Where can I find a good textbook for special relativity?

[Taylor_1989]

@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

$$t'_2-t'_1=0$$

 

[PeroK]

@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

$$t'_2-t'_1=0$$

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?

 

[Taylor_1989]

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?

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]

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?

I like T M Helliwell's book on SR, and it's available at a reasonable price in the UK.