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Minute Physics: Why E=mc² is Incomplete

Here’s another great video from the folks at Minute Physics. One of the most famous equations from one of the world’s most famous scientists is a bit more complicated than many people realize. E=mc² only describes objects with mass that aren’t moving. But what about massless particles – like light – that are moving? Check out the video for a quick explanation!

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  • Todd Deatherage November 1, 2012, 12:48 PM

    That doesn’t make sense. The math is wrong. The equation doesn’t balance.

    • Torbjörn Larsson November 1, 2012, 6:38 PM

      Which equation? And why, the presented ones do balance and they are known to make sense (describe the physics)?

  • Nirmalendu Das November 1, 2012, 2:53 PM

    E = mc^2 is a well known equation. E = composed of photons or quanta. But how many photons are responsible to create this energy, Actually, we do not know. Because, we don’t know the correct mass of a photon. So, we do not know the internal functions of m during excited state of matter. We can get this answer from Complete Unified Theory (page-424, 1998), written by me.

    Real formation of E = mc^2 is:

    E = (Avogadro number)^2 x root of mass of populated photons x velocity of light or photon / Curie constant. Where, equation of populated photons = mass of electron x [ (mass of
    matter)^2 – (mass of Alfa particle)^2] / Pi^2 x Avo. Number x (mass of Alfa particle)^2
    .
    In this way matter is converting to energy.

    The value of Pi is very important in the case of excited
    state. It will differ slightly than normal value of Pi. This will depend on the
    mass of matter. Then we will get the result same to E = mc^2.

    Nirmalendu Das.
    Email: nirmalgopa@gmail.com
    Dated: 01-11-2012.

  • Scott Yost November 1, 2012, 3:05 PM

    It’s only incomplete if you consider m to be the rest mass. When writing E = m times c-squared, it is normally assumed that m includes a time-dilation factor, taking into account the increase in inertia as a massive object approaches the speed of light.

  • lcrowell November 1, 2012, 6:54 PM

    The equation comes from the invariant interval. Distance in four dimensions is

    d^2 = (ct)^2 – x^2 – y^2 – z^2.

    This is invariant for all observers in any frame. If you watch a particle in motion and measure off the length of its path in space plus time = spacetime, this appears the same to all possible observers. If we set y = 0 and z = 0 and we consider the motion of a particle along the x direction x = vt we get

    d^2 = (ct)^2 – (vt)^2 = (c^2 – v^2)t^2.

    If we pull c out of the parentheses we get d^2 = (1 – (v/c)^2)(ct)^2. The distance d is the proper time of a clock on that moving particle d= c? and we see that the proper time is related to our coordinate time as ? = sqrt{1 – (v/c)^2}t, which is the time dilation of relativity.

    In physics there are conjugate variables to distance called momentum. The invariant quantity is the rest mass of a particle and this is related to the energy and momentum as

    (mc^2)^2 = E^2 – (pc)^2,

    where energy is the conjugate variable to time. This leads to the full equation

    E = sqrt{(pc)^2 + (mc^2)^2}.

    If the momentum part is small pc << mc^2 we may use binomial theorem to write

    E = (mc^2) sqrt{1 + (pc)^2/(mc^2)^2} ~= (mc^2)(1 + (1/2)p^2/(mc)^2

    = mc^2 + p^2/2m

    which is the rest mass part plus the standard classical mechanical energy.

    LC

  • Nirmalendu Das November 7, 2012, 12:44 PM

    Real
    formation of E = mc^2 is:

    E = (Avogadro number)^2 x root of mass of populated photons
    x velocity of light or photon / Curie
    constant. Where, equation of populated photons = mass of electron x [ (mass of
    matter)^2 – (mass of Alfa particle)^2] / Pi^2 x Avo. Number x (mass of Alfa
    particle)^2 .

    In this way matter converting to energy.

    The value of Pi is very important in the case of excited
    state. It will differ slightly than normal value of Pi. This will depend on the
    mass of matter. Then we will get the result same to E = mc^2.

    Nirmalendu Das

    Email: nirmalgopa@gmail.com

    Dated: 07-11-2012

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