Re: OT:Tempted to get this book
The basic energy equation:
E = sqrt(1/(1-(v^2/c^2)))mc^2.
Forget the mc^2 part for a moment, and focus on the stuff inside the sqrt
1/(1-(v^2/c^2))
Now, for light, v = c. So, we get, in the innermost set of parentheses,
c^2/c^2
which is, of course, 1.
So, we replace the innermost parenthesis with the result, and get
1/(1-1)
inside the sqrt. 1-1 = 0, so when we make that replacement, we get
1/0
which, other than being an odd comic, is mathamatically undefined. However, we do know that in the equation
y = 1/x, as x approaches 0, y approaches infinity. So, if we replace 1/0 with infinity, we get infinity inside the square root.
sqrt(infinity)
as the sqrt of infinity is still infinity, we can drop the sqrt function entierly, and the energy equation then becomes
E = infinity*mc^2
As m represents the rest mass, it's 0. If we make that replacement:
E = infinity*0*c^2.
In math, infinity * 0 isn't defined, and the c^2 isn't germain to this conversation (if you like, we can say the 0 eats it up and doesn't notice). The universe, however, makes it's own definitions, and comes up with a result for light contigent on the wavelength of the photon in question. However, that answer only applies when the photon is traveling at the speed of light. Plug any lower real velocity in there (well, any real velocity between c and -c, not inclusive of the endpoints), and the sqrt function comes up with a real answer, and the m=0 eats up everything, leaving a big fat 0 for E.
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Of course, by the time I finish this post, it will already be obsolete. C'est la vie.
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