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Spacetime diagrams can show the geometry underlying phenomena like time dilation and length contraction without mathematical equations. The history of an object's location through time traces out a line or curve on a spacetime diagram, referred to as the object's world line .
Time dilation is the difference in elapsed time as measured by two clocks, either because of a relative velocity between them (special relativity), or a difference in gravitational potential between their locations (general relativity). When unspecified, "time dilation" usually refers to the effect due to velocity.
A clock that is stationary with respect to the observer has a world line that is vertical, and the elapsed time measured by the observer is the same as the proper time. For a clock traveling at 0.3 c , the elapsed time measured by the observer is 5.24 meters ( 1.75 × 10 −8 s ), while for a clock traveling at 0.7 c , the elapsed time measured ...
Equation is a fundamental and much-quoted differential equation for the relation between proper time and coordinate time, i.e. for time dilation. A derivation, starting from the Schwarzschild metric, with further reference sources, is given in Time dilation § Combined effect of velocity and gravitational time dilation.
In the Schwarzschild solution, it is assumed that the larger mass M is stationary and it alone determines the gravitational field (i.e., the geometry of space-time) and, hence, the lesser mass m follows a geodesic path through that fixed space-time. This is a reasonable approximation for photons and the orbit of Mercury, which is roughly 6 ...
The proper time interval between two events on a world line is the change in proper time, which is independent of coordinates, and is a Lorentz scalar. [1] The interval is the quantity of interest, since proper time itself is fixed only up to an arbitrary additive constant, namely the setting of the clock at some event along the world line.
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The purple (dashed) line shows the path of a photon emitted from the surface of a collapsing star. The green (dot-dash) line shows the path of another photon shining at the singularity. In flat spacetime, the future light cone of an event is the boundary of its causal future and its past light cone is the boundary of its causal past .
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