A Transactional Analysis of Interaction-Free Measurements

The transactional interpretation of quantum mechanics is applied to the “interaction-free” measurement scenario of Elitzur and Vaidman and to the Quantum Zeno effect version of the measurement scenario by Kwiat et al. It is shown that the non-classical information provided by the measurement scheme is supplied by the probing of the intervening object by incomplete offer and confirmation waves that do not form complete transactions or lead to real interactions.     

Complementarity Relations for Multi-Qubit Systems

No Heading We derive two complementarity relations that constrain the individual and bipartite properties that may simultaneously exist in a multi-qubit system. The first expression, valid for an arbitrary pure state of n qubits, demonstrates that the degree to which single particle properties are possessed by an individual member of the system is limited by the bipartite entanglement that exists between that qubit and the remainder of the system. This result implies that the phenomenon of entanglement sharing is one specific consequence of complementarity. The second expression, which holds for an arbitrary state of two qubits, pure or mixed, quantifies a tradeoff between the amounts of entanglement, separable uncertainty, and single particle properties that are encoded in the quantum state. The separable uncertainty is a natural measure of our ignorance about the properties possessed by individual subsystems, and may be used to completely characterize the relationship between entanglement and mixedness in two-qubit systems. The two-qubit complementarity relation yields a useful geometric picture in which the root mean square values of local subsystem properties act like coordinates in the space of density matrices, and suggests possible insights into the problem of interpreting quantum mechanics.     

The Electrodynamic 2-Body Problem and the Origin of Quantum Mechanics

We numerically solve the functional differential equations (FDEs) of 2-particle electrodynamics, using the full electrodynamic force obtained from the retarded Lienard–Wiechert potentials and the Lorentz force law. In contrast, the usual formulation uses only the Coulomb force (scalar potential), reducing the electrodynamic 2-body problem to a system of ordinary differential equations (ODEs). The ODE formulation is mathematically suspect since FDEs and ODEs are known to be incompatible; however, the Coulomb approximation to the full electrodynamic force has been believed to be adequate for physics. We can now test this long-standing belief by comparing the FDE solution with the ODE solution, in the historically interesting case of the classical hydrogen atom. The solutions differ. A key qualitative difference is that the full force involves a delay torque. Our existing code is inadequate to calculate the detailed interaction of the delay torque with radiative damping. However, a symbolic calculation provides conditions under which the delay torque approximately balances (3rd order) radiative damping. Thus, further investigations are required, and it was prematurely concluded that radiative damping makes the classical hydrogen atom unstable. Solutions of FDEs naturally exhibit an infinite spectrum of discrete frequencies. The conclusion is that (a) the Coulomb force is not a valid approximation to the full electrodynamic force, so that (b) the n-body interaction needs to be reformulated in various current contexts such as molecular dynamics.     

Making Sense of a World of Clicks

In a recent article, O. Ulfbeck and A. Bohr [Found. Phys. 31, 757 (2001)] have stressed the genuine fortuitousness of detector clicks, which has also been pointed out, in different terms, by the present author [Am. J. Phys. 68, 728 (2000)]. In spite of this basic agreement, the present article raises objections to the presuppositions and conclusions of Ulfbeck and Bohr, in particular their rejection of the terminology of indefinite variables, their identification of reality with the world of experience, their identification of experience with what takes place on the spacetime scene, and the claim that their interpretation of quantum mechanics is entirely liberated from classical notions. An alternative way of making sense of a world of uncaused clicks is presented. This does not invoke experience but deals with a free-standing reality, is not fettered by classical conceptions of space and time but introduces adequate ways of thinking about the spatiotemporal aspects of the quantum world, and does not reject indefinite variables but clarifies the implications of their existence.     

A Critique of Atomistic Definitions of the Stress Tensor

Current interest in nanoscale systems and molecular dynamical simulations has focussed attention on the extent to which continuum concepts and relations may be utilised meaningfully at small length scales. In particular, the notion of the Cauchy stress tensor has been examined from a number of perspectives. These include motivation from a virial-based argument, and from scale-dependent localisation procedures involving the use of weighting functions. Here different definitions and derivations of the stress tensor in terms of atoms/molecules, modelled as interacting point masses, are compared. The aim is to elucidate assumptions inherent in different approaches, and to clarify associated physical interpretations of stress. Following a critical analysis and extension of the virial approach, a method of spatial atomistic averaging (at any prescribed length scale) is presented and a balance of linear momentum is derived. The contribution of corpuscular interactions is represented by a force density field f. The balance relation reduces to standard form when f is expressed as the divergence of an interaction stress tensor field, T ⁻. The manner in which T ⁻ can be defined is studied, since T ⁻ is unique only to within a divergence-free field. Three distinct possibilities are discussed and critically compared. An approach to nanoscale systems is suggested in which f is employed directly, so obviating separate modelling of interfacial and edge effects.      

Molecular orbital calculations based on linear combinations of fragment orbitals

A semiempirical MO method based on localized fragment orbitals has been developed, which is particularly suited for the construction of orbital correlation diagrams for the discussion of the electronic structure of complex molecules in terms of fragments and their interactions. The method allows for the inclusion of experimental ionization potentials and electron affinities of the fragments within the calculation of the Fock matrix elements and may thus form the basis of an interpretation of photoelectron spectra, comparable to the interpretation of UV spectra by means of the MIM method of Longuet-Higgins and Murrell. Several levels of approximation are discussed using the acrolein molecule as an example.     

Molecular interpretation of the linear relationship between the entropy and the enthalpy of activation of charge transfer reactions in polar liquids

The well-known linear relationship (TΔS# =αΔH# +β, where 1 >α > 0,β > 0) between the entropy (ΔS#) and the enthalpy (ΔH#) of activation for reactions in polar liquids is investigated by using a molecular theory. An explicit derivation of this linear relation from first principles is presented for an outersphere charge transfer reaction. The derivation offers microscopic interpretation for the quantitiesα andβ. It has also been possible to make connection with and justify the arguments of Bell put forward many years ago     

Functional interpretation and the existence property

It is shown that functional interpretation can be used to show the existence property of intuitionistic number theory. On the basis of truth variants a comparison is then made between realisability and functional interpretation showing a structural difference between the two. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Why the Hamilton Operator Alone Is not Enough

In the many worlds community there seems to exist a belief that the physics of quantum theory is completely defined by it’s Hamilton operator given in an abstract Hilbert space, especially that the position basis may be derived from it as preferred using decoherence techniques. We show, by an explicit example of non-uniqueness, taken from the theory of the KdV equation, that the Hamilton operator alone is not sufficient to fix the physics. We need the canonical operators , as well. As a consequence, it is not possible to derive a “preferred basis” from the Hamilton operator alone, without postulating some additional structure like a “decomposition into systems”. We argue that this makes such a derivation useless for fundamental physics.