- #1
joriarty
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Lorentz transformations ("synchronising" reference frames?)
A particle moves from (x,y,z,t) = (0 m,0 m,0 m,0 s) to (1 m,1 m,0 m,10 ns).
The usual Lorentz transformation equations:
I understand that the answer to part (i) is just 1.414×108 ms−1, that's just simple trigonometry. However I do not understand how to do part (ii).
My lecturer gives the following answer to the problem:
But I don't understand the answer. What does he mean by "synchronise clocks" and how did he calculate those answers? (unfortunately my lecturer is away for another 2 weeks so I can't ask him!)
Thank you
Homework Statement
A particle moves from (x,y,z,t) = (0 m,0 m,0 m,0 s) to (1 m,1 m,0 m,10 ns).
- i. What is the speed of the particle in this reference frame?
- ii. What is the speed of the particle in a reference frame moving along the x-axis at 0.7c?
Homework Equations
The usual Lorentz transformation equations:
- β ≡ V/c
- γ ≡ 1/sqrt(1 − β2)
- x′ = γ(x − tβc)
- t′ = γ(t − xβ/c)
- x = γ(x′ + t′βc)
- t = γ(t′ + x′β/c)
- c ≈ 3×108 ms−1
The Attempt at a Solution
I understand that the answer to part (i) is just 1.414×108 ms−1, that's just simple trigonometry. However I do not understand how to do part (ii).
My lecturer gives the following answer to the problem:
Synchronise clocks and rulers at (0, 0, 0, 0). Then we travel to (−1.54, 1, 0, 1.07×10−8) so speed is 1.71×108 ms−1 or β(v) = 0.57. Note that the x component of the velocity comes out negative.
But I don't understand the answer. What does he mean by "synchronise clocks" and how did he calculate those answers? (unfortunately my lecturer is away for another 2 weeks so I can't ask him!)
Thank you