In plane wave the H and E are in phase. So the pointing vector disappears regularly every pi. How is energy conservation validated ? Is it through the uncertainty of energy and time ?
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4I suspect you are looking at the wave in a static view (at a single $t$). Consider it's evolution in time. There are nodes but like the anti-nodes they move. – dmckee --- ex-moderator kitten Aug 27 '13 at 03:16
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Here is a paragraph on conservation of energy and maxwell's equations paragraph 1.6.
On average there is no problem. An instantaneous slice , where both E and B are zero, is misleading because they are changing in time in such a way as to build up the E and B of the next slice in t+dt.
In the framework where the plane wave is an ensemble of photons whose coherent stepping creates the E and B fields there is no problem of energy conservation even instantaneously, since the photons are not interacting and are each carrying their h*nu part of the energy of the wave. It is their synchronization in space time that creates the mathematical confluence of a zero in the classical formulation of the energy, that is why the classical discussion keeps to the average values of E and B..
anna v
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Would a single photon interact with itself to create this pattern .. ? – Anonymous Sep 09 '13 at 04:49
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No. A single photon is by definition a particle, and has a definite (x,y,z,t) and (p_x,p_y,p_z,E) within the Heisenberg uncertainty principle. It does not have an electric or magnetic field other than the one that appears when it gets into a coherent state with a multitude of other photons. see http://motls.blogspot.gr/2011/11/how-classical-fields-particles-emerge.html . – anna v Sep 09 '13 at 05:25