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Discuss the three models of spacetime. Aristotelian spacetime. Galilean spacetime. Einstein’s spacetime. “ The test of a first-rate intelligence is the ability to hold two opposing ideas in mind at the same time and still retain the ability to function. ” —F. Scott Fitzgerald.
In three dimensions, the distance from (x;y;z) to (x+ x;y+ y;z+ z) is given by s2 = x2 + y2 + z2. In spacetime, it turns out to be extremely useful to regard s 2= 2c 2 t + x + y + 2z as expressing an invariant notion of \distance squared" between two events. Students usually want to know \Why does the c2 t2 have a minus sign?" The best answer I ...
a geometric spacetime approach, where the di erences between Newtonian physics and relativity are encoded into the geometry of how space and time are modeled. I believe that understanding the di erences in the underlying geometries gives a
Minkowski space-time (or just Minkowski space) is a 4 dimensional pseudo-Euclidean space of event-vectors (t, x, y, z) specifying events at time t and spatial position at x, y, z as seen by an observer assumed to be at (0, 0, 0, 0). The space has an indefinite metric form depending on the velocity of light c:
Two ways spacetimes can differ: Different ways of specifying distances between points yield different types of spacetimes. Classical spacetimeshave separatespatial and temporal metrics: only one way to split time from space (spatial and temporal distances are absolute).
We can describe an event by a four numbers: E = (t, x, y, z). Just as there are vectors in 3-space which have a direction and a length, and are typified by the separations of neighboring points, there are 4-vectors in spacetime which are typfied by the separation of neighboring events: dx = (dt, dx, dy, dz).
The mathematics gives us an insight into how space and time are inextricably mixed and the most natural way to see this is in a representation of the world with four dimensions, three spatial and one temporal.
