De Broglie wavelength and velocity

[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.

 

[Vanadium 50]

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

 

[jtbell]

And how we connect this with special relativity where the velocity depends on the frame of reference.

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.

 

[Vanadium 50]

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.

 

[DrClaude]

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.

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/

 

[Heinera]

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/

That is correct.

An english translation of the thesis can be found here: https://www.relativitycalculator.com/pdfs/On_Theory_Quanta.pdf

 

[DrClaude]

An english translation of the thesis can be found here: https://www.relativitycalculator.com/pdfs/On_Theory_Quanta.pdf

That link doesn't work.

 

[Heinera]

That link doesn't work.

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

 

[Vanadium 50]

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.

 

[DrClaude]

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

Server not found.

 

[Heinera]

Server not found.

Ok. See if you have better luck with this server:

http://www.plasma.uaic.ro/topala/articole/De_Broglie%201927.pdf

 

[DrClaude]

Ok. See if you have better luck with this server:

http://www.plasma.uaic.ro/topala/articole/De_Broglie%201927.pdf

Yes, it works.