A Moving Body must “appear” Cool

Abstract

LANDSBERG has recently suggested¹ replacing Einstein's law T_lab = T_cm (1 − w²/c²)½ with the law T_lab = T_cm, where T_lab is the temperature of a body as measured in laboratory co-ordinates, T_cm is the temperature of the body measured in its rest frame, and w is the velocity of the body relative to the laboratory. The word “appear” was placed in quotation marks in the title becasue T_lab may not be the temperature as observed by the casual laboratory observer at all, just as the Lorentz contraction is not seen by a laboratory observer under ordinary visual inspection, no matter how large it is, but is replaced by a rotation². A black body at some temperature T_cm will emit a black body spectrum appropriate to T_cm in its rest frame, which will be seen Doppler-shifted to another temperature by other observers. An observer in front will see a blue-shift and one behind will see a red-shift, in neither case by a factor (1 − w²/c²)½.