Re: Eric Gisse insists Temperature is Not a Tensor!


Eric Gisse wrote:
On Apr 22, 4:06 am, "Juan R." <juanrgonzal...@xxxxxxxxxxxxxxxxxxxx>
wrote:
On Apr 22, 4:16 am, Eric Gisse <jowr...@xxxxxxxxx> wrote:



On Apr 21, 4:30 pm, "g...@xxxxxxxxxxx" <g...@xxxxxxxxxxx> wrote:

On Apr 21, 6:23 pm, Eric Gisse <jowr...@xxxxxxxxx> wrote:

On Apr 21, 8:43 am, "g...@xxxxxxxxxxx" <g...@xxxxxxxxxxx> 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...

http://en.wikipedia.org/wiki/Scalar_(physics)
QUOTE:
"For example, the distance between two points in space is a scalar, as
are the mass, charge, and kinetic energy of an object, or the
temperature and electric potential at a point inside a medium.

Scalars in relativity theory
In the theory of relativity, space and time are related (intp so
called Minkowski space-time) and as a consequence, scalar quantities
related to time (like energy, etc) and vector quantities related to
space (like momentum, etc) can be combined and treated mathematically
as ******four-dimensional vectors (four-vectors) or even
tensors.****** For example, the charge *****density***** at a point in
a medium, which is a scalar in classical physics, can be combined with
the local current density (a 3-vector) to make a relativistic 4-
vector. Similarly, mass density can be combined with momentum density
and pressure into the energy tensor.

Examples of scalar quantities:

electric charge and charge density (the latter nonrelativistically; in
relativity it must be combined with current density to comprise a 4-
vector)
spacetime interval
mass and mass density (the latter nonrelativistically; in relativity
it must be made part of the energy tensor in combination with momentum
density and pressure)
speed, but not velocity or momentum
******temperature ******
energy and energy density (the latter nonrelativistically)
" :END_QUOTE

(density and temperature are functions of each other)


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 *** 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 relavistic, T is invariant
M' = gamma M

M' is relavistic
M is invariant

X' = gamma X

X' is relavistic
******X is spacetime's invariant coordinate interval****

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.

.

Quantcast