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Mathematical Proof that Photons have No Rest Mass

  1. Feb 14, 2016 #1
    Using these equations I am about to prove that photons have a rest mass of zero (mathematically)
    E=hc/λ Photon Energy Equation

    E2=(pc+mc2)2 Mass-Energy Equivalence with Momentum Equation

    p=h/λ Momentum of a Photon Equation


    Set the First 2 equations equal to eachother...
    E=hc/λ ------------------------------------------------> E2=(pc+mc2)2




    h22= (p2c2/c2)+(m2c4/c2)






    (Enter in the Momentum of a Photon Equation)





    m(photon) = 0

    Is my math correct?
    If so, is this legible?
    And if so again, has this been proved yet and I am just completely unaware that it has?
    I also made a video on YouTube about this if you want to check it out...

    Last edited by a moderator: Feb 14, 2016
  2. jcsd
  3. Feb 14, 2016 #2


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    Second line does not follow from first, (right side is wrong).
    Last edited by a moderator: Feb 14, 2016
  4. Feb 14, 2016 #3
    Thanks. I didn't see that until you pointed it out. So I just did the math again (the right way) and it comes out to be...

    0 = m2c2

    Could this also prove that the the mass of a photon is zero since we already have a set velocity for the speed of light (2.99x108 m/s)?
  5. Feb 14, 2016 #4


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    What you have done is simply proving a circular argument. For example

    "p=h/λ Momentum of a Photon Equation"

    is ALREADY an assumption that the momentum does NOT depend on ANY mass. In other words, you didn't show that this is true, but rather you adopt this form for the photon.

    What you have done is simply doing a mathematical derivation from a known set of criteria, rather than showing that those starting criteria or description is correct. This is not a mathematical proof, but rather a logical consequence.

  6. Feb 14, 2016 #5
    So in simple terms, are you saying that p=h/λ is an equation DERIVED from the other two equations (and possibly others) ?
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