Why is motion in spacetime impossible? It has to do with the definitions of
space and time and the equation of velocity v = dx/dt. What the
equation is saying is that, if an object moves over any distance x, there is
an elapsed time t. Since time is defined in physics as a parameter for
denoting change (evolution), changing position from one point in a time
dimension (time axis) to another is self-referential. Why? Because the
equation for velocity along the time axis would have to be v =
dt/dt which is meaningless, of course. It is logically impossible for
the t coordinate of an object to change in spacetime. Et
voil´! It's that simple. No time travel, no motion in spacetime, no
spacetime and no time dimension.
I've always been unconfortable with the notion of time being considered the
fourth dimension. You just don't have the freedom of motion as with the
other three spatial dimentions and that wierd things start happening if you
reverse time or otherwise can affect the past. The fourth dimention as
another spatial dimention I can live with.
But I'm not about to go calling Richard Feynman a crackpot though!
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