Thread: verify that gamma = 1 + p^2/[(m^2)(c^2)]

Verify that 1/sqrt(1-(v^2)/(c^2)) = 1 + p^2/[(m^2)(c^2)]

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OK, so on the right side I changed p^2 into (m^2)(v^2) and cancelled out the m^2 in the numerator and denominator. This leaves me with:

1 + (v^2)/(c^2) = 1/sqrt(1-(v^2)/(c^2))

This seems tantalizingly close, but I have no clue what to do next.

Any guidance would be appreciated.

Yes, this is a homework problem, but homework isn't turned in. I'd still like to know how to do it though.

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By the way, how do you guys type math? I'd like to make it more readable.

Are you sure you're not supposed to be using the relativistic definition of momentum here: . After all, you are dealing with the lorentz factor here.

Also, it looks like your right hand expression turns out to be . Are you sure you typed in the question correctly?

Thanks for the prompt response.

I thought of using the relativistic definition, but it seems the nonrelativistic one got me closer. When using p = gamma mv, I get 1+gamma^2-gamma^4 for the right hand side. Can't factor that . . . or can I?

Yes, I typed it as it appears in the book. I'll look for a list of errata, though.
I'm taking gamma to be one over the square root of (1-(v^2)/(c^2))

Although your two expressions look similar, they are not equal. Just plug in some values of and you'll find out for yourself.

As for your problem, start with the RHS:


Keep going with this. Combine the fractions and simplify. You should end up with .

Yes, I do end up getting gamma squared. After combining the fractions, I multiplied top and bottom by 1/(c^2).

So I guess it was a bad problem then. International editions do have a lot of errors (probably intentional).