Generally covariant geometro-stochastic quantum gravity

Prugovečki, Eduard

doi:10.1007/bf02730756

Cited by 10 publications

(6 citation statements)

References 47 publications

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“…In other words, the propagation of the quantum frame field ~b in (18) from the initial-data hyperplane ~o is then deterministically governed by the Klein-Gordon equation. Therefore the same is true of the propagation of the quantum frames {~.f} defined in (20), and hence by (17) also of the propagation of any other quantum state. The same conclusion follows from (25) or (28), since for flat M parallel transport is path independent.…”

Section: Apx F=exp[-(1/2)(flf)+(~+)(xf)]wo;~ F~fxmentioning

confidence: 78%

“…As we shall demonstrate in this paper, by following a program of gradual extrapolation from nonrelativistic quantum mechanics rooted in this principle, one can arrive at a purely quantum notion of spacetime, which in its ultimate form (17) incorporates quantum gravity, and is mathematically provided by superfiber bundles over supermanifolds. These supermanifolds incorporate Lorentzian manifolds in their structure, but additional degrees of freedom of a quantum origin are also unavoidably present.…”

Section: Nonrelativistic Versus Special Relativistic Quantum Localitymentioning

confidence: 99%

“…The application (12)(13)(14)(15)(16)(17) of this principle of geometric locality to the stochastic quantum mechanics program of Ref. 11 has resulted in a geometro-stochastic framework based on a geometrically local notion of quantum states that are described in terms of wave functions over TxM X Vx c T~M (~ T'M, where TxM, T'M, and Vx denote, respectively, the tangent space, the cotangent space, and the 4-velocity hyperboloid above a given point x e M. From the point of view of the framework for quantum gravity discussed in Sec.…”

Section: Geometric Versus Topological Locality In Curved Spacetimementioning

confidence: 99%

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Geometro-stochastic locality in quantum spacetime and quantum diffusions

Prugovečki

1991

Found Phys

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The issue of the intrinsic nonlocality of quantum mechanics raised by J. S. Bell is examined from the point of view of the recently developed method of geometrostochastic quantization and its applications to general relativistic quantum theory. This analysis reveals that a distinction should be made between the topological concept of locality used in formulating relativistic causality and a type of geometric locality based on the concept of fiber bundle, which can be used in extending the strong equivalence principle to the quantum domain. Both play an essential role in formulating a notion of geometro-stochastic propagation based on quantum diffusions, which throws new light on the EPR paradox, on the origin of the arrow of time, and on other fundamental issues in quantum cosmology and the theory of measurement.

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Section: Apx F=exp[-(1/2)(flf)+(~+)(xf)]wo;~ F~fxmentioning

confidence: 78%

Section: Nonrelativistic Versus Special Relativistic Quantum Localitymentioning

confidence: 99%

Section: Geometric Versus Topological Locality In Curved Spacetimementioning

confidence: 99%

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Geometro-stochastic locality in quantum spacetime and quantum diffusions

Prugovečki

1991

Found Phys

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“…The invariance under diffeomorphisms of the pre-geometry for General Relativity has been discussed in [176][177][178][179].…”

Section: Discussionmentioning

confidence: 99%

Semiclassical Length Measure from a Quantum-Gravity Wave Function

Lecian

2017

Technologies

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Abstract:The definition of a length operator in quantum cosmology is usually influenced by a quantum theory for gravity considered. The semiclassical limit at the Planck age must meet the requirements implied in present observations. The features of a semiclassical wave-functional state are investigated, for which the modern measure(ment)s is consistent. The results of a length measurement at present times are compared with the same measurement operation at cosmological times. By this measure, it is possible to discriminate, within the same Planck-length expansion, the corrections to a Minkowski flat space possibly due to classicalization of quantum phenomena at the Planck time and those due to possible quantum-gravitational manifestations of present times. This analysis and the comparison with the previous literature can be framed as a test for the verification of the time at which anomalies at present related to the gravitational field, and, in particular, whether they are ascribed to the classicalization epoch. Indeed, it allows to discriminate not only within the possible quantum features of the quasi (Minkowski) flat spacetime, but also from (possibly Lorentz violating) phenomena detectable at high-energy astrophysical scales. The results of two different (coordinate) length measures have been compared both at cosmological time and as a perturbation element on flat Minkowski spacetime. The differences for the components of the corresponding classical(ized) metric tensor have been analyzed at different orders of expansions. The results of the expectation values of a length operator in the universe at the Planck time must be comparable with the same length measurements at present times, as far as the metric tensor is concerned. The comparison of the results of (straight) length measures in two different directions, in particular, can encode the pertinent information about the parameters defining the semiclassical wavefunctional for (semiclassicalized) gravitational field.

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“…71 and in Chapter 11 of Ref. 15) to quantum cosmology leads to the introduction of a "universal cosmic wave packet" that represents a conterpart of the "wave function of the universe ''(81's2) which describes all matter and gauge fields in existence.…”

Section: Elementary Particle and Cosmological Aspects Of Quantum Geommentioning

confidence: 99%

Realism, positivism, instrumentalism, and quantum geometry

Prugovečki

1992

Found Phys

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75he roles of classical realism, logical positivism, and pragmatic" instrumentatism in the shaping of fundamental ideas in quantum physics are examined in the light of some recent historical and sociological studies of the factors that influenced their development. It is shown that those studies indicate that the conventionalistic form of instrumentalism that has dominated all the major post-World War H developments in quantum physics is not an outgrowth of the Copenhagen school, and that despite the "schism" in twentieth century physics created by the Bohr-Einstein "disagreements" on foundational issues in quantum theory, both their philosophical stands were very much opposed to those of conventionalistic instrumentalism. Quotations .from the writings of Dirac, Heisenberg, Popper, Russell, and other influential thinkers, are provided, illustrating the fact that, despite the various divergencies in their opinions, they all either opposed the instrumentalist concept of "truth'" in general, or its conventionalistic version in post-World War H quantum physics in particular. The basic epistemic ideas of a quantum geometry approach to quantum physies ate reviewed and discussed from the point of view of a quantum realism that seeks to reconcile Bohr's "positivism" with Einstein's "reatism" by emphasizing the existence of an underlying quantum reality, in which the), both believed. This quantum geometry framework seeks to introduce geometro-stochastic concepts that are specifically designed for the systematic description of that underlying quantum reality, by devetop#~g the conceptual and mathematical tools that are most appropriate for such a use.

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Generally covariant geometro-stochastic quantum gravity

Cited by 10 publications

References 47 publications

Geometro-stochastic locality in quantum spacetime and quantum diffusions

Geometro-stochastic locality in quantum spacetime and quantum diffusions

Semiclassical Length Measure from a Quantum-Gravity Wave Function

Realism, positivism, instrumentalism, and quantum geometry

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