E2=m2c4+p2c2 not simply E=mc2
To the not here nation,
because only I am here.
Eons ago I asked the group to find error in a little book I wrote and posted on the blog of my think atheist page. I knew of one error, a science/math error I learned after the book was copywrite published.
My obvious intent was to have anyone on this site read the little book, "The Odd Average Atheist Bible." If there is any errors I need corrections. Anywho, that doesn't seem popular. That is asking for help.
The error I found is the formula E=mc2 is only valid for matter that has rest mass. The m is strictly rest mass. As photons only when emitted travel at the speed of light they are never at rest. If E=mc2 is used to calculate the mass of photons and energy, infinte mass for the photon result.
But with the formula: E times E = m2xc4 + p2xc2 or E2=m2c4+p2c2 the energy of the photon reduces to E2=p2c2 or E=pc or E = p times c.
p is momentum a valid value for photons. momentum equals "not at rest mass" time velocity.
davo
link for above:
Replies to This Discussion
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Permalink Reply by Radu Andreiu on -
Yeah, it's all right here. Quite interesting, but I guess it doesn't make much sense for most people.
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Permalink Reply by Brad Snowder on -
But isn't it really that when doing relativistic calculations you are almost always allowed to choose the frame of reference? If you choose the FoR with the same vector as the momentum then the momentum is zero and the whole second term is zero so E=mc^2. When doing real stuff it isn't always that simple but reducing it makes it fit on a t-shirt better.
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Permalink Reply by Brad Snowder on
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Unless you already know the rest mass of the photon, you generally find its energy from the wavelength first. Then you take that and divide by c^2 to get the rest mass (mass equivalence of a photon's energy). To calculate the momentum stored in the EM field; divide E by c. Rest mass by definition has no momentum so equivalence reduces to E=mc^2. So E/c=mc and mc=p for a photon. Or become a theist and just have faith that it all works out.
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Permalink Reply by Isaac on -
@Brad
p=mc is invalid for photons. In relativity, the kinetic energy of a particle is given by K=mc^2/(1-v^2/c^2)^1/2-mc^2, meaning that it takes an infinite amount of energy to accelerate a particle with mass to the speed of light. Thus, particles which do travel at the speed of light have no mass, and since the speed of light is invariant (in vacuum) for all frames of reference, it's the mc^2 term that vanishes in E^2=(mc^2)^2+(pc)^2, not the pc term. Therefore, for light, we get E=pc, which means that light has momentum at all times. Using planks formula, E=hf, E=pc reduces to p=hf/c or p=h/L, aka De Broglie's formula (I'm using L for wavelength here). Light's momentum depends on it's wavelength, which can change due to the Doppler effect, but the invariance of the speed of light guarantees that light will always have momentum.
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