I took a look through the relativity text and found it to be a very nice text. There's one mistake in it that people make all too often and that's the belief that Einstein never used or believed in using relativistic mass (RM). This is incorrect. RM, m, is defined as momentum, p, over speed, v. I.e. m = p/v. If the object is a particle which moves slower than light then the RM can be written as m = gamma*m_0 where m_0 is the particles proper mass. If the particle is moving in a gravitational field and is moving slowly then m does not equal m_0. m is a function of the gravitational potential. This can be found in Moller's text. I've derived it and placed it on my website at: http://home.comcast.net/~peter.m.brown/gr/uniform_force.htm
Einstein used this in his text "The Meaning of Relativity" on page 102.
In his GR paper of 1916 he wrote that mass and energy are essentially the same thing and is fully described by the "energy tensor" which we now refer to as the "stressenergymomentum tensor". He also assigned a mass density to EM energy density in one of his papers. So asserting that he never used RM is quite misleading. Actually he had to depend on it in his argument regarding Mach's principle. Einstein alsoCS: Dear Pete, in the book you mention, Einstein uses m to mean "rest mass", what you call m_0 ! In fact, he always did so, as far as I know. There is no paper where he used both m_0 for rest mass and m for relativistic mass. Also in the book you cite, Einstein does not use "relativistic mass" at all. And on page 102, there is nothing of what you are claiming. Furthermore, in the 1916 paper you mention, Einstein just says in §16 that "träge Masse nichts anderes ist als Energie", but not that relativistic mass should be used. In fact, the statement means "Inertial mass is nothing else than energy"! Of course, E/c^2 is a mass value, and that is what the statement expresses; but most researchers agree that is not useful to give it a special name. (By the way, your statement on Mach's principle is mistaken. The quantity m does not depend on the gravitational potential, whatever you may mean by "m".) But a fact remains: "Relativistic mass" was never used by Einstein; it is a concept only used by tabloids and by grandstanding authors.
