## Sunday, April 8, 2012

### Photons and their relation to the waves in the electric / magnetic fields

When I was in college and I first heard about the concept of photons in physics, I initially guessed that a photon would correspond to the field (electric / magnetic) between 2 nodes of the wave:
I was told this was not correct, and I left it at that, but recently I figured I would investigate why it was wrong.  That is what this post is about.

The energy of a photon is given by:
E = h * ν

h is Planck's constant 6.626e-34 [J*s]
ν is frequency [Hz]

I looked up the energy carried by electromagnetic waves in my go-to book:  "Introduction to Electrodynamics" by David J. Griffiths:
S = c * εo * Eo * cos^2(k*z - ω*t + δ)

c is the speed of light
εo is the permittivity of space
Eo is the (rms? max?) magnitude of the electric field
cos^2 is cosine squared
k is the wavevector, defined by the relationship between frequency and the speed of light
ω is the frequency of the radiation
δ is the phase

We can simplify this by assuming z = 0,  δ = 0 - this just says we are looking at what happens at z = 0, and there is no phase offset..
S = c * εo * Eo * cos^2(ω*t)

This equation defines the energy per unit time, per unit area.  So for the above, we would choose as our unit of time one cycle, or one half cycle of the wave.  But that still leaves the problem of the area.  Also, there is no classical restriction on the magnitude of the electric field (Eo).  The question then becomes, for a given area, is it possible to have Eo be so low that the energy of the photon spans more than 1 cycle?  There is nothing in the equations to prevent this.  Is there experimental evidence of it?

This essentially comes down to "single photon" experiments - experiments in which photons are measured one at a time.  I start by reading the wikipedia entry on the double slit experiment:

and will post my thoughts of this and other reading separately.

Update:
Single photon experiments with red photons from a He-Ne laser are not too hard to do:

The separation between individual photons is 2 km, which is much longer than the wavelength of the radiation (~700 nm) therefore, given the above framework the photon would be spanning billions of nodes!!

lowest measured forces (and by extension, electric fields):

review of some single photon experiments:

single photon and complementarity:

proof of single photon existence - single photon hitting beam splitter, arriving at only one detector: