A reproducibility principle is formulated and adopted as the guiding criterion for the acceptance of an experimental procedure as a simultaneous measurement of several observables. It is pointed out that this criterion can be applied to classical as well as quantum physics, and that it incorporates compatible as well as incompatible observables. The concept of fuzzy probability measure is presented as a possible mathematical tool for the description of statistical processes involving measurements of incompatible observables.

A notion of quantum space-time is introduced, physically defined as the totality of all flows of quantum test particles in free fall. In quantum space-time the classical notion of deterministic inertial frames is replaced by that of stochastic frames marked by extended particles. The same particles are used both as markers of quantum space-time points as well as natural clocks, each species of quantum test particle thus providing a standard for space-time measurements. In the considered flat-space case, the fluctuations in (...) coordinate values with respect to stochastic frames are described by coordinate probability amplitudes related to irreducible stochastic phase space representations of the Poincaré group. Lagrangian field theory on quantum space-time is formulated. The ensuing equations of motion for interacting fields contain no singularities in their nonlinear terms, and therefore can be handled by methods borrowed from classical nonlinear analysis. (shrink)

The geometro-stochastic quantization of a gauge theory based on the (4,1)-de Sitter group is presented. The theory contains an intrinsic elementary length parameter R of geometric origin taken to be of a size typical for hadron physics. Use is made of a soldered Hilbert bundle ℋ over curved spacetime carrying a phase space representation of SO(4, 1) with the Lorentz subgroup related to a vierbein formulation of gravitation. The typical fiber of ℋ is a resolution kernel Hilbert space ℋ $_{\bar (...) \eta }^{(\rho )} $ constructed in terms of generalized coherent states $\bar \eta $ ρ related to the principal series of unitary irreducible representations of SO(4, 1), namely de Sitter horospherical waves for spinless particles characterized by the parameter ρ. The framework is, finally, extended to a quantum field-theoretical formalism by using bundles with Fock space fibers constructed from ℋ $_{\bar \eta }^{(\rho )} $. (shrink)

It is shown that the time operatorQ 0 appearing in the realization of the RCCR's [Qμ,Pv]=−jhgμv, on Minkowski quantum spacetime is a self adjoint operator on Hilbert space of square integrable functions over Σ m =σ×v m , where σ is a timelike hyperplane. This result leads to time-energy uncertainty relations that match their space-momentum counterparts. The operators Qμ appearing in Born's metric operator in quantum spacetime emerge as internal spacetime operators for exciton states, and the condition that the metric (...) operator should possess a ground exciton state assumes the significance of achieving minimal spacetime4-momentum uncertainty in fundamental standards for spacetime measurements. (shrink)

The foundational difficulties encountered by the conventional formulation of quantum electrodynamics, and the criticism by Dirac, Schwinger, Rohrlich, and others, aimed at some of the physical and mathematical premises underlying that formulation, are reviewed and discussed. The basic failings of the conventional methods of quantization of the electromagnetic field are pointed out, especially with regard to the issue of local (anti)commutativity of quantum fields as an embodiment of relativistic microcausality. A brief description is given of a recently advanced new type (...) of approach to quantum electrodynamics, and to quantum field theory in general, which is epistemically based on intrinsically quantum ideas about the physical nature of spacetime, and is mathematically based on a fiber theoretical formulation of quantum geometries, aimed in part at removing the aforementioned difficulties and inconsistencies. It is shown that these ideas can be traced to a conceptualization of spacetime outlined by Einstein in the last edition of his well-known semipopular exposition of relativity theory. (shrink)

The roles of classical realism, logical positivism, and pragmatic instrumentalism 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 II 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 II quantum physics in particular. The basic epistemic ideas of a quantum geometry approach to quantum physics are reviewed and discussed from the point of view of a quantum realism that seeks to reconcile Bohr's “positivism” with Einstein's “realism” by emphasizing the existence of an underlying quantum reality, in which they 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 developing the conceptual and mathematical tools that are most appropriate for such a use. (shrink)

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 geometro-stochastic 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. (shrink)

The concept of probability space is generalized to that of stochastic probability space. This enables the introduction of representations of quantum mechanics on stochastic phase spaces. The resulting formulation of quantum statistical mechanics in terms of Γ-distribution functions bears a remarkable resemblance to its classical counterpart. Furthermore, both classical and quantum statistical mechanics can be formulated in one and the same master Liouville space overL 2(Γ). A joint derivation of a classical and quantum Boltzman equation provides an illustration of the (...) practical uses of these formalisms. (shrink)

Theories of free fields describing spin zero and1/2 extended particles are derived within the stochastic quantum field theory (SQFT) framework. Covariant SQFT analogs of free Schwinger functions and Feynman propagators are obtained, and explicit expressions for charge and four-momentum operators are derived which exhibit a remarkable formal resemblance to their local counterparts. It is shown that the essential results of the LSZ formalism for interacting fields also have their counterpart in SQFT, and that the same holds true of Wightman's reconstruction (...) theorem. Fields on quantum space-time do not obey the local (anti)-commutativity postulate, but we argue that due to the uncertainty principle this postulate cannot be operationally justified as an expression of microcausality despite the customary identification of the two notions. An operationally consistent microcausality condition is proposed instead. (shrink)

The measurement of one or more observables can be considered to yield sample points which are in general fuzzy sets. Operationally these fuzzy sample points are the outcomes of calibration procedures undertaken to ensure the internal consistency of a scheme of measurement. By introducing generalized probability measures on σ-semifields of fuzzy events, one can view a quantum mechanical state as an ensemble of probability measures which specify the likelihood of occurrence of any specific fuzzy sample point at some instant. These (...) sample points are the possible outcomes of any infinitely rapid succession of measurements at that instant of any sequence of observables of the system. (shrink)

The physical concept of locality is first analyzed in the special relativistic quantum regime, and compared with that of microcausality and the local commutativity of quantum fields. Its extrapolation to quantum general relativity on quantum bundles over curved spacetime is then described. It is shown that the resulting formulation of quantum-geometric locality based on the concept of local quantum frame incorporating a fundamental length embodies the key geometric and topological aspects of this concept. Taken in conjunction with the strong equivalence (...) principle and the path-integral formulation of quantum propagation, quantum-geometric locality leads in a natural manner to the formulation of quantum-geometric propagation in curved spacetime. Its extrapolation to geometric quantum gravity formulated over quantum spacetime is described and analyzed. (shrink)

The various physical aspects of the general relativistic principles of covariance and strong equivalence are discussed, and their mathematical formulations are analyzed. All these aspects are shown to be present in classical general relativity, although no contemporary formulation of canonical or covariant quantum gravity has succeeded to incorporate them all. This has, in part, motivated the recent introduction of a geometro-stochastic framework for quantum general relativity, in which the classical frame bundles that underlie the formulation of parallel transport in classical (...) general relativity are replaced by quantum frame bundles. It is shown that quantum frames can take over the role played by complete sets of observables in conventional quantum theory, so that they can mediate the natural transference of the general covariance and the strong equivalence principles from the classical to the quantum general relativistic regime. This results in a geometrostochastic mode of quantum propagation in general relativistic quantum bundles, which is mathematically implemented by path integration methods based on parallel transport along horizontal lifts of geodesics for the vacuum expectation values of a quantum gravitational field in a quantum spacetime supermanifold. The covariance features of this field are embedded in a quantum gravitational supergroup, which incorporates Poincaré as well as diffeomorphism invariance, and resolves the issue of time in quantum gravity. (shrink)