# De Broglie wavelength and velocity

1. Feb 7, 2016

### durant35

I was wondering about the equation for the de Broglie wavelength which indicates that the wavelength of any object is shorter when the object is moving faster. Why does this occur? And how we connect this with special relativity where the velocity depends on the frame of reference.

2. Feb 7, 2016

Staff Emeritus
The wavelength is shorter because the momentum is higher. De Broglie was developed before SR, so it is not a relativistic theory.

3. Feb 9, 2016

### Staff: Mentor

The wavelength also depends on the frame of reference. Note that velocity and wavelength depend on the frame of reference, even in non-relativistic mechanics.

Last edited: Feb 9, 2016
4. Feb 9, 2016

Staff Emeritus
Doc Al pointed out that I was wrong about the sequence of events - DeBroglie was after SR. However, it is still a non-relativistic theory.

5. Feb 10, 2016

### Staff: Mentor

I'm sorry, but de Broglie's thesis from 1924 starts from $E = mc^2$. It is then by combining this with Planck's $E = h \nu$ that he ends up with a wavelength for a matter wave. I don't see how this is not a relativistic theory.

A reproduction of the thesis (in French) can be found at https://tel.archives-ouvertes.fr/tel-00006807/en/

6. Feb 10, 2016

### Heinera

7. Feb 10, 2016

### Staff: Mentor

8. Feb 10, 2016

### Heinera

Hm. Works here. What kind of error do you get?

9. Feb 10, 2016

Staff Emeritus
DeBroglie essentially takes a fundamentally NR equation and stick in the relativistic expression for momentum in it. That doesn't make it a relativistic equation. (If it did, GR would have been invented a decade earlier.) As pointed out earlier, it doesn't transform right. In modern language, it takes one component of a 4-vector and relates it to three components of a different 4-vector.

10. Feb 10, 2016