# Mechanistic explanation of de Broglie wavelength

1. Apr 22, 2014

### alexepascual

I am not proposing a particular explanation and just in case you suspect I have something in mind, I must tell you that I don't. I was wondering if anybody here has some ideas.
I understand that you may have objections to my question. One of them might be that a mechanistic model would not work because that would be classical mechanics and the de Broglie wavelenght is a quantum mechanical thing. But I am not trying to find a derivation or anything precise. I was just thinking that there might be some intuitive model that would help understand why a particle with larger momentum has a shorter wavelength. I am not looking for standard explanations such as the ones we find in textbooks, but some kind of intuitive paradigm.
Why there is a wave associated to a particle (you may also object this) probably nobody knows yet and is taken as a postulate. But lets consider a massive particle and its associated wave. If we look at a particle with twice the mass (moving at the same speed), its wavelength will be half the one of the original particle. Now, what happens if we look at this particle as being composed by two of the original particles next to each other? Each would have the original wavelenght but somehow they combine to form a single wave with half the wavelength. How can this be explained? Remember that I am looking for some picture of this and not some formula.
Also, if we take the original particle going at certain speed and having some wavelength according to its momentum, and then we increase the speed to twice its original value, then the wavelength will also be half the original one as we have doubled its momentum. How can this be explained? Do you have some ideas?

Last edited: Apr 22, 2014
2. Apr 22, 2014

### Staff: Mentor

Sure - there are a number of interpretations along those lines Bohmian Mechanics, Nelson Stochastics and Primary State Diffusion come to mind.

You can look them up to see how they relate to your idea.

But I have to tell you unless you can figure out how to experimentally test it its just another interpretation - we have tons of those.

Thanks
Bill

3. Apr 22, 2014

### akhmeteli

I wonder if the following thread may be of interest for you: https://www.physicsforums.com/showthread.php?p=3617237#post3617237

4. Apr 23, 2014

### alexepascual

Thanks a lot for your suggestions. I already saved some of the pdfs on my machine and will look into them. This thing of the walking bubbles is something interesting I had never heard. With respect to Bohmian mechanics, although I never discarded it, I never felt so attracted as to dig deeply into it. It always sounded to me as too complex. But I may someday change my mind. The picture that I have used so far has been that of the wave being just a probability wave which might be due to superposing trajectories of the particle (many-worlds-style). But I think the many-worlds approach still does not explain Born's rule. It is simpler though, and I was hoping some day an explanation for Born's rule could be found using some modification of many-worlds. I understand this may sound bad to those of you with a realist inclination. (realist in the sense of a one-world reality, because in a way the many-worlds approach is also realist or super-realist as it just implies a larger universe). Well, I'll look into the walking droplet thing. Thanks again.

5. Apr 23, 2014

### Staff: Mentor

Check out Gleasons theroem:
http://kof.physto.se/cond_mat_page/theses/helena-master.pdf [Broken]

Also the following:
http://arxiv.org/pdf/quantph/0101012.pdf

Basically the modern view is QM is what is called a generalised probability model, and its the simplest one that allows continuous transformations between pure states.

The argument goes something like this. Suppose we have a system in 2 states represented by the vectors [0,1] and [1,0]. These states are called pure. These can be randomly presented for observation and you get the vector [p1, p2] where p1 and p2 give the probabilities of observing the pure state. Such states are called mixed. Probability theory is basically the theory of mixed states where the pure states are the usual basis vectors.

Now consider the matrix A that say after 1 second transforms one pure state to another with rows [0, 1] and [1, 0]. But what happens when A is applied for half a second? Well that would be a matrix U^2 = A. You can work this out and low and behold U is complex. Apply it to a pure state and you get a complex vector. This is something new. Its not a mixed state - but you are forced to it if you want continuous transformations between pure states.

QM is basically the theory where pure states are complex vectors, and its the theory that makes sense out of such weird pure states. There is really only one reasonable way to do it - by the Born rule (you make the assumption of non contextuality - ie the probability is not basis dependant, plus a few other things need to go into it) - as shown by Gleason's theorem.

Thanks
Bill

Last edited by a moderator: May 6, 2017
6. Apr 24, 2014

### PhilDSP

One conceptual picture, given with the understanding that modern QM generally doesn't sponsor or support conceptual pictures, is to harken back a bit to Maxwell's idea that space may be somewhat like an energy reservoir that exhibits a very substantial amount of energy pressure or potential stress when the energy is locally disturbed by the presence of a particle. The particle obviously consists of a highly compact amount of energy.

If you interpret the mass term as a component of the energy being transported, that contributes greatly to the relativistic momentum term which really determines the wavelength. In effect as you push more energy faster, space responds more intensely in an effort to equalize the disturbance. The faster more energy is transported, the faster space responds. In other words, the transport of energy invokes elasticity.

Again, this is just one possible interpretive picture that sympathizes with a Maxwellian view.

Last edited: Apr 24, 2014
7. Apr 24, 2014

### craigi

This is exactly what this paper is about.

http://arxiv.org/abs/1008.1066

Under this interpretation, the different worlds are real.

The conceptual leap that the reader must take is to accept that we have no well defined location in the universe.

8. Apr 25, 2014

### alexepascual

Well, now I have a lot of material to read. I'll take some time though. As soon as I take at least a quick read and do some thinking I will post some comments. Thanks again to all of you.