74 research outputs found
Common Axioms for Inferring Classical Ensemble Dynamics and Quantum Theory
The same set of physically motivated axioms can be used to construct both the
classical ensemble Hamilton-Jacobi equation and Schrodingers equation. Crucial
roles are played by the assumptions of universality and simplicity (Occam's
Razor) which restrict the number and type of of arbitrary constants that appear
in the equations of motion. In this approach, non-relativistic quantum theory
is seen as the unique single parameter extension of the classical ensemble
dynamics. The method is contrasted with other related constructions in the
literature and some consequences of relaxing the axioms are also discussed: for
example, the appearance of nonlinear higher-derivative corrections possibly
related to gravity and spacetime fluctuations. Finally, some open research
problems within this approach are highlighted.Comment: Final proceedings version. 6 pages. Presented at the 3rd QTRF
conference at Vaxjo, Sweden, June6-11 200
Why is Schrodinger's Equation Linear?
Information-theoretic arguments are used to obtain a link between the
accurate linearity of Schrodinger's equation and Lorentz invariance: A possible
violation of the latter at short distances would imply the appearance of
nonlinear corrections to quantum theory. Nonlinear corrections can also appear
in a Lorentz invariant theory in the form of higher derivative terms that are
determined by a length scale, possibly the Planck length. It is suggested that
the best place to look for evidence of such quantum nonlinear effects is in
neutrino physics and cosmology.Comment: 3 pages; Presented at the DICE 2004 workshop; Sept 2004, Piombino
Italy. Minor corrections: this is the proceedings Versio
Nonlinear Dirac Equations
We construct nonlinear extensions of Dirac's relativistic electron equation
that preserve its other desirable properties such as locality, separability,
conservation of probability and Poincar\'e invariance. We determine the
constraints that the nonlinear term must obey and classify the resultant
non-polynomial nonlinearities in a double expansion in the degree of
nonlinearity and number of derivatives. We give explicit examples of such
nonlinear equations, studying their discrete symmetries and other properties.
Motivated by some previously suggested applications we then consider nonlinear
terms that simultaneously violate Lorentz covariance and again study various
explicit examples. We contrast our equations and construction procedure with
others in the literature and also show that our equations are not gauge
equivalent to the linear Dirac equation. Finally we outline various physical
applications for these equations
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