The high energy limit of the trajectory representation of quantum mechanics

The trajectory representation in the high energy limit (Bohr correspondence principle) manifests a residual indeterminacy. This indeterminacy is compared to the indeterminacy found in the classical limit (Planck's constant to 0) [Int. J. Mod. Phys. A 15, 1363 (2000)] for particles in the classically allowed region, the classically forbiden region, and near the WKB turning point. The differences between Bohr's and Planck's principles for the trajectory representation are compared with the differences between these correspondence principles for the wave representation. The trajectory representation in the high energy limit is shown to go to neither classical nor statistical mechanics. The residual indeterminacy is contrasted to Heisenberg uncertainty. The relationship between indeterminacy and 't Hooft's information loss and equivalence classes is investigated.Comment: 12 pages of LaTeX. No figures. Incorporated into the "Proceedings of the Seventh International Wigner Symposium" (ed. M. E. Noz), 24-29 August 2001, U. of Maryland. Proceedings available at http://www.physics.umd.edu/robo

Quantum Transformations

We show that the stationary quantum Hamilton-Jacobi equation of non-relativistic 1D systems, underlying Bohmian mechanics, takes the classical form with $\partial_q$ replaced by $\partial_{\hat q}$ where $d\hat q={dq\over \sqrt{1-\beta^2}}$. The $\beta^2$ term essentially coincides with the quantum potential that, like $V-E$, turns out to be proportional to a curvature arising in projective geometry. In agreement with the recently formulated equivalence principle, these ``quantum transformations'' indicate that the classical and quantum potentials deform space geometry.Comment: 19 pages, LaTeX. Extended version to be published in Phys. Lett.

Canadian Monetary Policy and Real and Nominal Exchange Rates [Revised]

Abstract: This paper analyzes the relationship between Canadian Monetary Policy and the movements of Canada's real and nominal exchange rates with respect to the U.S. A broad-based theory is developed to form the basis for subsequent empirical analysis. The main empirical result is that the Canadian real exchange rate has been determined in large part by capital movements into and out of Canada as compared to the U.S. and world energy prices. Additional important determinants were world commodity prices and Canadian and U.S. real GDPs and employment rates. No evidence of effects of unanticipated money supply shocks on the nominal and real exchange rates is found. Under conditions where exchange rate overshooting is likely to occur in response to monetary demand or supply shocks, this suggests that the Bank of Canada follows an orderly-markets style of monetary policy and the conclusion is that this is the best approach under normal conditions. Finally, it is shown that in response to a domestic inflation rate that has become permanently too high or a catastrophic situation in the U.S., the Bank of Canada can induce a one-percent short-run change in the unemployment rate by pushing the nominal and real exchange rates in the appropriate direction by between five and six percent.Canadian Monetary Policy Real Exchange Rates

Canadian Monetary Policy and Real and Nominal Exchange Rates [Revised]

Abstract: This paper analyzes the relationship between Canadian Monetary Policy and the movements of Canada's real and nominal exchange rates with respect to the U.S. A broad-based theory is developed to form the basis for subsequent empirical analysis. The main empirical result is that the Canadian real exchange rate has been determined in large part by capital movements into and out of Canada as compared to the U.S. and world energy prices. Additional important determinants were world commodity prices and Canadian and U.S. real GDPs and employment rates. No evidence of effects of unanticipated money supply shocks on the nominal and real exchange rates is found. Under conditions where exchange rate overshooting is likely to occur in response to monetary demand or supply shocks, this suggests that the Bank of Canada follows an orderly-markets style of monetary policy and the conclusion is that this is the best approach under normal conditions. Finally, it is shown that in response to a domestic inflation rate that has become permanently too high or a catastrophic situation in the U.S., the Bank of Canada can induce a one-percent short-run change in the unemployment rate by pushing the nominal and real exchange rates in the appropriate direction by between five and six percent.Canadian Monetary Policy Real Exchange Rates

Canadian Monetary Policy and Real and Nominal Exchange Rates

This paper analyzes the relationship between Canadian Monetary Policy and the movements of Canada's real and nominal exchange rates with respect to the U.S. A broad-based theory is developed to form the basis for subsequent empirical analysis. The main empirical result is that the Canadian real exchange rate has been determined in large part by capital movements into and out of Canada as compared to the U.S. and world energy prices. Additional important determinants were world commodity prices and Canadian and U.S. real GDPs and employment rates. No evidence of effects of unanticipated money supply shocks on the nominal and real exchange rates is found. Under conditions where exchange rate overshooting is likely to occur in response to monetary demand or supply shocks, this suggests that the Bank of Canada follows an orderly-markets style of monetary policy and the conclusion is that this is the best approach under normal conditions. Finally, it is shown that in response to a domestic inflation rate that has become permanently too high or a catastrophic situation in the U.S., the Bank of Canada can induce a one-percent short-run change in the unemployment rate by pushing the nominal and real exchange rates in the appropriate direction by between five and six percent.Real Exchange Rate Canadian Monetary Policy

Interference, reduced action, and trajectories

Instead of investigating the interference between two stationary, rectilinear wave functions in a trajectory representation by examining the two rectilinear wave functions individually, we examine a dichromatic wave function that is synthesized from the two interfering wave functions. The physics of interference is contained in the reduced action for the dichromatic wave function. As this reduced action is a generator of the motion for the dichromatic wave function, it determines the dichromatic wave function's trajectory. The quantum effective mass renders insight into the behavior of the trajectory. The trajectory in turn renders insight into quantum nonlocality.Comment: 12 pages text, 5 figures. Typos corrected. Author's final submission. A companion paper to "Welcher Weg? A trajectory representation of a quantum Young's diffraction experiment", quant-ph/0605121. Keywords: interference, nonlocality, trajectory representation, entanglement, dwell time, determinis

The Equivalence Postulate of Quantum Mechanics

The Equivalence Principle (EP), stating that all physical systems are connected by a coordinate transformation to the free one with vanishing energy, univocally leads to the Quantum Stationary HJ Equation (QSHJE). Trajectories depend on the Planck length through hidden variables which arise as initial conditions. The formulation has manifest p-q duality, a consequence of the involutive nature of the Legendre transform and of its recently observed relation with second-order linear differential equations. This reflects in an intrinsic psi^D-psi duality between linearly independent solutions of the Schroedinger equation. Unlike Bohm's theory, there is a non-trivial action even for bound states. No use of any axiomatic interpretation of the wave-function is made. Tunnelling is a direct consequence of the quantum potential which differs from the usual one and plays the role of particle's self-energy. The QSHJE is defined only if the ratio psi^D/psi is a local self-homeomorphism of the extended real line. This is an important feature as the L^2 condition, which in the usual formulation is a consequence of the axiomatic interpretation of the wave-function, directly follows as a basic theorem which only uses the geometrical gluing conditions of psi^D/psi at q=\pm\infty as implied by the EP. As a result, the EP itself implies a dynamical equation that does not require any further assumption and reproduces both tunnelling and energy quantization. Several features of the formulation show how the Copenhagen interpretation hides the underlying nature of QM. Finally, the non-stationary higher dimensional quantum HJ equation and the relativistic extension are derived.Comment: 1+3+140 pages, LaTeX. Invariance of the wave-function under the action of SL(2,R) subgroups acting on the reduced action explicitly reveals that the wave-function describes only equivalence classes of Planck length deterministic physics. New derivation of the Schwarzian derivative from the cocycle condition. "Legendre brackets" introduced to further make "Legendre duality" manifest. Introduction now contains examples and provides a short pedagogical review. Clarifications, conclusions, ackn. and references adde