AMERICAN JOURNAL OF PHYSICS

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 VOLUME 33, NUMBER 1. Jan 1965

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Evidence Against Emission Theories

J.G. Fox

Another proof, more closely related to the present discussion, may be made by the following modification of a demonstration due to Langevin.  Consider a source which is at rest with respect to an observer O and which radiates a simultaneous, oppositely directed pair of equal quanta, hu, e.g., annihilation radiation. While the total energy radiated is ΔE = 2hu, the total momentum radiated is zero, so the source remains at rest with respect to O.

Now, consider this phenomenon from the point of view of an observer O' who moves with respect to O with the constant velocity v = bc along the line defined by the radiation.  On account of the first-order Doppler effect O' observes two quanta with the frequencies hu (1 + b) and hu (1 - b).  He thus concludes that a net amount of momentum hu(1+b)/c - hu (1-b)/c = 2hub/c is emitted in the direction in which the source and O appear to move with respect to him.  From the conservation principle for momentum he concludes that the source loses this same quantity of momentum.  Now the velocity of the source with respect to O' does not change since it remains at rest with respect to O, as has been seen.  Thus O' is forced to conclude that the mass of the source has decreased by an amount  Dm, where (Dm)u = 2hub/c.  Thus, Dm = DE/c².