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The most well-known class of spacetime diagrams are known as Minkowski diagrams, developed by Hermann Minkowski in 1908. Minkowski diagrams are two-dimensional graphs that depict events as happening in a universe consisting of one space dimension and one time dimension. Unlike a regular distance-time graph, the distance is displayed on the ...
The term that accounts for the failure of absolute simultaneity is the vx/c 2. A spacetime diagram showing the set of points regarded as simultaneous by a stationary observer (horizontal dotted line) and the set of points regarded as simultaneous by an observer moving at v = 0.25c (dashed line)
A spacetime diagram is typically drawn with only a single space and a single time coordinate. Fig. 2-1 presents a spacetime diagram illustrating the world lines (i.e. paths in spacetime) of two photons, A and B, originating from the same event and going in opposite directions. In addition, C illustrates the world line of a slower-than-light ...
Where Einstein referred to "an observer who takes the train as his reference body" or "an observer located at the origin of the coordinate system", this group of modern writers says, for example, "an observer is represented by a coordinate system in the four variables of space and time" [3] or "the observer in frame S finds that a certain event ...
The solution to the apparent paradox lies in the relativity of simultaneity: what one observer (e.g. with the garage) considers to be two simultaneous events may not in fact be simultaneous to another observer (e.g. with the ladder). When we say the ladder "fits" inside the garage, what we mean precisely is that, at some specific time, the ...
Two world lines that start out separately and then intersect, signify a collision or "encounter". Two world lines starting at the same event in spacetime, each following its own path afterwards, may represent e.g. the decay of a particle into two others or the emission of one particle by another.
Frame fields of a Lorentzian manifold always correspond to a family of ideal observers immersed in the given spacetime; the integral curves of the timelike unit vector field are the worldlines of these observers, and at each event along a given worldline, the three spacelike unit vector fields specify the spatial triad carried by the observer.
Consider how a static observer at R=0 might determine his distance to a ring riding observer at R = R 0. At event C he sends a radar pulse toward the ring, which strikes the world line of a ring-riding observer at A′ and then returns to the central observer at event C″. (See the right hand diagram in Fig. 7.) He then divides the elapsed ...