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## Main Question or Discussion Point

Consider a stationary observer and an emitter of light radiation that may be either receding or approaching at a variety of nonrelativistic velocities, with the velocity of the emitter having only a radial component and no transverse component.

I was wondering whether the Doppler Effect, specifically for light, is observed for

If it did, how would the following paradox be resolved? Consider a sample of gas with N hydrogen atoms, where N is very large, and the absolute temperature T of the gas is nonzero so that the atoms are all moving in a multitude of directions. Let one of these N atoms be in its first excited state and all N-1 others be in their ground state, with the N hydrogen atoms as a whole comprising an isolated system. Let these hydrogen atoms also be spread out over a large enough space that the mean free path for a collision is long enough for its probability to be close to zero for the time-scale of this thought experiment.

That hydrogen atom in its excited state now drops down to its ground state, emitting a photon of fixed frequency. Since all of the other N-1 hydrogen atoms are moving with respect to this one, they have a nonzero velocity, and hence also a nonzero radial velocity with respect to the hydrogen atom that emitted the photon. If the Doppler Effect is exhibited for arbitrarily small radial velocities, then the frequency shift and consequent energy shift of the emitted photon will result in none of these N-1 hydrogen atoms being able to absorb this photon even in principle, since quantization of electron energy levels defines an

This implies that photons that are emitted by an atom of a particular element cannot be absorbed by another atom of that same element, and that emitted light essentially becomes "tired, dead, or unreactive," in that emitted photons are degraded and must forever hence propagate through space, unable to ever be absorbed again. One can fairly surmise that a

Therefore, assuming that there is no minimum radial recessional or approaching velocity required for the Doppler Effect (for light/radiation) to come into effect leads to the absurdity just mentioned; hence, there is such a minimum "threshold" velocity, which then implies that Doppler shifts are

Is it possible that physicists haven't noticed that Doppler shifts could be quantized since the phenomenon has only been measured with recessional or approaching radial velocities that are "too large?"

Thanks,

Jay

I was wondering whether the Doppler Effect, specifically for light, is observed for

*any*recessional or approaching purely radial velocity, no matter how small the magnitude of that velocity. For example, if the emitter is receding at 0.00000001 m/s, will some tiny red shift exist?If it did, how would the following paradox be resolved? Consider a sample of gas with N hydrogen atoms, where N is very large, and the absolute temperature T of the gas is nonzero so that the atoms are all moving in a multitude of directions. Let one of these N atoms be in its first excited state and all N-1 others be in their ground state, with the N hydrogen atoms as a whole comprising an isolated system. Let these hydrogen atoms also be spread out over a large enough space that the mean free path for a collision is long enough for its probability to be close to zero for the time-scale of this thought experiment.

That hydrogen atom in its excited state now drops down to its ground state, emitting a photon of fixed frequency. Since all of the other N-1 hydrogen atoms are moving with respect to this one, they have a nonzero velocity, and hence also a nonzero radial velocity with respect to the hydrogen atom that emitted the photon. If the Doppler Effect is exhibited for arbitrarily small radial velocities, then the frequency shift and consequent energy shift of the emitted photon will result in none of these N-1 hydrogen atoms being able to absorb this photon even in principle, since quantization of electron energy levels defines an

*transition energy requirement.***exact**This implies that photons that are emitted by an atom of a particular element cannot be absorbed by another atom of that same element, and that emitted light essentially becomes "tired, dead, or unreactive," in that emitted photons are degraded and must forever hence propagate through space, unable to ever be absorbed again. One can fairly surmise that a

*reductio ad absurdum*has been reached.Therefore, assuming that there is no minimum radial recessional or approaching velocity required for the Doppler Effect (for light/radiation) to come into effect leads to the absurdity just mentioned; hence, there is such a minimum "threshold" velocity, which then implies that Doppler shifts are

**.***quantized*Is it possible that physicists haven't noticed that Doppler shifts could be quantized since the phenomenon has only been measured with recessional or approaching radial velocities that are "too large?"

Thanks,

Jay