Talk:Special relativity: mechanics

Reviewer A report

This is an excellent article on relativistic mechanics, and an excellent follow-up to the author's contribution on relativistic kinematics. Professor Rindler is a recognized authority on these matters, and the author of a number of textbooks on this subject. He makes an excellent choice of author for these Scolarpedia entries.

My only concern is with the introduction of a velocity-dependent mass in the section on relativistic mechanics. There is a long tradition of doing so in the older literature, but my observation is that this practice has long been given up by the vast majority of textbook authors. The marked preference these days is to keep the mass (rest-mass) as a relativistic invariant, and not to confuse things with a second notion of mass (relativistic mass) which increases with velocity. The author acknowledges this practice in his A WORD OF CAUTION, but blames mainly the particle physicists for rejecting the old tradition. I believe, however, that most relativists would join ranks. I would strongly recommend that the author revise his article to eliminate the relativistic mass from discussion, to replace instead it with rest mass.

Reviewer B report

I think that the section on the equivalence of mass and energy needs a revision.

Indeed the first lines of the sections appear exceedingly sloppy and more suited for a philosophical/historical text than a scientific one.

In my opinion the reason for that is that nowhere before in the text it has been stated that in a consistent Galilean theory the total mass, which is identified with the rest mass, must be conserved in an isolated system since otherwise momentum conservations is inconsistent with Galilei invariance. Energy conservation is an independent fact. Thus, in a Newtonian framework, the total rest mass acquires the meaning of “quantity of matter” which is conserved in isolated systems together with energy.

After the introduction of the Einstein formula the consistency of above considerations with special relativity should be verified by the \( c\rightarrow\infty \) expansion of the relativistic energy \(\sum^* m_0\gamma (u) c^2 \) as it is done in Eq.(46) however multiplying the equation by c^2 and commenting on the fact that the \(\sum^*m_0 c^2\) contributions “diverges” and hence this divergence should violate Eq.(46) if \(\sum^*m_0\) does not vanish.

Other comments

• March 23, 2011 -> Minor edit affecting Eq. (44). Changed \lambda(u) by \gamma(u).