Question

I think I understand this. https://users.sussex.ac.uk/~waa22/relativity/Complete_Derivation_files/derivation.pdf
Is there more to it than assuming that time is not an absolute thing and the speed of light is the absolute thing?

Answer 1

we arent helping u figure it out urself

Answer 2

isnt time absolute as well?

Answer 3

according to special theory of relativity, no \(\color{#0cbb34}{\text{Originally Posted by}}\) @Florisalreadytaken
isnt time absolute as well?
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 4

@Florisalreadytaken
what do you mean by "more to it"

I mean any other assumptions?

Answer 5

what about this

\[ (c t)^{2}=(v t)^{2}+\left(c t_{0}\right)^{2}\]
\[c^{2} t^{2}=v^{2} t^{2}+c^{2} t_{0}^{2} \]
\[\Rightarrow c^{2} t_{0}^{2}=\left(c^{2}-v^{2}\right) t^{2} \]
\[\Rightarrow t_{0}^{2}=\left(1-\frac{v^{2}}{c^{2}}\right) t^{2} \]
\[t \sqrt{1-\frac{v^{2}}{c^{2}}}=t_{0} \]
\[\Rightarrow t=\frac{t_{0}}{\sqrt{1-\frac{v^{2}}{c^{2}}}}\]

Answer 6

Where do you get this from ?

\[(c t)^{2}=(v t)^{2}+\left(c t_{0}\right)^{2}\]

Answer 7

If a spherical light wave is produced at the origin of the S and S' inertial frames at t = 0, the statement about the constant velocity of light in different inertial frames can be expressed using that formula

Answer 8

I'm confused. What do you mean by spherical? Is it as in spherical wave, like light originated from a point source?

Answer 9

yes, thats right

Answer 10

what does have to do with the derivation. I was thinking more of a photon bouncing from one mirror to another back and forth.

Answer 11

because it emerges from one point and then when it hits the mirror, it reflects and so on

Answer 12

still not clear how it matters. We are thinking this is in photon level aren't we? Is there any importance in thinking about spherical wave fronts?

Answer 13

anyway let's just forget about what I said -- what you got on that pdf file is very well explained,
and, based on what you're asking for, I don't believe there's anything more.

Answer 14

My suspicion was if it is a toned down version of a more advanced version. Ok thanks for help.