Relativistic Thermodynamics
Sven Gelbhaar
13 November 2007 (Update: 4 January 2008)
Einstein’s special theory of relativity has formulas, called Lorentz
transformations, that convert time or distance intervals from a resting frame of
reference to a frame zooming by at nearly the speed of light. But how about
temperature? That is, if a speeding observer, carrying her thermometer with her,
tries to measure the temperature of a gas in a stationary bottle,what
temperature will she measure? A new look at this contentious subject suggests
that the temperature will be the same as that measured in the rest frame. In
other words, moving bodies will not appear hotter or colder.
You’d think that such an issue would have been settled decades ago, but this is
not the case. Einstein and Planck thought, at one time,that the speeding
thermometer would measure a lower temperature,while others thought the
temperature would be higher. One problem is how to define or measure a gas
temperature in the first place.
James Clerk Maxwell in 1866 enunciated his famous formula predicting that the
distribution of gas particle velocities would look like a Gaussian-shaped curve.
But how would this curve appear to be for someone flying past? What would the
equivalent average gas temperature be to this other observer? Jorn Dunkel and
his colleagues at the Universitat Augsburg (Germany) and the Universidad de
Sevilla (Spain) could not exactly make direct measurements (no one has figured
out how to maintain a contained gas at relativistic speeds in a terrestrial
lab), but they performed extensive simulations of the matter.
Dunkel (joern.dunkel@physik.uni-augsburg.de ) says that some astrophysical
systems might eventually offer a chance to experimentally judge the issue. In
general the effort to marry thermodynamics with special relativity is still at
an early stage. It is not exactly known how several thermodynamic parameters
change at high speeds. Absolute zero, Dunkel says, will always be absolute zero,
even for quickly-moving observers. But producing proper Lorentz transformations
for other quantities such as entropy will be trickier to do. (Cubero et al.,
Physical Review Letters, 26 October 2007)
-http://www.aip.org/pnu/2007/split/843-1.html
I will tackle this issue in two parts; one will assume that the Theory of
Special Relativity is correct as-is, and the other in which my Revised Theory of
Relativity is the One True Theory.
Einstein’s Theory of Special Relativity would limit high speed inertial frames’
thermodynamics, as according to it matter is limited to the speed of light.
Therefore a body moving at the speed of light can only lose speed, and this
restricts the body’s thermal energy (its constituent parts vibrating) into a
cone of permitted movement away from the over-all body’s trajectory. This would
result in the body actually losing mass, as the elements which vibrate contrary
to the body’s trajectory could never catch up with the rest of its sister
elements. All thermal energy does here is act as a kind of attrition. Thermal
energy is inherently limited in this paradigm.
My Revised Theory of Relativity makes no such curtailment, as matter is
permitted to travel faster than the speed of light, and therefore the
superluminal body would experience no such attrition of its constituent
elementary particles.
A problem to be dealt with in both theories, however, is that both
interpretations are hard to test, as when we accelerate a body of mass to the
speed of light the sheer inertia would drain the thermal energy, as all mass
would concentrate right behind the thruster, leaving little room to vibrate. The
only foreseeable test is to measure a body of mass already in a high-speed
inertial frame.
As for Einstein’s and Planck’s predictions that measuring the temperature of an
extremely fast moving body of mass will read it to be lower than if it were
measured from the body’s own perspective (inertial frame), I disagree. I suspect
that the reasoning behind their predictions is that the light we’d be observing
coming from this body (in order to gauge its temperature) would be red or blue
shifted, depending on the observer’s position relative to the trajectory of the
body. What this assumption fails to consider is that the body’s constituent
parts vibrating away from the observer will be inversely shifted, thereby
statistically levelling out the otherwise errant temperature reading.
[06 September 2008: Upon re-reading this and giving it another modicum of
thought I’d like to recant the above claim, for it fails to take into
consideration that the particles travelling/’vibrating’ in the opposite
direction of the trajectory of the body as a whole would still be blue-shifted,
and therefore it would do little to negate the doubly-blue-shifted particles
diametrically opposed in their vector. In other words: a body of mass coming
toward the observer would appear warmer than it really is, and colder heading
away from the observer. This has little impact on actual temperature, but is
merely an illusion inherent from how we measure such things.]