De Broglie wavelength and it's dependence of the frame of reference

[Dweirdo]

Hello,
I've always wondered about the "relativity" of the De Broglie wavelength.

The wavelength depends on the momentum of the specific thing we are observing, thus on different frames of reference(F.O.R from now on :P) we might get different answers.
I have been looking through the web to find an answer for "how can it be , it's so weird",and found some not-actually-answered answers ,so I won't even ask cause it involves our understanding of "particles"/"waves" and their nature,nor about the "infinite wavelength" issue.


but I do want to ask about a some sort of a paradox:
as postulated by De Broglie :
The only way to ‘fit a wave’ around a nucleus is when the wavelength fits the circumference a whole-number of times,aka a standing wave.
However, the wavelength depends on the F.O.R so ,in a F.O.R moving 100 m/s relative to an atom the wavelength of the electron is different ,thus it's orbit should be different, and we've come up to a great way to find absolute velocity(?) ,I hope you guys see the paradox here,or the not-so-obvious interpretation of the De Broglie wavelength,seems like we have to add a "relative to..." when we talk about wavelength as we do with velocity ,momentum and kinetic energy.

like
"The only way to ‘fit a wave’ around a nucleus is when the wavelength relative to the nucleus fits the circumference a whole-number of times,aka a standing wave." but it's really weird to say...

so if anyone can help me "Solve" the paradox if there is any paradox,or it's just me not getting it... any ideas are welcome.

Thanks
Dw

 

[sophiecentaur]

Is this really a problem? If you say the atom is moving wrt your FOR then the de B wavelength will not be constant all around the atom from your (the observer's) point of view. That would mean that the wave pattern of the electron would be distorted. However, the concept of an "orbit" may be a bit too simplistic for such a discussion so the idea of the wavelength on one side being different from the wavelength on the other, as it 'goes round' may not have a lot of meaning - the model being too approximate for any real conclusions to be drawn.

 

[Dweirdo]

"Is this really a problem? If you say the atom is moving wrt your FOR then the de B wavelength will not be constant all around the atom from your (the observer's) point of view. That would mean that the wave pattern of the electron would be distorted. "

It is a great problem, even bigger with what you've just pointed out about the wavelength not being constant.
It is an EVENT that doesn't happen on one FOR but happens on another FOR while they have constant relative velocity, which is a major contra-diction of the most obvious principles of relativity(leaving SR behind).

I sure think that it is a problem,I would really appreciate if you could show me otherwise.

thanks,
dw

 

[cragar]

wouldn't this be the same as the doppler effect of light , Different observers would see different colors of light based on how fast they were going .

 

[Dweirdo]

cragar,you have a good point...it is a really good analogy.
but I still have a problem understanding "if the electron has a different wavelength in one frame of reference how can it still be a "standing wave""

 

[sophiecentaur]

cragar,you have a good point...it is a really good analogy.
but I still have a problem understanding "if the electron has a different wavelength in one frame of reference how can it still be a "standing wave""

A practical, mechanical, example of this would be having a guitar string which is of one thickness at one end and another thickness at the other. You can set up a standing wave on it but the wavelength will change half way along because the speeds of propagation are different. (the frequencies being the same). Or imagine a circular metal tube with a standing sound wave set up in it (tiny loudspeaker placed in there), spinning around its axis and moving past you. If you could observe the vibrations at different points in the tube, you would get different frequencies all around it but, as far as the tube is concerned, thee would be a single frequency / wavelength involved in the standing wave. All that's necessary for a standing wave is for the phases of the oscillations, in the region it exists, to be right to sustain it.

I still think SR is, actually a bit of a red herring here (on a first level of analysis). The electron is behaving itself quite 'properly' in its bound state around the atom - it's just that an 'observer' would see some distortion in its behaviour because of their relative motion. This would happen even in a classical model because there is nothing invariate about the speed of an electron.

@Dweirdo: I can see that you have a problem with this but, maybe you are applying 'rules' to standing waves that are more restrictive than necessary.
I have just thought of the Michelson Morley experiment which, effectively, does the same sort of thing with light (and you can do it with lasers and standing waves in fibre optic rings) and there is no problem with SR there.

 

[Dweirdo]

Cool,the first paragraph actually makes sense ,but I wonder if it is applied to our specific situation if there is still a standing wave..

When I mentioned SR, I meant that I'm not taking it into account, just the general principles of relativity such as "two observers moving with a constant velocity relative to each other can't have an experiment that agrees if some one moves/rests.".

I still have my doubts,but it is definitely clearer now,thank You :)

 

[sophiecentaur]

Cool,the first paragraph actually makes sense ,but I wonder if it is applied to our specific situation if there is still a standing wave..

But there is a standing wave. A moving observer would still, in principle, see nodes and antinodes (a probability distribution, if you are talking QM). The actual shape could be changed (as in the case of the discontinuous guitar string) but what you could see would still satisfy the requirements for calling it a standing wave. As I said at the start, it would just be distorted compared with the wave that the atom, itself, would see.

 

[Dweirdo]

I got that,thanks :)