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## Main Question or Discussion Point

I made a post yesterday in the thread "question regarding explanation of the impossibility of faster then(sic) light travel"

In that thread, I concluded that if something could be accelerated to the speed of light, then "time in that things frame" is slowing down, so that at the speed of light, all relative motion in that frame ceases, and the object is at absolute zero degrees kelvin.

So now I am thinking about whether or not SR is consistent with thermodynamics.

Consider the time dilation formula:

[tex] \Delta t = \frac{\Delta t'}{\sqrt{1-v^2/c^2}} [/tex]

By the axioms of algebra, v cannot equal c, unless [tex] \Delta t' = 0[/tex].

The basic argument I was thinking of is this.

Consider an object which is currently at rest in some inertial reference frame F, so in this frame v=0 right now. Now, of course this object has some temperature in this frame T. Now, suppose the object begins to accelerate in this frame, because some force is being applied to it. The speed v is now increasing. My next question is, is the temperature of this object relative or absolute?

Now, as the object moves faster and faster v gets closer to c. As the speed of this object increases, the quantity [tex] \sqrt{1-v^2/c^2} [/tex] is a fraction whose value decreases.

With this in mind, as a body accelerates through some inertial reference frame, time for the body passes slower and slower, so that if this body finally reached the speed of light, time for it wouldn't pass at all. The way to interpret that mechanically, is to say that all the particles in it have stopped moving relative to each other. Using thermodynamics, that would mean that the temperature of the body reached absolute zero, in the inertial reference frame. Thus, a body starting at temperature T when its speed equals 0, and accelerating to the speed of light c, would have to have its temperature slowly approach absolute zero, and would reach absolute zero if the object ever reached speed c in the frame. However, by thermodynamics, no body can ever reach a temperature of absolute zero degrees kelvin, and so no body can be acclerated to the speed of light (interesting way to draw this conclusion).

It is tempting to think that in the object's frame, the temperature of the ship is always T, and that things outside the object appear to be getting colder, because the time dilation formula is relativistic. If that were the case, then we could clearly say that temperature is relative, rather than absolute. But, I realize that the object is accelerating, and that SR doesn't strictly apply, because of this asymmetry between the two frames. Thus, relativity theory (generalized to accelerating frames), should predict that temperature is absolute, but is a function of speed. Thus, as the speed of the object increases, its temperature decreases, but its temperature in its frame is equal to its temperature in another frame.

The problem I see though, is that from relationship "E=Mc^2", it follows that as the object moves faster and faster, its total energy is increasing. Thus, if SR is correct, and thermodynamics is correct, then as a body's speed increases, its temperature is both increasing and decreasing, which is impossible. Hence, SR and thermodynamics are inconsistent. (Note that the rest energy of the object is a constant, and it is the kinetic energy that is increasing, but so then if the rest energy of an object is proportional to the temperature of an object, then that should be constant as the body speeds up.)

I would welcome anyone elses opinions on how relativity and thermodynamics interrelate. My whole point, is that there hasn't been much mathematical work on how relativity and thermodynamics work together. The total energy of a body is Mc^2, but where is there room for discussing the internal energy of a body, and the temperature of a body? Relativity simply doesn't adequately address thermodynamic issues (IMO).

One more thing:

Wouldn't this also mean that if a photon has internal parts, that those parts aren't in relative motion to each other? Thus, the temperature of any photon must equal absolute zero, which is impossible according to thermodynamics?

In that thread, I concluded that if something could be accelerated to the speed of light, then "time in that things frame" is slowing down, so that at the speed of light, all relative motion in that frame ceases, and the object is at absolute zero degrees kelvin.

So now I am thinking about whether or not SR is consistent with thermodynamics.

Consider the time dilation formula:

[tex] \Delta t = \frac{\Delta t'}{\sqrt{1-v^2/c^2}} [/tex]

By the axioms of algebra, v cannot equal c, unless [tex] \Delta t' = 0[/tex].

The basic argument I was thinking of is this.

Consider an object which is currently at rest in some inertial reference frame F, so in this frame v=0 right now. Now, of course this object has some temperature in this frame T. Now, suppose the object begins to accelerate in this frame, because some force is being applied to it. The speed v is now increasing. My next question is, is the temperature of this object relative or absolute?

Now, as the object moves faster and faster v gets closer to c. As the speed of this object increases, the quantity [tex] \sqrt{1-v^2/c^2} [/tex] is a fraction whose value decreases.

With this in mind, as a body accelerates through some inertial reference frame, time for the body passes slower and slower, so that if this body finally reached the speed of light, time for it wouldn't pass at all. The way to interpret that mechanically, is to say that all the particles in it have stopped moving relative to each other. Using thermodynamics, that would mean that the temperature of the body reached absolute zero, in the inertial reference frame. Thus, a body starting at temperature T when its speed equals 0, and accelerating to the speed of light c, would have to have its temperature slowly approach absolute zero, and would reach absolute zero if the object ever reached speed c in the frame. However, by thermodynamics, no body can ever reach a temperature of absolute zero degrees kelvin, and so no body can be acclerated to the speed of light (interesting way to draw this conclusion).

It is tempting to think that in the object's frame, the temperature of the ship is always T, and that things outside the object appear to be getting colder, because the time dilation formula is relativistic. If that were the case, then we could clearly say that temperature is relative, rather than absolute. But, I realize that the object is accelerating, and that SR doesn't strictly apply, because of this asymmetry between the two frames. Thus, relativity theory (generalized to accelerating frames), should predict that temperature is absolute, but is a function of speed. Thus, as the speed of the object increases, its temperature decreases, but its temperature in its frame is equal to its temperature in another frame.

The problem I see though, is that from relationship "E=Mc^2", it follows that as the object moves faster and faster, its total energy is increasing. Thus, if SR is correct, and thermodynamics is correct, then as a body's speed increases, its temperature is both increasing and decreasing, which is impossible. Hence, SR and thermodynamics are inconsistent. (Note that the rest energy of the object is a constant, and it is the kinetic energy that is increasing, but so then if the rest energy of an object is proportional to the temperature of an object, then that should be constant as the body speeds up.)

I would welcome anyone elses opinions on how relativity and thermodynamics interrelate. My whole point, is that there hasn't been much mathematical work on how relativity and thermodynamics work together. The total energy of a body is Mc^2, but where is there room for discussing the internal energy of a body, and the temperature of a body? Relativity simply doesn't adequately address thermodynamic issues (IMO).

One more thing:

Wouldn't this also mean that if a photon has internal parts, that those parts aren't in relative motion to each other? Thus, the temperature of any photon must equal absolute zero, which is impossible according to thermodynamics?

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