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Gordon N. Fleming

Publications and source records attributed to Gordon N. Fleming.

5 recordsLinked to original sources
arXiv2011

On the Quantum Deviations from Einstein Dilation of Unstable Quanton Decay Evolution and Lifetimes

For over a decade several workers have argued for the existence of quantum deviations from the classical, Einstein dilation of the decay evolution of moving or Lorentz boosted unstable particles. While the general claim is correct, the discussions have been incomplete and, sometimes, misleading. The discussions have been of three kinds. Type 1 examines the time dependence of the survival probability for 3-momentum eigenstates of the unstable quanton (Khalfin). Type 2 does the same for velocity eigenstates, obtaining an outrageous result which then discredits velocity eigenstates (Shirokov / Hegerfeldt). Type 3 examines arbitrary boosts of 3-momentum eigenstates (Stefanovich). Type 1 is incomplete since the momentum eigenstates are not the boosts of one another. Type 2 is misleading since the outrageous result is due to misinterpreting the initial conditions of the velocity eigenstates (as I have previously argued). Type 3 is the most satisfactory, but has failed to recognize and implement the unification of all three types of discussion that can be achieved. In this paper I will provide that unified treatment, beginning with a recapitulation of Type 1 and offering further clarification of Type 2 in the process. The unified treatment fully reinstates velocity eigenstates as essential contributors to unstable quanton states. Besides discussing the time evolution of survival probabilities I also focus on the concept of lifetime defined as the average time of decay. This quantity is helpful in order to display the inequivalent dependence of dilation on momentum and boosts most sharply and the deviation from Einstein dilation most cleanly.

quant-ph↗
arXiv2009

Observations on Unstable Quantons, Hyperplane Dependence and Quantum Fields

There is persistent heterodoxy in the physics literature concerning the proper treatment of those quantons that are unstable against spontaneous decay. Following a brief litany of this heterodoxy, I develop some of the consequences of assuming that such quantons can exist, undecayed and isolated, at definite times and that their treatment can be carried out within a standard quantum theoretic state space. This assumption requires hyperplane dependence for the unstable quanton states and leads to clarification of some recent results concerning deviations from relativistic time dilation of decay lifetimes. In the course of the discussion I make some observations on the relationship of unstable quantons to quantum fields.

quant-ph↗
arXiv2007

Correlation coefficients and the Robertson-Schroedinger uncertainty relations

Calling the quantity; 2delta(A)delta(B)/|<[A, B]>|, with non-zero denominator, the uncertainty product ratio or UPR for the pair of observables, (A, B), it is shown that any non-zero correlation coefficient between two observables raises, above unity, the lower bound of the UPR for each member of an infinite collection of pairs of incompatible observables. Conversely, any UPR is subject to lower bounds above unity determined by each of an infinite collection of correlation coefficients. This result generalizes the well known Schroedinger strengthening of the Robertson uncertainty relations (with the former expressed in terms of the correlation coefficient rather than the anticommutator) where the UPR and the correlation coefficient both involve the same pair of observables. Two, independent, derivations of the result are presented to clarify its origins and some examples of its use are examined.

quant-ph↗
arXiv2001

Uses of a Quantum Master Inequality

An inequality in quantum mechanics, which does not appear to be well known, is derived by elementary means and shown to be quite useful. The inequality applies to 'all' operators and 'all' pairs of quantum states, including mixed states. It generalizes the rule of the orthogonality of eigenvectors for distinct eigenvalues and is shown to imply all the Robertson generalized uncertainty relations. It severely constrains the difference between probabilities obtained from 'close' quantum states and the different responses they can have to unitary transformations. Thus, it is dubbed a master inequality. With appropriate definitions the inequality also holds throughout general probability theory and appears not to be well known there either. That classical inequality is obtained here in an appendix. The quantum inequality can be obtained from the classical version but a more direct quantum approach is employed here. A similar but weaker classical inequality has been reported by Uffink and van Lith.

physics.atom-ph↗