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...