# Confused about Lorentz Transformations

BWV
I thought Lorentz Transformations left Δt2-Δx2 invariant
but, for example a frame moving at .5C for Δt =1 has Δx = .5 so
Δt2-Δx2 = .75

If this is transformed by :

to a rest frame
Δt =0.65 has Δx = 0 and Δt2-Δx2≠ 0.75

not sure where I have gone wrong here, any help would be appreciated

## Answers and Replies

Samshorn
I thought Lorentz Transformations left Δt2-Δx2 invariant but, for example a frame moving at .5C for Δt =1 has Δx = .5 so
Δt2-Δx2 = .75. If this is transformed by [Lorentz Transformation] to a rest frame [then] Δt =0.65 has Δx = 0 and Δt2-Δx2≠ 0.75
Not sure where I have gone wrong here, any help would be appreciated

You made a mistake with your arithmetic. If you plug your numbers into the Lorentz Transformation equation that you quoted, the result is Δt' = sqrt(0.75) and Δx' = 0, so the quantity Δt'2-Δx'2 equals 0.75, just as before.