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English-Spacetime-Geometry Dictionary

Highly Recommended for Spacetime-Travel
It is unfortunate that Spacetime concepts often defy our physical intuition. (That's what you get when you spend most of your life within a narrow pencil of worldlines.)

However, it is quite remarkable that many of these Spacetime concepts have precise analogues in geometry. Thus, rather than reason with our unrefined physical intuition, it has been quite useful to reason with our better-refined geometrical intuition. Thus, it is often useful to think in geometrical terms when discussing concepts in relativity.

For the sake of the reader, we distinguish "public" universally-agreed-upon notions from "private" observer-dependent notions.

I highly recommend that you refer to this page often.

ENGLISH SPACETIME CONCEPT GEOMETRICAL CONCEPT
History of the Universe Spacetime certain 4-dimensional space (Lorentz manifold)
Finger-snap Event point
History of an Observer Worldline Timelike curve
History of an Inertial Observer Freely-falling Worldline Timelike geodesic curve (a curve that is as straight as it can be)
History of a Quick flash of light Light-Ray Lightlike geodesic curve
The elapsed-time you measure between two events. Private-Time elapsed between two events. Do a radar measurement. One-half the difference of your clock-time.
The separation-distance you measure between two events. Private-Distance between two events. Do a radar measurement. One-half the sum your clock-times. (i.e., the average of your clock-times>
Time read off a Wristwatch Proper-Time along Worldline Spacetime-length along a timelike curve
Your speed and direction of travel (through spacetime) Velocity Vector Unit timelike tangent-vector
How fast the other guy seems to be moving Relative-velocity of one observer with repsect to another observer Spacetime-Angle between two lines. Decompose his velocity-vector into a spatial-part and a temporal-part. Divide the spatial-part by the temporal-part.
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