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Hi,

The minkowski metric, which is relativistically invariant (meaning that changing the orientations of objects embedded within it in a relativistic way leave the metric unchanged), has a special part of it that can either be written (ict)^2 or -(ct)^2 this is part of the geometry that describes how the intervals of time are left unchanged by a relativistic transformation (in this space). The paradox you state is interesting, but I don't think it's correct. Time is a dimension, just like the other dimensions, except if you consider the psychological perception of time. The psychological perception of time does present a paradox. This paradox is that how can something that describes a distance, like the minkowski metric, not evolve over time. Time itself must evolve over time. To see why this is true, consider the function t^4 = t^2 + 3 (t^2 = 3), which is a curve for the sake of argument let's say, embedded in minkowski space. In order to generate the full curve, you must change the time parameter. This itself requires time! Now that's the paradox. Philosophers have stated this in various ways. Augustus invoked the presence of God as an argument for why time is so mysterious. Einstein thought the passage of time is psychological and we sit in a block of space-time, but if we do, then why do we see the seasons change like they do? Why is every season different from the next in an unpredictable way? The answer to to the unpredictability is entropy, but that still doesn't get at the root of what time actually is. At least, afaik. I am still learning from the greats, with Roger Penrose's book and Jeffrey Weeks' book.


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