Optical Interference: Photon Energy Conservation & Vector E

[Wishbone]

If you have two photons traveling in opposite directions, that destructivly interfere witheachother, is energy conserverd0? Is the E, in E=hf a vector quantity, that will take in account the directions in which they are travelling? I believe the answer has something to do with treating the light as a particle at that point, and not a wave, however I am not sure. Also, at the point of intersection, is can there be no detection of light?

 

[masudr]

My first point would be that a photon is not really a bit of an electromagnetic wave. This is essentially a classical EM question, since a classical EM wavepacket carries energy.

Secondly, even if a photon were a bit of an EM wave (I should call it a wavepacket I suppose), after the two wavepackets have destructively interferes, the waves emerge afterwards, still carrying the same energy. In fact, at the point of interference, all the energy is held in the magnetic field and the electric field is zero at that point in space and time.

 

[Wishbone]

why is the eletric field 0?

 

[masudr]

It precisely depends on the relative phase shifts of the waves at various points. But since you said "destructively interferes" then that's what it means: where the two electric field vectors are pointing in opposite directions but with the same magnitude giving a total of 0 at that precise point.