# e=mc^2

by alchemist
Tags: emc2
 P: 51 what is the actual equation of e=mc^2? this is only the simplified equation, and i have forgotten the actual one already...
 PF Patron Sci Advisor Emeritus P: 10,400 You probably mean E2 = p2c2 + m2c4 - Warren
 P: 21 what does the P stand for? and is that equation homogenous?
PF Patron
Emeritus
P: 10,400

## e=mc^2

It's a lowercase p, and it stands for (linear) momentum. I don't know what you mean by "homogenous."

- Warren
 P: 383 It all depends on whether you are a massist or an energist. ------ A massist is willing to attribute mass values to anything, in any state of motion. For a massist, this m is really m0, a mass attributed to something in its rest frame of reference. For a massist E2 = p2c2 + m02c4 p = mv are always true in any inertial frame. For light quanta, E = pc p = mc , because m0 = 0 for light quanta. But m = p/c = E/c2, a mass value dependent upon total energy of a quantum. So E = mc2 is true for a light quantum as well as a particle with a non-zero rest mass. ------ An energist is willing to attribute energy values to anything, in any state of motion. For an energist, m can only be attributed to something in its rest frame, so the subscript 0 is never needed. For an energist, p2 = E2/c2 - m2c2 is always true in any inertial frame. The energy E must come from other physics. For light quanta, p = E/c is a given, so p2 = p2 - m2c2 , so m2c2 = 0 . Since c > 0, m = 0 for a light quantum. So, E = mc2/(1 - v2/c2)1/2 only in the case of a particle with non-zero rest mass. ------ Most modern day physicists, especially high-energy physicists, tend to be energists rather than massists.
 P: 383 I said: So, E = mc2/(1 - v2/c2)1/2 only in the case of a particle with non-zero rest mass. I should have said: So, E = mc2/(1 - v2/c2)1/2 only in the case of a particle with non-zero mass.
P: n/a
 Originally posted by alchemist what is the actual equation of e=mc^2? this is only the simplified equation, and i have forgotten the actual one already...
The equation E = mc2 is the mass-energy equation relating the mass m of a particle to the free-particle energy E. The proof can be found here

http://www.geocities.com/physics_wor...ergy_equiv.htm

If the particle is a tardyon (i.e. a particle which travels at speeds less than light) then

m = m0/sqrt[1-(v/c)2]

Multiply both sides by c2

mc2 = m0c2/sqrt[1-(v/c)2]

Substitute in E = mc2 to get

E = m0c2/sqrt[1-(v/c)2]

This equation can be rewritten as

E2 - (pc)2 = (m0c2)2

Pete