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Pretty coincidental that time happens to be like the three spatial dimensions.. or is it?

Time is one dimensional with past and future, similar to left and right, up and down, back and forward of the other dimensions.

jerullibo
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Time is fundamentally different from the spatial dimensions in that you can only move forward, not backward. Mathematically in relativity this is expressed as a sign difference. The total spacetime distance $d$ between two nearby points is given by:

$$ d^2 = -\Delta t^2 + \Delta x^2 + \Delta y^2 + \Delta z^2 $$

Which is a version of the Pythagorean Theorem but where time intervals are opposite sign from space intervals.

RC_23
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    It is correct to say the signature of the $dt$ term is different, but it is not correct to say the difference is because you can can only move forward in time and not backwards. Both special and general relativity are time symmetric and neither have any concept of a flow of time in the forward direction. This seems to be an artefact of human consciousness. – John Rennie Oct 14 '23 at 07:35
  • I thought the hyperbolic nature of the metric implies this. Inside a black hole the signature changes from (–,+,+,+) to (+,–,+,+), and so the $r$ coordinate becomes "one way" and the $t$ becomes "two way." – RC_23 Oct 14 '23 at 15:04
  • The signature change is an artefact of the coordinates. Use Kruskal-Szekeres coordinates and there is no signature change. – John Rennie Oct 14 '23 at 15:13