What is the shortest wavelength of all? >0 or h?

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Discussion Overview

The discussion revolves around the question of the shortest possible wavelength in theoretical physics, exploring concepts related to quantum mechanics, general relativity, and the implications of high-velocity observers. The scope includes theoretical considerations and interpretations of fundamental constants.

Discussion Character

  • Exploratory, Debate/contested, Conceptual clarification

Main Points Raised

  • Some participants propose that the shortest wavelength could be related to Planck's constant or could be anything greater than zero, depending on the theoretical framework.
  • Others argue that quantum mechanics imposes a minimum limit defined by the Planck length, while general relativity allows for infinitely divisible energy, suggesting gravity waves can theoretically have any size.
  • A participant claims there is no minimum wavelength, asserting that an observer moving at high velocity could perceive a wave with a significantly shorter wavelength.
  • Another participant clarifies that the Planck length (a measure of distance) should not be confused with the Planck constant (which relates to angular momentum).
  • One participant mentions that using De Broglie's formula, a fast-moving heavy particle could theoretically have a wavelength smaller than the Planck length.

Areas of Agreement / Disagreement

Participants express multiple competing views on the existence and definition of a minimum wavelength, indicating that the discussion remains unresolved.

Contextual Notes

There are limitations regarding the definitions of terms like Planck length and Planck constant, as well as the assumptions underlying the different theoretical frameworks being discussed.

Daniel Petka
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Theoretically of course, what is the shortest wavelength of all? Is it the size of the Planck's constant or just anything over zero?
 
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Daniel Petka said:
Theoretically of course, what is the shortest wavelength of all? Is it the size of the Planck's constant or just anything over zero?
Depends on what framework you are working with. Quantum mechanics has a minimum limit, which is the Planck length, General Relativity has smooth space and infinitely divisible energy, so gravity waves can be any size (theoretically.)
 
There is no minimum wavelength. Not even the Planck length. In the frame of reference of an observer traveling at a high velocity opposite the direction the wave is traveling, the wave would have a significantly shorter wavelength.
 
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Daniel Petka said:
Theoretically of course, what is the shortest wavelength of all? Is it the size of the Planck's constant or just anything over zero?

You should not confuse the Planck length (which has units of distance) with Planck constant (which has units of angular momentum).
 
With De Broglie's formula a fast moving heavy particle would have a wavelength smaller than Plank's length. (yeah not constant :p)
 

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