Spacetime Diagrams Why spacetime To fully describe the
Spacetime Diagrams
Why spacetime. To fully describe the occurrence of an event we need to describe where and when it happened. This means we need to provide three dimensions of spacial coordinates and a time that the event occurs. For example: North 53°, West 2°, 38 m above sea level at 7. 30 a. m. This means we have 4 numbers that uniquely locate an event in space-time. Spacetime is therefore a four dimensional space: three space axes and one time axis.
An object’s position in Spacetime can be represented on a Minkowski diagrams are two dimensional and consist of: • One is the object’s spacial coordinates plotted on the horizontal spacial (x) axis and • The other is the time multiplied by the speed of light, ct, plotted on the vertical time (y) axis. • The origin represents the present.
Any single event is a point on the diagram. time Object travelling at the speed of light ct 45° o x Note: x and ct axes must be scaled the same for 45 o to be speed of light travel. space An object travelling at the speed of light between two points is a 45° line. (As the speed of light is the maximum possible speed no line on this diagram can be less than 45°. ) An object at rest is a vertical line. Constant velocity would have a constant gradient more than 45°. Accelerating object is a curved line. A line on these diagrams is called the “world line” of a motion and is the succession of events corresponding to the motion of the object.
Stationary object. time o o Slow moving object constant speed. space time Fast moving object constant speed. Object at speed of light. time o o space Object faster than the speed of light!! time This object/event does not exist. o space
Accelerating objects An object that is accelerating / decelerating will have a curved line on a Minkowski diagram. time Accelerating object 0 space decelerating object 0 space Note: any part of an accelerating line cannot have a gradient greater than 1, since this implies v > c
The world line of an object in Circular motion. • e. g. the orbit of the Earth in space is approximately a circle, a threedimensional (closed) curve in space: the Earth returns every year to the same point in space. However, it arrives there at a different (later) time. The world line of the Earth is helical in space-time (a curve in a four-dimensional space) and does not return to the same point. See use of geodesics In general relativity.
Two world lines that start out separately and then intersect, signify a collision or "encounter. “ Two world lines starting at the same point in space-time, each following its own path afterwards, may represent the decay of a particle into two others or the emission of one particle by another.
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