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In what fields can the consideration of four perpendicular vectors be useful to making theories and models in physics? Is the concept of four dimension restricted to spatial dimensions?

user289661
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  • Our concept of spatial dimensions is still restricted to three dimension. In some of our theories we treat time like it's a dimension, which works for some things and doesn't for others. – CuriousOne Feb 25 '16 at 03:58

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It's already in use; Minkowski introduced the four dimensional geometry of spacetime shortly after Einstein's first papers on Special Relativity. Three spacial and one temporal dimension; the metric is not Euclidean, but instead is Lorentzian, with signature +++- or ---+, depending on choice of convention.

Higher dimensional spaces occur naturally I mechanical systems, which have one dimension per degree of freedom; then the state of the system is completely specified by a single point and it's velocity in this space.

And quantum mehanics has a superabundance of situations demanding higher dimensional spaces, including ones with infinite dimensions.

Peter Diehr
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