Einstein's energy equation (after substituting the equation of relativistic momentum) takes this form: $$E = \frac{1}{{\sqrt {1 - {v^2}/{c^2}} }}{m_0}{c^2} % $$ Now if you apply this form to a photon (I know this is controversial, in fact I would not do it, but I just want to understand the consequences), you get the following: $$E = \frac{1}{0}0{c^2}% $$ On another note, I understand that after dividing by zero:
- If the numerator is any number other than zero, you get an "undefined" = no solution, because you are breaching mathematical rules.
- If the numerator is zero, you get an "indeterminate" number = any value.
Here it seems we would have an "indeterminate" [if (1/0) times 0 equals 0/0], although I would prefer to have an "undefined" (because I think that applying this form to a photon breaches physical/logical rules, so I would like the outcome to breach mathematical rules as well...) and to support this I have read that if a subexpression is undefined (which would be the case here with gamma = 1/0), the whole expression becomes undefined (is this right and if so does it apply here?).
So what is the answer in strict mathematical terms: undefined or indeterminate?
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