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The derivation is explained here

- #3

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The derivation is explained here[/url]

Thank you, however I am still in high school and therefore my knowledge of physics is obviously still small. Is there any simpler way of explaining it?

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Think of it like this: A body emits radiation in frame S in the positive and negative x-direction of equal quantities (but opposite directions). The total momentum of radiation emitted in S is zero. Now look at the same situation as viewed in a frame moving with respect. The total momentum of radiation emitted by the body is now non-zero. The body must account for that change in momentum. Calculation shows that the only way for this to happen is for the mass of the body to decrease. Calculation shows that the amount of energy emitted by the body E is related to the magnitude of the amount of decrease in the mass, m, as E = mcThank you, however I am still in high school and therefore my knowledge of physics is obviously still small. Is there any simpler way of explaining it?

Pete

- #5

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Think of it like this: A body emits radiation in frame S in the positive and negative x-direction of equal quantities (but opposite directions). The total momentum of radiation emitted in S is zero. Now look at the same situation as viewed in a frame moving with respect. The total momentum of radiation emitted by the body is now non-zero. The body must account for that change in momentum. Calculation shows that the only way for this to happen is for the mass of the body to decrease. Calculation shows that the amount of energy emitted by the body E is related to the magnitude of the amount of decrease in the mass, m, as E = mc^{2}.

Pete

Thanks, that helps a lot. But I'm still struggling slightly. Does anyone have any good analogies which might help me understand?

- #6

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E=mc^2 comes from the relativistic kinetic energy formula

KE = ymc^2 - mc^2

y is gamma, the Lorentz factor.

From that you get

KE + mc^2 = ymc^2 = Mc^2

From that point one can infer that there's a TOTAL energy (ymc^2), made up of kinetic energy plus mc^2. So E=Mc^2 usually means total energy, omitting the gamma and considering relativistic rather than invariant mass.

Now, as for the derivation of the kinetic energy formula, the derivation is identical to Newton's except that relativistic momentum (ymv) rather than ordinary momentum (mv) is used.

As for analogies, just think of matter and energy being equivalent, and c^2 simply being a conversion factor between the kilogram and the joule.

KE = ymc^2 - mc^2

y is gamma, the Lorentz factor.

From that you get

KE + mc^2 = ymc^2 = Mc^2

From that point one can infer that there's a TOTAL energy (ymc^2), made up of kinetic energy plus mc^2. So E=Mc^2 usually means total energy, omitting the gamma and considering relativistic rather than invariant mass.

Now, as for the derivation of the kinetic energy formula, the derivation is identical to Newton's except that relativistic momentum (ymv) rather than ordinary momentum (mv) is used.

As for analogies, just think of matter and energy being equivalent, and c^2 simply being a conversion factor between the kilogram and the joule.

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