Is Wave Theory the Key to Understanding All Physical Phenomena?

[DrChinese]

I don't believe this answers my question. I asked how we supposedly know that an electron can be confined to an arbitrarily small volume. You have given me a reference for the experimentally determined electron radius. I really can't make the connection.

A vanishingly small radius is clearly incompatible with your wave-only description (and it should be obvious why). I expect you'll have another non sequitur for that. (Maybe next time you could make it funny too, as this has become otherwise tiring.)

 

[eoghan]

Because there is a wave and an accompanying particle, rather than one thing which is somehow both. I mean, is this just too simple or something?

Wow... this discussion is very interesting! But I'd like to change my original question:
Why should I think the electron is a wave?
I know from the double slit experiment that an electron couldn't be described as a wave (each electron hits a point of the detector) nor as a particle (after a lot of electrons fired, I get a diffraction shape).
But I think, as Zenith8 said, that the experiment could be explained considering the electron as a particle which trajectory is determined by a wave. I don't understand: why I have to think that every electron is a wave?
Isn't simpler to think that the bodies are particles but they don't move in straight directions, but according to their wave (where the wave is something associated but separated from the body)?

 

[conway]

A vanishingly small radius is clearly incompatible with your wave-only description (and it should be obvious why). I expect you'll have another non sequitur for that. (Maybe next time you could make it funny too, as this has become otherwise tiring.)

No. A small but finite radius would indeed be very hard to explain with a wave theory. But if a wave-wave interaction gives the correct scattering function for low energies, then it only makes sense that you get the same type of distribution as you raise the energy without limit. What you choose to interpret as coulomb scattering of two point-charges is equally conistent with a wave interpretation. (And it should be obvious why.)

 

[zenith8]

Wow... this discussion is very interesting! But I'd like to change my original question:
Why should I think the electron is a wave?
I know from the double slit experiment that an electron couldn't be described as a wave (each electron hits a point of the detector) nor as a particle (after a lot of electrons fired, I get a diffraction shape).
But I think, as Zenith8 said, that the experiment could be explained considering the electron as a particle which trajectory is determined by a wave. I don't understand: why I have to think that every electron is a wave?
Isn't simpler to think that the bodies are particles but they don't move in straight directions, but according to their wave (where the wave is something associated but separated from the body)?

Hi Eoghan,

Welcome to the world of de Broglie-Bohm theory - come on in, the water's lovely..

Basically, no-one will dare to agree with you - they think that if it were that simple, someone ought to have noticed sometime over the last 80 years. And they're right, they ought to have. But, astonishingly, they didn't.

That's the power of charisma - well done Bohr and Feynman. 'Nobody understands quantum mechanics..', remember? Well, it's their choice.

Z.

 

[conway]

A vanishingly small radius is clearly incompatible with your wave-only description (and it should be obvious why). I expect you'll have another non sequitur for that. (Maybe next time you could make it funny too, as this has become otherwise tiring.)

I have listed all the postings of mine so far in this thread. I looked up the meaning of "non-sequitur" in Wikipedia but I am unable to identify any in this list. Perhaps you could point them out.

-----------------------
8. I don't know what you mean by this.

27. I wonder if you can come up with a specific experimental scenario which illustrates this difficulty.

29. I thought you were going to give an example of how to confine an electron to a volume too small for a wave.

31. I don't think I've asked for anything else except for an explanation of how we supposedly know this.

34. I don't believe this answers my question. I asked how we supposedly know that an electron can be confined to an arbitrarily small volume. You have given me a reference for the experimentally determined electron radius. I really can't make the connection.

35. Just to keep this on track, the original statement by Dr. Chinese was to the effect that the position of an electron can be determined to arbitrary precision. I am still asking what this means and how we supposedly know it to be true.

38. Exactly. (In response to Lightarrow).

 

[WaveJumper]

Hi Eoghan,

Welcome to the world of de Broglie-Bohm theory - come on in, the water's lovely..

Basically, no-one will dare to agree with you - they think that if it were that simple, someone ought to have noticed sometime over the last 80 years. And they're right, they ought to have. But, astonishingly, they didn't.

That's the power of charisma - well done Bohr and Feynman. 'Nobody understands quantum mechanics..', remember? Well, it's their choice.

Z.

Hi Zenith8,

I know next to nothing about BM and I am interested in the structure of the atom according to BM. Charged particles that travel through space give off energy. You said the electron is supposed to be both a wave and a particle at the same time. So, why don't the electrons fall into the nucleus if they are traveling continuously around the nucleus?

 

[sokrates]

Hi Eoghan,

Welcome to the world of de Broglie-Bohm theory - come on in, the water's lovely..

Basically, no-one will dare to agree with you - they think that if it were that simple, someone ought to have noticed sometime over the last 80 years. And they're right, they ought to have. But, astonishingly, they didn't.

That's the power of charisma - well done Bohr and Feynman. 'Nobody understands quantum mechanics..', remember? Well, it's their choice.

Z.

You are an obvious fan of de Broglie-Bohm theory (if that can be called a 'theory at all) but you have very little knowledge of the modus operandi of science, i.e scientific method.

The problem of de Broglie-Bohm is not that it's simple , the problem with it is it's stupendously naive... To get away from the probabilistic nature of things with a desire to make atomic world resemble the macroscopic world... It's a purely humane theory... It is understandable. It really is... It's like: Oh, I see why you want to think like that... It's the theory that a confounded beginner proposes in his 10th thread in Physics Forums yet, it is the same theory that has eluded the giants for 80 years... It has no connection with reality (tell me a table-top experiment that can detect the existing wave and the particle at the same time...) it is just the imagination at work ... A valiant attempt to solve the greatest mysteries of physics. Too bad nobody takes it seriously...

Beginners can easily buy into this fantasy, but there's not even a hint for the rest of the world to believe in it for two important reasons:

1.) There is NO experimental evidence to favor it AT ALL.
2.) It is an extraneous, and complicated idea (in terms of Occam)- and theorists know from hundreds of years' experience that 99.999% of the time, "simple" & "elegant" ideas work instead of complicated ones.

Therefore, you can delude yourself by thinking that you understand it but at least, stop misleading and biasing beginners (who have not even mastered the standard interpretation) by ridiculing Bohr,Feynman and others who have FOUNDED the standard quantum mechanics, which is by any standard, one of the most successful theories ever produced.

Remember at times, that without them you wouldn't even be talking about different interpretations, let alone a solid QM theory.

 

[sokrates]

I have listed all the postings of mine so far in this thread. I looked up the meaning of "non-sequitur" in Wikipedia but I am unable to identify any in this list. Perhaps you could point them out.

-----------------------
8. I don't know what you mean by this.

27. I wonder if you can come up with a specific experimental scenario which illustrates this difficulty.

29. I thought you were going to give an example of how to confine an electron to a volume too small for a wave.

31. I don't think I've asked for anything else except for an explanation of how we supposedly know this.

34. I don't believe this answers my question. I asked how we supposedly know that an electron can be confined to an arbitrarily small volume. You have given me a reference for the experimentally determined electron radius. I really can't make the connection.

35. Just to keep this on track, the original statement by Dr. Chinese was to the effect that the position of an electron can be determined to arbitrary precision. I am still asking what this means and how we supposedly know it to be true.

38. Exactly. (In response to Lightarrow).

Dr. Chinese's point was very clear and elementary even from the beginning.

I am not sure whether you are really not understanding it; or you are pretending so as he gave clear experimental facts related to the point-like nature of electrons, as well as their wave-like properties.

Non-sequitur is Latin for "It does not follow" - and it relates to your replies, as you are stubbornly avoiding to address what has been nicely explained to you. (Ironically all your posts are not logically related to what's preceded by them , i.e, they are all non-sequitur)

If you are really interested in why the wave-like properties CANNOT overlap with the particle-like properties, you can read Dr.Chinese's g-factor post again (#32), or you could familiarize yourself more with phenomena like Compton's scattering, Photoelectric Effect or Double-Slit experiment.

 

[DrChinese]

Dr. Chinese's point was very clear and elementary even from the beginning.

I am not sure whether you are really not understanding it; or you are pretending so as he gave clear experimental facts related to the point-like nature of electrons, as well as their wave-like properties.

Non-sequitur is Latin for "It does not follow" - and it relates to your replies, as you are stubbornly avoiding to address what has been nicely explained to you. (Ironically all your posts are not logically related to what's preceded by them , i.e, they are all non-sequitur)

Thanks sokrates, you express my thoughts precisely.

 

[Mentz114]

...

The problem of de Broglie-Bohm is not that it's simple , the problem with it is it's stupendously naive... To get away from the probabilistic nature of things with a desire to make atomic world resemble the macroscopic world... It's a purely humane theory... It is understandable. It really is... It's like: Oh, I see why you want to think like that... It's the theory that a confounded beginner proposes in his 10th thread in Physics Forums yet, it is the same theory that has eluded the giants for 80 years... It has no connection with reality (tell me a table-top experiment that can detect the existing wave and the particle at the same time...) it is just the imagination at work ... A valiant attempt to solve the greatest mysteries of physics. Too bad nobody takes it seriously...

Beginners can easily buy into this fantasy, but there's not even a hint for the rest of the world to believe in it for two important reasons:

1.) There is NO experimental evidence to favor it AT ALL.
2.) It is an extraneous, and complicated idea (in terms of Occam)- and theorists know from hundreds of years' experience that 99.999% of the time, "simple" & "elegant" ideas work instead of complicated ones.

...

This is mostly inaccurate and based on ignorance. The predictions of BM are the same as 'standard' QM. It is a probabilistic theory so there's no trying 'To get away from the probabilistic nature of things'. It is not compicated at all to people who understand Hamilton and Jacobi's theory. It does not confuse beginners.

 

[sokrates]

This is mostly inaccurate and based on ignorance. The predictions of BM are the same as 'standard' QM. It is a probabilistic theory so there's no trying 'To get away from the probabilistic nature of things'. It is not compicated at all to people who understand Hamilton and Jacobi's theory. It does not confuse beginners.

OK, I agree that I am ignorant when it comes to BB, now will you please give me a single experiment that favors BM over Copenhagen, even at the slightest sense??

Otherwise, I'll stick to my points.

 

[conway]

Dr. Chinese's point was very clear and elementary even from the beginning...he gave clear experimental facts related to the point-like nature of electrons, as well as their wave-like properties.

No, I don't think that was his point. He said that the position of an electron can be determined to arbitrary precision. That's pretty much an exact quote. And I still don't know what he means by this. I suspect that he is alluding to scattering experiments which are consistent with Coulomb scattering at arbitrarily high energies. I don't believe that in these experiments the actual position of the electron is determined to any precision at all.

But maybe he's talking about different experiments. I find his answers hard to pin down, what with the quantum eraser being thrown around for reasons I don't understand. Is the position of an electron determined to arbitrary precision in the quantum eraser? I don't think so. But that's why I have to keep asking the same question over and over.

 

[1Truthseeker]

I believe that my post in this new thread has also touched on some of the questions here:

https://www.physicsforums.com/showthread.php?t=344783

I also am interested in the actual structure of the atom and its constituents. I have been following along just recently on this thread and I have some questions that might interest some of the posters to the original poster's question(s).

I had brought up the structure of the atom in relation to electron microscopy and attosecond spectroscopy. If we are all seeing the same images, how do these QM interpretations apply to them? That was the basis for my questions after seeing them.

The theory that the electron is a wave is acceptable to me. I gather that any point we are discussing is a mathematical one and that it existing as a physical and discrete particle is not the reality. Much like how there are an infinite number of points on a number line, yet they have no radius, nor take up any volume, save for their illustrative description. It has been explained that in our ability to slice time, our temporal resolution, we see quanta of an electron wave so small that they appear to be point like, but that they are a fraction/sample/wavelet of their wave.

I think what the original poster is getting at (at least now) is what I am trying to get at: What is the actual physical structure of an atom? To answer that we need to know the structure of an electron, if the word structure can even be applied to it. If by structure, we can only infer it, since it may be nothing more than a fermion field of energy, how is it that we should even rightly teach the concept of an electron as a singular entity at all?

There are a lot more questions I have in the original thread, as it relates to this discussion as well, with links to the photographed atoms.

 

[Dmitry67]

I see 2 fundamental problems with BM:

1. Laplace determinism: me, typing this post right now, must be pre-coded in the initial conditions at the Big Bang.

2. While it manages to be compatible with 'standard' QM, when used outside of that framework - say, Hawking/Unruh radiation, it fails because the observers disagree if particle is real or virtual in different frames. Demystifier had addresses that issue inventing 'dead particles', but for me it is a beginning of curve fitting.

 

[sokrates]

Is the position of an electron determined to arbitrary precision in the quantum eraser? I don't think so. But that's why I have to keep asking the same question over and over.

If you understood the quantum eraser experiment, or bothered to check the wikipedia article on quantum eraser when Dr.Chinese first brought it up, you'd see that "the position of an electron is determined to extreme precisions (that is possible by today's experimental apparati)" which is another way of saying that "electron behaves as a particle".

He was kind and trying to make it clear. But let me say this upfront: The particle nature of electron is a very well established experimental fact, and the validity of it is not a matter of semantics or interpretations. Any interpretation has to accommodate itself to include this duality. So instead of trying to refute everything that is pointed out to you, maybe you could start looking up things like, wave-particle duality, and photoelectric effect and Compton scattering, etc... as I said in my earlier post. It is NOT a matter of high energies. It is NOT limited to Coulomb scattering. It is a fundamental observation.

 

[Mentz114]

OK, I agree that I am ignorant when it comes to BB, now will you please give me a single experiment that favors BM over Copenhagen, even at the slightest sense??

Otherwise, I'll stick to my points.

No I can't. Can you give me a single experiment that favours any interpretation of QM ?

As I understand it, there's nothing predicted to be different so experimental evidence
is irrelevant.

 

[Mentz114]

I see 2 fundamental problems with BM:

1. Laplace determinism: me, typing this post right now, must be pre-coded in the initial conditions at the Big Bang.

2. While it manages to be compatible with 'standard' QM, when used outside of that framework - say, Hawking/Unruh radiation, it fails because the observers disagree if particle is real or virtual in different frames. Demystifier had addresses that issue inventing 'dead particles', but for me it is a beginning of curve fitting.

The wave equation evolves deterministically in all quantum theories that have one. So they all require some intial conditions.

What's wrong with the 'dead particle' model ? are you saying that the Born treatment of mixed states is more intuitive ? I find Dr Nikolic's explanation of mixed states and measurement entirely harmonious with the Schrodinger/Heisenberg/Born/Dirac type thinking.

 

[Dmitry67]

The wave equation evolves deterministically in all quantum theories that have one. So they all require some intial conditions.

Yes, but non-deterministic theories and MWI can have very simple or null initial conditions
These theories can be compatible whit "God had no choice" while BM is not
BM is dragging us back to the nightmare of the laplace determinism

 

[conway]

If you understood the quantum eraser experiment, or bothered to check the wikipedia article on quantum eraser when Dr.Chinese first brought it up, you'd see that "the position of an electron is determined to extreme precisions (that is possible by today's experimental apparati)" which is another way of saying that "electron behaves as a particle".

But I did read the Wikipedia article and I didn't see anything about electrons. I even went back and searched for the word "electron" and it said "phrase not found". Isn't the quantum eraser experiment done with photons?

 

[conway]

Sokrates, who are you quoting when you say "the position of an electron is determined to extreme precisions..."? I googled the whole phrase and it doesn't appear anywhere on the Internet except in your post.

 

[Dale]

Hi Mentz114 and zenith8, you two are confusing me:

The predictions of BM are the same as 'standard' QM.

This is what I had understood previously, that it was an interpretation of QM, not a separate theory. But zenith8 disagrees:

De Broglie-Bohm is indeed a different theory; it is based on a different set of axioms to orthodox QM and it makes different predictions which in principle - though with great difficulty - could be observed (in the so-called quantum non-equilibrium case).

So which is correct? Does it make different experimentally testable predictions from standard QM (therefore being a different theory) or does it make the same experimentally testable predictions (therefore being a different interpretation).

 

[Dale]

I know from the double slit experiment that an electron couldn't be described as a wave (each electron hits a point of the detector) nor as a particle (after a lot of electrons fired, I get a diffraction shape).

I would say this differently. I would say: "I know from the double slit experiment that an electron couldn't be described as a classical wave (each electron hits a point of the detector) nor as a classical particle (after a lot of electrons fired, I get a interference shape)." The answer is that they are quantum mechanical particles which have a single unified mathematical description in QM that predicts both features of the experiment that you have identified.

 

[Mentz114]

DaleSpam:

So which is correct? Does it make different experimentally testable predictions from standard QM (therefore being a different theory) or does it make the same experimentally testable predictions (therefore being a different interpretation).

My understanding is that deBroglie-Bohm is an interpretation of QM and makes the same predictions. Whether an experimental test exists to distinguish dBB and orthodox QM is an arguable point. People have looked for something in the hope of resolving this but there's no easy way to do it. dBB is based on the Schroedinger equation, after all.

The answer is that they are quantum mechanical particles which have a single unified mathematical description in QM that predicts both features of the experiment that you have identified.

Yes, understanding QM with purely classical analogies is doing things upside down. One of the strengths of QM ( any flavour you like ) is that classical mechanics is recovered as average behaviour in large ensembles. So QM is a 'bigger' theory than classical mechanics, even a replacement for CM.

 

[Dmitry67]

What's about mysterious and elusive 'nonequilibrium states'?

 

[Demystifier]

I see 2 fundamental problems with BM:

1. Laplace determinism: me, typing this post right now, must be pre-coded in the initial conditions at the Big Bang.

2. While it manages to be compatible with 'standard' QM, when used outside of that framework - say, Hawking/Unruh radiation, it fails because the observers disagree if particle is real or virtual in different frames. Demystifier had addresses that issue inventing 'dead particles', but for me it is a beginning of curve fitting.

1. It's very strange that somebody who preferres the many-world interpretation (MWI) objects that, because in MWI it is also the case that everything is precoded in initial conditions.
Anyway, BM is the simplest known way to make QM compatible with the existence of objective reality. (In fact, MWI is even simplest, but unlike BM if fails to explain the Born rule.) It is not that BM is constructed so because somebody WANTS to restore determinism. Instead, determinism emerges as a bonus from a desire to restore objective reality in the simplest possible way.

2. The dead particles appear in the theory automatically, even before invoking the bohmian interpretation. The dead particles are a natural consequence of the requirement that all states in QFT should be described by wave functions in the relativistic configuration space.
Besides, in this relativistic version of BM based on such wave functions, it is no longer true that everything is precoded in the initial conditions at the big-bang. Instead, the "initial" conditions are distributed at all times.

 

[Demystifier]

OK, I agree that I am ignorant when it comes to BB, now will you please give me a single experiment that favors BM over Copenhagen, even at the slightest sense??

There isn't any. Just as there isn't any experiment that favors Copenhagen over Bohm too.

Anyway, you might like these papers
http://xxx.lanl.gov/abs/quant-ph/0505143 [Found.Phys.Lett. 19 (2006) 553-566]
http://xxx.lanl.gov/abs/0707.2319 [AIPConf.Proc.962:162-167,2007]
showing that even classical mechanics can be formulated in terms of (probabilistic) waves only.

 

[Cthugha]

Hi Mentz114 and zenith8, you two are confusing me:This is what I had understood previously, that it was an interpretation of QM, not a separate theory. But zenith8 disagrees:[...] So which is correct? Does it make different experimentally testable predictions from standard QM (therefore being a different theory) or does it make the same experimentally testable predictions (therefore being a different interpretation).

Let me give an answer from the position of someone, who tries to stay out of these "religious" debates. For several dozen years the standard qm interpretation and Bohmian interpretations made exactly the same predictions. One might argue, which one is more elegant, but the majority of people cares less about elegance and more about how complicated the math involved is. The math is usually easier in standard qm. Whether this is a consequence of the formalism itself or just a consequence of more people using standard formalism can be discussed as well. However, this also does not bother the majority of physicists.

However in order to reproduce the predictions of standard qm de-Broglie-Bohm needs the quantum equilibrium hypothesis, which states that if for some variable $$\rho (q,t_0)=\left|\psi(q,t_0)^2\right|$$ is valid, then $$\rho (q,t)=\left|\psi(q,t)^2\right|$$ is also valid. If one assumes this hypothesis, the predictions of standard qm and Bohmian mechanics are the same. However one guy called Valentini assumes that this equilibrium situation is just the limiting case of a more general theory, which can also treat nonequilibrium cases and assumes that there should have been some nonequilibrium condition shortly after the big bang. If that was true, the cosmic background radiation should show some signatures of this. Whether modern detectors are sensitive enough to detect this difference is however unclear. See this overview from Science for a short summary of his work http://www.sciencemag.org/cgi/reprint/324/5934/1512.pdf.

So I think Valentini is the first guy really doing physics (by really making predictions) when it comes to Bohmian mechanics instead of just some funny calculations. Nevertheless I do not know, whether he is right or not and I also do not know, whether it is possible to extend standard qm so that it can reproduce the results predicted by Valentini.

So until there is really some experimental evidence for any of those theories, I will just continue to just not care about these discussions.

 

[Demystifier]

Yes, but non-deterministic theories and MWI can have very simple or null initial conditions
These theories can be compatible whit "God had no choice" while BM is not
BM is dragging us back to the nightmare of the laplace determinism

Why laplace determinism is a nightmare?

 

[Dmitry67]

1. MWI can have null initial conditions.
The difference is not that MWI does not require inital conditions , but it can start from very simple initial conditions, say, vacuum in the pre-inflation BB era.
So in terms of the amount of information the information in BM is huge even at the BB, while in MWI universe become simpler and simpler when we rollback the film back to the BB.

2. And what's about the superstring - non-zero-sized 'particles'? Does BM has anything specific to predict in LQG or Superstring area?

 

[Dmitry67]

Why laplace determinism is a nightmare?

In MWI God is very lazy: he defined the laws, then pressed the Big Bang button and went away :) In BM He spent the enternity before pressing the big red "START" button carefully positioning the BM particles by his tweezers so 14 billions years later they form this very post.

 

[Demystifier]

1. MWI can have null initial conditions.
The difference is not that MWI does not require inital conditions , but it can start from very simple initial conditions, say, vacuum in the pre-inflation BB era.
So in terms of the amount of information the information in BM is huge even at the BB, while in MWI universe become simpler and simpler when we rollback the film back to the BB.

2. And what's about the superstring - non-zero-sized 'particles'? Does BM has anything specific to predict in LQG or Superstring area?

1. I disagree. If the initial condition is too simple (i.e., COMPLETELY symmetric and ordered), and if evolution is completely deterministic, then the state CANNOT evolve into something with a nontrivial structure. You need at least small initial non-homogeneities in order to get large non-homogeneities during the evolution. (If you claim the opposite, give me a reference which shows that.)

2. If you want to describe particle creation without introducing "dead particles", then, in a certain sense, string theory is a PREDICTION of BM:
http://xxx.lanl.gov/abs/0705.3542 [Europhys. Lett.85:20003, 2009] (Section 5.)

 

[Demystifier]

In MWI God is very lazy: he defined the laws, then pressed the Big Bang button and went away :) In BM He spent the enternity before pressing the big red "START" button carefully positioning the BM particles by his tweezers so 14 billions years later they form this very post.

I see no nightmare in this.

 

[Dmitry67]

1. I disagree. If the initial condition is too simple (i.e., COMPLETELY symmetric and ordered), and if evolution is completely deterministic, then the state CANNOT evolve into something with a nontrivial structure.

Easy. MWI can break symmetry in symmetrical way.

Say, initial state is symmetric: 0:0
In MWI 2 branches can appear: -1:1 and 1:-1
Now in all sub-branches of these initial branches are assymetric, while the whole universe from a bird view is symmetric.

Another example. Take void infinite chessboard of the Conway's Game of Life. Add a block 2x2 somewhere (by somewhere you add an infinite number of branches). Then do it again, again, and again. (I add 2x2 blocks becuase isolated figures do not survive in a game of Life, but later you can add individual figures).

Sooner or later on some sub-branch you will get a turing machine!

So your claim - simple and symemtric can not deterministically evolve into complex and assymetric is true, but only for the single-history theories.

Again, this is important: Symmetry can not be broken deterministically in a single-history theory!
To break a symmetry you need:
* Randomness, like in CI
* Pre-coded assymetry (BM)
* Multi-history (each branch breaks symmetry symmetrically)

 

[Dale]

My understanding is that deBroglie-Bohm is an interpretation of QM and makes the same predictions. Whether an experimental test exists to distinguish dBB and orthodox QM is an arguable point. People have looked for something in the hope of resolving this but there's no easy way to do it. dBB is based on the Schroedinger equation, after all.

Until this thread that was my understanding also. If it is indeed an interpretation of QM then I take the same view of dBB as I do of all interpretations of any theory: use whatever interpretation you like whenever you like to use it, just be aware that there is never any evidence to support one interpretation over another.

 

[lightarrow]

...

Isn't simpler to think that the bodies are particles but they don't move in straight directions, but according to their wave (where the wave is something associated but separated from the body)?

And why do they move according to their wave? An electric charge, for example, moves according to an electric field; and in this case?