- #1

cianfa72

- 1,959

- 216

- TL;DR Summary
- On the physical meaning of Minkowski's spacetime model from the point of view of clocks and rulers

Hi, I was thinking about the following.

Suppose we have a geometric mathematical model of spacetime such that there exists a global map ##(t,x_1,x_2,x_3)## in which the metric tensor is in the form $$ds^2 = c^2dt^2 - (dx_1)^2 + (dx_2)^2 + (dx_3)^2$$ i.e. the metric is in Minkowski form ##(+,-,-,-)##.

What does it mean from a physical experimental point of view ? I believe the following is true:

We can single out congruences of clocks (i.e. a families of clocks each filling the spacetime such that their worldlines do not cross) such that:

Suppose we have a geometric mathematical model of spacetime such that there exists a global map ##(t,x_1,x_2,x_3)## in which the metric tensor is in the form $$ds^2 = c^2dt^2 - (dx_1)^2 + (dx_2)^2 + (dx_3)^2$$ i.e. the metric is in Minkowski form ##(+,-,-,-)##.

What does it mean from a physical experimental point of view ? I believe the following is true:

We can single out congruences of clocks (i.e. a families of clocks each filling the spacetime such that their worldlines do not cross) such that:

- for each congruence of such clocks we can synchronize them, adjust their rates and assign spatial labels to each of them in a way such that light propagation process happens to be isotropic and occurs with the same fixed invariant speed ##c## (note that such light propagation properties are time invariant i.e. do not change in time).

Last edited: