Can Energy Equal Mass if c=1 in Particle Physics?

[bert2002]

Since in particle physics c can be take to equal 1, does this mean that Energy can equal mass if we use electronvolts ?

 

[Einj]

Yes, exactly (of course this is an artifact of setting c=1 and you have to be careful in restoring the right units when needed). However, be careful on the definition of m. One usually says that m is the rest mass, i.e. a constant that only depends on the species of the particle and not on its momentum. In this case the equation becomes E=\sqrt{m^2+\vec{p}^2}, where \vec p is the three-momentum of you particle.

 

[e.bar.goum]

Sure. This is why you often see tables of the standard model with mass reported in eV/c^2. And why "mass excess" is normally in units of MeV in nuclear physics. Often, you leave out the /c^2. This frequently confuses students who are studying nuclear/particle physics for the first time - you've got to remember to restore units.

 

[jtbell]

Similarly, many physicists say things like "the electron's momentum is 300 keV" which technically has the wrong units. What they really mean is either p = 300 keV/c or pc = 300 keV.

My personal convention is to write all relativistic equations in such a way that m always appears together with c² as mc², and p always appears together with c as pc. Then I can calculate the energy of the electron above as $$E = \sqrt{(mc^2)^2 + (pc)^2) } \\ E = \sqrt {(511 \text{ keV})^2 + (300 \text{ keV})^2)} \\ E = 583.1 \text{ keV}$$