# Special relativity fundamental question

1. Aug 3, 2009

### 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)

2. Aug 3, 2009

### Staff: Mentor

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.

3. Aug 3, 2009

4. Aug 3, 2009

5. Aug 3, 2009

### krindik

thanks for correcting

6. Aug 4, 2009

### 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 $$v$$)
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...

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Last edited: Aug 4, 2009