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Should not all four dimensions, therefore, be mathematically interchangeable? Assuming that we are 3-dimensional bodies travelling through 4-dimensional space, perceiving 'slices' of the fourth dimension as instants or moments in time, surely there should be no reason to favour one particular dimension (the one we perceive as time).

Why, then, in the equations describing general relativity, can't duration (t) be interchanged with spatial distance? Why is there no mathematical framework that allows (as a simplistic example) the multiplication of duration and distance to produce area (dt ⇔ dd)?

I realise that the quantum mechanics describes time as fundamentally probabilistic, in which case this logic would not apply. But why does this logic not apply to the equations of GR?

If, indeed, time and space are separate structures (after all, the law of entropy would imply that time is asymmetrical, placing it at contrast with the homogeneity of space), is there any mathematical proof that this is the case?