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Concerning E=mc2

  1. Jul 6, 2012 #1
    E=mc2. I am an avid reader of physics and science in general and a question popped into my head concerning the squaring of the speed of light in the equation E=mc2. It is my understanding that the speed of light is constant it does not accelerate. What rule or mechanism or whatever allows for the squaring of the speed of light in this equation.
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  3. Jul 6, 2012 #2


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    The speed of light is used in this equation as a conversion between units of mass and energy. As energy is measured in units of Joules (kg*m^2/s^2) and mass is measured in kg, one needs to multiply a mass by units of velocity^2 in order to get units of energy. It turns out that the required conversion factor is exactly c^2 (requires a bit of special relativity to derive).

    One should view the factor of c^2 as simply a conversion factor. I has absolutely nothing to do with light actually moving around or accelerating or some such.
  4. Jul 7, 2012 #3


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    The mechanism is "arithmetic". It has nothing to do with physics. In this formula, c is just a number- there are plenty of numbers larger than "c" and [itex]c^2[/itex] happens to be one of them.
  5. Jul 7, 2012 #4
    So, the "energy" that any "matter" has is equal to that "matter" multiplied by the speed of light sqaured?

    Id love to see that equation worked out using some real number to come up with exact amounts and then recreate them perfectly in reality...I suppose I am a doubter too...E=mc2 has always seemed a bit dreamy to me.
  6. Jul 7, 2012 #5
    What does 1kg of matter equal in energy? And how do I muliply matter and c2 in reality? a match?
  7. Jul 7, 2012 #6


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    1 × 299,792,458 × 299,792,458 joules.
  8. Jul 7, 2012 #7


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    Or, more pedantically,

    1 kg × 299,792,458 m/s × 299,792,458 m/s

    = (299,792,458)2 kg·m2/s2
    = (approximately) 9 x 1016 joules
  9. Jul 7, 2012 #8


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    Which is the energy released in the explosion of a 20 megaton thermonuclear weapon...
  10. Jul 8, 2012 #9
    Do not confuse "matter" with "mass". They are not the same thing nor interchangeable. (This is actually a pretty common mistake that many people make.)

    The proper way of expressing the above would be "the energy that any matter has is equal to its mass multiplied by c squared". Big difference.

    As already mentioned, the formula would not work as "E = mc", and one clear-cut way of determining why that formula is incorrect is to see that the units on both sides of the equation do not match. This is always a good test to check if a physics equation is invalid: If the units on both sides of the equation do not match, then you know that the equation is bogus. (Of course note that the same does not hold in the inverse case. In other words, just because the units match doesn't necessarily mean the equation is correct. The units matching is a requirement, but of course it's not all in itself sufficient to determine the validity of the equation.)

    Could someone post a short summary on how the "E=mc^2" equation is derived?
  11. Jul 8, 2012 #10
    Good info...thanks!

    I'm more interested to see the equation proven in the real world...

    Someone mentioned that 1kg of mass creates the energy of a 20 megaton bomb...why wouldnt it create the energy of a 1 kilogram bomb?
  12. Jul 8, 2012 #11


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    A nuclear fission or fusion bomb converts only a small fraction of its original mass into energy. (but a much larger fraction than with TNT)
  13. Jul 8, 2012 #12


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    All the "tonnes" in bomb making are given with respect to TNT bombs. E.g. 20 million tons of TNT.

    The largest thermonuclear bomb ever detonated was the Tsar bomba which had a yield of 50 million tons of TNT. Obviously the bomb itself did not weigh anywhere near 50 million tons.
  14. Jul 8, 2012 #13
    Thanks everybody for the replies. E=mc2 looks a lot like F=ma to me. Since electromagnetic waves to not accelerate I'm curious as to why squaring the speed of light works in the equation. But correct me if I'm wrong please about the EM waves. It's my understanding that photons move at 300,000 km/s from the moment of thier creation.
  15. Jul 8, 2012 #14
    They are completely different equations, with completely different meaning. The only thing they have in common is the mass.

    Square of speed has nothing to do with acceleration. They have exactly zero in common.

    In vacuum, approximately, yes. The exact value for vacuum is 299,792,458 m/s and is denoted c.
  16. Jul 8, 2012 #15
    You are correct that electromagnetic waves (or photons) always travel at the speed of light c. However E=mc^2 is a (static) relation concerning the energy contained in a body with mass m, i.e. the energy due to it having mass. It is not a dynamical equation telling us how things move (like F=ma). Therefore it is totaly alright to have c^2 in the equation.
  17. Jul 10, 2012 #16
    Disabuse yourself of the notion that squaring c has anything to do with acceleration. c is a constant, and c squared is another constant. It has absolutely nothing to do with acceleration.

    (Besides, m2/s2, which is the unit of c2, is not the unit of acceleration. It's still the unit of speed.)
  18. Jul 10, 2012 #17


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    To avoid confusion, no, [itex]m^2 / s^2[/itex] is not a unit of velocity. It simply is what it is. One might say it's a unit of Energy per mass.
  19. Jul 10, 2012 #18
    Are you sure? Is there any difference between saying "that car is traveling at 4 [itex]m/s[/itex]" and "that car is traveling at 16 [itex]m^2/s^2[/itex]" (other than the latter being quite unconventional and needlessly complicated but, ultimately, the same thing as the former)?

    Where is that coming from?
  20. Jul 10, 2012 #19
    It's not the same. Why would it be? The latter is a square of the former.
  21. Jul 10, 2012 #20


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    Yes there is quite a difference. The first way is correct, the second way is wrong.

    Would you say "the length of this table is 9 m^2"? No you would not, m^2 is a unit of area not length. You can only say "the length of this table is 3m".
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