# Is special relativity consistent with thermodynamics?

## 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:

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

By the axioms of algebra, v cannot equal c, unless $$\Delta t' = 0$$.

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 $$\sqrt{1-v^2/c^2}$$ 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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Njorl
One measure of temperature is the average kinetic energy (KE) of particles in the system. Since KE is dempendent upon velocity, and velocity is dependent on time, and time is dilated in the system in question, the average velocity of the particles seems lower, making it appear colder. This is also seen in the blackbody radiation from the object. It is doppler-shifted to a lower frequency, indicating a colder object. However, we do not generally speak of this in terms of a relativistic temperature shift. We generally allow for the difference in reference frames, and calculate what the temperature would be in that frame.

There are things in thermodynamics that are inconsistant with SR. Thermo, and stat mech in general, make assumptions about mass behavior of particles to allow predictions to be made about large systems. In gas diffusion, it is assumed that some arbitrarily small number of molecules can move an arbitrarily long distance in an instant. The assumptions imply some movement at speeds greater than c. The theory could be redone, putting relativistic limits on particle speeds, but it would not be appreciably more accurate.

Njorl

Njorl,

If we assume SR is correct, then it follows that the temperature of an accelerating body should decrease, as the object approaches the speed of light, for the reason I gave. Time passes slower for the object, internal KE is a measure of its temperature, the speed of the particles in the body must be decreasing, hence the temperature is approaching absolute zero, hence photons emitted from the body should reflect a colder temperature, etc.

So I ask you this. What if SR is wrong? Can we use a thermodynamic argument to conclude that SR is wrong? It would have to be an utterly simple argument, in order to carry any weight. You stated that you are well aware that SR and thermodynamics are inconsistent. So which has the problem?

Thermodynamics is statistical, so I don't see any problem with it, that pushes the error to SR.

Suppose that SR is wrong, what can we now say about the temperature of an accelerating body? As a force is applied to that body, the body accelerates. Now this force is 'distributed' to all the particles in the body, they all have the same net acceleration. So each particle in the body is being subjected to a force. One result is that the overall kinetic energy of the body is increasing Mv^2/2, but this isn't a statement about the internal energy. Now, since newtons third law must be satisfied, for any particle in the body which is subjected to a force, there is another particle outside the body which was subjected to an equal but opposite force. Hence, I acceleration alone should not increase the internal kinetic energy of a body. And thus, the temperature of a body is independent of its speed, at least classically.

Thus, if SR is correct, then as a body accelerates its temperature approaches absolute zero, and if SR is incorrect then as a body accelerates, its temperature does not change.

The above statement means that relativity is empirically falsifiable.

There are now many questions I have about relativity and thermodynamics, and I would appreciate any clear thoughts at all on the whole matter.

Thank you

Njorl
Originally posted by StarThrower
Njorl,

You stated that you are well aware that SR and thermodynamics are inconsistent. So which has the problem?

Thermodynamics is statistical, so I don't see any problem with it, that pushes the error to SR.

No, the error is in the diffusion theory of thermo. It is in the assumption that particles in a diffusing fluid can have arbitrarily high velocity. It is a false assumption. It is correctable, but yields virtually no additional accuracy, so no one bothers.

Njorl

Originally posted by Njorl
No, the error is in the diffusion theory of thermo. It is in the assumption that particles in a diffusing fluid can have arbitrarily high velocity. It is a false assumption. It is correctable, but yields virtually no additional accuracy, so no one bothers.

Njorl
Before you say the error is in diffusion theory of thermos, consider only the facts which are being used from thermodynamics in the above argument. One thermodynamic fact which is being used in the above argument, is that as the internal kinetic energy of a body decreases, the temperature of that body approaches absolute zero. Another fact which is being used, is that it is impossible for the temperature of any body to reach absolute zero.

Really, we should not regard either of these two statements as 'facts of thermodynamics' rather they are facts about the real universe, which we have learned from countless experiments, and then we think of statistical mechanics as explaining the results of these experiments.

Do you question either of these two facts? Neither of them has to do with 'diffusion theory' (at least I dont see how), so can you please explain what you mean?

I recall doing the mathematical analysis, of why two bodies in thermal contact reach thermal equilibrium. I even recall a nifty integration that I did using the gamma function. The text I used was written by 'Kittel' I think was the name, and I didn't really care much for his symbolism. At any rate, consider a gas of particles. They are bouncing around, not really at random since the universe is deterministic, but we choose to think about the gas using the mathematical theory of probability, which will let us reach statistical conclusions.

Let me try to recall some thermo (bear with me)

The entropy of a body is defined as:

$$\sigma = k ln(g)$$

Where k is the Boltzmann constant, and g is the number of accessible states of the system.

Now, if we place two bodies in thermal contact, we can use the definition of entropy given above, to prove that statistically they will reach the same temperature, with an extrodinarily high probability. The temperature of one body will rise, and the temperature of the other body will fall, and they will finally reach an intermediate temperature, at which the bodies are said to be at thermal equilibrium. I am sure you remember these formulas more than I, but I carried out the detailed analysis long ago, and I am speaking from memory. The probability that the two systems will reach thermal equilibrium is extrodinarily high. So what point am I going to be able to make here.

My point is this. The mathematical theory of thermodynamics does not allow for the entropy of a system to decrease unless that system is brought into contact with another system of lower entropy. And thus, no isolated body can have its entropy reach zero by magic, hence no isolated body can have its temperature reach absolute zero. And even if you tried to bring a body down to a temperature of absolute zero, that wouldnt happen, because of tiny collisions at the point of contact. So really then, it isn't thermodynamics which says that a body cannot reach a temperature of absolute zero, it is reality which says this. And so this was one of the facts which I was using, I dont see that it has anything whatsoever to do with diffusion theory.

The other fact which I was using, is that as the internal kinetic energy of a body goes down, so does its temperature. Does this fact have anything at all to do with diffusion theory? For this not to be a fact, it would have to be the case that as the internal kinetic energy of a body goes down, its temperature either increases or stays the same. This isn't what really happens, and thermodynamics predicts this fact.

So here is how I would argue.

1) It is a fact that if the internal energy of a body decreases, then its temperature decreases.

2) It is a fact that no body can reach a temperature of absolute zero.

(both of these facts happen to be predicted by thermodynamics, but neither of these facts have anything to do with theory)

The theory of SR contradicts these facts. It does so when one analyzes the time dilation formula. As a body accelerates in an inertial reference frame, time for the body passes slower, eventually stopping altogether if the body reached speed c. Now, thermodynamics says that no body can ever reach a temperature of absolute zero, so by thermodynamics, no body can ever be accelerated to the speed of light (which conclusion is consistent with relativity specifically E=mc^2) so we don't have a problem yet.

The problem is encountered, when we realize that according to relativity, as the body accelerates, its total energy is increasing, by the formula E = mc^2, but by the time dilation formula, the internal kinetic energy of that body should be decreasing. Mathematically, here is my argument:

$$E = Mc^2 = T + mc^2$$

T is the kinetic energy of the body, and mc^2 denotes the rest energy of the body, which is a constant.

Now think about things relativistically, but using the time dilation formula instead. According to that formula, the temperature of the ship should be going DOWN, not up, and specifically it is the internal kinetic energy of the body which is decreasing. So then, another part of the theory of relativity predicts that the total energy should be decreasing. I see this error as being in SR.

I would appreciate you pointing out any errors that I have made.

Thank you very much Njorl.

PS: Also, what on earth is the Gizmonics institute, and what is this red jumpsuit thing all about?

Njorl
Last things first, because they're easier...

There was a show on Comedy Central I used to watch. It was about a guy who was shot into space and forced to watch bad movies ... um, it was better than it sounds. This was its theme song:

In the not too distant future,
Next Sunday A.D.
There was a guy named Joel,
Not too different from you or me
He worked at Gizmonics Institute,
Just another face in a red jumpsuit
He did a good job cleaning up the place,
But his bosses didn't like him,
So they shot him into space!

"We'll send him cheesy movies,
"The worst we can find (la-la-la)
"He'll have to sit and watch them all,
"And we'll monitor his mind (la-la-la)
Now keep in mind Joel can't control,
Where the movies begin or end (la-la-la)
Because he used those special parts,
To make his robot friends

Robot Roll Call: (Come on, let's go)
Cambot (Pan left)
Gypsy (Hi girl)
Tom Servo (What a cool guy)
Croooow! (You little wisecracker)

If you're wondering how he eats and breathes,
And other science facts (la-la-la)
Then repeat to yourself, "It's just a show,
I should really just relax".
For... MYSTERY SCIENCE THEATER 3000!

Njorl

David
Originally posted by StarThrower
Consider the time dilation formula:
Consider this 1907 Einstein SR thermodynamics statement:

"Thus, the temperature of a moving system is always lower with respect to a reference system that is in motion relative to it than with respect to a reference system that is at rest relative to it."

krab

Originally posted by David
Consider this 1907 Einstein SR thermodynamics statement:

"Thus, the temperature of a moving system is always lower with respect to a reference system that is in motion relative to it than with respect to a reference system that is at rest relative to it."
That's basically what Njorl said. Are you making a point here? What is it?

David

Originally posted by krab
That's basically what Njorl said. Are you making a point here? What is it?

Njorl said: “There are things in thermodynamics that are inconsistent with SR.”

And that is correct, because the original 1905-07 SR theory contains errors that are not consistent with reality. So my point is, Einstein’s “temperature” statement of 1907 contains a paradox and in fact is self-conflicting nonsense.

He later corrected many of his early SR mistakes with his GR theory.

One must learn to study Einstein’s theories and statements not as if he was born with all the complete SR and GR ideas already inside his mind. He actually developed the ideas over time, and he made a few mistakes in the early years in the Kinematical part of the SR theory, which he later corrected with the GR theory. So we can’t take all his 1905 statements and assume they are the “absolute truth”, since he gradually changed his mind about many SR issues. Therefore, most of his later statements were far more accurate than his earlier statements, and some of his earlier statements were downright wrong.

Take for example, his “curved space” and “hypersphere” concept of 1915, for a totally “fixed” universe in which all the stars and galaxies are “fixed” and the universe is not expanding, which is what he believed in 1915, since that is what all the astronomers told him was true. But that concept was made obsolete in the late 1920s by the Hubble discovery and the Lemaitre big bang theory. So, in 1932 Einstein wrote a paper with de Sitter in which he retracted his original 1915 “curved space – hypersphere” idea. He said in the 1932 paper:

“There is no direct observational evidence for the curvature, the only directly observed data being the mean density and the expansion, which latter proves that the actual universe corresponds to the non-statical case. It is therefore clear that from the direct data of observation we can derive neither the sign nor the value of the curvature, and the question arises whether it is possible to represent the observed facts without introducing a curvature at all.”

“Although, therefore, the density corresponding to the assumption of zero curvature and to the coefficient of expansion may perhaps be on the high side, it certainly is of the correct order of magnitude, and we must conclude that at the present time it is possible to represent the facts without assuming a curvature of three-dimensional space. The curvature is, however, essentially determinable, and an increase in the precision of the data derived from observations will enable us in the future to fix its sign and to determine its value.”

It is common error that many people make, including physics professors, to think that ALL of what Einstein said over his entire lifetime was ALL correct. This is simply not true. His later GR statements and observations tended to be far more accurate than his earlier SR ones.

Since the Electrodynamical part of the 1905 theory is vastly different from the Kinematical part, many of his 1905 electrodynamical statements tend to be accurate. It is the Kinematical part of the 1905 and 1907 papers that are filled with errors that he later corrected. For example, in 1918, when he finally realized that just “relative motion” alone could not alter any clock tick rate, he added “acceleration” to the 1905 paper, retroactively, by placing the K’ frame resting inside a gravitational field. The K’ frame still was the “moving one”, while the K frame was the “stationary one”, but in 1918 and thereafter, the real reason for the physical “slow-down” in the K’ frame’s clock was NOT because of “relative motion”, but because of the gravitational field in the K’ frame that placed a real “force” on the K’ clock.

This was thoroughly explained by W. Pauli in his 1921 relativity book, which stated:

”Equation (392) has the following physical meaning: Consider two equal, originally synchronous, clocks at rest and let one of them be placed in a gravitational field for a certain length of time. Afterwards they will no longer be synchronous; the clock which had been placed in the gravitational field will have lost. As mentioned by Einstein [in Naturwissenschaften, 6 (1918) 697], this is the basis of the explanation for the clock paradox described in section 5 [of this book]. In the coordinate system K’ in which the clock C2 is permanently at rest, a gravitational field exists during the time in which its motion is retarded, and the observer in K’ can regard this field as causing the clock C2 to lose.

In his book, Pauli said this paradox problem was discussed by “Langevin (1911), Laue (1912), and Lorentz (1914)”. And he said, just as I have said, that the only “solution” to the paradox is to add “acceleration” to the K’ frame clock, since just “relative motion” alone will not cause that clock to “time dilate”.

In another chapter of his book, Pauli said:

“Let us describe the process in terms of a reference system K’, always at rest with respect to C2. Clock C1 will then move relative to K’ in the same way as C2 moves relative to K. Yet, at the end of the motion, Clock C2 will have lost compared with C1, i.e. C1 will have gained compared with C2. The paradox is resolved by observing that the coordinate system K’ is not a Galilean reference system and that in such a system the effect of acceleration cannot be neglected, since the acceleration is not produced by an external force, but, in the terminology of Newtonian mechanics, by an inertial force.”

So, it actually takes a “force” to slow down a clock. Relative motion alone won’t do it.

You can find Einstein’s 1918 “patch” article to correct the error in the original 1905 theory, in Volume 7 of the Collected Papers of Albert Einstein, but the hard-bound book will cost you about $140, and the paperback will cost about$50. Maybe you can find Volume 7 in a large university library.

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David
Originally posted by StarThrower
So now I am thinking about whether or not SR is consistent with thermodynamics.

Here is what Max Planck said about the thermodynamic issues of two relatively moving frames:

"Let us imagine that the body is brought by some reversible, adiabatic
process from a state in which it is at rest with respect to the unprimed [stationary]
system into a second state, in which it is at rest with respect to the primed [moving]
reference system. If the body's entropy for the unprimed system in the
initial state is denoted by n1 and in the final state by n2, then, because
of the reversibility and adiabatic nature of the process, n1 = n2. But the
process is reversible and adiabatic for the primed reference system as well,
hence we will also have n2’ = n2’.

"Now, if n1’ were not equal to n1 but, say, n1’ > n1 this would mean
the following: The entropy of a body is larger for the reference system for
which it is in motion than for the reference system for which it is at rest.
But this proposition would also require that n2’ > n2, because in the latter
state the body is at rest for the primed reference system while in motion for
the unprimed one. However, these two inequalities conflict with the two
equalities established. Similarly, one cannot have n1’ > n1; consequently
n1’ = n1 and, in general, n’ = n, i.e., the entropy of the body does not
depend on the choice of the reference system."

This statement was actually quoted in Einstein’s 1907 paper, and the Planck statement is correct.

But a few paragraphs later, Einstein came to this conclusion:

“Thus, the temperature of a moving system is always lower with respect to a reference system that is in motion relative to it than with respect to a reference system that is at rest relative to it.”

But this is incorrect because it contains an obvious paradox, since the satement says that both of two “relatively moving” frames would be colder than the other.

Einstein’s equation to go with that paradoxical statement is equally paradoxical. He said that if To = the temperature of the body from which the observation is beng made, then T would be the “absolute temperature” of the moving body, in this amount:

T/To = √ 1- (v^2/c^2)

So even his 1907 math means that both of two relatively moving systems will be colder than the other.

This 1907 paper can be found in The Collected Papers of Albert Einstein – Volume 2.

krab
Daivid sez:
But a few paragraphs later, Einstein came to this conclusion:
“Thus, the temperature of a moving system is always lower with respect to a reference system that is in motion relative to it than with respect to a reference system that is at rest relative to it.”
But this is incorrect because it contains an obvious paradox, since the satement says that both of two “relatively moving” frames would be colder than the other.
This is exactly the same paradox as exists in the case of two observers moving away from each other. Each sees his own clock running fine, but the other's running slow. It is only a problem if you are implicitly assuming absolute time. So this is not evidence of Einstein (and everyone since him) making an error; it is evidence of your own inability to understand relativity.

David
Originally posted by krab
Daivid sez: This is exactly the same paradox as exists in the case of two observers moving away from each other. Each sees his own clock running fine, but the other's running slow. It is only a problem if you are implicitly assuming absolute time. So this is not evidence of Einstein (and everyone since him) making an error; it is evidence of your own inability to understand relativity.

The “moving clock time dilation” thing of SR theory was a 1905 error, as I’ve explained, since there is no physical “force” placed on either clock with just relative motion. And Einstein corrected this with GR theory, by adding a “gravitational field” to the K’ frame in “On the Electrodynamics of Moving Bodies”, in a 1918 paper he wrote, which Pauli referred to in his 1921 book. Also, see Newton’s First Law and his dissertation about “relative” and “absolute” motion in the Principia.

The 1907 “temperature” statement is also an SR error which was based on the original 1905 SR “relative motion” error. And he’s is not talking about Doppler theory in the 1907 paper. He calls “T” the “absolute temperature”, not the “Doppler shifted visual temperature”.

When you say, “Each sees his own clock running fine, but the other's running slow,” if you are referring to the Doppler theory of 1842, then you are correct, but you need to keep in mind that in Doppler theory (and also in real life) the two observers would see each other’s clocks as appearing to “speed up” when the observers and clocks are moving toward each other. Just ask any radio or TV technician.

When you speak about “relativity”, you need to make it clear whether you are talking about SR or GR, or Galilean/Newtonian/Doppler relativity, or Lorentz relativity.

Janus
Staff Emeritus
Gold Member
Originally posted by David
The “moving clock time dilation” thing of SR theory was a 1905 error, as I’ve explained, since there is no physical “force” placed on either clock with just relative motion.
Which just emphases the fact that you do not understand SR. Time dilation does not rely on any physical force acting on the clocks. It is a direct consequence of the fact that c is a constant for all observers.

You have claimed to read a lot of papers by Einstein, but it is clear that you have not understood them.

David
Originally posted by Janus
Which just emphases the fact that you do not understand SR. Time dilation does not rely on any physical force acting on the clocks. It is a direct consequence of the fact that c is a constant for all observers.

You have claimed to read a lot of papers by Einstein, but it is clear that you have not understood them.
You don’t seem to know or accept the fact that he changed the Kinematical part of the SR theory in 1918. He finally learned that there is no such thing as “time dilation” due only to “relative motion”. So he added a gravitational field to the K’ frame in the 1905 paper. Why do you suppose he did that? If you understand SR, surely you can tell me that. Which of Newton’s Laws of Motion did Einstein violate when he had the clocks “time dilate” in the 1905 paper due only to “relative motion”? Explain Pauli’s explaination. Why was the gravitational field added to the 1905 theory, retroactively? Exactly what is the difference between SR and GR? How is the Electrodynamical part of SR theory more like GR than the Kinematical part? Which part of the 1905 theory more closely resembles the 1904 Lorentz relativity theory? Why?

And why did the “peculiar consequence” thought experiment wind up as a paradox, while the earlier time dilation thought experiments in that paper did not? What specifically was different between the way he synchronized the clocks in that thought experiment, and the way he synchronized them in Section 2 of the paper?

He referred to the K and k frames in the 1905 paper, so which frame was the “moving clock” in, in the “peculiar consequence” thought experiment? And what frame did that frame’s observer see the B clock in?

What unusual thing did he say about the relationship between atomic clocks and the speed of light in his 1911 theory? What do you think the “U” clocks are in the 1911 theory? What purpose do they serve? Exactly why does light bend when it passes near the sun? What did he say about it in the 1911 theory? What was the formula he used for the two different speeds of light in the 1911 theory? Why did he have to use a distant clock, rather than a local clock, to measure the different speeds of the different points along the plane wave of light that passed near the sun in the 1911 theory?

In the 1905 paper, what did he mean by, “It is clear that the same results hold good of bodies at rest in the “stationary” system, viewed from a system in uniform motion.” And why did he put “stationary” in quotes, both in the English translation and in the original German paper?

Exactly where does the blueshift seen by the train observer in Chapter 9 of his 1916 book take place, at the source or at the observer?

What was the German word he used for “synchronous” in “On the Electrodynamics of Moving Bodies”? What German word did he use for “simultaneous”? What is the difference between “synchronous” and “synchronized”?

You can show me how I “don’t understand SR theory” and how “you do” by giving me the correct answers to these questions. Anybody can say, “You don’t understand the SR theory, but I do,” but that is meaningless unless you can prove it, so prove to me that you do, by answering these important questions.

jeff
Originally posted by StarThrower
...I am thinking about whether or not SR is consistent with thermodynamics...is the temperature of this object relative or absolute?
The key thing to realize is that the principle of relativity alone can't determine the precise form of thermodynamical relations in a moving frame. In particular, how the temperature of moving bodies should change under lorentz transformations is really a matter of convention. As a simple example, I'll demonstrate the freedom one has in choosing how to handle temperature relativistically by considering an emitting body whose spectrum is isotropic and follows planck's law

f(E,T) ~ (eE/T &plusmn; 1)-1

where p&mu; = (E,p) is the emitted particle four-momentum, the Boltzmann constant is taken as unity, and &plusmn; refers to emitted bosons and fermions respectively. For an emitting body moving with velocity v, this can be written covariantly in terms of the product of p&mu; with either a "4-temperature" T&mu; &equiv; T&gamma;(1,v)] or an inverse 4-temperature &beta;&mu; &equiv; T-1&gamma;(1,v) which in the rest frame are just (T,0) and (1/T,0) respectively. We may then express E/T covariantly as either

E/T = p&mu;&beta;&mu; or p&mu;T&mu;/T&nu;T&nu;.

We then have three ways - equally valid from the standpoint of SR - to define the temperature, each determining how it changes under lorentz transformations:

1) T &equiv; 1/&beta;0 &rArr; T' = &gamma;-1T.

2) T &equiv; T0 &rArr; T' = &gamma;T.

3) T &equiv; (T&mu;T&mu;)&frac12; or (&beta;&mu;&beta;&mu;)-&frac12; &rArr; T' = T.

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David,

I am more confused by some of your comments, even though I don't fully follow all of you yet.

As I understood, time delation caused by relative speed, not acceleration, does exist. For example, a certain solar meson's life expectation was used to prove this point. From an earthling's observer, its life is much longer than its life expectation at rest. This experiment is shown in many museums and I believe the meson's speed is considered pretty constant.

My understanding is this, for a rocket passing by earch in high speed close to light speed relative to an earth observers, it can reach a start 300 light years away from us in 30 years, even though we will see it arrived after 400 years. I used 'passing by' to make certain there is no acceleratin involved at all.

While the time delation truely exists, it does not make good meanings until an Earth observer can coincide the rocket at a point of the time-space continuum. As I understood, only way to synchroize and compare two clocks is to put the two clocks at the same point or event of the time-space continuum. So, in order to compare the clock at the rocket against the clock at the Earch again tis to bring the rocket back to the Earch. That's when acceleration getinvolved.

Is this correct? If it's not correct, please explain the famous meson experiement and why light speed will be measured unchanged by two observers in relative movement but not accelerated.

Thanks

Back to temperature, My view of temporature is that is just a way to measure the kinetic energy of groups of particles or molecules.

I have a stranger idea. Since E = Mc**2. Let's assume there is only one molecule bouncing in a closed box in a certain speed close to light speed, An outside observer observing this box will see higher mass in the box than the rest mass of the particle and the box. Isn't this correct?

If so, higher temperature means higher speed pouplation of a group of molecules; and will a box containing high temperature of molecules will be measured with higher mass than the rest mass of these moecules and the box.

So, at the same time temperature is a measure of Energy and Mass as well.

Hope somebody can tell me whether I am wrong.

David
Originally posted by Sammywu
David,

I am more confused by some of your comments, even though I don't fully follow all of you yet.

As I understood, time delation caused by relative speed, not acceleration, does exist. For example, a certain solar meson's life expectation was used to prove this point. From an earthling's observer, its life is much longer than its life expectation at rest. This experiment is shown in many museums and I believe the meson's speed is considered pretty constant.
Ok, keep in mind that I’m speaking only theoretically, as most of us are here.

My contention is that the meson’s life is extended by Lorentz forces and also perhaps by GR accelerative forces. GR forces are in effect Lorentz forces with acceleration being also considered.

Relative motion alone can not possibly cause any clock to either slow down or speed up, because the clock is not physically “aware” of the relative motion.

However, a moving meson or atom or whatever, is “aware” of accelerative forces and Lorentz forces, which are, essentially, forces “felt” or experienced while traveling at high speeds through fields. This is what caused the current flow inside the NASA tether. It was not the “relative motion” between the tether and the earth that did it, it was the physical motion of the tether through the earth’s gravitational field.

Study the 1905 SR theory again. The first half is fiction, based on speculation. The second half is real, based on Lorentz relativity theory. In the second half, one “frame” moves through the fields of the other frame. In the first half, the frames and their fields are moving only “relatively”, and, of course, if they are a great distance apart, their fields will not interact. Einstein cleared up this flaw with the Kinematical part of SR theory as he gradually developed GR theory. That’s why he had to add a “gravitational field” to the k frame clock of the 1905 theory, in 1918, so that the clock would have a force placed on it and so that it would have a real physical reason to “slow down”, and of course he converted the 1905 mechanical clocks all into atomic clocks, so it is not “time” that slows down, it is only the clocks.

Originally posted by Sammywu
My understanding is this, for a rocket passing by earch in high speed close to light speed relative to an earth observers, it can reach a start 300 light years away from us in 30 years, even though we will see it arrived after 400 years. I used 'passing by' to make certain there is no acceleratin involved at all.
If the rocket is traveling at less than the speed of light, and if it takes the light 300 years to reach us from the star, then how is the rocket going to get to the star in only 30 years? You are talking about a rocket traveling at 10 times the speed of light. If it travels at the speed of light, and if the star is 300 ly away from us, it will arrive at the star in 300 years. Just forget about that Kinematical part of the SR theory. That was his first attempt at a relativity theory, based on some ideas he got from Lorentz, but the Kinematical part turned out to be wrong. However, the Electrodynamical part is mostly ok.

Originally posted by Sammywu
While the time delation truely exists, it does not make good meanings until an Earth observer can coincide the rocket at a point of the time-space continuum. As I understood, only way to synchroize and compare two clocks is to put the two clocks at the same point or event of the time-space continuum. So, in order to compare the clock at the rocket against the clock at the Earch again tis to bring the rocket back to the Earch. That's when acceleration getinvolved.

Is this correct? If it's not correct, please explain the famous meson experiement and why light speed will be measured unchanged by two observers in relative movement but not accelerated.

Thanks
The clock tick rate changes are based on natural functions of classical physics. There is no such thing as “time dilation” as it was described in the Kinematical part of the SR theory. A biologist goes by thermodynamic time, not Einstein SR time, and the biologist is correct. In that regard, lower temperatures in a living organism can cause true “time dilation” in the organism, but just “relative motion” can not.

I’ve been trying to decypher his early writings for the past 12 years. I just recently learned how and when he added “acceleration” to the Kinematical part of his 1905 theory. As soon as I get a copy of his 1918 paper, I’ll post some of it here. We’ve all been taught the wrong information about the Kinematical part of the 1905 paper for the past 98 years, and very few people today know about his 1918 correction of the 1905 paper.

David
Originally posted by Sammywu
Back to temperature, My view of temporature is that is just a way to measure the kinetic energy of groups of particles or molecules.

I have a stranger idea. Since E = Mc**2. Let's assume there is only one molecule bouncing in a closed box in a certain speed close to light speed, An outside observer observing this box will see higher mass in the box than the rest mass of the particle and the box. Isn't this correct?

If so, higher temperature means higher speed pouplation of a group of molecules; and will a box containing high temperature of molecules will be measured with higher mass than the rest mass of these moecules and the box.

So, at the same time temperature is a measure of Energy and Mass as well.

Hope somebody can tell me whether I am wrong.
Interesting thought experiment. I’ll give it some thought. I’m not sure that a bunch of hot atoms inside a sealed box actually weigh more than a bunch of cold ones, so the alleged “mass increase” might be only virtual or just “relative”. The “mass increase” was Lorentz’s idea. See his 1904 relativity paper in the book, “The Principle of Relativity”, Dover press.

If E=mc^2 and if mass is directly connected to the strength of the gravitational field of an astronomical body, then as the body gives off radiation, then its gravitational field grows weaker.

I read on a NASA website that the earth is gaining more mass than it is radiating into space, because it is accumulating additional mass from meteorites and space debris.

marcus
Gold Member
Dearly Missed
Originally posted by Sammywu
Back to temperature, My view of temporature is that is just a way to measure the kinetic energy of groups of particles or molecules.

I have a stranger idea. Since E = Mc**2. Let's assume there is only one molecule bouncing in a closed box in a certain speed close to light speed, An outside observer observing this box will see higher mass in the box than the rest mass of the particle and the box. Isn't this correct?
Yes, it is correct. The additional kinetic energy inside the box gives the box additional mass. It will weigh slightly more on the scales than it would if the contents were at lower temperature. The box will also have greater inertia.

A hot piece of iron weighs more than the same object would if allowed to cool down. The heat inside the sun contributes to its mass and therefore to gravitational attraction it exerts. But these effects are percentagewise small. Ordinary weighing scales are not sensitive enough to detect the difference in mass associated with temperature.

Originally posted by Sammywu
If so, higher temperature means higher speed population of a group of molecules; and will a box containing high temperature of molecules will be measured with higher mass than the rest mass of these molecules and the box.

So, at the same time temperature is a measure of Energy and Mass as well.

Hope somebody can tell me whether I am wrong.
You are not wrong. Sammywu I would like to provide some hyperlinks to confirm what you say, but I dont know of a specific link. What you are saying is not controversial. It is just a routine straightforward fact. So there should be a link on the web! Perhaps some other PF poster can supply one. Any online Special Relativity textbook should have an example similar to your box-with-molecules, or like the block of iron. Can anyone help us out with a link?

David
Originally posted by marcus
A hot piece of iron weighs more than the same object would if allowed to cool down.

Originally posted by Sammywu
Back to temperature, My view of temporature is that is just a way to measure the kinetic energy of groups of particles or molecules.

I have a stranger idea. Since E = Mc**2. Let's assume there is only one molecule bouncing in a closed box in a certain speed close to light speed, An outside observer observing this box will see higher mass in the box than the rest mass of the particle and the box. Isn't this correct?

If so, higher temperature means higher speed pouplation of a group of molecules; and will a box containing high temperature of molecules will be measured with higher mass than the rest mass of these moecules and the box.

So, at the same time temperature is a measure of Energy and Mass as well.

Hope somebody can tell me whether I am wrong.
you can google on Meisner Effect, here is an interesting link:http://www.rci.rutgers.edu/~williebo/n14superconductivity.pdf [Broken]

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Dave,

I will get back to the issue of why I gave an example of speed seems to be higher than light speed later. Actually my readings told me that shall not violate the issue of light speed as maximum. I will explain later.

Another imaginary experiment could be thought like this. First, build a rocket as long as 3 light seconds in some remote space away from all gravity and a tunnel as long as 4 light seconds; They shall be built far away from each other. Put a light source ( a laser ) at one end and a light detector at the other end. Fire the rocket toward the tunnel, and after it reaches its required speed, keep it fly in constant speed. We will have three synchronizable events: Evenet A, when the rocket head reaches the open end of the tunnel. Event B, when the rocket tail reaches the open end of the tunnel. Event C, when the rocket head reaches the close end of the tunnel. At the event B, we can turn on and off the lasers. If we have the right speed, the light will reach the rocket head and the close end of the tunnel at the event C. In that way, the light has travelled 3 seconds from the rocket light detector's point of view, while the tunnel detactor will believe the light travelled 4 seconds. Through calculation of SR, you can figure out a correct speed that we want.

Any way, I am not in totally disagreement with you. SR does bother me and most laymen like me. Not to mention the twin paradox. But if you are right, can you prove the meso experiment with your theory? That will help the whole Physic world a lot, in me opinion.

Marcus, I would like to hear your opinion if you don't mind. Do you also think the time delation due to just relative speed is purely wrongly percepted?

Also, I have seen your involvement in the discussion of the SR effects and the GR effects about the orbiting objects. The GR effect , which is opposite to the direction of SR effect, is brand new to me. Is it true? I have read Dennis Revell's document. Is his deduce of his formula correct?

Last question: If I spin a top to very high spin speed, not only now it possess angular mometum, will it be measured with higher mass just as the hot iron experiment. I recalled I might have seen that hot iron experiment in Physic World.

Thanks

marcus
Gold Member
Dearly Missed
Originally posted by Sammywu
...
Marcus, I would like to hear your opinion if you don't mind. Do you also think the time delation due to just relative speed is purely wrongly percepted?...
Sammywu, I must appeal to Janus about this. He is the PF mentor and has more experience and authority.
I only came into this thread because I heard you say that the mass of an object increases with its temperature (any object but a chunk of iron is one way to visualize it.)
Curiously enough I am absolutely certain about this but I do not know of a link that explains it and offers experimental confirmation!

It is actually a bit embarrassing! Usually when I feel completely sure about something I expect to be able to produce some evidence. But in this case I have no link to give you. I hope someone else here can supply a link to online evidence!

The original insight was in a 1905 paper of Einstein called
"Ist die Trägheit eines Körpers von seinem Energieeinhalt abhängig?"
(I cite this from memory so it may have errors)
"Is the Inertia of a Body dependent on its Energy content?"

and in effect what he was talking about was just this lump of iron (with an energy content dependent on temperature). put some heat in and it will have more inertia---that is, mass---and therefore weigh more.

the original idea back in 1905 was not about high-tech stuff like the atom bomb or cyclotrons accelerating particles to relativistic speeds---it was somehow very ordinary: heat an object and it gets heavier.
(and generalizations of this idea involving other kinds of energy-content).

There have been high tech verifications of the E=mc^2 idea but I dont know of any confirmation at a homely everyday level.
The difficulty, I guess, is that in the case of putting ordinary amounts of energy into an ordinary object (like a block of iron) the change in inertia is just TOO DARN SMALL to measure!

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marcus
Gold Member
Dearly Missed
Atomic clocks in GPS satellites run fast

Sammywu, you mentioned two effects on time---a GR effect and a SR effect.

Again I shouldnt be talking because I dont have a really good link
but I think it is really interesting that each GPS satellite has an atomic clock in it

and these satellites are in roughly 12 hour orbits (IIRC "if I remember correctly") which means they are really high up.

so their clocks are at a higher gravitational potential than we are at the surface of the earth. So by the GR effect these clocks run FASTER than they would at the earth's surface.

there is also the relative motion effect of SR, but actually I think they are in such high orbit they are not moving all that fast relative to us on this rotating ball and maybe the SR "dilation" effect is not so important.

Anyway you have probably used one of those GPS locators, or played with one, and amazingly (to me) each satellite must send orbit information with its time signal because the time signal must be CORRECTED for the GR effect of faster running clocks at higher altitudes. It is actually not a negligible effect!!! It is a real effect that you have to take account of and adjust for if you want the GPS system to work right and give correct locations.

A general reference on this could be this 1997 paper
http://www.allanstime.com/Publications/DWA/Science_Timekeeping/TheScienceOfTimekeeping.pdf
It is by David Allan an expert on timekeeping (and the GPS applications) at Hewlett-Packard---they make the atomic clocks in the GPS satellites, I believe, and supply a lot of the instrumentation for standardized timekeeping worldwide. So they are used to taking account of these little GR and SR effects.
but maybe this is not perfect for your needs so I hope Janus or somebody else has a better online reference for GPS and the GR effect on time.

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