# Q & A: Lorentz transformed temperature

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Most recent answer: 02/17/2017
Q:
Besides the well known Lorentz transformations across coordinate systems moving with respect to each other, could one conjecture that there would also be observable temperature transformation? If temperature is the measure of the motion of the molecular or atomic constituents of a moving object, then those constituents should move more slowly than the same object at rest because of time dilation. So if it were possible to measure the temperature of an object moving at 1/2 the speed of light for example, the temperature should be lower than the same object at rest. Admittedly a difficult experiment, but does it make sense theoretically?
- PHILIP LANKS (age 67)
57719
A:

Yes, that's a very good point. To separate out the effects of the Lorentz time dilation from Doppler effects of the object getting nearer or farther, think of some object (say a hot rock emitting black-body radiation) whizzing past, and consider what you'd see from the point where it made its closest approach. Everything coming from it would be slowed by the Lorentz factor sqrt(1-0.52)=sqrt(0.75). The frequencies of the radiation are reduced by that factor, so it looks like the temperature is reduced by the same factor. This effect is part of the relativisitic Doppler calculation routinely used to understand light from stars. It's called the transverse Doppler shift. In general, the total Doppler shift of the radiation involves both the transverse motion and the longitudinal part due to the object approaching or receding.

Mike W.

(published on 02/17/2017)