- #1
PhDeezNutz
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- TL;DR Summary
- This is an extension of a homework problem. (That I already solved)
https://www.physicsforums.com/threads/superluminal-moving-points-4-velocity.988718/
See post 2
I solved the problem (got the right answer) but I would like some insight. My answer seems contingent on choice of signature. I had to specifically choose (-,+,+,+) in order for the quantity under the square root to be positive.
I guess my question boils down to "Is choice of signature important when dealing with superluminal 4-velocities"? I wanted to show for superluminal velocities that
##\tilde{U} = \left( \frac{c}{\sqrt{\frac{u^2}{c^2} - 1}}, \frac{\dot{x}}{\sqrt{\frac{u^2}{c^2} - 1}}, \frac{\dot{y}}{\sqrt{\frac{u^2}{c^2} - 1}}, \frac{\dot{z}}{\sqrt{\frac{u^2}{c^2} - 1}}\right)##
(This is Rindler Problem 5.4 btw)
And I was successful using (-,+,+,+) and unsuccessful using (+,-,-,-). I was always under the impression that choice of signature did not matter as long as you were consistent but now I have my doubts.
Thank you in advanced for your insights.
I hope I am not breaking any forum rules by asking for insight on a homework problem in a non-homework section. In my defense I already solved it and now I'm asking for general insight that goes beyond the scope of the homework problem. I only used my homework problem to motivate it.
##\tilde{U} = \left( \frac{c}{\sqrt{\frac{u^2}{c^2} - 1}}, \frac{\dot{x}}{\sqrt{\frac{u^2}{c^2} - 1}}, \frac{\dot{y}}{\sqrt{\frac{u^2}{c^2} - 1}}, \frac{\dot{z}}{\sqrt{\frac{u^2}{c^2} - 1}}\right)##
(This is Rindler Problem 5.4 btw)
And I was successful using (-,+,+,+) and unsuccessful using (+,-,-,-). I was always under the impression that choice of signature did not matter as long as you were consistent but now I have my doubts.
Thank you in advanced for your insights.
I hope I am not breaking any forum rules by asking for insight on a homework problem in a non-homework section. In my defense I already solved it and now I'm asking for general insight that goes beyond the scope of the homework problem. I only used my homework problem to motivate it.