What?
A common synonym for rest mass is invariant mass. Look it up. It doesn't change under the Lorentz transformation. (Another quantity---formerly called "relativistic mass" but now more commonly called "energy"---does change under a Lorentz transform, and I hope that's what you're thinking of.)
Other than "look it up" I don't really know what to say.
One thing we can say is that
Farsight, like
johanfprins, is arguing with Albert Einstein even as he claims to use Einstein as his authority.
- What quantity do you call "rest mass"?
- If you've reserved "rest mass" as a term for some other quantity, what do you call the absolute, Lorentz-invariant, gauge-invariant quantity that is predicted by theory and confirmed by experimental observation, that everybody else calls "rest mass"?
This division of an object's energy into rest mass and kinetic energy goes back to Einstein's papers of 1905 and 1906. One of those papers happens to be the paper in which Einstein describes the relativistic length contraction that both
Farsight and
johanfprins have been denying:
A Einstein. Zur Elektrodynamik bewegter Körper. Annalen der Physik 17 (10), pages 891-921. 30 June 1905.
I'll use John Walker's translation:
I will also refer to one of my freshman-level textbooks:
A P French. Special Relativity, from The MIT Introductory Physics Series. Norton & Company, 1968.
But in relativity that kinetic energy is the mass-energy. Johan was referring to special relativity repeatedly.
...snip...
I went back and read page 60 and didn't see anything that I thought was untoward from Johan. The gist of what he's saying is that the kinetic energy is now mass-energy. So go with the flow and say that a massless particle where the kinetic energy is rotational exhibits mass. But you can't then have your cake and eat it. Once you call it a massive particle you can't say it's got kinetic energy any more.
Farsight is telling us we can't call it kinetic energy, but Einstein called it "the energy of motion W" and derived this formula for that kinetic energy:
[latex]
\[ W = m c^2 \left\{ \frac{1}{\sqrt{1 - v^2 / c^2}} - 1 \right\} \]
[/latex]
In French's textbook, that's equation (1-19) on page 22:
A.P.French said:
But the kinetic energy of a particle, so valuable a quantity in classical dynamics, now takes on a secondary status. It is merely the difference between the total energy
E and the rest energy
E0:
[latex]
\[ K = m_0 c^2 \left\{ \frac{1}{(1 - v^2 / c^2)^{1/2}} - 1 \right\}
\hbox{\ \ \ \ (1-19)} \]
[/latex]
Backtracking a couple of pages to understand how the rest energy
E0 was derived, Einstein's
E=mc2 combines with the Newtonian momentum
p=mv to produce
E=c2p/v. If you apply a force
F, the resulting increase in kinetic energy is
[latex]
\[ dE = F \; dx = \frac{dp}{dt} dx = v \; dp \]
[/latex]
Combining that with
E=c2p/v, integrating both sides, and multiplying through by 2 yields
[latex]
\[ E^2 = c^2 p^2 + E_0^2 \]
[/latex]
where
E02 is the constant of integration written as the square of some rest energy
E0. (For readers who remember page 65 or thereabouts, that equation should look familiar.)
For a while there,
johanfprins responded to many of our calculations by alluding to boundary conditions he falsely claimed we had been ignoring. Here, however, there really is a relevant boundary condition: The relativistic equation above must converge to the Newtonian limit as the momentum
p approaches zero. That boundary condition implies
[latex]
\[ m_0 = \frac{E_0}{c^2} \]
[/latex]
which is more famously known as
E0=m0c2.
All of the above is covered in chapter 1 of French's textbook. Although the textbook doesn't cover length contraction until chapter 4, Einstein deduced the fact of length contraction in the same paper that contains his derivation of the equation above for kinetic energy.
First, let's recall what
johanfprins and
Farsight have been saying about length contraction:
You can also check the length of the rod within K by using a srop watch which you activate when the front end passes you and stop when the rear end passes you. This is what you have to do when you cannot see OR observe the front and rear end simultaneously. You will then also find that the length within K is the same as the length within K/. Clinger go and get yourself a goldfish and become wise.
Note well that
johanfprins is saying there is neither length contraction nor length expansion.
Farsight appears to think he agrees with
johanfprins on this point, but
Farsight says there is length
stretching, which you just happen to perceive as length
contraction. I am not making this up:
Mind you, he was right about this:
"If you apply the Lorentz transformation correctly for a passing rod, you will find time dilation and length-stretching".
That's a bit of a surprise, it certainly sounds like "boutique" SR, but honestly it isn't, and it's quite simple to see why. Imagine you're in a gendanken spaceship looking at a star. It appears spherical. Press the accelerator, and now you see the star looking flattened. It's too far away from you for light to have travelled back and forth, you know that your action cannot have changed the star. So you know your action has changed your observation of the star. You know that it looks flattened because you've changed. And you've changed in that you're "smeared out". You're length-stretched rather than length-contracted, and as a result everything you see outside your spaceship looks length-contracted. I know that isn't what's taught,
The reason that isn't what's taught is that it's a confusingly cock-eyed way to look at it, and the "smeared out" business is just wrong.
Farsight's story is such a confusing way to think about length contraction that
Farsight has apparently talked himself into believing that
johanfprins's unequivocal denials of length contraction are compatible with Einstein's equally unequivocal derivation of length contraction.
Einstein said:
(b) By means of stationary clocks set up in the stationary system and synchronizing in accordance with § 1, the observer ascertains at what points of the stationary system the two ends of the rod to be measured are located at a definite time. The distance between these two points, measured by the measuring-rod already employed, which in this case is at rest, is also a length which may be designated “the length of the rod.”
In accordance with the principle of relativity the length to be discovered by the operation (a)—we will call it “the length of the rod in the moving system”—must be equal to the length l of the stationary rod.
The length to be discovered by the operation (b) we will call “the length of the (moving) rod in the stationary system.” This we shall determine on the basis of our two principles, and we shall find that it differs from l.