A reinterpretation of von Neumann's theory of measurement

Von Neumann's theory of measurement in quantum mechanics is reinterpreted so that the experimental arrangement specifies the location of the cut by calling for the separate observation of the object and the measuring apparatus after the initial measurement interaction. The measurement ascertains which element of the mixture describing the final state of the apparatus is actually present. The relevance and feasibility of observing the final coherent state of the object plus apparatus is criticized and the paradoxes of Schrödinger's cat and Wigner's friend are discussed.Work performed under the auspices of the U.S. Atomic Energy Commission.     

Generalization of von Neumann's theorem to nonreproducible measurements in the framework of quantum field theory. I

One of von Neumann's three theorems - the one on the reduction of the wave packet – is extended to the most general case of nonreproducible measurements in the framework of quantum field theory. The proof of the generalization uses only the most general principles of theory: unitarity of the operator and the standard probability interpretation of the state vector of a physical system.Lecture at the Fall School 1976 on Axiomatic Quantum Field Theory (Uzhgorod, September 15–21, 1976) and at the Nuclear-Physics Section Session of the Academy of Sciences of the USSR (Moscow, February 1–4, 1978).Uzhgorod Branch of Hadron Theory. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 108–113, April, 1978.I am very grateful to Academician N. N. Bogolyubov for approval of the resulta of this paper (preliminary publications of some results were given in [16–22]), to Professors M. I. Podgoretskii (JINR, Dubna), V. Ya. Fainberg (P. N. Lebedev Physics Institute, Moscow) for numerous fruitful and stimulating discussions, to Professor Yu. M. Shirokov (V. A. Steklov Mathematics Institute, Moscow) for valuable comments, and to L Yu. Krivskii and E. P. Sabada for helpful discussions.     

Generalization of von Neumann's theorem to irreproducible measurements within the framework of quantum field theory. V

Various papers in the series are summarized and the results are extended to the general possibility of mutual self-measurement in a closed macrosystem whose state is specified not by a vector but by some statistical operator in Hilbert space. All the nonconservative effects still apply. Further, these effects occur in a microsystem that remains in a mixed state.Report to a meeting of the Division of Nuclear Physics, Academy of Sciences of the USSR, Moscow, February, 1978.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 85–92, September, 1979.I am indebted to I. Krivskii for a valuable discussion.     

Quantum decision theory as quantum theory of measurement

We present a general theory of quantum information processing devices, that can be applied to human decision makers, to atomic multimode registers, or to molecular high-spin registers. Our quantum decision theory is a generalization of the quantum theory of measurement, endowed with an action ring, a prospect lattice and a probability operator measure. The algebra of probability operators plays the role of the algebra of local observables. Because of the composite nature of prospects and of the entangling properties of the probability operators, quantum interference terms appear, which make actions noncommutative and the prospect probabilities nonadditive. The theory provides the basis for explaining a variety of paradoxes typical of the application of classical utility theory to real human decision making. The principal advantage of our approach is that it is formulated as a self-consistent mathematical theory, which allows us to explain not just one effect but actually all known paradoxes in human decision making. Being general, the approach can serve as a tool for characterizing quantum information processing by means of atomic, molecular, and condensed-matter systems.     

EPR-relations,von Neumann's standard forms and a proof concerning a conjecture of E. Scheibe

In the first part of this paper it is shown how EPR-situations are correlated with von Neumann's standard form of quantum mechanical states describing a system consisting of two dynamical independent subsystems. These standard forms are the mathematical tools for a proof of a conjecture of E. Scheibe: If the 4 selfadjoint operators in Bell's — inequality are pairwise EPR — related, then this inequality is valid in the strong form (with the same upper bound as in statistical mechanics). In the last section the question is discussed whether observations made on the two subsystems together with EPR-relations between them, determine the state of the composed system.Retired, however for a time back at     

Magnetotransport in manganites and the role of quantal phases: theory and experiment

While low-temperature Hall resisitivity rhoxy of La2/3(Ca,Pb)1/3MnO3 single crystals can be separated into ordinary (OHE) and anomalous (AHE) contributions, no such decomposition is possible near the Curie temperature Tc. Rather, the rhoxy data collapse to a single function of the reduced magnetization m=M/Msat, with an extremum at approximately 0.4 m. A new mechanism for the AHE in the inelastic hopping regime is identified that reproduces the scaling curve. An extension of Holstein's model for the hopping OHE, the mechanism arises from the combined effects of the double-exchange-induced quantal phase in triads of Mn ions and spin-orbit interactions.     

Quantum theory as a theory in a classical propositional calculus

Classical logic and Boolean algebras are, of course, very intimately related. It is, however, possible to show that lattices of propositions isomorphic to the lattice of all the closed subspaces of a separable Hilbert space arise quite naturally within the classical propositional logic. This was first shown by the author in 1987 in connection with a certain type of theories calledtheories with orthocomplementation. These theories are not easy to interpret physically and it is shown that simpler theories, which are more amenable to physical interpretation, can also be used. It is then possible to assume that quantum theory is such a theory and, as a result, to formulate a new approach that provides a way of looking at the wave-particle duality and touches upon the foundations of quantum field theory.     

Microscopic,quantal theory of Brownian motion applied to deep inelastic heavy-ion collisions

The present understanding of the statistical features of deep inelastic heavy ion collisions can be improved considerably by following the lines of modern molecular theory of Brownian motion. Only a few assumptions are necessary, which are direct consequences of the underlying physical picture. The physical interpretation of these assumptions leads to simple estimates of their validity. The theory is a quantum mechanical, strong coupling, transport theory. Collective vibrations can be included in a simple and straightforward manner.     

Quantum theory as a universal physical theory

The problem of setting up quantum theory as a universal physical theory is investigated. It is shown that the existing formalism, in either the conventional or the Everett interpretation, must be supplemented by an additional structure, the interpretation basis. This is a preferred ordered orthonormal basis in the space of states. Quantum measurement theory is developed as a tool for determining the interpretation basis. The augmented quantum theory is discussed.     

Yang-Mills theory in three dimensions as a quantum gravity theory

We perform the dual transformation of theYang-Mills theory in three dimensions using the Wilson action on the cubic lattice. The dual lattice is made of tetrahedra triangulating a 3-dimensional curved manifold but which is embedded into a flat 6-dimensional space [for the SU(2) gauge group]. In the continuum limit, the theory can be reformulated in terms of 6-component gauge-invariant scalar fields having the meaning of the external coordinates of the dual lattice sites. These 6-component fields induce a metric and a curvature of the 3-dimensional dual-color space. The Yang-Mills theory can also be rewritten as a quantum gravity theory with the Einstein-Hilbert action but with a purely imaginary Newton constant plus a homogeneous “ether” term. The theory can be formulated in a gauge-invariant and local form without explicit color degrees of freedom.     

Quantum theory of Ur-objects as a theory of information

The quantum theory of ur-objects proposed by C. F. von Weizsäcker has to be interpreted as a quantum theory of information. Ur-objects, or urs, are thought to be the simplest objects in quantum theory. Thus an ur is represented by a two-dimensional Hilbert space with the universal symmetry groupSU(2), and can only be characterized asone bit of potential information. In this sense it is not a spatial but aninformation atom. The physical structure of the ur theory is reviewed, and the philosophical consequences of its interpretation as an information theory are demonstrated by means of some important concepts of physics such as time, space, entropy, energy, and matter, which in ur theory appear to be directly connected with information as the fundamental substance. This hopefully will help to provide a new understanding of the concept of information.     

A unified quantum theory of mechanics and thermodynamics. Part III. Irreducible quantal dispersions

This part of the paper concludes the presentation of the unified theory. It is shown that the theory requires the existence of, and applies only to, irreducible quantal dispersions associated with pure or mixed states. Two experimental procedures are given for the operational verification of such dispersions. Because the existence of irreducible dispersions associated with mixed states is required by Postulate 4 of the theory, and because Postulate 4 expresses the basic implications of the second law of classical thermodynamics, it is concluded that the second law is a manifestation of phenomena characteristic of irreducible quantal dispersions associated with the elementary constituents of matter.Parts I, IIa, and IIb of this paper appeared inFound. Phys. 6, 15, 127, 439 (1976), respectively. The numbering of the sections, equations, and references in this part continues from the previous parts.     

String theory as a theory of quantum gravity: a status report

We review the status of string theory as a quantum theory of gravity. Our emphasis is on outstanding questions and remaining challenges rather then on well-established results and successes.     

Four-dimensional BF theory as a topological quantum field theory

Starting from a Lie group G whose Lie algebra is equipped with an invariant nondegenerate symmetric bilinear form, we show that four-dimensional BF theory with cosmological term gives rise to a TQFT satisfying a generalization of Atiyah's axioms to manifolds equipped with principal G-bundle. The case G=GL(4,) is especially interesting because every 4-manifold is then naturally equipped with a principal G-bundle, namely its frame bundle. In this case, the partition function of a compact oriented 4-manifold is the exponential of its signature, and the resulting TQFT is isomorphic to that constructed by Crane and Yetter using a state sum model, or by Broda using a surgery presentation of four-manifolds.     

Partial measurement in the Bohm-Bub hidden-variable theory

The Bohm-Bub hidden-variable theory is able to predict the results of measuring a quantum system only in the special case where the set of commuting observables being measured is complete. To handle the much more common case where the set is incomplete, Tutsch has proposed a generalization of the Bohm-Bub model. Unfortunately, as we show here, Tutsch's original method does not yield the correct quantum mechanical transition probabilities. On the other hand, Belinfante's modification of Tutsch's method does yield the correct probabilities, and it gives a satisfactory hidden-variable theory of partial measurement for the case where one or more commuting variable(s) are measured at a single space-time point. In the case where the variables are measured at different space-time points, the theory is inadequate, due to the fact that it is not relativistically covariant, and does not take relaxation of the hidden variables into account.     

Multicolor QCD as a dual-resonance theory

The quantum chromodynamics with massless quarks and an infinite number of colors is represented as a theory of the noninteracting mesons which lie on rising Regge trajectories. The perturbation theory for these trajectories is developed. The expansion parameter (effective coupling) is calculated and appears to be about $\text{1}\text{2}$. The expansion coefficients can also be calculated analytically as functions of spin and other quantum numbers. The calculations are carried through to the end in the zeroth and first order. The resulting trajectories look reasonable and are in qualitative agreement with experiment. The corrections from finite numbers of colors and from quark masses can also be found, but are not considered here.