably it is a difference on a philosophical level; so I don’t think we can prove something, but again, for me TOE=equations+initial conditions.

 

[Demystifier]

For me TOE *must* include the initial conditions. Otherwise it is not a Theory of EVERYTHING.

Probably it is a difference on a philosophical level; so I don’t think we can prove something, but again, for me TOE=equations+initial conditions.

In this sense, TOE must also explain consciousness, answer the question whether God exists or not, explain why your brain prefers MWI and why my brain prefers BM, ... for otherwise it is not a theory of EVERYTHING.

Too much for any theory existing so far.

 

[DrChinese]

For me TOE *must* include the initial conditions. Otherwise it is not a Theory of EVERYTHING.

Probably it is a difference on a philosophical level; so I don’t think we can prove something, but again, for me TOE=equations+initial conditions.

I would agree with Demystifier: A TOE does not need to explain initial conditions. Presumably the laws of physics could be specified without knowing WHY those initial conditions arose.

On the other hand, I think most TOEs won't go very far unless it is clear that some initial conditions lead to the universe we see today. In other words, the TOE must be feasible considering what conditions are today. Otherwise, the TOE would be considered falsified out of hand.

 

[Dmitry67]

Demystifier - yes, I need to add "EVERYTHING fundamental"

Demystifier, DrChinese, that what part of science should answer the question about the initial conditions? How is it called?

 

[Demystifier]

Demystifier, DrChinese, that what part of science should answer the question about the initial conditions? How is it called?

If any existing branch of science should answer it, then it is - cosmology.

 

[Dmitry67]

So you believe that an ultimate TOE will not cover Cosmology?

 

[Demystifier]

So you believe that an ultimate TOE will not cover Cosmology?

No. All I am saying is that the currently existing theories do not successfully cover this PART of cosmology. (And please, don't try to twist this statement!)

 

[DrChinese]

So you believe that an ultimate TOE will not cover Cosmology?

It should have a cosmological component. But it is not considered a reasonable requirement of a TOE that it actually specify initial conditions directly. In a similar vein: it is not a requirement of a TOE that it answer such questions as the following:

a) Are there universes outside our own?
b) Could the laws of physics have been created any other way?
c) If a) and b) are yes, are there other universes in which the laws of physics are different?

I think you can see that having a TOE is not intended to imply that we will know everything. We can potentially discover a TOE and still have plenty of unanswered questions (such as above). So there is no need to take the "everything" part literally. A TOE is a step.

 

[Dmitry67]

DrChinese, questions a) b) c) can be replied ONLY by MUH/MWI, because if you don't accept MUH/MWI then any answers to a) b) c) are not falsifiable in principle. Do you agree?

 

[WaveJumper]

The initial conditions cannot be explained unless physicists come to know what Time, Space and Matter are. With a vague understanding of such fundamental concepts, speculations about the initial conditions would not even scratch the surface.

 

[DrChinese]

DrChinese, questions a) b) c) can be replied ONLY by MUH/MWI, because if you don't accept MUH/MWI then any answers to a) b) c) are not falsifiable in principle. Do you agree?

I don't think the interpretation matters for these questions. They are just too big. You don't need to believe in MWI to believe in the existence of other universes. Or that the laws of physics may not be the same in other universes. (The generally accepted theoretical mechanism of spontaneous symmetry breaking could be considered evidence that they would not.)

 

[WaveJumper]

Demystifier - yes, I need to add "EVERYTHING fundamental"

Demystifier, DrChinese, that what part of science should answer the question about the initial conditions? How is it called?

You may be interested to see this article on the ideas of cosmologist Andrei Linde and Alan Guth about the initial conditions in New Scientist:

http://www.ipod.org.uk/reality/reality_universe2.asp

 

[jambaugh]

What, physically, does a pilot wave in itself consist of?

It's elephants all the way down! ;)

You always run into this dilemma when looking for/at foundational substance. To "explain" electromagnetism you can propose an aether as a medium because we are used to thinking of waves as fluctuations of the medium. One must then ask about the components of this medium and mediators of its interaction and you are back where you started except you've moved beyond observable phenomena.

If one starts with quantum mechanics and one describes the behavior of quanta one will invoke a Hilbert space with "vectors" represented by wave-functions. At this level these wave-functions are not real but just mathematical constructs (like a force vector or real number line). The direct operational interpretation of the wave-function is a function yielding probability amplitudes for the observation of the quantum at each spatial point at a given time. It is thus effectively a probability distribution but encoding more information (the way a velocity vector encodes more information than just its magnitude=speed).

Understand this first and then consider the question of (ontological) interpretation of quantum theory. In trying to describe an objective reality underlying the phenomena we see in elementary quantum experiments and describe with these wave-functions you have some interesting historic proposals. Everett's MWI and Bohm's Pilot Wave being two such. The Bohmian's assert that the wave-function itself corresponds to some existent wave phenomenon guiding the classical$$^*$$ particle and thus "explaining" quantum interference phenomena.

(* classical in the sense of having always an objective state of reality with position and momentum well defined but not known to the observer.)

As far as what underlies this wave the supposition stops there treating both pilot wave and elementary particles as foundational objects out of which other things are made.

For myself I am a Copenhagenist and deny the need to reify the wave-function. I see pilot-waves as analogous to the luminiferous aether invented by Newton.

Actually I just looked up Newton's aether on the web and it would seem he invented pilot waves before Bohm to explain the same phenomena of interference, diffraction and refraction along with his particulate light theory. I didn't realize the question went back that far!

So I guess the best answer to your question is...

Pilot waves are undulations of the aether.

 

[zenith8]

It's elephants all the way down! ;)

Any comments on my post #15 then?