What is the actual equation of e=mc^2?

[alchemist]

what is the actual equation of e=mc^2? this is only the simplified equation, and i have forgotten the actual one already...

 

[chroot]

You probably mean

E² = p²c² + m²c⁴

- Warren

 

[mceddy2001]

what does the P stand for? and is that equation homogenous?

 

[chroot]

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

- Warren

 

[quartodeciman]

It all depends on whether you are a massist or an energist.

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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.

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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.

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Most modern day physicists, especially high-energy physicists, tend to be energists rather than massists.

 

[quartodeciman]

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.

 

[pmb]

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

www.geocities.com/physics_world/sr/mass_energy_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