Deriving Lorentz Transformation

  • Thread starter Arman777
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  • #1
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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.
 

Answers and Replies

  • #2
PeroK
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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.
 
  • #3
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That term is from the relativity of simultaneity. You need that as well to derive Lorentz.
But how. How can I derive it ?
 
  • #4
PeroK
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But how. How can I derive it ?
You have to derive the "leading clocks lag" rule and using this along with time dilation and length contraction you can derive Lorentz.
 
  • #5
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okay I manage to derive it thanks.
 

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