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

  • Thread starter Thread starter manvirsingh
  • Start date Start date
  • Tags Tags
    Derive Terms
manvirsingh
Messages
9
Reaction score
0
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.
 
Physics news on Phys.org
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)?
 
x=stationary observer
x1=moving observer
c2= c squared
v= velocity
 
manvirsingh said:
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<br /> \begin{align}<br /> t_1 &amp;= \frac{t - vx/c^2}{\sqrt{1-v^2/c^2}} \\<br /> x_1 &amp;= \frac{x - vt}{\sqrt{1-v^2/c^2}} \\<br /> t &amp;= \frac{t_1 + vx_1/c^2}{\sqrt{1-v^2/c^2}} \\<br /> x &amp;= \frac{x_1 + vt_1}{\sqrt{1-v^2/c^2}}<br /> \end{align}<br />
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).
 
I asked a question here, probably over 15 years ago on entanglement and I appreciated the thoughtful answers I received back then. The intervening years haven't made me any more knowledgeable in physics, so forgive my naïveté ! If a have a piece of paper in an area of high gravity, lets say near a black hole, and I draw a triangle on this paper and 'measure' the angles of the triangle, will they add to 180 degrees? How about if I'm looking at this paper outside of the (reasonable)...
Thread 'Relativity of simultaneity in actuality'
I’m attaching two figures from the book, Basic concepts in relativity and QT, by Resnick and Halliday. They are describing the relativity of simultaneity from a theoretical pov, which I understand. Basically, the lightning strikes at AA’ and BB’ can be deemed simultaneous either in frame S, in which case they will not be simultaneous in frame S’, and vice versa. Only in one of the frames are the two events simultaneous, but not in both, and this claim of simultaneity can be done by either of...
Back
Top