Electromagnetic radiation and Flaw of De-Broglie Equation

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Discussion Overview

The discussion revolves around the implications of the De-Broglie equation in the context of electromagnetic radiation, particularly focusing on the properties of photons and the relationship between wavelength, momentum, and energy. Participants explore theoretical aspects, including relativistic considerations and classical electrodynamics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether the wavelength of light becomes infinite due to the zero mass of photons when applying the De-Broglie equation, suggesting a contradiction with the finite wavelength observed in light.
  • Another participant clarifies that the momentum of a photon is given by the relation E/c, rather than the classical mv, emphasizing the need to consider massless particles in relativistic contexts.
  • A further contribution notes the relationship between energy and momentum densities in electromagnetic waves as described by Maxwell's equations, reinforcing the relativistic framework.
  • One participant presents an argument based on the Lorentz transformation, asserting that if an object has a frequency proportional to its energy, it must also have a wavelength inversely proportional to its momentum, citing experimental support for this relationship.

Areas of Agreement / Disagreement

Participants express differing views on the implications of the De-Broglie equation for photons, with some supporting the traditional interpretations and others challenging them. The discussion remains unresolved regarding the apparent contradiction raised about the wavelength of light.

Contextual Notes

There are limitations in the assumptions made about the application of the De-Broglie equation to massless particles, and the discussion does not fully resolve the mathematical implications of these assumptions.

curious bishal
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By De-Broglie,light also exibits matter property. According to him, wavelength=planck's constant/ momentum. And again momentum is the product of mass and velocity. We again know that, mass of light i.e. photon is zero. Then from De-Broglie's equation, is the wavelength of light infinity?
If so,from wave property of light,wavelength of light is finite. Is such contradiction allowed?
 
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The momentum of a photon is not [itex]mv[/itex], it's [itex]E/c[/itex]. This follows from Einstein's [itex]E^2=p^2c^2+m^2c^4[/itex] for a massless particle.

(In addition, the relation [itex]p=\gamma mv[/itex] should be used in relativity for the three-momentum of massive particles, where m is the invariant mass, but that's not very relevant in this case. Just so you know.)
 
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Note also that in Maxwell's classical electrodynamics (which is fully relativistic even though Maxwell knew nothing about Einstein's relativity!), the energy and momentum densities of an electromagnetic wave are related by E = pc.
 
What I got from reading DeBroglie's paper is a very simple argument. If an object has a frequency proportional to its energy, then the laws of relativity require that it also have a wavelength which is (inversely) proportional to its momentum.

This is because of how the Lorentz transformation works. If you have some object that say, changes colors periodically in time (say, moving from uniformly red to uniformly blue and back again), and you change to a moving reference frame, you will see that the object is not all the same color at the same time. It changes from red to blue and back again over the length of the object (and also in time). This is the relativity of simultaneity in action.The faster you're moving, the quicker the colors appears to oscillate over the length of the object (and in time).

What it means is that if an object has a characteristic frequency, it must have a characteristic wavelength as well, and since that frequency is proportional to energy, the momentum must be inversely proportional to the wavelength in order for everything to work out correctly.

Since then lots of experiments have been done to back this up, so it's not just theoretical speculation.
 

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