De Broglie wavelength and velocity

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Discussion Overview

The discussion centers on the de Broglie wavelength and its relationship with velocity, particularly in the context of special relativity. Participants explore how the wavelength of an object changes with its speed and the implications of frame of reference on both velocity and wavelength.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • Some participants propose that the de Broglie wavelength is shorter for faster-moving objects due to higher momentum.
  • Others argue that de Broglie's theory is fundamentally non-relativistic, despite its development occurring after special relativity.
  • A participant asserts that de Broglie's thesis incorporates relativistic concepts, starting from the equation \(E = mc^2\) and combining it with Planck's equation \(E = h \nu\) to derive a wavelength for matter waves.
  • Some participants discuss the dependence of wavelength and velocity on the frame of reference, noting this applies even in non-relativistic mechanics.
  • There is contention regarding whether de Broglie's approach can be considered relativistic, with some stating that it does not transform correctly under relativistic conditions.
  • Participants share links to de Broglie's thesis and translations, with some experiencing issues accessing the provided resources.

Areas of Agreement / Disagreement

Participants express differing views on whether de Broglie's theory should be classified as relativistic or non-relativistic, indicating a lack of consensus on this point. The discussion remains unresolved regarding the implications of frame of reference on the de Broglie wavelength.

Contextual Notes

There are unresolved questions about the definitions and assumptions underlying the classification of de Broglie's theory, as well as the implications of using relativistic expressions in a non-relativistic framework.

durant35
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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.
 
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The wavelength is shorter because the momentum is higher. De Broglie was developed before SR, so it is not a relativistic theory.
 
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durant35 said:
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.
 
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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.
 
Vanadium 50 said:
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/
 
DrClaude said:
That link doesn't work.
Hm. Works here. What kind of error do you get?
 
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.
 
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Heinera said:
Hm. Works here. What kind of error do you get?
Server not found.
 
  • #11
DrClaude said:
Server not found.
Ok. See if you have better luck with this server:

http://www.plasma.uaic.ro/topala/articole/De_Broglie%201927.pdf
 
  • #12
Heinera said:
Ok. See if you have better luck with this server:

http://www.plasma.uaic.ro/topala/articole/De_Broglie%201927.pdf
Yes, it works.
 

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