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x, y, z should not commute if t does not
October 22, 2008
by Halliday,
1 year 4 weeks ago
Comment: 32501
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The primary problem I have with the non-commutativity relation expressed in the article is it's lack of general invariance (transform x, y, z, and t in any general way and you get something that doesn't match). What I would expect would be something like
xμ xν - xν xμ = xσ Cσμν
where Cσμν = -Cσνμ is some appropriate tensor field (with appropriate characteristics with regards to complex conjugation).
This still indicates that determining the location and time simultaneously is impossible (due to the non-commutativity, for non-vanishing C), though it also means that one cannot determine all three components of position either. This seems more realistic to me.
David
P.S. Thankfully, we can now use <sup> and <sub>!!!! :-)