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

[John Denker <jsd@av8n.com>]

I'm not sure there is a specific question on the table, so let
me throw out some non-specific possibly-helpful ideas....

On 12/08/2010 02:37 PM, Folkerts, Timothy J wrote:

> Someone else (off-list) said: " Strictly speaking, it is not possible
> to measure the temperature other than in the rest frame of each
> object. One can infer the temperature by observing the emitted
> radiation, but to do so one has to make certain assumptions – such as
> that the radiation one observes is thermal and has not been doppler
> shifted – that are not always valid.

I disagree with that philosophy.  In my book, practically all
measurements are inferences.  Even using a ruler to measure a
piece of paper requires making either (a) making assumptions
or (b) applying calibration factors and other corrections to 
compensate for non-idealities.

> the two objects are made of a single material that has a melting
> point above the temperature of the shell but below that of the
> planet. The shell will remain solid; the planet will melt."

Yes, that is what we would expect ... although I don't know of 
anybody who has done the experiment.

>   So can we conclude the melting point is suppressed 

I wouldn't say that.  The stuff melts at a perfectly well
defined temperature.  In fact NIST uses various melting points
as calibrated secondary standards for temperature.  Again,
there might be calibration issues and various non-idealities, 
but nothing major and nothing different in principle from any
other measurement.

> where
> gravity is stronger = where acceleration is greater?

According to the Tolman relation, the temperature is redshifted
according to the depth of the potential, not the local strength
of the field.  In a suitable "parallel plate" geometry you could
have a (nearly) constant field strength (constant acceleration 
everywhere) but the potential would vary considerably from place 
to place.

> The discussion went on to: "... it demonstrates how an object at one
> temperature can heat another to a higher temperature; so this cannot
> be what the second law prohibits." 

That seems OK to me.  We can define temperature as T := ∂E/∂S ... 
and given that E is not relativistically invariant we shouldn't be
toooo surprised to find that T is not relativistically invariant.

=========

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