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Worldli nes: History as Geometry

If a ``point" in Minkowski space is an EVENT, what is a ``line"? Well, it is a continuous sequence of events, which in our personal life we might call a history. In Physics, however, we are usually focussed on the history of an object's motion through space, which in the is known (somewhat pretentiously, perhaps) as a WORLDLINE. gif

  
Figure: An event A can be located in spacetime using either of two coordinate systems O (ct, x) and O' (ct', x') with a common origin at (0,0) that differ from each other by a ``boost" (Lorentz transformation) corresponding to O' moving at u with respect to O along the positive x axis. If ct and x are plotted on the same scale (as they always are), then the WORLDLINE of a beam of light moving along the x axis after starting from the origin will be a straight line making the same angle to both axes. Unlike the rotation shown in Fig. gif, however, the Lorentz transformation is not orthogonal (does not preserve right angles) -- so that this graphical construction cannot be used in quite the same simple intuitive way.



Jess Brewer
Fri Aug 16 17:01:55 PDT 1996