# I Establishing consistency between a wave model of the photon and a particle model

1. Jul 22, 2017

Note: added to the title should be "and a particle description". $\\$ The intensity (energy density) of an electromagnetic wave is proportional to the second power of the electric field amplitude, i.e. intensity $I=n \, E^2$, apart from proportionality constants. Meanwhile the energy contained in N photons is $U=N \, E_p$, where $E_p=\hbar \omega$ is the energy of a single photon. It may be a poor physics to consider the electomagnetic field $E_i$ of a single photon, but assuming we can, the superposition of $N$ photons in the same mode all in phase with each other results in a state that has $N^2$ that of the initial energy, since $E_{total}=NE_i$ in that case. One explanation that avoids this dilemma is to have the phases of each of the individual photons to be random when all of the photons are in the same photon mode, so that the phasor diagram to compute the resultant $E_{total}$ is that of a 2-D random walk. For large $N$, $E_{total}$ will be proportional to $\sqrt{N }$ and the energy will be proportional to $N$, (i.e. $E_{total} \approx \sqrt{N} E_i$), as it needs to be. The question I have is if this explanation is consistent with the presently accepted way of how the photon is modeled, by QED for example?

Last edited: Jul 22, 2017
2. Jul 22, 2017

Staff Emeritus
Then why are you doing it?

You are taking a quantum mechanical system that is not in an eigenstate of electric field and treating it as if it were. Why should that produce anything helpful?

3. Jul 22, 2017

In some ways, it may be like doing what Bohr did by assuming circular electron orbits in the Bohr model of the atom. Letting $E_i(t)=E_i cos(\omega t +\phi)$ for some random but constant $\phi$ does give a result that gives consistency (for energy computations) to the classical model of the electromagnetic field. $\\$ Additional comment: The Bohr model may not be completely correct, but it is still the quickest way to compute the wavelengths of the principal transitions in the hydrogen atom.

Last edited: Jul 22, 2017
4. Jul 22, 2017

Staff Emeritus
This sounds a lot like a personal theory.

Anyway, you have your answer. No, this is not something consistent with QED because it's not even consistent with QM.

5. Jul 22, 2017

Thank you for the input. It probably does then fall into the category of a personal theory. Unless anyone else has anything that keeps it from being that, it appears under the Physics Forum rules, further discussion would not be favored and/or not allowed, which is really ok with me. :) :)

6. Jul 22, 2017

### Staff: Mentor

Done.
(and in the future if you need a correction of this sort, just report your own post - that brings it to the attention of the mentors so that one of us can fix it for you).

7. Jul 23, 2017

One additional comment: I just did a quick google of the subject of Quantum Phase Operators and the following paper showed up: Quantum Phase and Quantum Phase Operators, Some Physics and Some History by Michael Martin Nieto dated 1993 I believe. Here is a "link" : http://cds.cern.ch/record/567453/files/9304036.pdf Some of the mathematics and some of the conclusions are above my present level, but I found it of much interest. At the time of the writing of the paper, it appears there is still no good answer for what the phase of the photon wave function might be for small $N$.