# Deriving Lorentz Transformation

Gold Member

## Homework Statement

How can we derive Lorentz Transformation using the length contraction and time dilation equations of relativity ?

## Homework Equations

##γ = 1/ (\sqrt{1-u^2/c^2})##
##t = t_0γ##
##L = L_0/γ##

## The Attempt at a Solution

[/B]
In position Lorentz Transformation calculations, simply I thought that the distance will get shorter since theres length contraction.
So in galilean transformation the position transformation is ##x= x_0-ut##. So this "length" will get shorther by the amount of ##γ##.
So we have ##x = γ(x_0-ut)##

For the time part I am kind of stuck. I didnt understand where the ##ux/c^2## comes from.

PeroK
Homework Helper
Gold Member
2021 Award

## Homework Statement

How can we derive Lorentz Transformation using the length contraction and time dilation equations of relativity ?

## Homework Equations

##γ = 1/ (\sqrt{1-u^2/c^2})##
##t = t_0γ##
##L = L_0/γ##

## The Attempt at a Solution

[/B]
In position Lorentz Transformation calculations, simply I thought that the distance will get shorter since theres length contraction.
So in galilean transformation the position transformation is ##x= x_0-ut##. So this "length" will get shorther by the amount of ##γ##.
So we have ##x = γ(x_0-ut)##

For the time part I am kind of stuck. I didnt understand where the ##ux/c^2## comes from.

That term is from the relativity of simultaneity. You need that as well to derive Lorentz.

Gold Member
That term is from the relativity of simultaneity. You need that as well to derive Lorentz.
But how. How can I derive it ?

PeroK