The discussion revolves around understanding concepts in special relativity, particularly related to measuring lengths and time intervals in different frames of reference. Participants are exploring the implications of the light clock thought experiment and the equations governing Lorentz transformations.
There is an active exploration of the concepts, with some participants providing guidance on measurement techniques and the significance of simultaneous measurements. Various interpretations of the problem are being discussed, and participants are encouraged to think critically about the definitions and implications of the concepts involved.
Some participants express confusion regarding the notation and the fundamental concepts of special relativity, indicating a need for further clarification on the definitions of time intervals and frames of reference.
Taylor_1989 said:@PeroK so now for part b using that I can use the Lorentz transformations like so:
$$L=x_2-x_1$$ $$L'=x'_2-x_1'$$ $$t'_1=t'_2$$
$$x_2-x_1=y((x'_2-x'_1)-(ut'_2-ut'_1))$$
$$L=yL'$$
This is because
$$t'_2-t'_1=0$$
Yes I do and many thanks. Could you recommend a textbook? I am a first year physics undergrad. I taught myself A-level math, and was not allowed to A-level physics as a private candidate. Which I am regretting now. As I feel if I actually I missed out on a lot of theory and now trying to play catch. Would it be worth me getting a a-level book that contains special relativity or just find a first year?PeroK said:Those are the correct algebraic steps in the right order. So, perhaps that's good enough! Let me give you the explanation (and tidy up the notation a bit):
Suppose the two ends of the rod in ##S'## are simultaneously at ##x'_1## and ##x'_2## at some time ##t'##.
The length of the rod in ##S'## is therefore given by ##L' = x'_2 - x'_1##.
These two events transform to positions ##x_1## and ##x_2## in ##S## given by:
##x_1 = \gamma (x'_1 + Vt'), \ x_2 = \gamma (x'_2 + Vt')##
(Note the sign of ##V## in the Lorentz Transformation, as we are going from ##S'## to ##S##.)
Note: as the rod is stationary in ##S## the times of those two events are not important for a length measurement in ##S##, which is:
##L = x_2 - x_1 = .\gamma (x'_2 - x'_1) = \gamma L'##
Do you understand the logic of this?
I like T M Helliwell's book on SR, and it's available at a reasonable price in the UK.Taylor_1989 said:Yes I do and many thanks. Could you recommend a textbook? I am a first year physics undergrad. I taught myself A-level math, and was not allowed to A-level physics as a private candidate. Which I am regretting now. As I feel if I actually I missed out on a lot of theory and now trying to play catch. Would it be worth me getting a a-level book that contains special relativity or just find a first year?