Probably best to start with the globally rigid conformal de Sitter group i.e. 16 parameters including / =/= 0. There is no gravity, i.e. no dynamical curvature until you localize at least its T4 subgroup.
The 4 tetrads e^I and the 6 spin-connections w^I,^J formally live on a non-dynamical Minkowski space-time (at least when / = 0).
Geometrodynamic field (e^I, w^I^J) is on equal ontological par with U1xSU2 & SU3 forces.
From: Paul Zielinski
To: Jack Sarfatti
Sent: Wed, July 6, 2011 2:45:56 PM
Subject: Re: de Broglie waves as the generator of spacetime
Regarding (5), if you start with Minkowski spacetime as an axiom, then how can you end up with emergent curved spacetime geometry and no background?
Don't you mean that you start with de Sitter space in the complete absence of gravitating matter?
Or are you taking about SR kinematics?
I don't understand either version.
Look I think you are confused over the difference between mathematics and theoretical physics.
In pure math you can do anything you like.
Quantum theory (OQT) used pure math with additional constraints linking symbols to operational procedures.
In particular OQT assumes only Hermitian operators with real eigenvalues and orthogonal eigenfunctions. These eigenfunctions correspond to Bohr's "total experimental arrangement" of detectors at the classical level.
A unitary change of basis is an actual change in the configuration and settings of the detectors. It leaves inner products invariant and it requires similarity transformations of the operators.
A non-orthogonal set of eigenfunctions will correspond to some new physical conditions e.g. laser beams, phase transitions with new order parameters etc.
Henry Stapp may want to say this is new physics beyond OQT?
The observables need not be Hermitian, if the Hamiltonian is not Hermitian then it generates a non-unitary time evolution with imaginary energy part i.e., dissipation & pumping - open not closed systems. decaying states, and growing states & dissipative meta-stable structures - far from thermal equilibrium etc.
We have seen in the density matrix formalism for an entangled system the use of a non-orthogonal basis allows entanglement signaling - there must be a physical reason why the non-orthogonal basis MUST be used. It's not an abstract formal whim the way Zielinski believes.
From: Paul Zielinski <
To: Jack Sarfatti <
Sent: Wed, July 6, 2011 3:22:55 PM
Subject: Re: OK I think I see where Zielinski makes his false premise on physical meaning of base eigenvectors in quantum theory
Change to:
"My point is that the physical motivation for the choice of non-orthogonal state vectors to represent the physical states of a QM system does not legitimize the
use of non-orthogonal bases for the direct computation of observable quantities from the associated Hilbert space operators."
On 7/6/2011 3:19 PM, Paul Zielinski wrote:
My point is that the motivation for the choice of state vector to represent the physical
state of a QM system does not legitimize the use of a non-orthogonal basis for the direct computation of observable quantities from the associated Hilbert space operators.