![]() ![]() Thus, for example, the path of a planet orbiting a star is the projection of a geodesic of the curved four-dimensional (4-D) spacetime geometry around the star onto three-dimensional (3-D) space. In physics, spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional. Using the same language we can define a notion of distance along a curve (a 'metric') and with a given metric we can distinguish particular curves called 'geodesics' which generalize the notion of a straight line. In general relativity, gravity can be regarded as not a force but a consequence of a curved spacetime geometry where the source of curvature is the stress–energy tensor (representing matter, for instance). All of this language is imported from the mathematical field of geometry, and specifically the geometry of differential manifolds. Also remember that the o 1 spacetime is infinite in extent so the conformal space-time diagram can go on far beyond our past lightcone, as shown above. In other words, a freely moving or falling particle always moves along a geodesic. Note that a constant SouthEast course is a straight line on the Mercator chart which is analogous to having straight line past lightcones on the conformal space-time diagram. And it is the attempt of things to go along straight lines in this curved space-time which makes them move the way they do. According to him, space and timewhich must be put together as space-timeare near heavy masses. The analog of a straight line in space is for space-time a motion at uniform velocity in a constant direction. Importantly, the world line of a particle free from all external, non-gravitational forces is a particular type of geodesic. Einstein had a different interpretation of the law of gravitation. This may seem like playing with words, but actually if the geometry is non-Euclidean then there is no simple definition of a straight line. So for example a thrown object actually follows a straight line - it just looks like a parabola to us. In general relativity, a geodesic generalizes the notion of a "straight line" to curved spacetime. Objects, from photons to planets, moving in general relativity, obey the geodesic equation, so a curved line can be a 'straight line', that is, if you define a straight line as the shortest distance between two points. Basically it's that we define a straight line as the trajectory followed by a freely moving particle.
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