Date: Winter 2011-2012
How do photons annihilate other photons? If two photons each had an energy of 500 KeV and they annihilated each other, how much energy would the two photons resulting from the annihilation have? (If there is a mathematical formula that would answer my question, I would appreciate that as well.)
The two photons join together and then fly apart as two other particles, usually a particle and an antiparticle. A common result is an electron and an anit-electron (often called a positron). The total energy of the photons (1000keV) becomes the total energy of the electrons. In the electrons, however, some of the energy takes on the form of mass (E=mc^2). If this is enough energy for the electrons, then the electrons will probably fly apart. If it is not enough, then the electrons might join back together and fly apart as two photons again.
Dr. Ken Mellendorf
Illinois Central College
Photons do not annihilate, they interfere.
Where they have opposite amplitude, yes they cancel out, but!
they always pop out somewhere else,
because there is always someplace their wave-patterns add constructively.
Just try to design two wave-patterns that don't do that...
Also, destructive interference is not really a reaction like electron-positron annihilation;
nothing really changes.
Photons are pure energy, so with photons in and photons out,
there is no change to any sum of quantum-numbers of massy particles of matter.
In contrast, when electron and positron annihilate,
there are two less leptons in the universe (and God counts these daily;)
and their rest-mass is converted to photons, mobile pure energy,
We say that photons are pure energy, not matter,
because photons have no rest-mass.
Their total mass-energy is only that which they have in momentum and frequency and EM-fields.
If they are gradually slowed to zero kinetic energy, they are no more, there is nothing left.
For any particle, mass_energy = Rest_Mass + (Kinetic_Energy/c^2) (just like E=mc2).
For photons, the first term is zero.
Also true for gravitons, and almost true for neutrinos.
Since photons are pure energy going into the annihilation,
and the result of an annihilation is pure energy,
yes there is no change. No reaction.
Annihilation converts rest-mass, bound energy called matter, into mobile energy.
That is not happening here. No rest-mass to convert!
So photons are quite transparent to each other.
They never interact with each other in empty free-space.
They require the non-linear effects of some matter to interact with each other.
With matter in the wave-patterns, you can get wave-mixing and frequency doubling and
two-photon absorption and fluorescence and triggered fluorescence and
stimulated emission (laser emission)...
But in empty space, they just sail through each other.
You could imagine the peaks and troughs of the waves interfering,
but they would not mean much of anything, because the initially separate wave-fronts
always come out of the crossing-zone going the same direction they had at first.
In fact, the interference you are thinking of can only be detected by something made of matter,
such as a photo-diode or surface photo-emission of electrons or an atom being ionized.
I am not sure, but I think that represents a non-linear effect too.
"Detection" measures the square of wave-amplitude,
and then flips a coin with appropriately weighted probability
to say "I got one" or "I do not".
It does this many times real fast, then we get to start averaging
and calling it a real number like "intensity".
That square-law above is the non-linear function that made the two waves mix
and showed you the interference pattern.
So the energy they had at the beginning is simply conserved.
In fact each leaves with the same energy it entered with,
if they do not get caught by your detector on their way through your experiment zone.
Also, conservation of energy is a whole different truth.
If 1 MeV total mass-energy goes in with all the pieces
then 1MeV total mass-energy comes out,
just maybe on different pieces.
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Update: June 2012