Worldline

This article is about the path an object traces through spacetime. For the branching-track sense used in secret space program accounts, see

Timeline branching

A worldline is the path a particle or object traces through spacetime — not a route through space alone, but the complete record of where it is at every moment of its existence. A stationary object still has a worldline: it moves through time while standing still in space. The idea was introduced by Hermann Minkowski in 1908 and is now the standard way of describing motion in special relativity and general relativity.

Minkowski's formulation

Minkowski presented the idea on 21 September 1908, in an address to the 80th Assembly of German Natural Scientists and Physicians at Cologne. His argument was that Albert Einstein's 1905 relativity paper had made separate notions of space and time untenable, and that physics should instead work in a single four-dimensional continuum in which each object is a curve.

The practical consequence is that questions about simultaneity, ageing and causality become questions about the shape of curves. Two observers who disagree about whether events were simultaneous are not disagreeing about facts; they are slicing the same four-dimensional structure at different angles.

Timelike, spacelike and null

A worldline is classified by how it sits relative to the light cone at each point:

timelike — the object travels slower than light. Every massive object's worldline is timelike, and its length is the proper time elapsed on a clock carried along it.
null (or lightlike) — the path of a photon, lying exactly on the light cone.
spacelike — a separation no signal can bridge. No object has a spacelike worldline.

This classification is what makes the twin paradox unmysterious: the travelling twin's worldline is a different curve between the same two events, and proper time along it is shorter.

Closed timelike curves

A worldline that returns to its own past is a closed timelike curve — an object that is its own ancestor in the causal order. Certain exact solutions of Einstein's field equations admit them, including the Gödel universe and the interiors of rotating black holes.

Stephen Hawking proposed in 1992 that quantum effects diverge in precisely the way needed to prevent such curves forming, a proposal he named the chronology protection conjecture and summarised as keeping the universe "safe for historians." The conjecture is unproven, and whether it holds is one of the open questions on which time travel proposals turn.

The secret space program usage

The word is also used, in a different and unrelated sense, in secret space program accounts: a "worldline" there means a branching track of experienced reality that a person can be moved between, rather than a curve in spacetime. That usage belongs to Timeline branching, which encompasses the Looking Glass device and the probability-stream claims of Dan Burisch and Bill Uhouse.

The two senses share a word and nothing else. Minkowski's worldline is a description of an object's history and carries no claim that history could have gone otherwise; the secret space program sense is exactly a claim that it could, and that the alternative branches are reachable. Nothing in relativity's use of the term supports the second reading, and no source in the branching literature derives its usage from Minkowski.

Open questions

References

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