Fra
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I'm curious if anyone has and physical intuition that would lead to non commutative geometry?
I mean on one hand we have NCG as a branch of math, which explores what mathematics you get if you try to replace som commutativity requirements in normal geometry etc. This may or many not interest people for reasons not relevant to physicists.
OTOH, there are some vague arguments and expectations of QG where it seems clear that spacetime as classical background needs to be replaced.
There are also the usual analogies with extending symplectic phase-space geometry to non-commuting things when we quantize. But there at least superficially one can argue that we understand why the coordinates doens't commute. It takes a definite history of q to infer p, when defined as the conjugate momenta in QM. Thus, q and p are not independent like they are in classical physics.
Is there someone that has published anything that similarly provides some rational arguments for an explicit reconstruction for spacetime that does match how it's likely to actually by inferred? I mean spacetime is usually just and INDEX of events. What is the origin of this INDEX?
To just play the what if game and consider "what of coordinate functions" doesnt' commute doesn't provide any predictive value, unless one complements it with some ideas of HOW it doesn't commute? IE. exactly how is the index constructed, and how does this explain non-commutativity?
Maybe the starting point is better to question how any index emerges. I mean, how come suddently you use several independent indexes in n-tuples to index an event? AS long as we are dealing only with distinguishable state, why not just label all distinguishable permutations of the indexes.
So from a basic starting point of distinguishable evetnts, how does sets of grouped indexes emerge from a non-grouped starting point? Is it somehow more favourable for an encoding structures to decompose an index into n-tuples? Does it allow storing more information in the same memory? It seems to me that this must have to do with ordering and representation of information, and how that's implemented in encodings in matter?
I expect that a NCG-motivation for a physicist would be found somewhere down this hole? I feel frustration when I don't find this.
Paolo commented on a similar question in https://www.physicsforums.com/showthread.php?p=2715420 which gave much great comments, but there was not much motivation in the form I seek.
/Fredrik
I mean on one hand we have NCG as a branch of math, which explores what mathematics you get if you try to replace som commutativity requirements in normal geometry etc. This may or many not interest people for reasons not relevant to physicists.
OTOH, there are some vague arguments and expectations of QG where it seems clear that spacetime as classical background needs to be replaced.
There are also the usual analogies with extending symplectic phase-space geometry to non-commuting things when we quantize. But there at least superficially one can argue that we understand why the coordinates doens't commute. It takes a definite history of q to infer p, when defined as the conjugate momenta in QM. Thus, q and p are not independent like they are in classical physics.
Is there someone that has published anything that similarly provides some rational arguments for an explicit reconstruction for spacetime that does match how it's likely to actually by inferred? I mean spacetime is usually just and INDEX of events. What is the origin of this INDEX?
To just play the what if game and consider "what of coordinate functions" doesnt' commute doesn't provide any predictive value, unless one complements it with some ideas of HOW it doesn't commute? IE. exactly how is the index constructed, and how does this explain non-commutativity?
Maybe the starting point is better to question how any index emerges. I mean, how come suddently you use several independent indexes in n-tuples to index an event? AS long as we are dealing only with distinguishable state, why not just label all distinguishable permutations of the indexes.
So from a basic starting point of distinguishable evetnts, how does sets of grouped indexes emerge from a non-grouped starting point? Is it somehow more favourable for an encoding structures to decompose an index into n-tuples? Does it allow storing more information in the same memory? It seems to me that this must have to do with ordering and representation of information, and how that's implemented in encodings in matter?
I expect that a NCG-motivation for a physicist would be found somewhere down this hole? I feel frustration when I don't find this.
Paolo commented on a similar question in https://www.physicsforums.com/showthread.php?p=2715420 which gave much great comments, but there was not much motivation in the form I seek.
/Fredrik