On Bohr's response to EPR: II

In my reconstruction of Bohr's reply to the Einstein-Podolsky-Rosen argument, I pointed out that Bohr showed explicitly, within the framework of the complementarity interpretation, how a locally maximal measurement on a subsystem S₂ of a composite system S₁+S₂, consisting of two spatially separated subsystems, can make determinate both a locally maximal Boolean subalgebra for S₂ and a locally maximal Boolean subalgebra for S₁. As it stands, this response is open to an objection. In this note, I show that meeting the objection requires a modification of the complementarity thesis concerning what propositions can be taken as determinate, or what observables can be raken to have values, in a given measurement context.     

The EPR Paper and Bohr's Response: A Re-Assessment

For many years after Bohr's response to the EPR argument, Bohr was considered to have provided an authoritative rebuttal of the ideas of the paper, and more generally of Einstein's stance on quantum theory. More recently, however, there has been great difficulty even in achieving general agreement on Bohr's meaning. Two recent papers, by Dickson, and by Clifton and Halvorson, have sought to establish the structure of Bohr's argument. In the present paper, the papers of EPR and Bohr are re-assessed in the light of these recent papers, and also in light of the development and presentation of quantum information theory.     

On the logical structure of quantum mechanics

Croc lattices are of central importance in the mathematical foundation of quantum mechanics. They reflect the structure of the logical calculus of propositions concerning microphenomena. In this context, the mathematical consequences resulting from the special structure of the lattice are of particular interest. Beginning with the notion of hemimorphism of a croc lattice, we get, in a natural way, an extension of the structure of the lattice by the Baer *-semigroup. We embed the Baer *-semigroup in an algebra with generalized *- and -operations and prove some theorems as consequences of the particular properties of the underlying croc lattice.Work supported by the Swiss National Science Foundation.     

On the logical foundations of the Jauch-Piron approach to quantum physics

We make a critical analysis of the basic concepts of the Jauch-Piron (JP) approach to quantum physics. Then, we exhibit a formalized presentation of the mathematical structure of the JP theory by introducing it as a completely formalized syntactic system, i.e., we construct a formalized languageL _e and formally state the logical-deductive structure of the JP theory by means ofL _e . Finally, we show that the JP syntactic system can be endowed with an intended interpretation, which yields a physical model of the system. A mathematical model endowed with a physical interpretation is given which establishes (in the usual sense of the model theory) the coherence of the JP syntactic system.     

A non-completeness argument for quantum mechanics (analysis of the EPR paper)

This paper aims at a clarification of the interrelations of the fundamental ideas in the EPR paper [2]. Through a logical analysis of the completeness condition and the physical reality criterion, we show how the premises of the EPR argument are obtained and explicate in what sense the conclusion that quantum mechanics is a non-complete theory follows.     

Quantum logical solution to the measurement problem of quantum mechanics

In this paper I propose a reformulation and solution of the measurement problem of quantum mechanics. The reformulation depends on a quantum logical interpretation of quantum mechanics, broadly construed. The solution depends on a theorem about partial Boolean algebras which is proved here.     

A logical analysis of physical theories

La Rivista del Nuovo Cimento (1971-1977) -     

A quantum computer in the scheme of an atomic quantum transistor with logical encoding of qubits

A scheme of a multiqubit quantum computer on atomic ensembles using a quantum transistor implementing two qubit gates is proposed. We demonstrate how multiatomic ensembles permit one to work with a large number of qubits that are represented in a logical encoding in which each qubit is recorded on a superposition of single-particle states of two atomic ensembles. The access to qubits is implemented by appropriate phasing of quantum states of each of atomic ensembles. An atomic quantum transistor is proposed for use when executing two qubit operations. The quantum transistor effect appears when an excitation quantum is exchanged between two multiatomic ensembles located in two closely positioned QED cavities connected with each other by a gate atom. The dynamics of quantum transfer between atomic ensembles can be different depending on one of two states of the gate atom. Using the possibilities of control for of state of the gate atom, we show the possibility of quantum control for the state of atomic ensembles and, based on this, implementation of basic single and two qubit gates. Possible implementation schemes for a quantum computer on an atomic quantum transistor and their advantages in practical implementation are discussed.     

DNA transistor and quantum bit element: Realization of nano-biomolecular logical devices

Based on the theoretical prediction that chemical bonds can act as tunnel junctions in the Coulomb blockade regime, and on the technical ability to coat a DNA strand with metal, we suggest that DNA can be used to built nano-logical devices. We discuss two explicit examples: a single-electron tunneling transistor (SET) and a quantum bit element. These devices would be literally in the nano-meter scale and would be able to operate at room temperature. In addition they would be highly stable and have a self ably property.     

On the quantum logic approach to quantum mechanics

A quantum logic structure for quantum mechanics which contains the concepts of a physical space, localizability, and symmetry groups is formulated. It is shown that there is an underlying Hilbert space which mirrors much of this axiomatic structure. Quantum fields are defined and shown to arise naturally from the quantum logic structure. The fields ofHaag andWightman are generalized to this theory and an attempt is made to find a local equivalence for these fields.     

On the zigzagging causility model of EPR correlations and on the interpretation of quantum mechanics

Being formalized inside the S-matrix scheme, the zigzagging causility model of EPR correlations has full Lorentz and CPT invariance. EPR correlations, proper or reversed, and Wheeler's smoky dragon metaphor are respectively pictured in spacetime or in the momentum-energy space, as V-shaped, A-shaped, or C-shaped ABC zigzags, with a summation at B over virtual states |B B|. An exact correspondence exists between the Born-Jordan-Dirac wavelike algebra of transition amplitudes and the 1774 Laplace algebra of conditional probabilities, where the intermediate summations |B) (B| were over real hidden states. While the latter used conditional (or transition) probabilities (A|C) = (C|A), the former uses transition (or conditional) amplitudes A|C = C|A*. The formal parrallelism breaks down at the level of interpretation because (A|C) = |A|C|². CPT invariance implies the Fock and Watanabe principle that, in quantum mechanics, retarded (advanced) waves are used for prediction (retrodiction), an expression of which is | U | = | U = U|, with | denoting a preparation, | a measurement, and U the evolution operator. The transformation | = |U or | = |U^–1 exchanges the preparation representation and the measurement representation of a system and is ancillary in the formalization of the quantum chance game by the wavelike algebra of conditional amplitude. In 1935 EPR overlooked that a conditional amplitude A|C = A|BB|C between the two distant measurements is at stake, and that only measurements actually performed do make sense. The reversibility A|C = C|A* implies that causality is CPT-invariant, or arrowless, at the microlevel. Arrowed causality is a macroscopic emergence, corollary to wave retardation and probability increase. Factlike irreversibility states repression, not suppression, of blind statistical retrodiction—that is, of final cause.Dedicated to Professor David Bohm, proponent of the EPRB version of nonseparability.     

On the linear response theory of infinite quantum systems

The perturbation of a C¹-dynamics α by a time-dependent unbounded 1-derivation of the form μ?(t)δ′ is considered. The existence of the perturbed dynamics and that of the linear responce oftthe C¹-dynamical system ($\text{A}$, $\text{R}$, α) is shown. The existence of the corresponding generalized susceptibility and some convergence problems are discussed.     

A classical model of EPR experiment with quantum mechanical correlations and bell inequalities

A simple model of a classical break-up process is given in which the correlation E(a,b) of the components A and B of the spins of the two subsystems along directions a and b gives precisely the quantum mechanical result $\text{?cos(}\text{a·b}\text{)}$. The model is “local”, but the normalization procedure of correlation functions in terms of “hidden variables” is different from that used in deriving Bell's inequalities. A discretization procedure of the classical spins is then given which reproduces fully the dichotomous quantum mechanical results both for probabilities and for correlation functions. This procedure illustrates particularly clearly the difference between quantum and classical spins and provides a possible intuitive picture for the notion of the “reduction of the wave function”.     

On logical gates in precipitating medium: Cellular automaton model

We study a two-dimensional semi-totalistic binary cell-state cellular automaton, which imitates a reversible precipitation in an abstract chemical medium. The systems exhibits a non-trivial growth and nucleation. We demonstrate how basic computational operation can be realized in the system when the propagation of the growing patterns is self-restricted by stationary localizations. We show that precipitating patterns of different morphology compete between each other and thus implement basic logical gates.     

A multifrequency EPR approach to travertine characterisation

The understanding of processes that give rise to travertine deposits is important. This is so because of its widespread use as decorative material, but more so in environmental studies due to the significance, by proxy, of travertine in climatology. In this paper, a multifrequency EPR spectroscopy study of the behaviour of an ubiquitary vicariant of Ca in calcite, Mn(II), is presented. EPR spectra were obtained from a natural sample at 9.5 (X-band), 95, 190, and 285GHz, and interpreted through numerical simulation. An analysis of the distribution of the zero-field splitting interaction revealed the source of some unexpected spectral features in the width of the lines in the X-band. By contrast, the homogeneous broadening plays only a minor role. Moreover, field-dependent anisotropies of the Zeeman and hyperfine tensors were observed at higher frequency. On the basis of results garnered in this study, the ZFS interaction of Mn(II) has been ascribed to the microstructural anomalies of the Mn(II) distribution in calcite. This may be considered as the fingerprint of the physical-chemical conditions at the time of travertine deposition. As a consequence, X-band EPR spectroscopy represents a specific tool to investigate the genesis, and to check the homogeneity of Mn(II) distribution in travertines as well as in other calcite-based materials.     

On the response of a two-level quantum system to a class of time-dependent quasiperiodic perturbations

We study analytically the response of a two-level quantum system to a certain class of time-dependent quasiperiodic perturbations generated by a Fibonacci sequence. We show that the quasi-energy spectrum (Fourier transform of the evolution operator) generically is not a denumerable sum of delta functions. Hence the response is not quasiperiodic. Several numerical investigations (Poincaré sections, polarization fluctuation, etc.) suggest an intermediate kind of behavior between quasiperiodic and chaotic.     

A parametric approach to spectral-spatial EPR imaging

Continuous wave electron paramagnetic resonance imaging for in vivo mapping of spin distribution and spectral shape requires rapid data acquisition. A spectral-spatial imaging technique is presented that provides an order of magnitude reduction in acquisition time, compared to iterative tomographic reprojection. The proposed approach assumes that spectral shapes in the sample are well-approximated by members from a parametric family of functions. A model is developed for the spectra measured with magnetic field modulation. Parameters defining the spin distribution and spectral shapes are then determined directly from the measurements using maximum a posteriori probability estimation. The approach does not suffer approximation error from limited sweep width of the main magnetic field and explicitly incorporates the variability in signal-to-noise ratio versus strength of magnetic field gradient. The processing technique is experimentally demonstrated on a one-dimensional phantom containing a nitroxide spin label with constant g-factor. Using an L-band EPR spectrometer, spectral shapes and spin distribution are accurately recovered from two projections and a spectral window which is comparable to the maximum linewidth of the sample.     

On the zigzagging causality EPR model: Answer to Vigier and coworkers and to Sutherland

The concept of propagation in time of Vigier and co-workers (V et al.) implies the idea of a supertime; it is thus alien to most Minkowskian pictures and certainly to mine. From this stems much of Vet al.'s misunderstandings of my position. In steady motion of a classical fluid nobody thinks that momentum conservation is violated, or that momentum is shot upstream without cause because of the suction from the sinks! Similarly with momentum-energy in space-time and the acceptance of an advanced causality. As for the CT invariance of the Feynman propagator, the causality asymmetry it entails is factlike, not lawlike. The geometrical counterpart of the symmetry between prediction and retrodiction and between retarded and advanced waves, as expressed in the alternative expressions B|UA=BU|A=B|U|A for a transition amplitude between a preparation |A and a measurement |B, is CPT-invariant, not PT-invariant. These three expressions respectively illustrate the collapse, the retrocollapse, and the symmetric collapse-and-retrocollapse concepts. As for Sutherland's argument, what it falsifies is not my retrocausation concept but the hidden-variables assumption he has unwittingly made.