# Propagation of de Broglie waves

1. Dec 30, 2014

### Akash Pardasani

I had a doubt regarding the propagation of de Broglie waves.
How do we know the speed of propagation of these waves and also do there characteristics( speed and amplitude and frequency) depend on the source particle ( or they depend only on the motion(momentum) of the source and no whatsoever relation with the "type" of particle)?

2. Dec 30, 2014

### dextercioby

The concept of de Broglie waves is outdated, has been that way since the wave mechanics of Schrödinger has been reinterpreted correctly in the realms of serious QM (Born + Dirac + von Neumann). So your question has really no relevance. If you mean the deBroglie-Bohm <guiding waves> (the so-called <Bohmian mechanics>), that's a different (>1952) enchilada and here we have some very knowledgeable forum colleagues.

3. Dec 30, 2014

### Staff: Mentor

Dextercioby is correct.

The problem is the semi historical way QM is often taught. They don't go back and point out things like de-Broglie waves they use to motivate the QM formalism are no longer correct in that formalism. This leads to all sorts of confusion in beginning students, so much so I don't think its the correct way to go about teaching it - but then again other methods have issues as well so its basically loose loose doesn't matter what you do.

But just as an example of another approach check out:
http://www.scottaaronson.com/democritus/lec9.html

Also the following gives the correct historical account of how QM came about:

De-Broglies ideas lead to Schroedinger's equation when someone challenged Schroedinger that if you have waves you need a wave equation. But Heisenberg came up with a totally different approach based on matrices. It was thought they were equivalent and Schroedinger made an attempt to show such but it wasn't entirely successful. At the end of 1926 Dirac made a better fist of it and it is what generally goes by the name QM these days - but mathematically it has issues with the so called Dirac Delta function. Von-Neumann fixed those up in his famous Mathematical Foundations Of Quantum Mechanics published in 1932 but it wasn't as elegant as Dirac's approach so physicists stuck with Dirac despite its mathematical problem. Mathematicians then went hard to work and fixed up the issues with Dirac and these days either method is mathematically just as valid.

The point though is Dirac's version (he called it the transformation theory) meant the issues that birthed it like de-Broglies were consigned to the scrap heap, and except as part of the history of QM is best forgotten about.

Thanks
Bill

4. Nov 19, 2016

### afcsimoes

I have read that the today's mainstream QM is based on the infinite wave because it is the unique that has a defined frequency, with the sequente use of Fourier analisys. This lead to the lost of the locality.
I also has read that the wavelets math concept can bring the losted locality back again.

5. Nov 19, 2016

### vanhees71

Whereever you read that, through the source away ;-). In modern non-relativistic QM (there's only one QM not a mainstream or whateverelse) a particle can be described by a wave function, obeying the Schrödinger equation. It is well defined and not infinite. It's a complex valued field $\psi(t,\vec{x})$. Its modulus squared, $|\psi(t,\vec{x})|^2$ gives the probability density to find a particle at the position $\vec{x}$ at time $t$.

I also don't know, what you mean by "lost locality". The Schrödinger equation is a partial differential equation and as such a local concept.

6. Nov 19, 2016

### Quotidian

Hi there - I have been involved in a discussion of interpretations of physics on a philosophy forum. A question has come up, related to this thread, so I thought I might ask it here.

I am not a physics graduate. I have read documentry histories of the subject, like Manjit Kumar's 'Quantum' and David Lindley's 'Uncertainty', and have a reasonable grasp of some of the philosophical issues underlying the Bohr-Einstein debates, but I can't read physics equations.

Bearing that in mind, the question is this. The 'interference patterns' associated with the famous 'double-slit' experiment, are really patterns left on screens. The question is, what is causing those patterns? The answer is, sub-atomic particles. But if the particles are fired one-at-a-time, then how can they form an 'interference pattern'? How is a single particle interfering with itself? That seems to be the issue.

Could you say that when the particles are fired sequentially, they're still behaving as though they're part of a beam of particles.? It's as if time has been taken out of the equation, so that the sequence of particles behaves as though they're being fired together instead of being separated by time.

So is there any sense in which the probability distribution is causing the individual particle to behave as though it is part of a beam of particles? It seems as if the probability distribution is itself like the so-called 'pilot wave' - in other words, it determines all the possibilities, but only in the sense of constraining the possible paths that any individual particle takes, whether individually or as part of beam. But because it is simply probability, or possibility, it is not something that actually exists; it is on the borderline of potentiality and actuality.

Does this kind of thinking make any sense?

Last edited: Nov 19, 2016
7. Nov 19, 2016

### Staff: Mentor

The answer is the uncertainty principle and the principle of superposition. It is explained here:
https://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

Physics unfortunately goes through various levels depending on how advanced the audience is. At the start and in popularization's you have the wave particle duality as the explanation of the double slit. Unfortunately it is one of the many myths of QM:
https://arxiv.org/abs/quant-ph/0609163

Then you have an explanation like the above aimed at a slightly more advanced reader. Unfortunately, while much much better (otherwise I would not use it) it to is wrong to an even more advanced reader:
https://arxiv.org/abs/1009.2408

To make matters worse to the very advanced reader, some of whom post here it, to is wrong. Physics unfortunately can be like that and is a big issue for guys like you. At your level take the paper I linked to is the explanation - forget the more advanced stuff.

Not really. We know the why of the double slit very well and hopefully after reading my linked paper you will to.

If you REALLY want to learn QM get these three books in the following order:
https://www.amazon.com/Quick-Calculus-Self-Teaching-Guide-2nd/dp/0471827223
https://www.amazon.com/Theoretical-Minimum-Start-Doing-Physics/dp/0465075681
https://www.amazon.com/Quantum-Mechanics-Theoretical-Leonard-Susskind/dp/0465062903

Then if you want to learn the real basis of modern physics, the truth that students when they learn about it usually in graduate school leaves them it in stunned silence, the truth that basically left Einstein speechless when he heard about one of its foundation discoveries, Noethers Theorem, get the following:

But before that, to set the stage so to speak, get Landau Mechanics:
https://www.amazon.com/Mechanics-Third-Course-Theoretical-Physics/dp/0750628960
If physicists could weep, they would weep over this book. The book is devastingly brief whilst deriving, in its few pages, all the great results of classical mechanics. Results that in other books take take up many more pages. I first came across Landau's mechanics many years ago as a brash undergrad. My prof at the time had given me this book but warned me that it's the kind of book that ages like wine. I've read this book several times since and I have found that indeed, each time is more rewarding than the last.'The reason for the brevity is that, as pointed out by previous reviewers, Landau derives mechanics from symmetry. Historically, it was long after the main bulk of mechanics was developed that Emmy Noether proved that symmetries underly every important quantity in physics. So instead of starting from concrete mechanical case-studies and generalising to the formal machinery of the Hamilton equations, Landau starts out from the most generic symmetry and dervies the mechanics. The 2nd laws of mechanics, for example, is derived as a consequence of the uniqueness of trajectories in the Lagragian. For some, this may seem too "mathematical" but in reality, it is a sign of sophisitication in physics if one can identify the underlying symmetries in a mechanical system. Thus this book represents the height of theoretical sophistication in that symmetries are used to derive so many physical results.'

I could say more but best you discover it for yourself from the references I gave.

It will change your view of the world and hopefully start a discussion with your philosophy friends on the REAL foundations and meaning of physics.

Thanks
Bill

Last edited: Nov 19, 2016
8. Nov 19, 2016

### Quotidian

Hey Bill - thanks for that - I guess the answer is, I am not going to learn physics at this stage in life. I really ought to think about other things. Thanks.

Altough, I would like an answer to this question, if it's possible:

'Could you say that when the particles are fired sequentially, they're still behaving as though they're part of a beam of particles?'

9. Nov 19, 2016

### Staff: Mentor

In QM whats going on when not observed we do not know - the theory is silent. So the answer is - we don't know.

Thanks
Bill

10. Nov 19, 2016

### Quotidian

But, the result when you fire the beam of particles sequentially, and when you fire it all it once, is the same, is it not?

11. Nov 19, 2016

### hairyzussy

How do you produce a negative probability using an electron probability wave?

12. Nov 19, 2016

### Staff: Mentor

Obviously not - in a beam two or more can flash the screen at the same time.

If by behaving the same you mean it makes little difference to the analysis - yes (you do then have the possibility is collisions in a beam).

Thanks
Bill

13. Nov 19, 2016

### Staff: Mentor

Have you heard of the Kolmogorov axioms? If not look them up and you will see its impossible - probability is positive.

During the early days of QM in relativistic problems you got negative probabilities which indicated you were in deep do do. The reason is it was the positive probability of an antiparticle. But it was also found the extension of QM to Quantum Field Theory (QFT) was a much better way to handle the issue.

This however is way way off topic - if you want to discuss it further stat a new thread.

Thanks
Bill

14. Nov 19, 2016

### afcsimoes

So, if we made a first duble slit experiment using a beam and a second experiment firing the same amount of particles but in a one by one basis, then we wil finish with two conrete objective and real identical images of an interference patern?

15. Nov 19, 2016

### Staff: Mentor

Yes.

Thanks
Bill

16. Nov 20, 2016

### Quotidian

afcsimoes: So, if we made a first double slit experiment using a beam and a second experiment firing the same amount of particles but on a one by one basis, then we wil finish with two concrete objective and real identical images of an interference patern?

bhobba: Yes.

Thanks! So from this, can I presume that the interference pattern is not rate-dependent, i.e. the rate at which the photons are emitted doesn't affect the distribution?

17. Nov 20, 2016

### Staff: Mentor

Yes.

Thanks
Bill

18. Nov 20, 2016

### afcsimoes

What is the explanation for that? At the second experiment, fired one by one, how can each electron interfere with all the previous and with all the futures? Or interfere with himself?
Alternatively, can it be justified with some uncertainty/probabilistic quantic event at/in the shooter? Or at the double slit? A shootted electron interfering with the electrons of the slit edge substance? (e.g. as if the electron's wave was a 4D helicoide)

19. Nov 20, 2016

### Staff: Mentor

Its simply the same experiment done in parallel and repeated many times over.

I gave a link to the why of the double slit. The explanation works if there is one or many.

Thanks
Bill

20. Nov 20, 2016

### afcsimoes

I will try to read and understand.
Thank you Bill
Armando

21. Nov 21, 2016

### fanieh

Do particles in the deBroglie-Bohm have trajectories? It seems they are local particles yet it seems there is at the same time no trajectories. So do the particles just appear when measured? but is it not Bohmian mechanics is about trajectories?

22. Nov 21, 2016

### Quotidian

So, to recap the question I had: it is well known that if you set up a double-slit experiment, then send the particles through the slits one-at-a-time, you still get interference patterns. This is a paradox, because there's no question of the particles interfering with one another, as they're sent separately. This paradox is consequence of superposition.

As a consequence, if you ran two instances of a double-slit experiment, the first being one-photon-at-a-time, the second being all the photons being fired at once - given that in all other respects the set-up was identical, could you detect the difference between the two experiments, on the basis of the interference patterns alone? Answer is 'no'.

What I find interesting about that, is that if the same interference pattern is created by either 'slow' or 'instantaneous' transmission of energy, then the factor of 'duration of the event' doesn't seem to have any consequences for the formation of the pattern. So the 'interference pattern' is not actually a consequence of 'interference' at all, because when the single photon test is run, there is nothing to interfere with the single photon - yet it produces the same pattern as if it is run en masse.

So what I am taking from that, is that the cause of the interference pattern, is not actually 'interference' in the sense that water waves 'interfere' with each other. The kinds of waves associated with water, are only an analogy for the 'wave function' that determines the 'interference pattern'.

So what determines the interference pattern really is the probabilities expressed by the wave function equation, and this is not a function of time (otherwise, the rate would effect it.) But more to the point, it's an illustration of how mere probabilities can be causally effective.

23. Oct 2, 2017

### physics pfan

Hi bhobba,

Your wrote: "The point though is Dirac's version...meant the issues that birthed it like de-Broglies were consigned to the scrap heap"
Please explain the issues. A photon meets a slit, an electron meets a crystal lattice; both photon and electron diffract; hence small matter can assume a wave identity; this was de Broglie's main point.. What part of this goes to the scrap heap?

You also wrote: "...then again other methods have issues as well so its basically loose loose doesn't matter what you do." I think you meant 'lose' and not 'loose' and I don't think you can claim 'typo' here. You and the many are not clear on the difference...

physics pfan

24. Oct 2, 2017

### Staff: Mentor

All the phenomena which was explained by the so called wave particle duality was explained instead by Schrodinger's equation whose new explanation, while not known to Dirac (he derived from an assumption about Poisson brackets) is actually symmetry ie the probabilities of the Born Rule are frame independent which is so damn obvious nobody would really question it - but strictly speaking you are invoking Einsteins Principle Of Relativity - see Chapter 3 Ballentine. Note - its at the advanced undergraduate level - if you are not at that level you will just have to take my word for it. Schrodinger thought it was actually waves and his equation described those waves. As an aside he actually made two cancelling errors in his derivation, but that's another story - and his derivation was pretty much a crock anyway. But it soon became clear it wasn't about actual waves, and he became despondent because he thought that's what was going on - so despondent he wished he never had anything to do with it. To understand its not waves simply look at the hydrogen atom:
https://chemistry.stackexchange.com...-many-wave-functions-associated-with-hydrogen

None of those look like waves to me .

Auto correction - its not perfect and doesn't pick up words that are correct spelling for something different - its lose, lose.

In don't know what you mean by the many do not know the difference - even someone in grade 1 here would know the difference.

My English is terrible, my worst subject at HS - I failed it. But its not so bad I don't know that one - it's just carelessness in trusting spell checkers - it happens to the best of us, even people with much better literacy skills than me.

Thanks
Bill

Last edited: Oct 2, 2017
25. Oct 3, 2017

### Blue Scallop

Can you please elaborate what you meant by Schrodinger actually "made two cancelling errors in his derivation"? so the two errors cancel out to become right? weird.. what is it