Of Mass and Reference Frames

In his Reference Frame piece “Whence the Force of F = ma? II: Rationalizations” (Physics Today, December 2004, page 10 ), Frank Wilczek levels a critique against the zeroth law (conservation of mass) in an effort to dispel the culture of force. As it stands, his assessment falls short of a complete description of mass. Ironically, the problem is related to reference frames.

If the zeroth law is to apply solely to the Newtonian concept of mass, then it should be abolished, as Wilczek suggests, particularly since it is related to the more fundamental laws of conservation of momentum and energy. But Newtonian momentum is not simultaneously conserved in all inertial reference frames.

A more inclusive view is that energy and momentum are but two aspects of the singular beast we call four-momentum, which is conserved in all inertial reference frames. The importance of this notion comes from the fact that mass is the magnitude of the four-momentum vector. Thus, although “Newtonian” mass may not be conserved in all inertial reference frames, the broader concept of mass as the magnitude of four-momentum is.

In the most general terms, the zeroth law is perhaps not as expendable as Wilczek might have us believe.