Re: [Phys-l] A relativity/thermodynamics "dilemma"

["John Clement" <clement@hal-pc.org>]

But it is not dilemma because all observers agree that the outer shell
radiates to the inner planet.  But once they have reached thermal
equilibrium the radiation stops.  At that point the both observers "see"
themselves at the same temperature as the opposite.  But if the inner one
sends a message to the outer one they will disagree about the temperatures.
The outer one will claim a cooler temperature than the inner observer
claims.  By see of course I mean they see the same spectral radiation.

The apparent "paradox" is that the two observers do not agree on the
temperature.  But if one observer travels to the other place they will be
surprised to find the temperature has changed.

So your "temperature is the same" is looking at an observer who carries a
thermometer from one place to the other and measures the same temperature.
Of course an observer who is a physicist could compensate the measurements
for relativity and figure out what the other person would see.

It is a cute illustration of how relativity is in conflict with our ideas
drawn from classical physics.  I think the word paradox is perfectly
appropriate for something which seems in conflict with our natural
intuition.  This is sort of like Frederick who will not have his 21st
birthday until 84 years have passed, or he is 84 years old. It is a
linguistic paradox which "common sense defies" as I recall the song goes.

The classical prescription that no thermal energy flows when the two objects
are at the same temperature is not necessarily valid if you measure the
temperatures in different reference frames.0

John M. Clement
Houston, TX 

> > But when you say the shell and the planet are at the same
> > temperature, how do you measure this?
>
> I agree that this the the crux.  As with all relativity "dilemmas", the
> problem disappears when you look at things from the correct perspective.
> I was trying highlight the "dilemma" nature of the problem by being a
> little fast-and-loose with the wording of the problem.  I *think* in the
> discussion that followed I got to the crux of the dilemma more or less
> correctly.