Special relativity MOC

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 is an invariant metric.

In the interactive demonstration above, only one dimension of space, the -axis, is considered. The red hyperbola represents the line of all events of the same (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 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:

  1. If 1, i.e. , 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.
  2. If 1, i.e. , 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).
  3. If , i.e. , 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.

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Footnotes

  1. 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