How to derive t1 in terms of t and t in terms of t1

[manvirsingh]

1. (x=X1+vt1, x1=x-vt )

2.(t=t1+vx1/c2, t1=t-vx/c2 )


I know that 1. is x in terms x1 and x1 in terms of x.
I understand it very well, the adding and substracting of
velocity.

But i am unable to understand the 2.how these equation are
derived and what does they mean.

The mane problem is how they are derived.

Please help me.

 

[mfb]

c2 means c^2 (c squared)?
This looks like a classical formula, as time passes at the same rate for t and t1. They are just shifted by a constant value, which is meaningless in physics (there is no absolute time in physical equations, just time differences).

Edit: Ah, those are the moving x1, x? Sorry, I am confused by your equations. Can you provide the source, or at least write them in a clean way (with $$tag would be perfect, together with an explanation what the parameters are)?$$

 

[PeterDonis]

I assume you are talking about the Lorentz transformation formulas? You might try here for a start:

http://en.wikipedia.org/wiki/Lorentz_transformation#Derivation

 

[manvirsingh]

x=stationary observer
x1=moving observer
c2= c squared
v= velocity

 

[DrGreg]

x=stationary observer
x1=moving observer
c2= c squared
v= velocity

That still doesn't answer the question. I assume x is supposed to be a distance (not an observer) so you have to specify between what and what and measured by who. Similarly for the other terms.

The Lorentz transform is usually expressed in a form something like$$\begin{align}<br /> t_1 &= \frac{t - vx/c^2}{\sqrt{1-v^2/c^2}} \\<br /> x_1 &= \frac{x - vt}{\sqrt{1-v^2/c^2}} \\<br /> t &= \frac{t_1 + vx_1/c^2}{\sqrt{1-v^2/c^2}} \\<br /> x &= \frac{x_1 + vt_1}{\sqrt{1-v^2/c^2}}<br /> \end{align}$$
where

t = time between event O and event E as measured by observer A
x = distance between event O and event E as measured by observer A
t₁ = time between event O and event E as measured by observer B
x₁ = distance between event O and event E as measured by observer B
v = velocity of observer B relative to observer A

My equations look rather different to yours, so did you really mean what you wrote? And if you did, what do the letters mean (they can't be the same as the meanings I gave).