Special relativity fundamental question

[krindik]

Hi,
I'm very new to special relativity and have a very basic question.
A and B are moving from each other at a speed of v
at some instant a light flashes in the space.
A records: At time t a light flashed at x
B records: At time t' a light flashed at x'

Here is what I understood from SR theory,
A, at time t sees what B records (instantly, forgetting the delay to see B's record) and writes the relationship to match what he records (t, x) and B records (t', x')

x' = \gamma (x - vt)
t' = \gamma (t - v/c^2 x)
\gamma = 1/\sqrt{1 - v^2/c^2 }

Is my understanding correct?

I am reading the wikibook http://en.wikibooks.org/wiki/Special_Relativity (hope that'll help me in all of special relativity)

Thanks in advance

 

[jtbell]

Yes, that is correct. The equations you have written (the first two specfically) are the Lorentz Transformation which relates position and time coordinates of an event as measured by the observers A and B, provided that one event has x = 0, t = 0 and x^{\prime} = 0, t^{\prime} = 0. That is, the two coordinate systems are set up so their origins coincide.

 

[krindik]

Thanks.

But then is this in wikibook correct?
http://en.wikibooks.org/wiki/Special_Relativity/Spacetime#The_modern_approach_to_special_relativity
It says
t' = t/\gamma not t' = t\gamma

here the event is B's position at time t(in A's frame) and t'(B's frame)

 

[DrGreg]

Thanks.

But then is this in wikibook correct?
http://en.wikibooks.org/wiki/Special_Relativity/Spacetime#The_modern_approach_to_special_relativity
It says
t' = t/\gamma not t' = t\gamma

here the event is B's position at time t(in A's frame) and t'(B's frame)

That is correct, because B's position is x'=0, not x=0.

 

[krindik]

thanks for correcting

 

[krindik]

One more question related to the same scenario from wikibook

1) How do you interpret the leaning forward of the time and x axis?
Can you give some hints from the attached image?

2)
The book says (Bill and John are moving from each at v)

So distances between two points according to Bill are simple lengths in space (X) whereas John sees Bill's measurement of distance as a combination of a distance (x) and a time interval:
x^2 = X^2 - (cT)^2 -----(1)

But Bill's distance, x, is the length that he would obtain for things that John believes to be X metres in length. For Bill it is John who has rods that contract in the direction of motion so Bill's determination "x" of John's distance "X" is given from:
x = X\sqrt{1 - v^2/c^2} -----(2)

Eq. 2 is from the Lorentz tranform and Eq. 1 is from the space-time interval definition
But why does Eq. 1 has only T from B's frame but not t from John's frame?

Can u pls give some advice?

Actually I'm a bit confused as to how the interpretation that a moving objects are out of phase by T = (v/c^2) X is derived. From that onwards I tend to wonder whether
the wikibook is correct and questioning everything... really sorry if this is a silly question...