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## Homework Statement

We normally assume that the origins of two inertial frames coincide at t=t'=0. This way we find:

t' = γ(t - vx/c

^{2})

x' = γ(x-vt)

Suppose instead that when t=T the origin of S' (which is moving along the x-x' axis with speed v relative to S) has abscissa x=X (neglect y and z) and the S' clock at the origin of S' reads t'=0 at that moment.

a. How do the Lorentz transformations from S to S' need to be modified?

b. What about from S' to S?

c. Write these in matrix form.

Hint: you do not need to re-derive these transformations, try introducing an auxiliary frame that reduces the problem to the usual case.

## Homework Equations

Lorentz transformations (above)

## The Attempt at a Solution

I don't know how to start this problem...