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Light from a fast car

I hope you have the time to answer this question. It's been an on-going dispute between my friends and [me]. Theorhetical Question: If a vehicle was traveling at the speed of light and a light source was emitted from the vehicle would there be a visible beam of light?

Please help me. Thanks.

"Opinions expressed are mine and not those of Rohm and Haas Company"

The most likely reason for the dispute is that the question is not especially well-posed. By "vehicle" one understands a largish object with a nonzero mass. But objects with a mass cannot travel at the speed of light. So it makes no sense to ask about the properties of something emitted from it.

If you mean the vehicle is massless, yes it could emit a photon visible to the human eye, but (to conserve energy and momentum) only in the direction it was travelling. (Also, the energy of the vehicle would have to start out larger than the energy of the emitted photon.)

If you mean the (massive) vehicle is travelling just below the speed of light, it could emit a photon in any direction. Whether or not it is visible (to the human eye) depends on the wavelength of the photon, in the reference frame of the observer, i.e. on the wavelength as emitted and the relative velocity of vehicle and observer. (Of course, there is nothing special about the vehicle's speed, just about the relative speed.)

I hope this helps settle your friendly dispute.

Andreas Kronfeld
Theoretical Physics Department

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last modified 9/28/1998