Take the most simple academic example for interferences. Since it is not any real experiment, one can have shocking contradictions. For example: 2 monochromatic plane waves with (parallel) amplitudes propagating in the same direction. The Poynting vectors of the 2 waves without superposition are always constant. Once superposed, the resulting Poynting vector is constant, but is dependent on the phase difference. Thus, how to explain the energy balance? If there is an energy redistribution it may be easy perhaps, but when the three values are constant in space... What is the right explanation? –

Take the most simple academic example for interference. Since it is not any real experiment, one can have shocking contradictions. 

For example: 2 monochromatic plane waves with (parallel) amplitudes propagating in the same direction. The Poynting vectors of the 2 waves without superposition are always constant. Once superposed, the resulting Poynting vector is constant, but is dependent on the phase difference. 

Thus, how can we explain the energy balance? If there is an energy redistribution it may be easy perhaps, but when the three values are constant in space... What is the right explanation? –

Suppose two monochromatic waves of different amplitude propagating in the same direction (either same sense or opposed); then (except for phase difference pi/2) the resulting mean energy flow is not the sum (case of same sense) or the difference (opposed sense) of the interfering beams. Where the energy of the separate beams is gone? Depending on the phase difference between the waves the resulting energy flows change but (except for phase difference pi/2) the problem is that the total energy in space is not the sum of the two energies. In the case where the two amplitudes are equal, standing waves can be understood as an energy redistribution, but when amplitudes are different it seems there is energy creation or anihilation...

Take the most simple academic example for interferences. Since it is not any real experiment, one can have shocking contradictions. For example: 2 monochromatic plane waves with (parallel) amplitudes propagating in the same direction. The Poynting vectors of the 2 waves without superposition are always constant. Once superposed, the resulting Poynting vector is constant, but is dependent on the phase difference. Thus, how to explain the energy balance? If there is an energy redistribution it may be easy perhaps, but when the three values are constant in space... What is the right explanation? –

Suppose two monochromatic waves of different amplitude propagating in the same direction (either same sense or opposed); then (except for phase diffrence pi/2) the resulting mean energy flow is not the sum (case of same sense) or the difference (opposed sense) of the interfering beams. Where the energy of the separate beams is gone? Depending on the phase difference between the waves the resulting energy flows change but (except for phase diffrence pi/2) the problem is that the total energy in space is not the sum of the two energies. In the case where the two amplitudes are equal, standing waves can be understood as an energy redistribution, but when amplitudes are different it seems there is energy creation or anihilation...

Suppose two monochromatic waves of different amplitude propagating in the same direction (either same sense or opposed); then (except for phase difference pi/2) the resulting mean energy flow is not the sum (case of same sense) or the difference (opposed sense) of the interfering beams. Where the energy of the separate beams is gone? Depending on the phase difference between the waves the resulting energy flows change but (except for phase difference pi/2) the problem is that the total energy in space is not the sum of the two energies. In the case where the two amplitudes are equal, standing waves can be understood as an energy redistribution, but when amplitudes are different it seems there is energy creation or anihilation...