Minkowski spacetime

Minkowski spacetime is the formal name for the combination of euclidean space and time into a four-dimensional manifold, for which the Spacetime interval $(Δ 𝑠) 2$ is an invariant metric.

In the interactive demonstration above, only one dimension of space, the $𝑥$ -axis, is considered. The red hyperbola represents the line of all events of the same $(Δ 𝑠) 2$ (taken with the origin). Therefore, it represents the set of possible co-ordinates that could be assigned in other inertial frames in standard configuration.

Subdivision

Since $(Δ 𝑠) 2$ is invariant for all inertial frames, it can be used to subdivide all of spacetime in relation to one event (taken as the origin). These regions are as follows:

If $(\Delta s)^2 < 0$ ¹, i.e. $(c \Delta t)^2 > (\Delta r)^2$ , the event is time-like separated from the origin. This means
- In all reference frames the events have the same order and never occur simultaneously, i.e. they may be causally related.
- There exists a reference frame where the events occur in the same place.
If $(\Delta s)^2 > 0$ ¹, i.e. $(\Delta r)^2 > (c \Delta t)^2$ , the event is space-like separated from the origin. This means
- In all reference frames the events have spacial separation i.e. they may be causally related.
- There exists a reference frame where the events occur simultaneously (see Relativity of simultaneity).
If $(\Delta s)^2 = 0$ , i.e. $(\Delta r)^2 = (c \Delta t)^2$ , the event is light-like separated. This means
- It is possible a photon to travel in a straight line between the events
- No object with mass can be present at both events.

#state/tidy | #SemBr | #lang/en

The $<$ and $>$ are reversed when the negative space convention is used (as is the case for PHYS1002). See the footnote in Spacetime interval for more discussion of convention. ↩ ↩²

Minkowski spacetime

Subdivision

Footnotes