Does my speedy spaceship (.999+C) have a temperature?

[Suppaman]

TL;DR Summary

Assume we measure the temperature as the ship passes, what will it be?

I assume that as time is moving much slower on the ship and that may affect the frequency of heat radiation. I am not sure how to phrase the question because I do not want to assume any answers. I did ask Mr. Google but no results.

 

[PeroK]

Summary: Assume we measure the temperature as the ship passes, what will it be?

I assume that as time is moving much slower on the ship and that may affect the frequency of heat radiation. I am not sure how to phrase the question because I do not want to assume any answers. I did ask Mr. Google but no results.

How do you define temperature?

How would you measure the temperature of a moving object?

 

[Suppaman]

Everything in the sky is moving and we can measure their temp so like that. And I asked if it had a temp, and you asked me two questions, please answer mine first.

 

[PeroK]

Everything in the sky is moving ...

I'll need to think about that!

 

[PeroK]

Try this:

https://physics.stackexchange.com/questions/83488/is-temperature-a-lorentz-invariant-in-relativity

 

[Ibix]

I think it depends how you choose to define temperature, as PeroK's link suggests. Certainly one can define "rest temperature" which is invariant, and it makes sense to do so. Certainly you will measure the radiation from a moving object as red- or blue-shifted, which would let you define a "relativistic temperature".

I'd prefer to define temperature as invariant, and as far as I'm aware that's the modern approach to more or less everything. I don't know if there is a consensus in this case or not - my only text on relativistic thermodynamics is over eighty years old.

So ultimately, I think you need to answer PeroK's questions - how are you defining temperature and what method are you using to measure it. When you've answered both, the answer to your question will be obvious. Until you've answered both, the answer is "could be anything".

For stars in the sky, generally we're trying to compare like with like. So I expect that we measure the apparent blackbody curve, correct for the Doppler shift by looking at spectral lines, and thereby measure "rest temperature".

 

[Suppaman]

The ship obviously has a temp, it is moving and that will not change that temp. If I take a photo with my IR camera as it passes in front of the camera, neither coming or going, just in passing, what will my camera measure? Let us say that if the ship was stopped it would reg 1000 deg F and now it is moving and time is slower on the ship it would still be 1000 deg F based on the ship's sensors but what would I see?

 

[PeroK]

The ship obviously has a temp, it is moving and that will not change that temp. If I take a photo with my IR camera as it passes in front of the camera, neither coming or going, just in passing, what will my camera measure? Let us say that if the ship was stopped it would reg 1000 deg F and now it is moving and time is slower on the ship it would still be 1000 deg F based on the ship's sensors but what would I see?

There's the transverse Doppler effect:

https://en.wikipedia.org/wiki/Relativistic_Doppler_effect#Transverse_Doppler_effect
Note that IR radiation is a measure of the heat an object is radiating and not its temperature. Two objects heated to the same temperature do not necessarily radiate the same heat. Compare a well insulated house with a poorly insulated one.

Also, more important, if you have several observers, all moving with respect to each other and all measuring different temperatures of the ship, then you can see that the concept becomes physically less meaningful.

You would have to say: "the temperature of that object relative to me is ...". In the same way that you say "the velocity of that ship relative to me is ...".

As @Ibix has pointed out, temperature is something that we would like to define as invariant - i.e. an inherent quantity of the object itself. Not dependent on the relative velocity of an observer to the object.

 

[Ibix]

If I take a photo with my IR camera as it passes in front of the camera, neither coming or going, just in passing, what will my camera measure?

It'll show a blackbody spectrum (edit: assuming your ship is a blackbody - see next post), related to the blackbody spectrum you would measure at rest by the transverse Doppler shift. So you'd see a blackbody temperature reduced by a factor of $\gamma$ compared to the at-rest measure.

Whether you regard this measure as "the temperature of the spaceship", or whether you correct for the motion of the ship (recovering the at-rest measure) and call this the temperature of the ship, is up to you.

The measurements are a matter of fact. How you label them follows consensus opinion and, as I said, I don't know what the modern consensus is. I expect it is for using "temperature" to mean invariant (or rest) temperature. But I do not know.

 

[Ibix]

It's also worth looking at the photo in this post to see the issues with IR for temperature measurement, quite apart from any relativistic effects. It works for blackbodies - not so much for very non-black things.

Nonetheless, whatever IR spectrum you measure will be related to the at-rest IR spectrum by the transverse Doppler effect.

 

[russ_watters]

Why is this even an Einsteinian relativity question? Temperature is not frame dependent in Galilean Relativity either. When you travel in a plane, you'd cook if it was.

 

[russ_watters]

Note that IR radiation is a measure of the heat an object is radiating and not its temperature. Two objects heated to the same temperature do not necessarily radiate the same heat. Compare a well insulated house with a poorly insulated one.

That's oddly put. It should be obvious that IR is a surface temperature measurement and there are limitations associated with that, but that doesn't make the measurement inaccurate, it just makes it different from an internal measurement.

What can make the measurement itself inaccurate is emissivity differences between materials.

 

[Suppaman]

Thank you all. I think I was looking for how we would view the observable properties of the speedy ship. For example, suppose there was a place that had a very high emission of energy, gigawatt laser, some super high power emitter of some kind that if a physical was in its focus for a super short time it would totally destroy the item. Now our speedy ship passes through this area very quickly, but the time exposed is long enough to do damage. But time on our ship is slow and it is so slow there is not enough time experienced by the ship for the energy beam to do damage. In the physical universe, we can have physical objects that are experiencing slow time, I am looking for information on what the rules are for interacting with them. We know gravity and speed can slow time but we do not know what time really is.

 

[Orodruin]

Why is this even an Einsteinian relativity question? Temperature is not frame dependent in Galilean Relativity either. When you travel in a plane, you'd cook if it was.

Again, this depends. If you mean the rest temperature, sure. If you mean the temperature that you would associate with the spectrum radiated from the body that will be affected by the Doppler effect and correspondingly red or blue shifted.

 

[Ibix]

For example, suppose there was a place that had a very high emission of energy, gigawatt laser, some super high power emitter of some kind that if a physical was in its focus for a super short time it would totally destroy the item. Now our speedy ship passes through this area very quickly, but the time exposed is long enough to do damage. But time on our ship is slow and it is so slow there is not enough time experienced by the ship for the energy beam to do damage.

You contradict yourself here. Either damage was done or it was not. It may be that you don't understand one frame's explanation for why damage was done (I'd have to work through it myself, but I'd suspect Doppler and angular aberration). But if you simply assume there's a contradiction then you are choosing to be confused.

 

[Suppaman]

You, someone, asked why this was " an Einsteinian relativity question? " Would it be best to ask a question and enclose it in a higher level question asking what category the question should be asked in? Perhaps there is a category or topic that can be used to ask a question and the powers that be are expected to assign it to an appropriate category or topic? I do not want to waste anyone's time. I also would appreciate having my question reworded to make proper sense rather than being criticized for asking a less than best question. Some times a really good question may not yet have a proper or universally accepted answer.

 

[jbriggs444]

We know gravity and speed can slow time

No they do not. They affect the way we associate time here measured against this reference frame with time there measured against that reference frame. But they do not "slow time". Time proceeds at one second per second regardless.

 

[Suppaman]

So there is no twin paradox?

 

[jbriggs444]

So there is no twin paradox?

The twin paradox does not involve time slowing down. It involves the comparison of time over here with time over there. And it involves the fact that the elapsed time between events depends on the path taken.

 

[Suppaman]

One twin is obviously older than the other. How did that happen?

 

[PeroK]

One twin is obviously older than the other. How did that happen?

There are numerous threads on here about the twin paradox.

In general, many people before they learn SR have a misapprehension that "speed makes time run slower". If they learn SR properly, they learn that this is a misapprehension. In fact, the first thing they learn is that all inertial motion is relative and that velocity-based time dilation is symmetric.

From your posts above and on previous threads, it's clear that you have never lost the misapprehension about motion and time. In fact, you seem quite subborn in resisting all attempts to explain this to you.

My honest advice is to take a step back, forget all you think you know about SR and to start learning it without any misapprehensions or false preconceptions about what it says. These are preventing you understanding SR and understnding the answers to your questions.

This question about motion and temperature is a case in point.

In particular: there is no physical difference between a spaceship at rest relative to the Earth and te same ship traveling at nearly the speed of light relative to the Earth. It's the same ship and there are no physical differences associated with relative motion. There cannot be as the Earth is likewise traveling at nearly the speed of light relative to the ship.

 

[Suppaman]

Twin paradox[edit]
Bailey et al. (1977) measured the lifetime of positive and negative muons sent around a loop in the CERN Muon storage ring. This experiment confirmed both time dilation and the twin paradox, i.e. the hypothesis that clocks sent away and coming back to their initial position are slowed with respect to a resting clock.[27][28] Other measurements of the twin paradox involve gravitational time dilation as well. See for instance the Hafele–Keating experiment and repetitions.

 

[Nugatory]

So there is no twin paradox?

It’s not a paradox, if that’s what you mean.
Time passes at the rate of one second per second for both the traveling twin and the stay at home twin.

Their clocks tick off different amounts of time between the separation and reunion events for the same reason that two cars driving along different routes between the same two points will generally record a different number of kilometers driven: the different routes have different lengths, not because anything funny is happening with their speedometers.

 

[PeroK]

Twin paradox[edit]
Bailey et al. (1977) measured the lifetime of positive and negative muons sent around a loop in the CERN Muon storage ring. This experiment confirmed both time dilation and the twin paradox, i.e. the hypothesis that clocks sent away and coming back to their initial position are slowed with respect to a resting clock.[27][28] Other measurements of the twin paradox involve gravitational time dilation as well. See for instance the Hafele–Keating experiment and repetitions.

There is no shortage of material which, through a general lack of precise language, can reinforce your misconceptions. This is not so much wrong as misleading, when taken out of context.

As a counter to this, you could try:

https://en.wikipedia.org/wiki/Twin_paradox#Resolution_of_the_paradox_in_special_relativity
It's not motion that causes differential aging, but changing from one inertial frame to another and, more generally, the shape of the path through spacetime.

 

[Nugatory]

Twin paradox[edit]
Bailey et al. (1977) measured the lifetime of positive and negative muons sent around a loop in the CERN Muon storage ring. This experiment confirmed both time dilation and the twin paradox, i.e. the hypothesis that clocks sent away and coming back to their initial position are slowed with respect to a resting clock.[27][28] Other measurements of the twin paradox involve gravitational time dilation as well. See for instance the Hafele–Keating experiment and repetitions.

And careless wording like this is part of the reason that Wikipedia is not, in general, an acceptable source here. This description isn’t exactly wrong but without a great deal more context it is terribly misleading - and it’s misled you.

A decent textbook might say something similar (the English language is not a precision instrument) but will also cover the other concepts that are needed to understand what’s going on: events; the spacetime interval; the distinction between proper time and coordinate time; relativity of simultaneity; frames as conventions for assigning coordinates to events; and the distinction between invariants and coordinate/frame-dependent quantities.

Wikipedia, even when it’s right, won’t always do this. Some Wikipedia articles are good, some aren’t, and the only way of knowing which are which is to ask someone who is already familiar with the subject.

 

[hmmm27]

So, the doppler effect will make the ship

- get (to the occupants) and appear (to a stationary observer) as being hotter at the front and colder at the rear...

while time dilation makes the ship

- get hotter while appearing colder, both all 'round.

 

[Orodruin]

get (to the occupants) and appear (to a stationary observer) as being hotter at the front and colder at the rear...

No. Occupants will not notice a thing. For the occupants, the ship is stationary.

 

[jbriggs444]

So, the doppler effect will make the ship

- get (to the occupants) and appear (to a stationary observer) as being hotter at the front and colder at the rear...

while time dilation makes the ship

- get hotter while appearing colder, both all 'round.

If I understand the thinking, the notion is of a photon gas which is isotropic in a particular "rest" frame. Within this gas, the moving ship sees an anisotropy -- blue-shifted high energy forward and red shifted low energy aft.

Special relativity is not responsible for the anisotropy. The setup of the universe is.

The thinking about time dilation is trickier. If you appear colder to the other guy, the other guy also appears colder to you. However there is some sense to be made of the conundrum.

Consider the situation with two parallel, infinitely long trains running on parallel tracks in opposite directions at high speed. Can the trains reach thermal equilibrium with one another? It seems to me that each will gain heat from the other due to relativistic beaming and a resulting net blue shift. There is no free lunch, of course. The gain in heat comes at the expense of each train's kinetic energy -- it is a fancy way of engaging in frictional mutual slow-down.

 

[russ_watters]

Again, this depends. If you mean the rest temperature, sure. If you mean the temperature that you would associate with the spectrum radiated from the body that will be affected by the Doppler effect and correspondingly red or blue shifted.

That's fine, I've just never heard of doppler shift being referred to as a temperature alteration. E.G., we don't say redshifted stars/galaxies are colder than blueshifted ones, do we?

But yeah, I guess the OP's wording implies that word usage.

 

[Heikki Tuuri]

Suppose that your spaceship is a black body in temperature T in the co-moving frame.

Let a static observer use an infrared telescope and measure the black body spectrum at a temperature T' with the correct surface brightness. Then we could say that the static observer "sees" the ship having the temperature T'.

I did some quick calculations, which might contain an error. If the spaceship is moving straight toward the static observer, then he does see the correct black body radiation for a temperature T' > T. If the spaceship is receding, T' < T. The spectrum is shifted because of the Doppler effect and time dilation.

If the spaceship is moving by, then the static observer sees it length-contracted. My calculations suggested that the surface brightness might appear too high for a black body at a temperature T / gamma.

 

[Vanadium 50]

I hesitate to jump in, because the detour suggests that this is really the start of an anti-relativity screed.

However...

Classically, there are several different definitions of temperature. They are equivalent in that they all give the same value for the same system. In relativity, these transform differently so do not agree. They will never agree.

It also doesn't matter. If I have a rocket moving at .99c with respect to my heat bath, it is not in thermal equilibrium with that heat bath. There's no way to say what its temperature "really is" since it doesn't fulfill the conditions to even have a temperature.

 

[pervect]

I gather there are a couple of relativistic treatments of temperature. One of them, as I recall, had inverse temperature as a 4-vector. So $\Delta Q$ became the change in a 4-vector (not just a scalar energy), and the change in inverse temperature also became a 4-vector. And $\Delta S$, which was still a scalar, became the dot-product of these two 4-vectors, the change in energy-momentum, and the inverse temeprature.

However, I was more comfortable with the treatments (which I've also seen) where temperature was always specified in the rest frame of whatever had the temperature.

The reference I recall was https://arxiv.org/abs/physics/0505004. Apologies if I messed up anything in my recollections, it's been a while since I read it. I don't know what the impact factor of this paper was, it looked like a decent place to start to me, but I'm not that familair with thermodynamics.