Re: A question on inelastic relativistic collisions

[Samuel Held <Held@RHIP.PHYS.UTK.EDU>]

Larry,
        The arguments for the formulas I put up were made on the basis
that heat is not just pure Energy but also carries some momentum.  When
Einstein and Planck (actually Planck first) made their calculations
based on the first law of thermo, they required a "fake force" that
carried the momentum.  However, the first law considers heat to be pure
energy.  this argument was made in the 1940's by H. Ott and the
reference is
        D.L. Steinert "An evaluation of relativistic thermodynamics"
(Ph.D. thesis - 1969 - Mich. State)
this may be a little hard to get a hold of for a high school teacher but
if there is a local college nearby with an interlibrary loan office they
may be able to track down a copy.  In fact, I think my undergrad college
got it from Cornell.
        I am sorry that I can offer no more than this.  It is too far
gone from me now to offer any more than this as an explanation.  Other
theories by others, P.T. Landsberg (previously mentioned by someone
else) and C. Moeller are more complex.  Landsberg's arguments rely on a
relativistically corrected first law and an argument that the partition
function is invariant.  Too much to explain here and back then.
        Another reason for so much confusion is trying to correctly
define heat and work.  Also, what do we consider in the system.  Ott
only considered a gas, while Planck and Einstein a gas and a container
(where I believe their force came from)  It is very hard to understand
so I will let you read up on the material.
Here are the rest of my references for any one who wants to look them up
J. Bicak "A note on relativistic heat engines"  Lett. Nuovo Cimento
vol.1 p.302-304, 1969
F.C. Jones "Relativity, heat and 'fictitious' forces" Nuovo Cimento
vol.57B p.307-314, 1968
P.T. Landsberg "Special relativistic thermodynamics: a review" 1969
Pittsburgh Symposium, in a "Critical review of Thermodynamics" Mono
Corp., Baltimore 1970
P.T. Landsberg and K.A. Johns "A relativistic generalization of
thermodynamics"  Nuovo Cimento vol.52B p.28-44, 1967
P.T. Landsberg and K.A. Johns "Work and heat in special relativity" J.
Phys. Soc. Japan vol. 26, Supp. p.310-312, 1969
C. Moeller "Thermodynamics in the special and general theory of
relativity" in "Old and New Problems in Elementary Particles"  Academic
Press, New York (1968)
P.J.E. Peebles and D.T. Wilkinson "Comment on the anisotropy of the
primeval fireball" Phys. Rev. 174 2168-2170 (1968)  (Before it split
into the different volumes - if not then most likely a Phys. Rev. Lett.)
P.J.E. Peebles "Cosmic black-body radiation" Astrophys.J. vol. 142
p.414-419 (1965)
N.G. van Kampen "Relativistic thermodynamics of moving systems" Phys.
Rev. vol. 173 p.295-301 (1968)
N.G. van Kampen "Relativistic thermodynamics" J. Phys. Soc. Japan vol.
26, Supp. p.295-301, 1969


Hope that helps.


Sam Held



-----Original Message-----
From: L. R. Cartwright (Larry) [mailto:physics@SCNC.CPS.K12.MI.US]
Sent: Saturday, February 20, 1999 10:03 PM
To: PHYS-L@LISTS.NAU.EDU
Subject: Re: A question on inelastic relativistic collisions


Up to now, the ex-engineer country bumpkin physics teacher was following
this thread with reasonable success.  David's remark about internal
energy
and mass gave him a jolt, but he recovered.  Now Sam's latest find has
Larry puzzled again.  Here's the problem:

I thought it was pretty well established that T is directly proportional
to Q by the relationship T = KQ/m where K is some constant determined by
the physical composition of the substance under consideration.  Given
that
m is going to take a relativistic hit (m = m_o / gamma), I do not see
how
both T and Q can be dilated by a factor of gamma.  It seems to me
that something besides K is going to have to remain constant,
and if T = gamma * T_o then it is not possible for Q = gamma * Q_o
and also m = m_o / gamma.

I want to be able to pass along as much of this thread as possible to my
students.  Can someone please help me see where I am screwing this up?

Best wishes,

Larry

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Larry Cartwright
Physics, Physical Science, Internet Teacher
Charlotte High School, 378 State Street, Charlotte MI 48813
<physics@scnc.cps.k12.mi.us> or <science@scnc.cps.k12.mi.us>

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

On Sat, 20 Feb 1999, Samuel Held wrote:

> Ed,
>         I finally found my paper from undergrad and I think some of
this
> will answer your question.  According to H. Ott, S = S_o where _o
> indicates rest frame.  Then both heat and temp receive a Lorentz
boost,
> Q = gamma * Q_o and T = gamma * T_o where gamma is the normal
> sqrt(1-(v^2/c^2)).  I can references later if people want, but the
work
> dates back to the 50's and 60's.  I can even try to scan the paper for
> people.  However, some of it is pretty complicated tensor equations
that
> do not give me an intuitive feel for the material.
>
>
> Sam Held