Special Theory of Relativity

frames. No experiment can be perfomed to decide who in a set of inertial frames is moving and who is at rest.
The speed of light in empty space is the same in all inertial frames

vx/c2)
γ = 1/ √(1-v2/c2)
y´= y z´= z
Vx ´=(Vx –V) /(1-VxV/c2)

x =γ (x´+vt´)
t = γ (t´ + vx´/c2)
γ = 1/ √(1-v2/c2)
y = y´ z = z´
Vx=(Vx´+ V) /(1+Vx ´V/c2)

Inertial frame at rest: O (x,y,z,t)
Inertial frame moving with velocity v: O´ (x´,y´,z´,t´)

t1´ = γ (t 1 – vx1/c2)= 0
t 2´ = γ (t 2 – vx2/c2) = γ (t 2 – v L/ c2)=0
t1 =0 and t2 = v L/ c2

We measure L = X2 - X1
at t1 = t2 = 0

x1´ = γ (x1 - vt1) = 0
x2´ = γ (x2 - vt2)= γ ( L– v2L/c2) = γ L(1-v2/c2)= L / γ
L´ = x2´ - x1´ = L / γ

L

t1 = t1´ = 0

= 0

t1´ = γ ( t 1 – V x1 / c2) = 0
t 2´ = γ (t 2 – Vx2/c2) = γ t 2
t1´- t2´= γ (t1 - t 2)

t1 = t1´ = 0