Jacobi's Principle and the Disappearance of Time

Jacobi's action principle is known to lead to a problem of time. For example, the timelessness of the Wheeler-DeWitt equation can be seen as resulting from using Jacobi's principle to define the dynamics of 3-geometries through superspace. In addition, using Jacobi's principle for non-relativistic particles is equivalent classically to Newton's theory but leads to a time-independent Schrodinger equation upon Dirac quantization. In this paper, we study the mechanism for the disappearance of time as a result of using Jacobi's principle in these simple particle models. We find that the path integral quantization very clearly elucidates the physical mechanism for the timeless of the quantum theory as well as the emergence of duration at the classical level. Physically, this is the result of a superposition of clocks which occurs in the quantum theory due to a sum over all histories. Mathematically, the timelessness is related to how the gauge fixing functions impose the boundary conditions in the path integral.Comment: Published version. Significant amendments to presentation. 27 page

Unsharp Quantum Reality

The positive operator (valued) measures (POMs) allow one to generalize the notion of observable beyond the traditional one based on projection valued measures (PVMs). Here, we argue that this generalized conception of observable enables a consistent notion of unsharp reality and with it an adequate concept of joint properties. A sharp or unsharp property manifests itself as an element of sharp or unsharp reality by its tendency to become actual or to actualize a specific measurement outcome. This actualization tendency-or potentiality-of a property is quantified by the associated quantum probability. The resulting single-case interpretation of probability as a degree of reality will be explained in detail and its role in addressing the tensions between quantum and classical accounts of the physical world will be elucidated. It will be shown that potentiality can be viewed as a causal agency that evolves in a well-defined way

Types of quantum information

Quantum, in contrast to classical, information theory, allows for different incompatible types (or species) of information which cannot be combined with each other. Distinguishing these incompatible types is useful in understanding the role of the two classical bits in teleportation (or one bit in one-bit teleportation), for discussing decoherence in information-theoretic terms, and for giving a proper definition, in quantum terms, of ``classical information.'' Various examples (some updating earlier work) are given of theorems which relate different incompatible kinds of information, and thus have no counterparts in classical information theory.Comment: Minor changes so as to agree with published versio

Diffuse venting at the ASHES hydrothermal field : heat flux and tidally modulated flow variability derived from in situ time-series measurements

Author Posting. © American Geophysical Union, 2016. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Geochemistry, Geophysics, Geosystems 17 (2016): 1435–1453, doi:10.1002/2015GC006144.Time-series measurements of diffuse exit-fluid temperature and velocity collected with a new, deep-sea camera, and temperature measurement system, the Diffuse Effluent Measurement System (DEMS), were examined from a fracture network within the ASHES hydrothermal field located in the caldera of Axial Seamount, Juan de Fuca Ridge. The DEMS was installed using the HOV Alvin above a fracture near the Phoenix vent. The system collected 20 s of 20 Hz video imagery and 24 s of 1 Hz temperature measurements each hour between 22 July and 2 August 2014. Fluid velocities were calculated using the Diffuse Fluid Velocimetry (DFV) technique. Over the ∼12 day deployment, median upwelling rates and mean fluid temperature anomalies ranged from 0.5 to 6 cm/s and 0°C to ∼6.5°C above ambient, yielding a heat flux of 0.29 ± 0.22 MW m−2 and heat output of 3.1± 2.5 kW. Using a photo mosaic to measure fracture dimensions, the total diffuse heat output from cracks across ASHES field is estimated to be 2.05 ± 1.95 MW. Variability in temperatures and velocities are strongest at semidiurnal periods and show significant coherence with tidal height variations. These data indicate that periodic variability near Phoenix vent is modulated both by tidally controlled bottom currents and seafloor pressure, with seafloor pressures being the dominant influence. These results emphasize the importance of local permeability on diffuse hydrothermal venting at mid-ocean ridges and the need to better quantify heat flux associated with young oceanic crust.NSF Grant Numbers: OCE-1131772, OCE-1131455, OCE-1337473; University of Washington, and the NSF award Grant Number: OCE-09579382016-10-2

Type-Decomposition of a Pseudo-Effect Algebra

The theory of direct decomposition of a centrally orthocomplete effect algebra into direct summands of various types utilizes the notion of a type-determining (TD) set. A pseudo-effect algebra (PEA) is a (possibly) noncommutative version of an effect algebra. In this article we develop the basic theory of centrally orthocomplete PEAs, generalize the notion of a TD set to PEAs, and show that TD sets induce decompositions of centrally orthocomplete PEAs into direct summands.Comment: 18 page

The Definition of Mach's Principle

Two definitions of Mach's principle are proposed. Both are related to gauge theory, are universal in scope and amount to formulations of causality that take into account the relational nature of position, time, and size. One of them leads directly to general relativity and may have relevance to the problem of creating a quantum theory of gravity.Comment: To be published in Foundations of Physics as invited contribution to Peter Mittelstaedt's 80th Birthday Festschrift. 30 page

Classical Vs Quantum Probability in Sequential Measurements

We demonstrate in this paper that the probabilities for sequential measurements have features very different from those of single-time measurements. First, they cannot be modelled by a classical stochastic process. Second, they are contextual, namely they depend strongly on the specific measurement scheme through which they are determined. We construct Positive-Operator-Valued measures (POVM) that provide such probabilities. For observables with continuous spectrum, the constructed POVMs depend strongly on the resolution of the measurement device, a conclusion that persists even if we consider a quantum mechanical measurement device or the presence of an environment. We then examine the same issues in alternative interpretations of quantum theory. We first show that multi-time probabilities cannot be naturally defined in terms of a frequency operator. We next prove that local hidden variable theories cannot reproduce the predictions of quantum theory for sequential measurements, even when the degrees of freedom of the measuring apparatus are taken into account. Bohmian mechanics, however, does not fall in this category. We finally examine an alternative proposal that sequential measurements can be modelled by a process that does not satisfy the Kolmogorov axioms of probability. This removes contextuality without introducing non-locality, but implies that the empirical probabilities cannot be always defined (the event frequencies do not converge). We argue that the predictions of this hypothesis are not ruled out by existing experimental results (examining in particular the "which way" experiments); they are, however, distinguishable in principle.Comment: 56 pages, latex; revised and restructured. Version to appear in Found. Phy