Is it possible for photons to interact with each other directly?
There is only one photon-photon-graviton vertex, but that is exceedingly small. Photon photon scattering is dominated by fermion loops.
the graviton is misleading here.
Have a look here: http://arxiv.org/PS_cache/hep-ph/pdf/0512/0512033v1.pdf Fig. 2.2 shows the lowest order of photon-photon coupling due to virtual fermions.
If photons can't couple with other photons , And if they obey the principle of superposition , when we fire photons through a double slit , then how are they interacting with each other , I have only begun to study QM so take it easy.
Yes, but the OP said "directly" - I would argue this excludes fermion loops.
I agree, "directly" excludes fermion loops or non-linear effects in active materials.
@cragar: "interference" and "coupling" are two different things. Measuring coupling means that you have to prepare (e.g.) a two-photon state ("colliding photons") and check if and how they scatter. Interference in quantum mechanics means that even one single photon = a one photon state can interfer with itself.
In a double slit experiment you do not need different photons to interfere with each other; you will observe an interference pattern even if you send only single photons through the double-sit. You can even do the following: Prepare a huge number of exact copies of one double-slit experiment. Now distribute them all over the earth in different laboratories. In each lab send exactly one photon through the experiment and register its position on the screen (x and y coordinate). Then collect all (x,y) tupels from all over the earth and plot them in one diagram. You will find an interference pattern.
Speaking of fermion loops - what does it mean for us? Can photons attract each other? Is there some change in the usual Coulomb force?
in QFT formulation of electrodynamics, photons can fluctuate into particle-antiparticle pairs, thus altering the classical picture of electromagnetism
One can try to express these QFT loop corrections as terms in an effective potential; that would imply quantum corrections to the Coulomb force. But I am not sure if this will always work.
Two things that I've found:
1. Two photon interference (Hong-Ou-Mandel effect)
Two photons are incident at a beamsplitter and you will observe that they both take the same path (possibility 1 and 4 in the picture).
2. Two-photon physics
Have a look at the external links
You can't exclude loops from tree level interactions in a meaningful way. A physical interaction will include all contributions, splitting them up in tree level and higher order loop contributions is unphysical, even though in perturbation theory the contributions appear separately. Well known example: You can have violations of unitarity at tree level while in reality no such violations are possible within quantum mechanics as it is a unitary theory by design.
Some nice expressions for the effective coefficient of refraction for light propagating through magnetic fields are http://arxiv.org/abs/hep-ph/9806417" [Broken]
W bosons couple to photons. Could there be an exchange YW -->YW bosons. if so would that sagest photon interaction.
DrZoidberg: One way to think of it is, photons cannot interact because each photon occupies a unique point in relativistic spacetime. In that context, photons do not move at all relative to one another and therefore could never achieve local contact.
This is misleading as it applies to massless gluons as well; but gluons DO interact.
If we looked at it as wave function there would be interaction? But as a particle I wouldn’t think it would interact directly.
Photons as wave functions do not interact
1) there is no wave function for a photon (and no Schrödinger equation)
2) wave functions do not interact; they can only interfer, but this is somethign totally different
I do agree with you in this context of a photon interaction being “single”. As a wave function though to say “they interfere” is an interaction. Direct or indirect it can be seen as an interaction.
I disagree. In order to see interference the photons involved must be indistinguishable. Therefore interference should not be interpreted as the interaction of two or more photons, but as a property of one single state containing more than one excitation.
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