The Minimal Modal Interpretation of Quantum Theory

We introduce a realist, unextravagant interpretation of quantum theory that builds on the existing physical structure of the theory and allows experiments to have definite outcomes, but leaves the theory's basic dynamical content essentially intact. Much as classical systems have specific states that evolve along definite trajectories through configuration spaces, the traditional formulation of quantum theory asserts that closed quantum systems have specific states that evolve unitarily along definite trajectories through Hilbert spaces, and our interpretation extends this intuitive picture of states and Hilbert-space trajectories to the case of open quantum systems as well. We provide independent justification for the partial-trace operation for density matrices, reformulate wave-function collapse in terms of an underlying interpolating dynamics, derive the Born rule from deeper principles, resolve several open questions regarding ontological stability and dynamics, address a number of familiar no-go theorems, and argue that our interpretation is ultimately compatible with Lorentz invariance. Along the way, we also investigate a number of unexplored features of quantum theory, including an interesting geometrical structure---which we call subsystem space---that we believe merits further study. We include an appendix that briefly reviews the traditional Copenhagen interpretation and the measurement problem of quantum theory, as well as the instrumentalist approach and a collection of foundational theorems not otherwise discussed in the main text.Comment: 73 pages + references, 9 figures; cosmetic changes, added figure, updated references, generalized conditional probabilities with attendant changes to the sections on the EPR-Bohm thought experiment and Lorentz invariance; for a concise summary, see the companion letter at arXiv:1405.675

Creation of macroscopic superpositions of flow states with Bose-Einstein condensates

We present a straightforward scheme for creating macroscopic superpositions of different superfluid flow states of Bose-Einstein condensates trapped in optical lattices. This scheme has the great advantage that all the techniques required are achievable with current experiments. Furthermore, the relative difficulty of creating cats scales favorably with the size of the cat. This means that this scheme may be well-suited to creating superpositions involving large numbers of particles. Such states may have interesting technological applications such as making quantum-limited measurements of angular momentum.Comment: 9 pages, 7 figure

Orbital eigenchannel analysis for ab-initio quantum transport calculations

We show how to extract the orbital contribution to the transport eigenchannels from a first-principles quantum transport calculation in a nanoscopic conductor. This is achieved by calculating and diagonalizing the first-principles transmission matrix reduced to selected scattering cross-sections. As an example, the orbital nature of the eigenchannels in the case of Ni nanocontacts is explored, stressing the difficulties inherent to the use of non-orthogonal basis sets and first-principles Hamiltonians.Comment: 5 pages, 5 figurs; replaced with final version, introduction revised; to be published in PR

A mathematical model of tumor self-seeding reveals secondary metastatic deposits as drivers of primary tumor growth

Two models of circulating tumor cell (CTC) dynamics have been proposed to explain the phenomenon of tumor 'self-seeding', whereby CTCs repopulate the primary tumor and accelerate growth: Primary Seeding, where cells from a primary tumor shed into the vasculature and return back to the primary themselves; and Secondary Seeding, where cells from the primary first metastasize in a secondary tissue and form microscopic secondary deposits, which then shed cells into the vasculature returning to the primary. These two models are difficult to distinguish experimentally, yet the differences between them is of great importance to both our understanding of the metastatic process and also for designing methods of intervention. Therefore we developed a mathematical model to test the relative likelihood of these two phenomena in the subset of tumours whose shed CTCs first encounter the lung capillary bed, and show that Secondary Seeding is several orders of magnitude more likely than Primary seeding. We suggest how this difference could affect tumour evolution, progression and therapy, and propose several possible methods of experimental validation.Comment: 20 pages, 4 figure

Pension funds. asset allocation and participant age: a test of the life-cycle model

This paper examines the impact of participants. age distribution on the asset allocation of Dutch pension funds, using a unique data set of pension fund investment plans for 2007. Theory predicts a negative effect of age on (strategic) equity exposures. We observe that pension funds do indeed take the average age of their participants into account. However, the average age of active participants has been incorporated much more strongly in investment behaviour than the average ages of retired or dormant participants. This suggests that both employers and employees, who dominate pension fund boards, tend to show more interest in active participants. A one-year higher average age in active participants leads to a significant and robust reduction in the strategic equity exposure by around 0.5 percentage point. Larger pension funds show a stronger age-equity exposure effect than smaller pension funds. This age-dependent asset allocation of pension funds aligns with the original life-cycle model by which young workers should invest more in equity than older workers because of their larger human capital. Other factors, viz. fund size, funding ratio, and average pension wealth of participants, influence equity exposure positively and significantly, in line with theory. Pension plan type and pension fund type have no significant impact.Pension funds, strategic equity allocation, lifecycle saving and investing

The Birth-Death-Mutation process: a new paradigm for fat tailed distributions

Fat tailed statistics and power-laws are ubiquitous in many complex systems. Usually the appearance of of a few anomalously successful individuals (bio-species, investors, websites) is interpreted as reflecting some inherent "quality" (fitness, talent, giftedness) as in Darwin's theory of natural selection. Here we adopt the opposite, "neutral", outlook, suggesting that the main factor explaining success is merely luck. The statistics emerging from the neutral birth-death-mutation (BDM) process is shown to fit marvelously many empirical distributions. While previous neutral theories have focused on the power-law tail, our theory economically and accurately explains the entire distribution. We thus suggest the BDM distribution as a standard neutral model: effects of fitness and selection are to be identified by substantial deviations from it

Measurement and Quantum Dynamics in the Minimal Modal Interpretation of Quantum Theory

Any realist interpretation of quantum theory must grapple with the measurement problem and the status of state-vector collapse. In a no-collapse approach, measurement is typically modeled as a dynamical process involving decoherence. We describe how the minimal modal interpretation closes a gap in this dynamical description, leading to a complete and consistent resolution to the measurement problem and an effective form of state collapse. Our interpretation also provides insight into the indivisible nature of measurement—the fact that you can't stop a measurement part-way through and uncover the underlying 'ontic' dynamics of the system in question. Having discussed the hidden dynamics of a system's ontic state during measurement, we turn to more general forms of open-system dynamics and explore the extent to which the details of the underlying ontic behavior of a system can be described. We construct a space of ontic trajectories and describe obstructions to defining a probability measure on this space