Throughout the book, there is an alleged distinction between mass and inertia. In the early chapters, in non-relativistic situations, this is a distinction without a difference ... but the intent becomes clear in connection with special relativity, culminating in equation 14.41 in section 14.7 on page 367.
Alas, equation 14.41 cannot be correct. It is ruled out by experiments, including Eötvös experiments, with many orders of magnitude to spare. More generally, the distinction between mass and inertia is inconsistent with the weak equivalence principle, as set forth on page 321.
Remark: There was a period in history when experts thought that special relativity could be explained with the help of velocity-dependent mass, but that only lasted a couple of years, and it was more than 100 years ago. It never really worked; there were proposals for "longitudinal" mass, "transverse" mass, "electromagnetic" mass, and who-knows-what else.
Suggestions:
Get rid of the alleged distinction between mass and inertia.
There is no need to introduce the term "inertia" at all; the term "mass" is conventional in physics.
In particular, the quantity defined in section 4.2 on page 79 should be called _mass_ not «inertia».
It might be good to change the section 4.2 section title to Mass (rather than inertia).
The discussion leading up to equation 14.41 needs to be extensively rewritten.
Sometimes factors of γ appear in the equations of motion. Although sometimes they belong there, in many cases they can be and should be eliminated. The solution is never to rewrite the equation using a worse definition of mass; in most case the solution is to rewrite the equation using a better definition of time, i.e. proper time.
References:
Misner / Thorne / Wheeler Gravitation
Nominally this is a book on general relativity, but it starts out with a clear, clean, modern exposition of special relativity.
See item #107 for a catalog of related issues.
Throughout the book, there is an alleged distinction between mass and inertia. In the early chapters, in non-relativistic situations, this is a distinction without a difference ... but the intent becomes clear in connection with special relativity, culminating in equation 14.41 in section 14.7 on page 367.
Alas, equation 14.41 cannot be correct. It is ruled out by experiments, including Eötvös experiments, with many orders of magnitude to spare. More generally, the distinction between mass and inertia is inconsistent with the weak equivalence principle, as set forth on page 321.
Remark: There was a period in history when experts thought that special relativity could be explained with the help of velocity-dependent mass, but that only lasted a couple of years, and it was more than 100 years ago. It never really worked; there were proposals for "longitudinal" mass, "transverse" mass, "electromagnetic" mass, and who-knows-what else.
Suggestions:
Sometimes factors of γ appear in the equations of motion. Although sometimes they belong there, in many cases they can be and should be eliminated. The solution is never to rewrite the equation using a worse definition of mass; in most case the solution is to rewrite the equation using a better definition of time, i.e. proper time.
References: