# On the Present Status of Quantum Mechanics

## – Speakers –

- Stephen L. Adler: Confronting Stochastic Localization Models in Nanomechanical Resonator and Gravitational Wave Detector Experiments

I discuss recent work, using exact solutions of the decoherent, non-dissipative forced harmonic oscillator, to set bounds on stochastic localization models for objective state vector reduction. Current and planned nanonmechanical resonator and gravitational wave detector experiments will give improved bounds on the stochastic model parameters, but are still 3 to 8 orders of magnitude away from the capability of seeing an effect at the level of the preferred CSL model parameters.

- David Albert: Physics and Narrative

T.b.a.

- Paolo Budinich: Pure Spinor Geometry and Quantum Mechanics

Pure spinors, discovered by Cartan (1938), who named them "simple" and by Chevalley (1954) who renamed them "pure", were recently (2002) rediscovered as instrumental for some progress in "the" problem of super gravity. This rediscovery is attracting the attention of both theoretical physicists and mathematicians on pure spinor geometry and of its possible fundamental role in quantum mechanics of elementary particles. Where in particular, it might be at the origin of strings, of the "standard group" of internal symmetry, of charges, and, if formulated in compact momentum space, it could allow the purely geometric formulation of quantum mechanics extending thus the programme started already in 1935 by Fock when he formulated, in the one point compactification S3 of momentum space, the problem of the Hydrogen atom stationary states. The possible relevance of this approach for the purely geometrical origin of quantum mechanics is underlined, and then both great revolutions of last century would have their roots in geometry, since for relativity it is already obvious.

- Giulio Casati: Classical Dynamical Chaos and Quantum Dephasing

We discuss the role played by internal dynamical chaos in the quantum dephasing process in the absence of any external environment. We first show, on a simple model, that the decay of the quantum Loschmidt echo is determined by the decay of an appropriate classical correlation function. We then report on the numerical simulation of the double-slit experiment, where the initial wave-packet is bounded inside a billiard domain with perfectly reflecting walls. If the shape of the billiard is such that the classical ray dynamics is regular, we obtain interference fringes whose visibility can be controlled by changing the parameters of the initial state. However, if we modify the shape of the billiard thus rendering classical (ray) dynamics fully chaotic, the interference fringes disappear and the intensity on the screen becomes the (classical) sum of intensities for the two corresponding one-slit experiments.

- Marisa Dalla Chiara, Roberto Giuntini and Giuliano Toraldo di Francia: Holistic Quantum Computational Semantics
and Gestalt-Thinking Processes

Human perception and thinking seem to be essentially synthetic. We never perceive an object by scanning it point by point; we instead form right away a Gestalt, a global idea of it. Gestalt-thinking processes cannot be adequately represented in the framework of classical semantics, which is basically compositional and analytical : the meaning of a whole is determined by the meanings of its parts, and not vice versa. Quantum computational semantics provides a mathematical formalism for an abstract theory of meanings where the following conditions are satisfied: 1) global meanings (which may correspond to a Gestalt) are intrinsically vague, because they leave semantically undecided many relevant properties of the objects under investigation; 2) any global meaning determines some partial meanings, which are generally more vague than the global one; 3) meanings (Gestalten) can be generally represented as superpositions of other meanings, possibly associated to probability-values; 4) like Gestalten, meanings are dealt with as intrinsically dynamic objects.

- Giacomo Mauro D'Ariano: Quantum Mechanics as a "Syntactic Manual" for the Experiment

The debate on the nature of quantum probabilities in relation to Quantum Non Locality has elevated Quantum Mechanics to the level of an "Operational Epistemic Theory". In such context the quantum superposition principle has an extraneous non epistemic nature. This lead us to seek purely operational foundations for Quantum Mechanics, from which to derive the current mathematical axiomatization based on Hilbert spaces. In the present work I present a set of axioms of purely operational nature, based on a general definition of "the experiment", the operational/epistemic archetype of information retrieval from reality. As we will see, this starting point logically entails a series of notions [state, conditional state, local state, pure state, faithful state, instrument, propensity (i.e. "effect"), dynamical and informational equivalence, dynamical and informational compatibility, predictability, discriminability, programmability, locality, a-causality, rank of the state, maximally chaotic state, maximally entangled state, informationally complete propensity, etc. ], along with a set of rules (addition, convex combination, partial orderings, ... ), which, far from being of quantum origin as often considered, instead constitute the universal "syntactic manual" of the operational/epistemic approach. The missing ingredient is, of course, the quantum superposition axiom for probability amplitudes: for this I propose some substitute candidates of purely operational/epistemic nature.

- Francesco De Martini: Realization of a Decoherence-Free Mesoscopic Quantum Superposition (Schrödinger Cat)

We report the realization of an entangled mesoscopic quantum superposition by multiple universal cloning of a single photon qubit via the high gain, quantum-injected optical parametric amplification. By modern tomographic methods the conditions of non-separability and quantum superposition are investigated for the mesoscopic output state of a dynamic ''closed system'' fully realizing the condition conceived in 1935 by Erwin Schrödinger in his paradigmatic "Cat" apologue, a fundamental quantum mechanical landmark.

- Lajos Diosi: Continuous wavefunction collapse in quantum-electrodynamics?

Time-continuous wavefunction collapse mechanisms __not__ restricted to Markovian approximation have been found only a few years ago, and have left many issues open. The results apply __formally__ to standard relativistic quantum-electrodynamics. I present a generalized Schrödinger equation guided by a certain complex stochastic field. The equation reproduces the __exact__ dynamics of the interacting fermions in QED.
The state of the fermions appears to collapse continuously, due to their interaction with the photonic degrees of freedom. Even the formal study is instructive for foundations of quantum mechanics and of field theory as well.

- Fay Dowker: Quantum Local Hidden Variables

Papers with the title "Bell was wrong" receive the same treatment from those in the physics and philosophy of physics communities as those claiming "Einstein was wrong". Rightly so - I am not crazy - Bell was right. But if one gives up one of the key assumptions in Bell's theorem - that there exists a classical probability distribution (a classical measure) on the hidden variables - and replaces it by the possibility that there is "quantum measure" (which I will define) then one can have local hidden variables compatible with the experimental outcomes in the standard EPRB setup.

- Ennio Gozzi: Quantization as a Dimensional Reduction Phenomenon

We briefly review a path-integral approach to Classical Mechanics which is the functional counterpart of the Koopman von Neumann operatorial approach to Classical mechanics. We then show that we can pass from this path-integral for classical mechanics to the one for quantum mechanics by freezing to zero two grassmannian partners of time.

- Lucien Hardy: Probabilistic Theories With Dynamic Causal Structure

Quantum theory is a probabilistic theory but one which assumes fixed background causal structure. General relativity, on the other hand, is deterministic but has dynamic causal structure (the causal relationship between events depends on the state). Hence it seems likely that a theory combining the two will be a probabilistic theory with dynamic causal structure. I will present a framework for such theories

- Giovanni Jona-Lasinio: Invariant Measures under Schrödinger Evolution and Analogs of Coherent States for Hamiltonians with non Quadratic Potentials

Gibbs measures invariant under the Schrödinger evolution viewed as an infinite dimensional dynamical system induce the classical distribution on the quantum expectations of coordinates and momenta of a system of oscillators. For non quadratic Hamiltonians, at low temperature the so called effective potential replaces the classical potential. The quantum states typical of this regime are the coherent states in the case of oscillators and states with similar properties in the non harmonic case.

- Adrian Kent: Causal Quantum Theory and the Collapse Locality Loophole

Causal quantum theory is an umbrella term for ordinary quantum theory modified by two hypotheses: state vector reduction is a well-defined process, and strict local causality applies. The first of these holds in some versions of Copenhagen quantum theory and need not necessarily imply practically testable deviations from ordinary quantum theory. The second implies that measurement events which are spacelike separated have no non-local correlations. To test this prediction, which sharply differs from standard quantum theory, requires a precise theory of state vector reduction, for example that given by the Ghirardi-Rimini-Weber spontaneous collapse models. Formally speaking, any precise version of causal quantum theory defines a local hidden variable theory. However, causal quantum theory is most naturally seen as a variant of standard quantum theory. For that reason it seems a more serious rival to standard quantum theory than local hidden variable models relying on the locality or detector efficiency loopholes. Some plausible versions of causal quantum theory, including those incorporating GRW models, are not refuted by any Bell experiments to date, nor it is obvious that they are inconsistent with other experiments. They evade refutation via a neglected loophole in Bell experiments, the "collapse locality loophole", which exists because of the possible time lag between a particle entering a measuring device and a collapse taking place. Fairly definitive tests of causal versus standard quantum theory could be made by observing entangled particles separated by about 0.1 light seconds.

- Ludovico Lanz: Quantum Macro-Objectivation: a Challenge for Quantum Field Theory

The modern formulation of axiomatics of quantum theory (POV measures, operations, instruments) already arose in Ludwig's approach to the foundations of quantum mechanics, based on a suitable schematization of sources and detectors employed in the experiment, giving evidence, at a statistical level, of a microsystem. This suggests that replacing the usual prevailingly phenomenological description of non-equilibrium macrosystems with a more fundamental one might also clarify the question of macro-objectivation in quantum theory, which plagues the measuring process. We show that local equilibrium macrosystems can be described in non relativistic quantum field theory by non equilibrium statistical operators, displaying classical state parameters. In this framework microsystems can be linked with a breakdown of deterministic time evolution of these state parameters and usual quantum mechanics arises for them if decoherence due to the macroscopic environment can be neglected. Preliminary discussion of the relativistic case will be given.

- Giuseppe Marmo: Differential Geometry of Density States: Open Systems

We show that a very high level of geometrization may be achieved also in the description of density states and composite systems. We shall use some of the geometrical structures to discuss entanglement and the dynamics for open systems.

- Hrvoje Nikolic: Relativistic Bohmian Interpretation of Quantum Mechanics

I present a relativistic covariant version of the Bohmian interpretation of QM and discuss the corresponding measurable predictions.

- Valerio Scarani: The Simulation of Entanglement with Non-Local Resources

The simulation of quantum entanglement with alternative ressources has been the object of several recent works. These studies allow a better understanding of the remarkable features of entangled states. Communication has sometimes been used to simulate entanglement; for instance, it is known that a single bit of communication needs to be added to local variables to simulate the maximally entangled state. However, communication has problematic features (e.g. it should be faster-than-light): this suggest that it is not the most suited resource for that task. Recently, another approach was developed. This approach is based on a theoretical object which could be assumed as a "unit of non-locality". I shall review the feats and (at least temporary) failures of this last approach.

- Roderich Tumulka: The Ghirardi-Rimini-Weber Model and Relativity

I review a recent relativistic variant of the GRW model, involving a stochastic evolution law for the wave function that deviates from the Schrödinger evolution by discrete spontaneous collapses.

- Hans Westman and Ward Struyve: Pilot-Wave Theory for the Standard Model

It is no problem to devise a pilot-wave model for bosonic field theories with fields as beables. For example, the electromagnetic field was already treated in this way in Bohm's seminal paper. For fermionic field theory it has proved less straightforward to devise a pilot-wave model with fields as beables. For this reason we explore the idea to introduce field beables only for bosons and not for fermions. Our approach is completely analogous to the situation in nonrelativistic quantum theory, where Bell treats spin not as a beable but only as a property of the wavefunction. In this way we may give a pilot-wave interpretation of the standard model.

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