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

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

    chroot 10,427
    Staff Emeritus
    Science Advisor
    Gold Member

    You probably mean

    E2 = p2c2 + m2c4

    - Warren
     
  4. what does the P stand for? and is that equation homogenous?
     
  5. chroot

    chroot 10,427
    Staff Emeritus
    Science Advisor
    Gold Member

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

    - Warren
     
  6. 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.
     
  7. 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.
     
  8. pmb

    pmb 0

    Re: e=mc^2

    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
     
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