Electromagnetic radiation and Flaw of De-Broglie Equation

[curious bishal]

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?

 

[DeIdeal]

The momentum of a photon is not $mv$, it's $E/c$. This follows from Einstein's $E^2=p^2c^2+m^2c^4$ for a massless particle.

(In addition, the relation $p=\gamma mv$ 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.)

 

[jtbell]

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.

 

[jfizzix]

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.