# Thinking obout The Principle of Special Relativity

1. Jun 19, 2012

### zhangyang

During this year, I was studing classic physics again ,which contain mechanics and electrodynamics.They are both irrelevant to thermodynamics,and irrelevant to statistics.

In mechanics ,we have the Newton's laws of motion,which can be in the same form in any inertial system,that is to say , Newton' laws obey Galelo's transformation .

But Einstein found that Maxwell's equations doesn't obey Galelo's transformation,so in classic physics ,Galelo's transformation is not universal.IN Maxwell's theory ,we know that the speed of light is only relevant to the nature of dieletric,it is controdict to the Galelo's transformation.(Yes,The principle of invariability of speed of light is contained in the Maxwell's theory)

There need a principle which is correct in both mechanics and thermodynamics.Lorentz's transformation is obeyed by Maxwell' theory ,but not obeyed by Newton's law.So Newton's law shoud be changed.Einstein gave mass a new meaning and made Newton's law obey The Lorentz's transformation.

So ,the Principle of special relativity is a result from mechanics and electrodynamics,which is not the whole physics,firstly it doesn't contain thermodynamics and it is not statistical.It gives us new conception such as the relativity of time and space.But is temperature relative?Or, is any statistical average relative ? Or can statistical average remove the relativity and arrive pure absolutivity?

Zhang Yang

2. Jun 19, 2012

### HallsofIvy

I don't know what "temperature is relative" could mean. Temperature of an object, of course, depends upon the motion relative to the center of mass in any case. That does not depend upon "relativity".

3. Jun 19, 2012

### GAsahi

I think he means about a relativistic treatment of temperature transformation. This subject is a very thorny one and, best I can remember, there are three schools of thought:

$$T'=T \gamma$$
$$T'=T/ \gamma$$
$$T'=T$$

I used to know who had the last word in this argument :-(

4. Jun 20, 2012

### zhangyang

Thank you. I'm very interested in the "temperature transformation" which you told.Can you give me more clues?

Motion of heat is in every direction,and the mean kenetic energy have no definite direction,and temperature is determined by mean kenetic energy,so can temperature has its transformation between two inertial system ?

I think motion of heat has its essential difference from one-body orbit motion,so the transformation can not be directly valid,it will bring some new concept.

Zhang Yang

5. Jun 20, 2012

### Naty1

We seem to have somewhat of a language barrier so I can't tell exactly what you are
questioning.

Temperature is a scalar:

http://en.wikipedia.org/wiki/Scalar_(physics [Broken])

Yet an accelerating observer reads a different theoretical temperature than an inertial
observer: [no experimental confirmation of this]

http://en.wikipedia.org/wiki/Unruh_effect

so "vacuum" and 'temperature ' is a relative concept that depends on the observer. The two observers will not agree on the number of particles they observe. To say it another way, the two observers can each construct quantum field theory but the theories will be different since they do not use the same notion of vacuum. But the effect is teased from different coordinate frames and different models in relativity.

Lots more on the Unruh effect in this discussion:

Last edited by a moderator: May 6, 2017
6. Jun 20, 2012

### Bill_K

He's not talking about the Unruh effect. As GAsahi said, there has been considerable disagreement on the transformation of temperature. See this article for a summary.

7. Jun 20, 2012

### GAsahi

Yes, this is the paper that I had in mind, thank you for tracking it down. Bottom line is that an experiment will be the deciding factor for choosing the transformation that reflects experimental reality.

8. Jun 20, 2012

### vanhees71

It depends on the definition of "temperature", how the various quantities transform. The definition, commonly used in my field of research (relativistic heavy-ion collisions, the quark-gluon plasma), we define temperature as a scalar (or scalar field in (ideal) fluid dynamics). This means the temperature is defined to be measured with a thermometer that is at rest relative to the fluid cell, of which the temperature is to be determined.

In statistical mechanics, the covariant definition of temperature is

$$\hat{R}=\frac{1}{Z} \exp[-\beta(x) u^{\mu} \hat{P}_{\mu}].$$

Here, $u^{\mu}(x)$ is the four-velocity field of the fluid cell with $u_{\mu} u^{\mu}=1$ and $\hat{P}_{\mu}$ the operator of the total momentum of the fluid cell, and $Z$ the partition sum,

$$Z=\mathrm{Tr} \exp[-\beta(x) u^{\mu} \hat{P}_{\mu}].$$

9. Jun 20, 2012

### Naty1

agreed, I realize, but I am. I could not tell exactly what the original post intended and thought maybe the poster picked up the T' = T, etc, theme because somebody replied that way or if THAT was the original interest. either way he's can follow up or not according to his interest.