B.G. Sidharth: LAW WITHOUT LAW (2007)
It must also be mentioned that spin half itself is relational and refers to three
dimensions, to a spin network infact [102, 42]. That is, spin half is not mean-
ingful in a single particle Universe.
While a relation like (24) above has been in use recently, in non commutative
models, we would like to stress that it has been overlooked that the origin of
this non commutativity lies in the original Dirac coordinates....
In the above considerations, we started with the Dirac equation and deduced
the underlying non commutative geometry of spacetime. Interestingly, start-
ing with Snyder’s non commutative geometry, based solely on Lorentz in-
variance and a minimum spacetime length, which we have taken to be the
Compton scale, (23), it is possible to deduce the relations (27), (26) and the
Dirac equation itself as we will see later.
We have thus established the correspondence between considerations start-
ing from the Dirac theory of the electron and Snyder’s (and subsequent)
approaches based on a minimum spacetime interval and Lorentz covariance.
It can be argued from an alternative point of view that Special Relativity
operates outside the Compton wavelength as we saw earlier.
We started with the Kerr-Newman black hole. Infact the derivation of the
Kerr-Newman black hole itself begins with a Quantum Mechanical spin yield-
ing complex shift, which Newman has found inexplicable even after several
decades [103, 104]
the question has now been answered. Complexified spacetime is symptomatic of fuzzy spacetime and a non commutative geometry and Quantum Mechanical spin and relativity
To conclude: the main message I wished to convey is that quantum gravity will require Quantum Spacetime. But also that Quantum Spacetime in turn requires quantum observers. This is of course true for quantum phase space as well. There we became (more or less) used to deal with the contradictions of the quantum/classical interaction. We learned how to deal with noncommuting observables for example.
No comments:
Post a Comment