It seems that the spatial dimensions are orthogonal: a particle can move along one axis without changing its position in relation to other two axes.
It seems that the temporal dimension is somewhat orthogonal:
- a particle can move along the time axis but not along the space axes by standing still
- if a particle is to move along space axes, it necessarily also moves along time axis
Is there something deep and meaningful in this seemingly incomplete orthogonality, or is it just a consequence of some theory (perhaps general relativity)?
If we take into account quantum mechanic, the above statements are not entirely correct. A particle cannot really be standing completely still (due to uncertainty principle). But does it matter?
Do we need to treat massive and massless particles separately in this deliberation?