Tuesday, April 26, 2011

Objection against zero energy ontology and quantum classical correspondence

The motivation for requiring geometry and topology of space-time as correlates for quantum states is the belief that quantum measurement theory requires the representability of the outcome of quantum measurement in terms of classical physics -and if one believes in geometrization- one ends up with generalization of Einstein's vision.

There is however a counter argument against this view and second one against zero energy ontology in which one assigns eigenstates of four-momentum with causal diamonds (CDs).

  1. One can argue that momentum eigenstates for which particle regarded as a topological inhomogenuity of space-time surface, which is non-localized cannot allow a space-time correlate.

  2. Even worse, CDs have finite size so that strict four-momentum eigenstates strictly are not possible.

On the other hand, the paradoxical fact is that we are able to perceive momentum eigenstates and they look localized to us. This cannot be understood in the framework of standard Poincare symmetry.

The resolution of the objections and of the apparent paradox could rely on conformal symmetry assignable to light-like 3-surfaces implying a generalization of Poincare symmetry and other symmetries with their Kac-Moody variants for which symmetry transformations become local.

  1. Poincare group is replaced by its Kac-Moody variant so that all non-constant translations act as gauge symmetries. Translations which are constant in the interior of CD and trivial at the boundaries of CDs are physically equivalent with constant translations. Hence the latter objection can be circumvented.

  2. The same argument allows also a localization of momentum eigenstates at the boundaries of CD. In the interior the state is non-local. Classically the momentum eigenstate assigned with the partonic 2-surface is characterized by its 4-D tangent space data coding for momentum classically. The modified Dirac equation and Kähhler action indeed contain and additional term representing coupling to four-momenta of particles. Formally this corresponds only to a gauge transform linear in momentum but Kahler gauge potential has U(1) gauge symmetry only as a spin glass like degenary, not as a gauge symmetry so that space-time surface depends on momenta.

  3. Conscious observer corresponds in TGD inspired theory of consciousness to CD and the sensory data of the observer come from partonic 2-surfaces at the boundaries of CD and its sub-CDs. This implies classicality of sensory experience and momentum eigenstates look classical for conscious perceiver.

The usual argument resolving the paradox is based on the notion of wave packet and also this notion could be involved. The notion of finite measurement resolution is key notion of TGD and it is quite possible that one can require the localization of momentum eigenstates at the boundaries of CDs only modulo finite measurement resolution for the position of the partonic 2-surfaces.

For background see the chapter Construction of Quantum Theory: M-matrix of "Towards M-matrix".

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