Message from discussion Eric Gisse insists Temperature is Not a Tensor!

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From: Eric Gisse <jowr...@gmail.com>
Newsgroups: sci.physics.relativity
Subject: Re: Eric Gisse insists Temperature is Not a Tensor!
Date: 22 Apr 2007 19:02:20 -0700
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On Apr 22, 4:06 am, "Juan R." <juanrgonzal...@canonicalscience.com>
wrote:
> On Apr 22, 4:16 am, Eric Gisse <jowr...@gmail.com> wrote:
>
>
>
> > On Apr 21, 4:30 pm, "g...@hotmail.com" <g...@hotmail.com> wrote:
>
> > > On Apr 21, 6:23 pm, Eric Gisse <jowr...@gmail.com> wrote:
>
> > > > On Apr 21, 8:43 am, "g...@hotmail.com" <g...@hotmail.com> wrote:
>
> > > > > Eric Gisse insists Temperature is Not a Tensor Rank_0 !!!!!!
>
> > > > Energy is a scalar. Is Energy a rank 0 tensor?
>
> > >http://en.wikipedia.org/wiki/Tensor
> > > Quote:"For example, mass, ***temperature***, and other scalar
> > > quantities are tensors of rank 0;"
>
> > Wikipedia is wrong and you are stupid for treating Wikipedia like a
> > comprehensive textbook on the subject.
>
> No wikipedia is not wrong when says that temperature is a zero rank
> tensor. He only problem is that ***you*** do not know that a tensor
> (i.e. the general concept of TENSOR) is.

I understand full well the concept and application of tensors.

Wikipedia, as usual, is being imprecise. Temperature is a Galilean-
invariant scalar but it is not a Lorentz-invariant scalar.

Not all scalars are rank 0 tensors. Remember energy? Its' a scalar...

>
> >From _Physical Properties as Tensors_ [1]:
>
> [BLOCKQUOTE
> The pyroelectric tensor, (essentially a vector) represents the
> relation between a first-rank tensor (the vector of electric
> polarization) and a zero-rank tensor (the temperature).
> ]
>
> See also [2].
>
> [1]  http://www.iucr.org/iucr-top/comm/cteach/pamphlets/18/node2.html
>
> [2]http://www.geol.umd.edu/pages/facilities/lmdr/press.html

Wow good job on using websites that are specifically referencing
classical mechanics in an argument that is obviously about
relativistic mechanics. Why do you continue to butt in on subjects you
simply _do not understand_ ?

The fact that temperature is not a Lorentz scalar follows from a quite
simple set of arguments.

Remember your thermodynamics - the second law can be expressed, when
changes in the system can be treated adiabatically, as dS = int [ dQ/
T].

Since entropy is simply a measure of the number of available states,
it will be the same from one reference frame to the next. With about
10 lines of algebra, it follows that dQ' = sqrt(1 - v^2/c^2) dQ for an
observer moving with a constant velocity v with respect to the system
under consideration.

Equating dS and dS' gives T' = sqrt(1 - v^2/c^2) T.

T is a scalar but it is not a rank zero tensor. A tensor is invariant
under a coordinate transformation - T does not qualify. Which is what
I have been saying _the entire fucking time_. I did not know the exact
argument when I said that it was not a Lorentz invariant scalar, I
just knew it could not be because T is defined as dE/dS [partials]
which means, via E, that T is a coordinate dependent number. Isn't
having an education a wonderful thing?

The argument I cribbed was taken from Relativity, Thermodynamics, and
Cosmology by Tolman. I could write out the entire argument and justify
every step for you, if you would like. It really is a short and sweet
argument from inarguable principles.