- #1
Higgsono
- 93
- 4
In SR why is the following length-interval invariant
(1) $$ 0 = (cdt)^{2}-dx^{2}$$
While,
(2) $$ 0 = (cdt)^{2}+dx^{2} $$
is not invariant?
The first expressions (1) measures the coordinates of a wavefront propagating away from the observer with the speed och light, and since c is a constant, this expression must be zero in all reference frames moving with constant velocity relative to it.
But why not use expression (2) as a way to measure distans?
(1) $$ 0 = (cdt)^{2}-dx^{2}$$
While,
(2) $$ 0 = (cdt)^{2}+dx^{2} $$
is not invariant?
The first expressions (1) measures the coordinates of a wavefront propagating away from the observer with the speed och light, and since c is a constant, this expression must be zero in all reference frames moving with constant velocity relative to it.
But why not use expression (2) as a way to measure distans?