E = mc^2: Identity or equality

pmb_phy

Some people refer to the relationship between inertial mass m (aka "relativistic mass") and inertial energy E as an identity and some refer to it as an equality. Inertial mass has never been defined as m = E/c².

Inertial mass is always defined as the m in p = mv (e.g. Tolman, Feynman, French etc. etc. etc.). The E in that equation is always defined as the total energy of a particle minus the potential energy of position, V(r) (although some people use different letters for, such as T, for E. E.g. Goldstein - 3rd Ed.). The relationship E = mc² must then be derived which thereby makes it an equality rather than an identity.

My question is to those who hold it to be an identiy is - Why?

Thanks

Pete

DW

Inertial mass is not relativistic mass as I have mathematically proven here in the past. Relativistic mass has no place in modern relativity as it is just a redundant name for relativistic energy which is defined as the time element of the momentum four-vector of the first kind. From the definition of the momentum four-vector of the second kind one has
[tex]P^{0} = p^{0} + (q/c)\phi ^{0}[/tex]
This yields
[tex]E_{R} = E_{tot} - E_{pot}[/tex]
[tex]E_{R}[/tex] is the relativistic energy and what is innapropriately called relativistic mass. You also missname energy parameter by total energy as well which is unfortunate, but even if by that mistake you have identified relativistic mass with the energy parameter instead of the total energy, you have still "identified" it with an energy. That should end your questioning whether it is an identity because even though you have identified it with the wrong energy, you have still "identified" it yourself.
To see more about what I am refering to conserning the different kinds of momentum four-vectors see
http://www.geocities.com/zcphysicsms/chap3.htm

chroot

Okay, pmb, how many threads do you intend to start that have no purpose other than discussing the semantics of the invariant mass view vs. the relativistic mass view? This same discussion has already been had countless times on this forum. I've given you the opportunity to write an essay supporting your views, which we will happy to host for you. You have ignored that opportunity, and continue to start threads about the same topics. I regard this thread as spamming.

- Warren