- #1
binbagsss
- 1,259
- 11
The question is : Let s be the speed of light through water. If water is flowing at speed v in a given frame, find the speed of light in that frame, were the light propagates in the same direction as the water?
My question:
I am having a sign issue.
I can not see how the following is flawed, derived from the Lorentz boosts:
x' = γ(x-Vt)
t'=γ(t-Vx/c^2)
Where I define frame O' to be that of the water moving at v, and O to be the stationary water.
Then V=v.
x is the position vector in frame O. x = st.
=> dx'/dt'= [itex]\frac{s-v}{1-\frac{sv}{c^{2}}}[/itex]
Which is not the correct answer : [itex]\frac{s+v}{1+\frac{sv}{c^{2}}}[/itex]Many thanks to anyone who can help shed some light on this.
My question:
I am having a sign issue.
I can not see how the following is flawed, derived from the Lorentz boosts:
x' = γ(x-Vt)
t'=γ(t-Vx/c^2)
Where I define frame O' to be that of the water moving at v, and O to be the stationary water.
Then V=v.
x is the position vector in frame O. x = st.
=> dx'/dt'= [itex]\frac{s-v}{1-\frac{sv}{c^{2}}}[/itex]
Which is not the correct answer : [itex]\frac{s+v}{1+\frac{sv}{c^{2}}}[/itex]Many thanks to anyone who can help shed some light on this.