- #1
Surya97
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- TL;DR Summary
- Two photons/EM wave packets traveling in a vacuum, in exactly the opposite direction, with equal frequency and amplitude and orientation, meet head-on while having a 180 degree phase offset, creating perfect destructive interference and thus a standing wave with a zero amplitude for the instant of the pulses overlapping, at which point they then continue moving after “passing through” each other. Where is the energy “stored” during this moment, and the “info” about the constituent waves?
Assume that this is a case where by sheer coincidence, two sources of coherent single-frequency EM wave pulses with equal duration are both fired in opposing directions, with both carrying the same frequency and amplitude and orientation. These two waves meet head-on while moving in opposing directions, and their phases are precisely offset by 180 degrees so that each trough of one wave meets with the crest of the other. This should be true for both the electric and magnetic components of both waves. Assume they are traveling through a vacuum, including at the point where they meet/overlap.
As such, when they overlap, their sum is zero, leading to complete destructive interference, with zero regions of constructive interference for the energy to “move to”. Additionally, please assume that this is not some sort of experimental setup but rather a natural coincidence, so there is no need to appeal to the idea that in practice there would have to be some shared original source with a beam splitter, as this is not an experiment.
Is my assumption correct that for the duration/region of the overlap of these two discrete pulses (not a continuous beam), this creates the appearance of a “zero amplitude” standing EM wave due to complete destructive interference in the entire overlapping region? If so, where does the energy stored in those two EM waves “go”? I understand that the wave can still be decomposed into the constituent parts and that the derivatives and individual momenta are nonzero, but their summation appears to have no momentum or amplitude, and thus there should be zero electromagnetic energy density in this overlapping region.
Also assume that the sum of these waves’ energies does not add up to a discrete multiple of the mass of any known antiparticle pair, so that these waves do not cause pair production upon collision. Where in the EM field is the energy “stored” for the duration of the overlap? Why doesn’t the zero amplitude result in zero energy, which implies some violation of conservation of energy, which doesn’t seem possible in this simple closed system? Also, where/how is the “tendency” of the two constituent waves to continue moving (as if passing through each other) and seemingly spontaneously reforming (after the complete destructive interference period) “remembered”? How is this information stored about the constituent waves and the energy/future state changes that they held? Am I right that they should pass through each other and continue moving as if nothing happened once the duration of full overlap/interference is over?
Is there some form of conversion to “EM potential energy” that exists in this case despite the lack of visible EM field amplitude? If not, I don’t see where the energy is stored in this summed zero-amplitude standing wave, or how the EM field maintains conservation of energy in this case, or how the info about the two individual waves and their future tendency to keep moving (and thus seemingly spontaneously reappear) is preserved after this “collision”.
In the case of physical waves on a string, the resulting destructive interference before the waves continue past each other is explained away with the idea that the “velocity” of the material of the string creates a tendency for the string to keep moving despite the instantaneous appearance of being stationary, which is where the kinetic energy goes, somehow. This explanation is also not satisfying, but it doesn’t seem to apply at all in the case of two EM waves due to there being no underlying “material” or constituent massive particles that have their own kinetic energy. Additionally, since this takes place in a vacuum, there is no medium for the energy to be transferred to as heat, other than maybe quantum fluctuations/virtual particles I suppose.
Where then does this energy go and how is the “information” about the future motion of the two constituent waves “stored”? Please do not appeal to the notion that this ideal situation cannot be set up in practice without the two wave sources being the same or something; I have not found a satisfying answer to any similar/related questions that do not make some appeal of this type. Please just assume that this situation is occurring exactly as stated, by pure coincidence, and help me figure out the explanation/reason for the resulting behavior not violating any conservation laws.
I appreciate the help!
As such, when they overlap, their sum is zero, leading to complete destructive interference, with zero regions of constructive interference for the energy to “move to”. Additionally, please assume that this is not some sort of experimental setup but rather a natural coincidence, so there is no need to appeal to the idea that in practice there would have to be some shared original source with a beam splitter, as this is not an experiment.
Is my assumption correct that for the duration/region of the overlap of these two discrete pulses (not a continuous beam), this creates the appearance of a “zero amplitude” standing EM wave due to complete destructive interference in the entire overlapping region? If so, where does the energy stored in those two EM waves “go”? I understand that the wave can still be decomposed into the constituent parts and that the derivatives and individual momenta are nonzero, but their summation appears to have no momentum or amplitude, and thus there should be zero electromagnetic energy density in this overlapping region.
Also assume that the sum of these waves’ energies does not add up to a discrete multiple of the mass of any known antiparticle pair, so that these waves do not cause pair production upon collision. Where in the EM field is the energy “stored” for the duration of the overlap? Why doesn’t the zero amplitude result in zero energy, which implies some violation of conservation of energy, which doesn’t seem possible in this simple closed system? Also, where/how is the “tendency” of the two constituent waves to continue moving (as if passing through each other) and seemingly spontaneously reforming (after the complete destructive interference period) “remembered”? How is this information stored about the constituent waves and the energy/future state changes that they held? Am I right that they should pass through each other and continue moving as if nothing happened once the duration of full overlap/interference is over?
Is there some form of conversion to “EM potential energy” that exists in this case despite the lack of visible EM field amplitude? If not, I don’t see where the energy is stored in this summed zero-amplitude standing wave, or how the EM field maintains conservation of energy in this case, or how the info about the two individual waves and their future tendency to keep moving (and thus seemingly spontaneously reappear) is preserved after this “collision”.
In the case of physical waves on a string, the resulting destructive interference before the waves continue past each other is explained away with the idea that the “velocity” of the material of the string creates a tendency for the string to keep moving despite the instantaneous appearance of being stationary, which is where the kinetic energy goes, somehow. This explanation is also not satisfying, but it doesn’t seem to apply at all in the case of two EM waves due to there being no underlying “material” or constituent massive particles that have their own kinetic energy. Additionally, since this takes place in a vacuum, there is no medium for the energy to be transferred to as heat, other than maybe quantum fluctuations/virtual particles I suppose.
Where then does this energy go and how is the “information” about the future motion of the two constituent waves “stored”? Please do not appeal to the notion that this ideal situation cannot be set up in practice without the two wave sources being the same or something; I have not found a satisfying answer to any similar/related questions that do not make some appeal of this type. Please just assume that this situation is occurring exactly as stated, by pure coincidence, and help me figure out the explanation/reason for the resulting behavior not violating any conservation laws.
I appreciate the help!
