Measurement as Absorption of Feynman Trajectories: Collapse of the Wave Function Can be Avoided

We define a measuring device (detector) of the coordinate of quantum particle as an absorbing wall that cuts off the particle's wave function. The wave function in the presence of such detector vanishes on the detector. The trace the absorbed particles leave on the detector is identifies as the absorption current density on the detector. This density is calculated from the solution of Schr\"odinger's equation with a reflecting boundary at the detector. This current density is not the usual Schr\"odinger current density. We define the probability distribution of the time of arrival to a detector in terms of the absorption current density. We define coordinate measurement by an absorbing wall in terms of 4 postulates. We postulate, among others, that a quantum particle has a trajectory. In the resulting theory the quantum mechanical collapse of the wave function is replaced with the usual collapse of the probability distribution after observation. Two examples are presented, that of the slit experiment and the slit experiment with absorbing boundaries to measure time of arrival. A calculation is given of the two dimensional probability density function of a free particle from the measurement of the absorption current on two planes.Comment: 20 pages, latex, no figure

A Path Intergal Approach to Current

Discontinuous initial wave functions or wave functions with discontintuous derivative and with bounded support arise in a natural way in various situations in physics, in particular in measurement theory. The propagation of such initial wave functions is not well described by the Schr\"odinger current which vanishes on the boundary of the support of the wave function. This propagation gives rise to a uni-directional current at the boundary of the support. We use path integrals to define current and uni-directional current and give a direct derivation of the expression for current from the path integral formulation for both diffusion and quantum mechanics. Furthermore, we give an explicit asymptotic expression for the short time propagation of initial wave function with compact support for both the cases of discontinuous derivative and discontinuous wave function. We show that in the former case the probability propagated across the boundary of the support in time $\Delta t$ is $O(\Delta t^{3/2})$ and the initial uni-directional current is $O(\Delta t^{1/2})$. This recovers the Zeno effect for continuous detection of a particle in a given domain. For the latter case the probability propagated across the boundary of the support in time $\Delta t$ is $O(\Delta t^{1/2})$ and the initial uni-directional current is $O(\Delta t^{-1/2})$. This is an anti-Zeno effect. However, the probability propagated across a point located at a finite distance from the boundary of the support is $O(\Delta t)$. This gives a decay law.Comment: 17 pages, Late

Matter wave pulses characteristics

We study the properties of quantum single-particle wave pulses created by sharp-edged or apodized shutters with single or periodic openings. In particular, we examine the visibility of diffraction fringes depending on evolution time and temperature; the purity of the state depending on the opening-time window; the accuracy of a simplified description which uses ``source'' boundary conditions instead of solving an initial value problem; and the effects of apodization on the energy width.Comment: 11 pages, 11 figure

Urinary Aminopeptidase Activities as Early and Predictive Biomarkers of Renal Dysfunction in Cisplatin-Treated Rats

This study analyzes the fluorimetric determination of alanyl- (Ala), glutamyl- (Glu), leucyl-cystinyl- (Cys) and aspartyl-aminopeptidase (AspAp) urinary enzymatic activities as early and predictive biomarkers of renal dysfunction in cisplatin-treated rats. Male Wistar rats (n = 8 each group) received a single subcutaneous injection of either saline or cisplatin 3.5 or 7 mg/kg, and urine samples were taken at 0, 1, 2, 3 and 14 days after treatment. In urine samples we determined Ala, Glu, Cys and AspAp activities, proteinuria, N-acetyl-β-D-glucosaminidase (NAG), albumin, and neutrophil gelatinase-associated lipocalin (NGAL). Plasma creatinine, creatinine clearance and renal morphological variables were measured at the end of the experiment. CysAp, NAG and albumin were increased 48 hours after treatment in the cisplatin 3.5 mg/kg treated group. At 24 hours, all urinary aminopeptidase activities and albuminuria were significantly increased in the cisplatin 7 mg/kg treated group. Aminopeptidase urinary activities correlated (p0.259) with plasma creatinine, creatinine clearance and/or kidney weight/body weight ratio at the end of the experiment and they could be considered as predictive biomarkers of renal injury severity. ROC-AUC analysis was made to study their sensitivity and specificity to distinguish between treated and untreated rats at day 1. All aminopeptidase activities showed an AUC>0.633. We conclude that Ala, Cys, Glu and AspAp enzymatic activities are early and predictive urinary biomarkers of the renal dysfunction induced by cisplatin. These determinations can be very useful in the prognostic and diagnostic of renal dysfunction in preclinical research and clinical practice.This study was supported by a grant (R1/12/2010/66) from the University of Jaén with the participation of Caja Rural of Jaén, and from the Carlos III Health Institute of the Spanish Ministry of Health and Consumer Affairs (Red de Investigación Renal, REDinREN RD06/0016/0017 and RD07/0016/2008), “FEDER una manera de hacer Europa.