Recent content by Kutuzov

Thank you. Works perfectly! I call that kind of expansion Taylor series expansion, and only say binomial expansion if I use the binomial theorem. But it might be the same thing.

I need an example of said binomial expansion to see what it's about. I'm sure I will recognize it straight away, it's just what I think is binomial expansion is stuff like (a+b)^3=a^3+3a^2b+3ab^2+b^3. In this case (1+vdv') the exponent is one, so an expansion like this would leave the...

Homework Statement In this thread the author performs the following calculation under "method 1": v+dv=\frac{v+dv'}{1+vdv'}=v+(1-v^2)dv'\implies dv'=\frac{dv}{1-v^2} He's set c=1 so the second expression is the relativistic velocity addition formula. What I don't understand is how he gets the...

Posting again in case you want to keep helping, read this topic by email and got sent my first more positive response before I edited it.

We can break out \gamma for one. That gives us \gamma (c^2-v^2)^{1/2}=\gamma c(1-\frac{v^2}{c^2})^{1/2}=\gamma^2 c Um wait... is this what we expect? Returning to my original quesiton, if this is the magnitude of \mathbf{V_1} and \mathbf{V_2}=c, we get V_1V_2cosh(\phi)=\gamma^3 c^2\neq \gamma...

Yes, in the rest frame we can write a 4-velocity as \left( 0, 0, 0, c \right) by choosing the inertial frame appropriately. My understanding is that the magnitude of \left( 0, 0, \gamma v, \gamma c \right) would be (\gamma^2 c^2-\gamma v^2)^{1/2}. I also don't know why we can assume that the...

But both velocities cannot be in the rest frame? I understand that one can always be written in this way, (0, 0, 0, \gammac). But not both at the same time? And only a timelike velocity written in such a way will have the magnitude c, right?

Homework Statement I'm confused about the difference between the following two statements: \mathbf{V_1}\mathbf{V_2}=V_1V_2\cosh (\phi) and \mathbf{V_1}\mathbf{V_2}=\gamma c^2 Where \gamma is the Lorentz factor of the relative speed between the two vectors. Both vectors are time-like. The...