- #1
Kaguro
- 221
- 57
Hello all.
I am having some small trouble with applying the lorentz transformations to calculate lorentz contraction. Here's what I did:
Let O be the rest system and O' be the system moving with velocity v w.r.t O along x axis. Consider a rod lying in the O' system with ends x1' and x2'.
Length of rod in O' system is:
L' = x2' - x1'
measured at the same instant t'.
In the O system,
x2 = ##\gamma##(x2'+vt')
x1 = ##\gamma##(x1'+vt')
So,
L = x2-x1 = ##\gamma##(x2-x1) = ##\gamma##(x2' - x1')
so,
L = ##\gamma##(L')
But... that's not quite right... L should always be smaller than L'...
Where did I go wrong?
I am having some small trouble with applying the lorentz transformations to calculate lorentz contraction. Here's what I did:
Let O be the rest system and O' be the system moving with velocity v w.r.t O along x axis. Consider a rod lying in the O' system with ends x1' and x2'.
Length of rod in O' system is:
L' = x2' - x1'
measured at the same instant t'.
In the O system,
x2 = ##\gamma##(x2'+vt')
x1 = ##\gamma##(x1'+vt')
So,
L = x2-x1 = ##\gamma##(x2-x1) = ##\gamma##(x2' - x1')
so,
L = ##\gamma##(L')
But... that's not quite right... L should always be smaller than L'...
Where did I go wrong?