Relative State Research Articles

On Explaining Experiences of a Quantum World

“the view advanced by H. W. Everett (1957)—that there simply is no reduction—quite fails to account for the actual phenomena of physics, which we may summarize as the appearance of reduction: namely, our experience of definite observations.” (Stein 1983, p. 573.)In an interesting recent paper, Geroch (1984) has sought to state the content of, “and to some extent to advocate” a view toward quantum mechanics which is at least closely akin to the view advanced by Everett, known popularly (but, arguably, misleadingly) as the many-worlds interpretation. While sensitive to objections along the lines of that by Stein quoted above, Geroch believes that these can adequately be answered. The key to answering such objections is to argue that physics is not responsible for accounting for our experience of physical phenomena—it is enough that it account for the physical phenomena themselves. It is this last argument that I wish to examine in this paper, both in general, and specifically in its application to Everett's interpretation of quantum mechanics.

Few-nucleon transfer reactions on 15N and 16O

We have studied one-, two- and three-particle transfer reactions induced by 115 MeV 11B and 12C, 126 MeV 18O and 105 MeV 13C ions on gas targets of 15N and 16O. These reactions are found to be very selective; in some cases only one excited state in the final nucleus is populated. The reactions on 16O excite mainly high spin states with n particles in the sd shell in a relative s-state. Reactions on 15N excite positive parity states by transferring one particle into the p-shell and n − 1 into the sd shell and negative parity states which have the structure p −1(sd) n . These latter states correspond to weak coupling of a p 1 2 hole to the states excited in the corresponding transfer reaction bn 16O. Shell model wave functions have been computed for the two-particle one-hole states of mass 17 and for the three-particle one-hole states of mass 18. The overlaps of these with weak coupling wave functions were calculated in order to justify the application of the weak coupling model in this mass region. The qualitative difference in the spectra of the T = 0 and T = 1 negative parity states of mass 18 is reproduced and explained in a simple fashion.

A note on the Everett interpretation of quantum mechanics

Three aspects of the Everett interpretation of quantum mechanics are considered. It is first shown that the proof of the metatheorem is not complete—thus it is an open question as to whether or not it is true. Next, some difficulties for the Everett interpretation and the metatheorem, which arise from consideration of the physics developed by observers in maverick universes, are discussed. Finally, it is shown that the universal state description of an ever-branching universe with each branch corresponding to a possible perceived universe fails completely in the limit of an infinite number of successive branchings.

Isobar configurations in closed shell nuclei

Explicit expressions for one- and two-N ∗ isobar configurations in closed shell nuclei have been derived in the impulse approximation and applied to 4He and 16O. Conventional transition potentials with π- and ϱ-exchange have been used and the influence of potential regularization and short-range correlations have been studied. The dominant isobar configurations are found to be the one- and two-Δ components and originate from two-nucleon pairs in a relative S-state. The probability for finding a nucleon as a Δ-isobar is about 4.5% in 4He and about 3.2% in 16O. These numbers should be considered as upper limits due to uncertainties in off-shell effects of the transition potentials.

Finite and infinite measurement sequences in quantum mechanics and randomness: The Everett interpretation

The quantum mechanical description of both a finite and infinite number of measurement repetitions, as interactions between copies of an object system and a record system, are considered here. States describing the asymptotic situation of an infinite number of repetitions are seen to have some interesting properties. The main construction of the paper is the association of states to sequential tests for randomness. To each such test T and each positive integer m one can associate states ΘnTm and Θ∞Tm corresponding respectively to those length-n and finite outcome sequences which pass test T at the significance level 2−m. Following the methods of Martin Löf, a universal sequential test V, which includes an infinity of sequential statistical tests for randomness, is given and the corresponding states ΘnVm and Θ∞Vm are discussed. Finally, a possible use of these states in the Everett interpretation of quantum mechanics is discussed.

Three-body bound-state calculation in momentum space

Thc determination of 3-body bound and scattering states for (( real ist ic , two-body and three-body interactions, which are in general not separable, is still a formidable task. One would like to have a clear and economic algorithm to allow an easy test of various nuclear-interaction models. To that aim we have looked into the method proposed by KIM (1) for the calculation of bound states. One is faced with a problem in two continuous variables Pz= 89 I/r k,I, qz = ~ Ik~ 89 (kin -~ k.)[, where kl, 1 = 1, 2, 3 are the momenta of the 3 particles. One gains a drastic reduction in the dimension of the problem if the p-dependence can be exhausted by a few suitably chosen basis functions ~v.(p), taken from a complcte set. We want to propose such a set, which is tightly adapted to the problem under consideration. With an eye towards mesontheoretical nucleon-nucleon interactions the method is developpcd in momentum space, however, demonstrated only for three identical bosons interacting in relative s-states. The Faddeev wave function amplitude then obeys the equation

Translationally invariant and non-translationally invariant empirical effective interactions

In this work we examine empirical deficiencies of the core-renormalized realistic effective interactions and seek simple corrective potentials. We note the inability of the current realistic interactions to account for the energies of isobaric analog states; likewise they are unable to reproduce the changes in the single-particle energies, as one goes from one closed shell to another. We note that the Schiffer interaction gives better results for these gross properties and we attribute this to a combination of several facts. First, to the inclusion of long range terms in the Schiffer potential, then to the presence of relative p-state terms ( l = 1), in addition to the usual relative s-state terms ( l = 0). We further attribute the strange shape of the above interaction to the fact that it is translationally invariant, whereas the theory of core-polarization yields non-translationally invariant potentials. Consequently, as a correction to the monopole deficiencies of the realistic interactions we propose the term V mon = ar 2(1) r 2(2)+ β[ r 4(1) r 2(2)+ r 2(1) r 4(2)].

Quantum Theory and Cosmolog

Interpretations, or generalizations, of quantum theory that are applicable to cosmology are of interest because they must display and resolve the “paradoxes” directly. The Everett interpretation is reexamined and compared with two alternatives. Its “metaphysical” connotations can be removed, after which it is found to be more acceptable than a theory which incorporates collapse, while retaining some unsatisfactory features.

A new analysis of angular distributions attributed to the neutron-proton final state interaction in the reaction pd → ppn

Recently measured angular distributions attributed to the neutron-proton final state interaction at zero relative energy in the reaction pd → ppn are analyzed with an exact threebody theory using spin-dependent separable potentials for relative S-states of two nucleons. The relation between the Watson factorization ansatz and the exact theory is demonstrated for the case of the angular distribution measured with an incident beam of 52 MeV deuterons.

Van Fraassen's Modal Model of Quantum Mechanics

Bas van Fraassen in [4] has recently tried to use modal logic to solve the measurement problem of quantum mechanics. His model is based on a method of expressing quantum states developed by Hugh Everett [1] called the “relative state formulation.” Unfortunately, Everett's mathematics cannot be generalized as van Fraassen requires. The difficulty itself is elementary enough. But a revision of van Fraassen's postulates (such as the one he adopted on p. 341 after he had been told of the problem) can save the mathematics only on pain of making the whole study irrelevant to the physics. I shall explain the dilemma in this note. In a later paper [5], van Fraassen avoids this dilemma by developing an abstract modal interpretation which does not rely on any expression for quantum states.

Philosophical Problems: The Many-Worlds Interpretation of Quantum Mechanics . A Fundamental Exposition. Bryce S. DeWitt and Neill Graham, Eds. Princeton University Press, Princeton, N.J., 1973. viii, 253 pp. Cloth, $12.50; paper, $5.50. Princeton Series in Physics.

Philosophical Problems: <i>The Many-Worlds Interpretation of Quantum Mechanics</i> . A Fundamental Exposition. Bryce S. DeWitt and Neill Graham, Eds. Princeton University Press, Princeton, N.J., 1973. viii, 253 pp. Cloth, $12.50; paper, $5.50. Princeton Series in Physics.

Finite-range calculation of two-neutron transfer reactions on rare-earth nuclei

Finite-range DWBA calculations have been done for (p, t) reactions on rare-earth nuclei. The perturbation interaction acting between the proton and each transferred neutron was assumed to have a Gaussian shape. At low incident energy, very good agreement with the zero-range calculation was found both in the shapes of the angular distributions and in the magnitudes of the cross sections for the 2 + and 4 + ground-band members relative to the ground-state transition. At high incident energy, however, the finite-range calculations produced considerable changes in the shapes of the angular distributions. The better agreement with the experimental data indicates the importance of the finite-range interaction at high incident energies. It was also found that the errors introduced by assuming a transferred pair to be in a relative s-state have surprisingly little effect on the shapes and the magnitudes of the cross sections.

Harmonic oscillator potential insertions in particle lines

Brueckner calculations of the binding energy of finite nuclei are usually performed with harmonic oscillator single-particle wave functions. Therefore it is computationally more convenient to keep the oscillator potential in intermediate states and then subtract out its effects by calculating higher-order diagrams involving potential insertions in particle lines. It is found that the lowest-order diagram involving a single potential insertion in a particle line can be approximated by — κ U ̄ c.m. , where κ is the wound integral and U ̄ c.m . is the average over the c.m. potential energy of the pairs of particles in the nucleus which occupy relative S-states.

Theoretical analysis of p+ 4He reactions at 46.7 MeV

Using the plane wave Born approximation (PWBA), angular distributions and energy spectra of p+ 4He reactions are analysed taking into account the final state interaction (FSI) between the final state nucleon pair in their relative S-state, Reasonable agreement with angular distributions can be obtained by introducing a lower cutoff in the radial overlap integrals. Effects of the cutoff in the energy spectra are discussed and found to be important. Results of a calculation with the distorted wave Born approximation (DWBA) of the 4He(p, d) 3He reaction are also presented.

Shell-model matrix elements from a realistic potential

We present a new method of calculating the effective matrix elements of a “realistic” two- body interaction. We assume that the unperturbed energies of the single-particle states are those of a harmonic oscillator. For two particles outside an inert core, the problem can in some instances be solved exactly; in other cases, it is necessary to approximate the Pauli principle (in a way that is later shown to be justified). The theory is applied to 6He, and for interaction energies involving relative s-state motion, our matrix elements are about 20% more attractive than those computed by use of the bare G-matrix. Since the G-matrix calculations assume free-particle energies for states outside the model space, this difference gives some measure of the sensitivity of the computed T = 1 matrix elements to assumptions about the single-particle energies used in intermediate states.

Absorption of stopped K$minus$ mesons by light nuclei

The non-mesonic and non-radiative capture processes of K− mesons in light nuclei, K−+2N -> Λ +N and K−+2N -> Σ+N, have been investigated using a pair-absorption model. It is shown that the ratio of the capture rate by the relative D-state pair to that by the relative S-state pair is very sensitive to the short-range nuclear correlations.

Trinucleon three-body photodisintegration

Corrections to the three-body photodisintegration cross section due to (i) the use of an S-state containing a soft core and the inclusion of admixed states of the S′ and D type in the ground state and (ii) final-state interactions between nucleons in relative s-states are calculated. A satisfactory fit to the data is obtained for energies up to the peak cross section.

Intrinsic states of deformed nuclei in the Hartree-Fock (HF) approximation

This paper deals with an application of the HF method to deformed nuclei. The two nucleon interaction used is a non-local separable potential which acts only in relative s-states. The HF equations are solved in the matrix formulation. Calculations are performed for 16O, 20Ne, 24Mg, 28Si, 32S, Ar and 40Ca. The 4p-4h state of 16O is also investigated. Solutions correponding to different kinds of deformation are investigated. Single-particle energies and wave functions are obtained. The intrinsic quadrupole moments are also calculated.

Calculation of binding energy of the 16O nucleus

A method to calculate binding energies of nuclei by K-matrix theory is presented and applied to 16O. A first-order approximation to the K-matrix is obtained by neglecting the Pauli principle and potential energies in intermediate states. Thus to first order we consider the Puff-Mohling reaction matrix. In light of recent work on the effect of the three-body interaction it seems a reasonable approximation to neglect potential energies in intermediate states. Thus the only correction term is due to the Pauli principle. The method is however easily extended to a more general energy spectrum. It can be applied to finite nuclei as well as to infinite nuclear matter. Formally our method to calculate the K-matrix is similar to the “reference spectrum” method of Bethe, Brandow and Petschek applied by them to infinite nuclear matter. We apply our method to 16O using harmonic oscillator single-particle wave functions and a nucleon-nucleon interaction represented by a spin independent exponential potential giving infinite scattering length and 2.5 fm effective range (Moszkowski-Scott potential) acting only in relative s-states. A binding energy of 2.77 MeV/nucleon is obtained. The Puff-Mohling K-matrix, i.e. our first-order K-matrix, gives 1.7 MeV/nucleon more binding. Comparison with the in principle more approximate separation method calculation gives perfect agreement.

A study of the Hartree-Fock approximation as applied to finite nuclei

Hartree-Fock calculations have been performed for the closed-shell nuclei 16O, 40Ca and 80Zr, and, with certain simple approximations, for the open-shell nuclei 12C, 28Si and 60Zn. The velocity-dependent, two-body force acts in relative s-states only. The force saturates nuclear matter at the correct energy and density and yields small second-order perturbation corrections, but has too large a range to be in good agreement with the two-body data. However the choice of this simple force enables us to study the Hartree-Fock approximation in detail which is the main purpose of this paper. We calculate wave functions, energy levels, binding energies and density distributions for the six nuclei and obtain rough agreement with the experimental results. A discussion is given of the non-local Hartree-Fock potential.