Limit of Quantum Mechanics: Classical Mechanics in High Entropy
Discover how classical mechanics emerges as a high-entropy limit of quantum mechanics. Explore the fundamental differences and the potential of recovering classical mechanics from the high-entropy state in this intriguing study by Carcassi, Landini, and Aidala.
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Classical mechanics as the high-entropy limit of quantum mechanics Gabriele Carcassi , Manuele Landini and Christine A. Aidala Physics Department University of Michigan Institut f r Experimental Physik und Zentrum f r Quantenphysik, Universit t Innsbruck
Main goal of the project Identify a handful of physical starting points from which the basic laws can be rigorously derived For example: Irreducibility Quantum state Infinitesimal reducibility Classical state https://assumptionsofphysics.org ? time time This also requires rederiving all mathematical structures from physical requirements For example: Science is evidence based scientific theory must be characterized by experimentally verifiable statements topology and ?-algebras https://assumptionsofphysics.org/
previous results Third law of thermodynamics ? 0 ? ? = 0 Physical entropy is absolute ? Statistical mechanics ? ?? = log ? ? Define as the support of a uniform distribution of zero entropy ? ? = ?log ????? Fixes units (i.e. log argument is a pure number) and zero of entropy https://assumptionsofphysics.org/
Lets plot entropy against uncertainty ? Gaussian maximizes entropy for a given uncertainty ? ? log2?????? ???? excluded by 3rd law of thermodynamics 2???? ?= ??? ? ???? ? 0 ???? ? Classical uncertainty principle https://assumptionsofphysics.org/
Quantum mechanics incorporates the third law while classical mechanics does not Is this the only difference? Suppose the lower bound on the entropy is the only difference, then in the limit of high entropy of quantum mechanics we should recover classical mechanics Can we? https://assumptionsofphysics.org/
06/01/2024 https://assumptionsofphysics.org/
Looking for a map ?(?) that increases entropy of all mixed states, such that every level set of entropy maps to another level set ? Unitary must be mapped to unitary ? ? Entropy increasing map Unitary map ???? excluded by 3rd law of thermodynamics classical quantum https://assumptionsofphysics.org/
In classical mechanics ? ? ? = ? ? + log? ? ? ,? ? = ?{?,?} In quantum mechanics Jacobian is a constant: all volumes rescaled by the same factor ? ? ,? ? = ? ?,? Stretching map ? ? = ? ? ? ? = ? ? Pure stretching map Need to take care of operator ordering!!! Infinitesimal pure stretching map Lindblad eq (open quantum system) ?? ??=? ?,? + ? ? ?? 1 2? ?,? ?? 2 ? ? = ? = ? = ? ? + ??? Anti-normal ordering and Husimi Q are preferred https://assumptionsofphysics.org/
Effects of stretching map on phase space representations Husimi Q is simply stretched Wigner function is stretched and convolved with a gaussian, and coincides with the Husimi Q in the limit https://assumptionsofphysics.org/
Another perspective: move the pure states to minus infinite entropy Instead of ? ? ,? ? = ?? ?,? = ? Redefine original space such that ?, ? =? ? ? ? ,? ? = ? ? 0 ? Mathematically equivalent to lowering the entropy of a pure state to , or 0 (group contraction) https://assumptionsofphysics.org/
Low speed Speed ? High entropy 0 Classical Mechanics Relativistic Mechanics Entropy Quantum Mechanics Quantum Field Theory No-mechanism limit (same as non-relativistic limit) https://assumptionsofphysics.org/
More about our project Project website https://assumptionsofphysics.org for papers, presentations, https://assumptionsofphysics.org/book for our open access book (updated every few years with new results) YouTube channels https://www.youtube.com/@gcarcassi Videos with results and insights from the research https://www.youtube.com/@AssumptionsofPhysicsResearch Research channel, with open questions and livestreamed work sessions GitHub https://github.com/assumptionsofphysics Book, research papers, slides for videos... https://assumptionsofphysics.org/
