Spacetime interval via time and distance

The spacetime interval is a combination of distance and time that is invariant under Lorentz tranformations. It has the property of being invariant in the sense that it has the same value for all observers in any inertial reference frame.

Notation:

1. \(c\) (c) is speed_of_light.

Notes:

1. If \(\Delta s**2 > 0\), the spacetime interval is said to be timelike. Events with a timelike separation can be causally connected, i.e. one can find an inertial reference frame in which both events happen at the same place at different times.

2. If \(\Delta s**2 = 0\), the spacetime interval is said to be lightlike. Events with a lightlike separation are exactly far enough from each other that light could be present at both events, and they are causally connected.

3. If \(\Delta s**2 < 0\), the spacetime interval is said to be spacelike. Events with a spacelike separation are causally disconnected, i.e. one can find an inertial reference frame in which both events happen at the same time in different positions.

Conditions:

1. The spacetime in which the two events occur is flat (special relativity case).

Links:

1. Wikipedia.

spacetime_interval

spacetime_interval between the two events.

Symbol:

s

Latex:

\(s\)

Dimension:

length

temporal_distance

time separation between the two events.

Symbol:

t

Latex:

\(t\)

Dimension:

time

spatial_distance

euclidean_distance between the two events.

Symbol:

d

Latex:

\(d\)

Dimension:

length

law

s^2 = (c * t)^2 - d^2

Latex:

\[s^{2} = \left(c t\right)^{2} - d^{2}\]