Re: Deriving space-time interval

On 1 Mar, 19:17, "Koobee Wublee" <koobee.wub...@xxxxxxxxx> wrote:
On Mar 1, 10:21 am, "Paul Whymark" <1337...@xxxxxxxxx> wrote:

How was the following formula derived? Is it related to the Lorenz
factor?

s^2 = r^2 - (ct)^2

Do you mean the following?

** ds^2 = c^2 dt^2 - dx^2 - dy^2 - dz^2

If so, start with the Lorentz transformation.

** dt' = (dt - B dx / c) / sqrt(1 - B^2)
** dx' = (dx - B c dt) / sqrt(1 - B^2)
** dy' = dy
** dz' = dz

Where

** B = v / c

You will find the following is true through simple algebra.

c^2 dt'^2 - dx'^2 - dy'^2 - dz'^2 =
c^2 dt^2 - dx^2 - dy^2 - dz^2 == ds^2

Thank you very much for explanation.

.