Which of the following is a Lorentz transformation? (Assume a system of units such that the velocity of light is 1.)
A.
B.
C.
D.
E. None of the above
A and B are FALSE since t' = t is Galilean.
Check answer C:
x' = (x − vt)γ = 1.25x − .75t
γ = 1.25 and vγ = .75
v = .75/1.25
t' = (t − vx/c²)γ = 1.25t − .75x
γ = 1.25 and (v/c²)γ = .75
v = .75c²/1.25 = .75/1.25, since c = 1
v is consistent → C is TRUE
Answer: C
A.
B.
C.
D.
E. None of the above
(GR9277 #94)
Solution:
| Galilean | Lorentz |
|---|---|
| x' = x − vt | x' = (x − vt)γ |
| y' = y | y' = y |
| z' = z | z' = z |
| t' = t | t' = (t − vx/c²)γ |
A and B are FALSE since t' = t is Galilean.
Check answer C:
x' = (x − vt)γ = 1.25x − .75t
γ = 1.25 and vγ = .75
v = .75/1.25
t' = (t − vx/c²)γ = 1.25t − .75x
γ = 1.25 and (v/c²)γ = .75
v = .75c²/1.25 = .75/1.25, since c = 1
v is consistent → C is TRUE
Answer: C
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