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E=MC^2 Logical connection

  1. Feb 2, 2005 #1
    Hi. I understand the equation, but I don't understand logically in my head why it is that way. Maxwell's equations, etc show it mathematically but I'm looking for a logical explanation of why it is this way. Like for instance, the logical connection for F=MA would be "more force is needed to move a bigger object, or to move it faster."...now, as far as E=MC^2...

    What I know so far is this:
    energy should be directly proportional to mass, because something of more mass should release more energy. The speed of light fits in because it's sort of a measure of pure energy that's already been converted into mass completely.

    However, I don't understand:
    Why the speed? How does speed fit in?
    Why squared?

    Now, I know you all could prove it with maxwell's equations and such, but I'm not asking for proof, I'm asking for a logical explanation so I can see in my head why it works this way.
  2. jcsd
  3. Feb 2, 2005 #2


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    All physical equations must have consistent units. The equation "E = m" does not have consistent units, because energy and mass are not the same quantity. To make this equation sensible, you must provide some kind of conversion factor.

    You are no doubt aware that the newton, the SI unit of force, is defined as

    [tex]\textrm{force (N)} = \frac{kg \cdot m}{s^2}[/tex]

    Energy can also be found by integrating a force over a distance:

    [tex]\textrm{energy (J)} = F \cdot d = \frac{kg \cdot m^2}{s^2}[/tex]

    As you can see, energy has the same units as mass times a squared velocity. So why is that velocity the speed of light? It's the only absolute velocity in the universe, measured the same by all observers, no matter how they are moving.

    - Warren
  4. Feb 2, 2005 #3
  5. Feb 3, 2005 #4
    There's a 100 year old proposition that explains why E=mcc; that proposition has never been put to rest. It is:

    The final irreducible constituent of all physical reality is the electromagnetic field.

    Understand that and you will understand all of the "WHY" questions we can't answer with our present day assumptions.
  6. Feb 3, 2005 #5


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    I'm interested in this. Can you provide a reference which discusses this concept? Guess I felt there was no irreducible constituent so I'd like to know about it.
  7. Feb 3, 2005 #6
    That is a quote from Einstein; I found it in one of Einstein's articles in "The World of Physics", Weaver. I can look it up if there is any question about its accuracy.

    Einstein was explaining how the theories of Maxwell, (Not Maxwell's EM theory) Lorentz, etc had basic flaws. He couldn't find a basic flaw in "final irreducible ...." concept but never used it in his work as far as I can understand.
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