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RoboSpy
2004-Oct-16, 04:24 AM
It just occured to me...

The temperature of an object is defined as the measure of the average kinetic energy of the particles in that object. Kinetic energy is defined as follows:

KE = (1/2)mv^2

Where m is mass and v is velocity.

If velocity is relative, however, doesn't this imply that the temperature of an object is also relative, and depends upon the relative velocity of the person taking the measurement? Or are we to presume that the measure of the average kinetic energy is the measure of the average kinetic energy taking the velocities of the particles in relation to one another and not with respect to the observer?

Also, my definition of temperature is coming out of chemistry classes, where we often deal with ideal gases, so maybe there are different definitions...though I imagine that would be terribly inconvenient.

Evan
2004-Oct-16, 07:00 AM
That seems pretty straight forward to me. If you could measure the temperature of something moving at relativistic velocity relative to your frame of reference (very big "if") it should measure colder than if you were in the same frame as the object. If time is slowed for the object then so is the apparent motion of atoms to someone not in the same frame. This can only be a thought experiment though. You can't measure the object without having your measuring gear in the same frame as the object. This is where the concept of simultaneity comes in. Interesting idea but not relevant. You are either in the same frame and then everything seems normal or you are not in the frame and can't examine it. For the object in the relativistic frame although time is slowed the distances are shorter (Fitzgerald Contraction).

Eroica
2004-Oct-16, 10:53 AM
If you could measure the temperature of something moving at relativistic velocity relative to your frame of reference (very big "if") ...
You could do it indirectly. For example, you can determine the surface temperature of a star from its spectrum (specifically by measuring the lambda-max of its light-curve). If you do this while approaching the star at relativistic speeds, the star's light will be blue-shifted and it will become hotter and bluer to you. If you are receding, the star will become cooler and redder.

Strangely, if you were travelling to, say, Sirius, at relativistic speeds, you might not be able to see the star with the naked eye, because most of its light would be blue-shifted into the UV region!

papageno
2004-Oct-16, 11:49 AM
The Cosmic Microwave Background has the spectrum of a black body at a temperature of a few Kelvin.
But when the radiation was emitted, the temperature was a lot higher.
It is observed to be lower because of red-shift.

You can't measure the object without having your measuring gear in the same frame as the object.

This is basically the case with temperature for chemical systems (where systems in physical contact are usually considered).

Observed kinetic energy does depend on frame of reference, but it is not a problem as long as frames of reference are used consistently.

A Thousand Pardons
2004-Oct-16, 07:50 PM
This can only be a thought experiment though. You can't measure the object without having your measuring gear in the same frame as the object. This is where the concept of simultaneity comes in. Interesting idea but not relevant. You are either in the same frame and then everything seems normal or you are not in the frame and can't examine it.
Frames are imaginary constructs, so it seems you mean that the object being measured is at a different velocity than the temperature-measuring instrument. I'm pretty sure that's possible.

Fortis
2004-Oct-16, 08:40 PM
It just occured to me...

The temperature of an object is defined as the measure of the average kinetic energy of the particles in that object. Kinetic energy is defined as follows:

KE = (1/2)mv^2

Where m is mass and v is velocity.

One of the key things that you might be missing is that heat is the energy tied up in the "random" motion of the particles, rather than the coherent motion in any one direction. If someone takes a cold snooker ball and throws it, its temperature doesn't increase (unless we have to take into account aerodynamic heating.) :)

A Thousand Pardons
2004-Oct-16, 10:19 PM
One of the key things that you might be missing is that heat is the energy tied up in the "random" motion of the particles, rather than the coherent motion in any one direction. If someone takes a cold snooker ball and throws it, its temperature doesn't increase (unless we have to take into account aerodynamic heating.)
No, RoboSpy is talking about the relativistic effects. Didn't Sam5 get into that pretty far?

swansont
2004-Oct-18, 11:20 AM
No, RoboSpy is talking about the relativistic effects. Didn't Sam5 get into that pretty far?

Postcount-wise, yes. Conceptually, no.

zebo-the-fat
2004-Oct-18, 08:06 PM
Strangely, if you were travelling to, say, Sirius, at relativistic speeds, you might not be able to see the star with the naked eye, because most of its light would be blue-shifted into the UV region!

Would not the infra-red light (Sirrius must emit IR) be shifted to the visible part of the spectrum?

Eroica
2004-Oct-18, 08:10 PM
Strangely, if you were travelling to, say, Sirius, at relativistic speeds, you might not be able to see the star with the naked eye, because most of its light would be blue-shifted into the UV region!

Would not the infra-red light (Sirius must emit IR) be shifted to the visible part of the spectrum?
Yes, but is it intense enough to be visible to the naked eye? And, anyway, if you were going fast enough, even the IR would be blueshifted into the UV. I doubt if Sirius emits enough radio-waves to be visible.

Andreas
2004-Oct-18, 11:49 PM
It just occured to me...

The temperature of an object is defined as the measure of the average kinetic energy of the particles in that object. Kinetic energy is defined as follows:

KE = (1/2)mv^2

Where m is mass and v is velocity.

If velocity is relative, however, doesn't this imply that the temperature of an object is also relative, and depends upon the relative velocity of the person taking the measurement?
Velocity decreases. Mass increases.

Sam5 did try to use the decreasing apparent temperature in an attempt to declare relativity theory self-contradicting. Something along the lines of "we should see relativistic water freeze, while it wouldn't from its own frame of reference" (and that for at least three or four dozen pages of discussion). At first it would seem that less velocity would cause the water to build the crystalline bonds, but then you have to consider the relativistic mass increase which would also break the bonds easier due to increased inertia. It cancels out and liquid water stays liquid in every frame of reference, regardless of apparent temperature.