Friends,
With Adrian Freed, I asked ca. 2010-2011 whether one could invert the conventional time-dependence of our measurable observables. Can we regard time (or more properly duration) not as an independent variable but as an outcome of dynamic material
process, e.g. as an observable, i.e. an operator? (Caveat, changing the question from pointwise time to duration may radically change the question because I do not assume that “time” must be modeled by a scalar field like
R or C (algebraist’s field, not physicist’s field!).)
I remember Mike Epperson’s first response in UC Davis last year was the reminder that in QM, such operators must be self-adjoint. Cold splash. However, hope springs eternal :) I have radically empirical as well as conceptual reasons to persevere
in this hunch.
The following may be relevant:
Abstract
We extend the concept of time operator for general semigroups and construct a non-self-adjoint time operator for the diffusion equation which is intertwined with the unilateral shift. We obtain the spectral resolution, the age eigenstates and a new shift representation of the solution of the diffusion equation. Based on previous work we obtain similarly a self-adjoint time operator for Relativistic Diffusion.
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Sha Xin Wei • Professor
and Director • School of Arts, Media and Engineering + Synthesis • Rhythmanalysis
Herberger Institute for Design and the Arts + Fulton Schools of Engineering • ASU
Fellow: ASU-Santa Fe Center for Complex Biosocial Systems
Affiliate Professor: Future of Innovation in Society; Computer Science; English
Founding Director, Topological Media Lab
Affiliate Professor: Future of Innovation in Society; Computer Science; English
Founding Director, Topological Media Lab
skype: shaxinwei • mobile: +1-650-815-9962
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