Freqeuncy of Matter Waves Approaches Infinity as Velocity Approaches c

In summary, the frequency of matter waves increases without bound as the velocity of a particle approaches the speed of light (c). This phenomenon is rooted in quantum mechanics, where the energy of a particle is directly related to its frequency. As the particle accelerates and nears the speed of light, its energy and, consequently, its wave frequency rise significantly, illustrating the fundamental relationship between velocity, energy, and wave behavior in the context of relativistic physics.
  • #1
hisgutsaysmaybe
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TL;DR Summary
If phase velocity = fλ, and as group velocity -> c, λ -> 0 but phase velocity -> c, then does this mean that f -> infinity as group velocity -> c?
I have heard that the phase velocity of matter waves can be represented as c^2/v. But if the wavelength of these matter waves goes to zero as momentum approaches infinity and v approaches c, then does this mean that the frequency of the matter waves approaches infinity, to give the matter wave a finite and nonzero speed?
In a way this might make sense, because E = ymc^2, so hf = ymc^2. However, the time of an event dilates for an observer which is moving with respect to the event, also by a factor of gamma. I had believed that these two phenomena might combine to appear to give the matter wave a constant frequency, regardless of the velocity of the observer.
 
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  • #2
hisgutsaysmaybe said:
I have heard
Where? Please give a reference.
 
  • #3
From De Broglie's 1924 paper, page 10 (445 of the journal):
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Taken from this PDF version: https://www.pwein.at/physics/Lectures/Famous-Papers/Phil-Mag-47-446-1924.pdf

I learned in school that the phase velocity was c^2/v, and I have taken it as fact without trying to understand why yet.
 
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