I already know the solution to this problem, but I'm not sure exactly why it works out the way it does, so I'm looking for an explanation.
Homework Statement
A particle accelerator accelerates electrons at 40 GeV in a pipe 2 miles (3218.69 metres) long, but only a few cm wide. How long is the...
Thank you so much. For part b), can I just plug numbers into a Lorentz equation, say, ##t' = γ(t - vx/c^2)##? And I'm assuming the resulting speed should be a significant fraction of c?
Should it not also equal 3m?
##\Delta s^2 = -c^2(0)^2 + (3)^2##?
##\Delta s'^2=-c^2(10^-8)^2 + \Delta x'^2##
But how can I solve that if both ##\Delta s'## and ##\Delta x'## are unknown?
I see. I hadn't thought to use that; the context it was used in the lecture was for four-vectors with multiple spatial dimensions.
So, ##\Delta s^2=-c^2(10^-8)^2 + (3)^2## (that should be 10^-8, but it won't show up properly)? From that I get ##\Delta s^2 = (-1) * (3 * 10^8)^2 * (10^-8)^2 +...
3 +/- 3, that is. I think it's +3? So, the new separation is 6 metres? Or am I completely off here...?
Apologies for the double post; I exceeded the post edit time limit.
1.
Two events occur simultaneously in an inertial reference frame, separated by a distance of 3 metres. Within a different inertial frame that is moving with respect to the first, one event occurs 10^-8 seconds later than the other.
(a) In the moving frame, what is the spatial distance between...