As I recall it is small, going basically in proportion to (v/c)^2, but what does this have to do with Temperature? Strictly speaking temperature is the average kinetic energy in an equilibrium state, not the average KE of any collection of atoms, whose individual energies or velocity distribution is changing. Because low mass particle colliding with a high mass particle tends to "bounce" off the high mass particle with little energy transfer AND because the low mass particles' mutual collisions rapidly re-distribute their total KE into a time constant distribution, (and same is true of collisions between the high mass particles) there is some sense in speaking of two different temperatures. For example, an "electron temperature" and "ion temperature" in a plasma. They will quickly (on human time scales) become the same if the plasma is "isolated," however, usually it is not. IE there may be energy flow into and from it, which even if a net of zero, can keep these two "temperatures" different. Molecular and not fully ionized ions, even helium ions, tend to "bleed radiant energy" and electric fields applied tend to heat the electrons more that the ions, so Te > Ti is possible to maintain.
Forgot to answer that bit from #15. Since the spectrum of ambient radiation seen in the rod's frame is biased and no longer isotropic Planck black-body distributed (as assumed holds in observer rest frame), things like surface emissivity/reflectivity, and the aspect ratio of rod will be factors. Without doing sums, it's not hard to figure qualitatively that high reflectivity and high aspect ratio will favor a lower mean rod temperature, and conversely for the opposite cases. The extremes would be a silvered thin rod bent into a hoop rotating about it's major axis (thus 'endless') vs a carbon blacked thin disk whose axis of symmetry is parallel to relative v. If there is a sneaking suspicion energy conservation might be violated, note that angularly biased net radiation implies conversion of relative KE to radiant. The opposite would imply violation of the 2nd law! [edit: above is based on rod having achieved 'thermal equilibrium' with it's biased heat bath environment]
If there is no friction with the hand and that hand's temperature is the rod's temperature, then there is no energy transfer, independent of the emissivity etc. coefficients of the rod surface.
For that particular case it is implicitly assumed an 'infinitely long' moving rod has already achieved thermal equilibrium with a heat bath that is isotropic for the rest frame observer and his/her hand? Then assuming further that heat transfer is radiative not via conduction ('frictionless' idealization implies that imo), then no, emissivity does indeed matter - there is an emission angle bias (lower at angles further from the surface normal), as outlined to some extent in various places e.g.: https://en.wikipedia.org/wiki/Emissivity A low emissivity ('silvered') rod surface implies reduced heat transfer from hand to rod - biased ambient spectrum in rod frame will increase the mean effective reflectivity - higher energy blue-shifted radiation hits at more rakish angles. Conversely, biased radiation from rod to relatively low reflectivity hand implies relatively higher hand thermal uptake. This assumes there is no time for thermal equilibrium between hand and passing rod to be established. If there were (say an 'infinite array of hands'), I would still expect a differential, but somewhat reduced. Basically, thermal equilibrium has a different interpretation to the usual case of stationary systems. I dimly recall coming across a lengthy debate on the topic back in a very old issue(s) of NewScientist, but no doubt it has been well handled in the peer-reviewed literature somewhere.
No my prior post, 24, is correct. Two bodies, both in thermodynamic equilibrium (have a temperature) and if that temperature is the same, then neither can get net energy from the other. Not by radiation nor by contact conduction and they can have very different (in both angle and wave length) emission coefficients. If net energy transfer were possible one could heat the other, making a temperature difference. That difference could power a "heat engine" violating both first and second laws of thermodynamics.
Wow, great responses all around! Thanks much. The transverse Doppler shift is exactly what I was thinking of, and I appreciate the references thereon. All the stuff about non-isotropic Doppler shifts goes well beyond what I had in mind - this is a surprisingly deep subject! And as for the contact temperature thing, I actually was talking about conductive heat transfer; I now realize that in a frictionless system, that's an ill-posed question. I'm glad it sparked some good discussion on radiative transfer, though.
The Doppler shift is a coordinate dependent measurement. The frequency is measured from remote coordinates. The frequency measured in the local proper frame where emitted isn't Doppler shifted. The measurement in the local proper frame is invariant and the remote measurement is frame dependent. Simple stuff. All the measurements are valid. The measurement in the local proper frame is a proper measurement while the remote measurement is coordinate dependent. I sound like a broken record but that's the way it works. The rod doesn't change temperature because it can be considered to be in relative motion. Temperature is a scalar which is measured at a specific local proper frame space time event. It doesn't change due to what coordinates you choose for the rod or the measurement device. Billy T mentioned friction. That's one of the physical processes that can result in a change of temperature. There's many more but choosing different coordinates isn't one of them. The reason I keep going over this is because you seem to think the temperature of the rod would be raised if the measurement device, the hand, stopped the rod before it's temperature was measured. This would mean the temperature change would be due to changing coordinates. This would be a violation of the principle of relativity. What difference would it make to the measurement in the local proper frame if you choose the rest frame for the rod instead of the hand?
I'm actually skeptical of this claim; I would love to see a citation. Insofar as temperature is related to atomic velocities, and velocity is a frame-dependent quantity, I don't see any reason why temperature should be frame-independent. I realize that if the observer stopped the rod before checking its temperature, that would be a local proper measurement. I apologize for being unclear about that. I was asking about the situation where the observer measures the rod's temperature without slowing it down, such that the measurement frame is spatially local but moving fast compared to the proper frame.
Assuming we are speaking of the atoms and or molecules in a confined volume, perhaps a solid, with no temporal changes in the velocity distribution, then the RANDOM total kinetic energy average is the temperature determining factor. Each and every particle could have a fixed velocity added to its velocity and the temperature remains unchanged, but the object has more KE in your frame - the one it was at rest in before each molecule got V added to it. A pan of boiling water on my stove has temperature T (roughly 100C) this despite it has a huge velocity thru space about the sun, etc. ONLY the random velocity makes the temperature. The random velocity is frame-independent so the temperature is too.
It doesn't matter whether the rod or the measurement device is modeled moving or at rest. For your case a choice of coordinates will decide that. The measurement result will be the same regardless which coordinates you choose. For example the LHC at CERN is a local proper frame where particle experiments are conducted. The choice of ocoordintes for the measurement devices in relative motion with particle beam collision remnants is at rest because it's easier to do the physics for this type of experiment. No way does the choice of coordinates change the result of the experiments. Temperature is a scalar. The measurement of temperature is a space time event conducted in the local proper frame. The physical measurement of the temperature of an object is conducted in the objects local proper frame. The measurement device also has to be physically in the rods local proper frame. It doesn't make any difference which one you think is moving. Inertial motion is relative. Accelerated motion is absolute. If some physical process associated with the acceleration causes the accelerated object to change temperature, such as increasing the objects total energy, so be it. For objects in inertial frames, following the natural geodesic inertial path, the total energy and momentum is a constant of the motion. The derivation of the relativistic energy equation confirms that both total energy and momentum are constants of inertial motion. It would be real magic if the temperature of an object changed due to a choice of coordinates initiated by a physicist. Anyway that's enough from me.
This is very interesting, on the lighter side I am inclined to give a name to this " The Relativistic Temperature Contraction", why not when we can have 'time dilation' and 'length contraction' ? In the thread, James R brings in relationship between Temperature and speed of atomic particles, Fednish48 raises the valid and pertinent point (even for argument sake) that speed is frame dependent so the Temperature must also be frame dependent, Brucep counters Fednish48 by bringing in Proper Frame and Remote Frame concepts, arguing that the transformation back to proper frame gives the invariant temperature, Is he being choosy ? Because would the same thing not happen if we were to do the same exercise for length and time ? Then Billy T, kind of agreeing with Fednish48 attempts to solve the riddle by saying that in random motion (of atomic particles) the reference frame speed will not matter, looks quite reasonable, but is it correct ? Try following Take a hollow packed lengthy rod, fill up the same with gaseous particles at Temperature T and make it move along the length. May be what Billy T says could be right at macroscopic level if we do statistical maths of collective individual random motion, but then length of this rod contracts in some frame, primarily reducing the volume and thus increasing either the pressure or Temperature ? Or can we say that length is contracting so the atomic particle should also contract, but then Billy T argument come in the way. I am not making any assertion, just creating few more points for positive academic discussions, you know science cannot be choosy barring duality of particle. Where is the catch ?
That's not my argument. It's a scientific fact but not part of my argument. My argument is both the rod and the measurement device are in the same local proper inertial frame when the temperature measurement is made. This is an invariant space time event and it doesn't matter what coordinates you choose to model the event with. Either the rod or measurement device at rest or either in relative inertial motion. The result would be the same. Fednis48 initimated that the temperature of the rod could be lower when it's in motion than when it was at rest. In point of fact there is no way of knowing anything beyond the two objects are in relative motion. So the way relativity theory works you get to choose the coordinates to model the physics with. Nothing physically happens associated with the choice of coordinates you model your local proper inertial frame with. Redshift, Blueshift, Doppler shift are all remote coordinate dependent measurements. None of physics associated with the 'shifts' has anything to do with local proper frame measurements. I could be loose and and just say local measurements but folks don't seem to get the differences between invariant and coordinate dependent. Probably because my attempts to explain become tiresome. Still fun. When the choice was made to predict the temperature would be lower it seemed that the local measurement was being conflated with remote coordinate measurements.
I was running a google search for a good definition of relativistic temperature, and I came across this thread over at stackexchange, which suggests that there's not actually a consensus regarding the relativistic definition of temperature. The basic problem is that if the object and the thermometer are moving quickly and inertially with respect to each other, they can't come to thermal equilibrium. As a result, the various measures of temperature that are equivalent in classical mechanics (mean kinetic energy in the proper frame? blackbody exponent over Boltzmann's constant? derivative of energy with respect to entropy?) no longer give the same result. Of particular importance to this thread, fast-moving objects cool down in the blackbody sense but (as brucep points out) maintain their temperature in the mean proper KE sense.
You either have a poor or highly selective memory - I suggest in regard to that last statement, you go back and read what I anticipated and dealt with in last para of #23. That a 'temperature differential' (ill-defined in SR) will in general exist does *not* automatically imply violation of either law. You are ignoring that KE acts as a 'pump' and 'reservoir'.
Yes that Stackexchange article I also came across, and as you say it does indicate a continued lack of consensus. But it's more than that - there is from the start there and elsewhere in the literature, very often a failure to tightly specify all aspects of an often vaguely assumed scenario. Typically, taken as a body with perfect black-body emissivity accelerated rapidly to a thereafter constant relative v, and one then asks what is the 'temperature' of such body - there having been negligible time for any possible heat transfer between such body and environment - i.e. a typically non-equilibrium scenario. I tried my best to indicate one needs to factor all possible variables when discussing 'temperature' and whether there is an unambiguous meaning to that in SR scenarios - cf my comments 2nd para in #26. Anyway, an example of an article that at least tries to cover many of the earlier controversy and reasoning that led to conflicting claims, see: http://www.numericana.com/answer/heat.htm Another article worth looking at is: http://arxiv.org/pdf/0910.0164 None of them afaik in skimming through, discuss the issue of e.g. angular-dependent emissivity and how that then combines with geometry in determining 'equilibrium thermodynamics' or lack thereof. A truly comprehensive general treatment appears to be lacking. As a simple example showing how the concept of 'a temperature', for a moving body immersed in a rest-frame isotropic black-body thermal bath is naive in general, I will revert to the 2nd extreme case given in #23 "a carbon blacked thin disk whose axis of symmetry is parallel to relative v." It should not need specific calculations to see that the 'front' disk face sees an overall blue-shifted spectrum thus higher energy density of impinging thermal radiation, than the back face for which general red-shifting applies. Consequently, there will be a temperature *differential* established and maintained between front and back faces - regardless of any final 'thermal equilibrium' being reached with the environment. Thus a continual heat flow from front to back face - seen in any frame. This hopefully makes it clear the subject is somewhat complex, with many variables to carefully consider - and which need tightly defining from the outset if confusion is to be avoided. Much of the commentary in certain earlier posts amounts to pretentious waffle. About the only unambiguous thing that can easily be said is that, like any form of internal energy, the thermal energy content of a moving body is - absent appreciable heat transfer with environment - boosted by the gamma factor. But that simple observation hardly covers the more interesting aspects of how such a moving body (again - geometry matters!) then thermally interacts with various possible environments (e.g., vacuum, close-by matter having some emissivity characteristics, etc.).
My, things have gotten quiet here. To round out a bit from last post #36, there is one situation for which the notion of 'temperature of a moving body' can be well defined in a certain sense. Strictly rectilinear motion of a mass moving at speed v wrt observer rest frame, in a vacuum environment at absolute zero, the environment being so extensive thermal back-reaction to the mass is zero. In the mass rest frame, there is a radiant power loss to the environment, j*, given by the Stefan-Boltzman law (https://en.wikipedia.org/wiki/Stefan–Boltzmann_law) ~ T^4. This proper rate j* must equal that found in observer frame since there cooling rate dT/dt ~ 1/gamma, and net thermal energy W ~ gamma, will exactly cancel each other. That is - net radiant power loss is an invariant in such circumstance. Hence, in terms of net radiant power loss, T = T'. Note this definition gives an average value based on net radiant power loss, and loses validity and indeed meaning as soon as any other condition or consideration enters. [edit: I have corrected an earlier claim above.]
