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

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

I suspect there is already a paper on this.  But when you say the shell and
the planet are at the same temperature, how do you measure this?  You can
not do it independently for the two objects.  You can only do it by looking
at the radiation from the two objects ftom some vantage point.  So you must
observe that the inner and outer objects have the same radiation spectrum if
there is no net thermal transfer.  So the person on the planet will observe
that their radiation is blue shifted and the radiation from the shell is
blue shifted.  But the person in the shell will say the radiation is more
reddish from both.  Each person will "observe" something different, but
consistent with no net energy transfer.  A person hovering half way between
will observe and in between spectrum for both.  All three will agree there
is no net energy transfer.

Your original analysis seemed to imply an absolute reference frame, but in
relativity there is no such thing.

John M. Clement
Houston, TX

> Here's a "dilemma" that came up in another discussion:
>
> "Suppose you have a planet at the center of a shell.  Both are
> blackbodies at the same temperature.  Photons from the planet will be
> red-shifted coming up, while photons coming down will be blue-shifted.
> Thus there will be more energy going down to the planet than up from it.
> Thus you have a net flow of energy even though the temperatures are the
> same."
>
> (Or make the outer object SLIGHTLY cooler.  Then you could have a net
> flow of energy from the cool shell to the warm planet, again in
> violation of the 2nd law.)
>
>
> I've never heard it discussed, but I conclude that "at the same
> temperature" is also relative.
>
> One line of reasoning looks at the clocks at the two locations.  The
> clock on the planet will run slower.  If the planet was radiating 400
> J/s/m^2, the shell "at the same temperature" would radiate 400 J/s/m^2
> -- but according to its own clock.  According to the clock on the
> ground, it would be radiating slightly more than 400 J/s/m^2.  So
> observer travelling from one to the other would measure the same
> temperatures in the proper frames.  But an observer at either location
> will see the planet as slightly cooler than the shell.  Thus there
> should be a net flow of thermal energy inward.
>
> You could also consider the speeds of the atoms.  In their own reference
> frame, both would have the same distribution of speeds --> same
> temperature.  But the observer on the planet would see the atoms in the
> shell moving faster --> higher temperature.
>
> In either line of reasoning, there will be a net flow of energy from the
> shell to the planet even though both are "the same temperature".
>
> 1) Have you ever run across this "dilemma" before?
> 2) Do my explanations seem right?
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