Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:physics/0701163

Physical unknowables

Karl Svozil

Published Jan 15, 2007• 5 citations
arXivHTMLPDF

Abstract

A variety of physical unknowables are discussed. Provable lack of physical omniscience, omnipredictability and omnipotence is derived by reduction to problems which are known to be recursively unsolvable. "Chaotic" symbolic dynamical systems are unstable with respect to variations of initial states. Quantum unknowables include the random occurrence of single events, complementarity and value indefiniteness.

DOI
10.48550/arxiv.physics/0701163

Related papers

Physical Unknowables

Karl Svozil

As we know, there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns – the ones we don't know we don't know. –United States Secretary of Defense Donald H. Rumsfeld at a Department of Defense news briefing on February 12, 2002 Ei mihi, qui nescio saltem quid nesciam! (Alas for me, that I do not at least know the extent of my own ignorance!) –Aurelius Augustinus, 354–430, “Confessiones” (Book XI, chapter 25) Rise and Fall of Determinism In what follows, a variety of physical unknowables will be discussed. Provable lack of physical omniscience, omnipredictability and omnipotence is derived by reduction to problems that are known to be recursively unsolvable. “Chaotic” symbolic dynamical systems are unstable with respect to variations of initial states. Quantum unknowables include the random occurrence of single events, complementarity, and value indefiniteness. From antiquity onward, various waves of (in)determinism have influenced human thought. Regardless of whether they were shaped by some Zeitgeist , or whether, as Goethe's Faust puts it, “what you the Spirit of the Ages call, is nothing but the spirit of you all, wherein the Ages are reflected,” their proponents have sometimes vigorously defended their stance in irrational, unscientific, and ideologic ways.

Cambridge University Press eBooks•Jun 6, 2011•5 citations

Physical (A)Causality: Determinism, Randomness and Uncaused Events

Karl Svozil

Part I Embedded observers, reflexive perception and representation: Intrinsic and extrinsic observation mode -- Embedded observers and self-expression -- Reflexive measurement -- Intrinsic self-representation -- Part II Provable unknowns: On what is entirely hopeless -- Forecasting and unpredictability -- Induction by rule inference -- Other types of recursion theoretic unknowables -- What if there are no laws? Emergence of laws -- Part III Quantum unknowns: "Shut up and calculate" -- Evolution by permutation -- Quantum mechanics in a nutshell -- Quantum oracles -- Vacuum fluctuations -- Radioactive decay -- Part IV Exotic unknowns: Classical continua and infinities -- Classical (in)determinism -- Deterministic chaos -- Partition logics, finite automata and generalized urn models -- Part V Transcendence: Miracles -- Dualistic interfaces -- Part VI Executive summary: Executive summary -- Appendix A: Formal (in)computability and randomness -- B: Two particle correlations and expectations

•Feb 14, 2018•16 citations

Indeterminism and Randomness Through Physics

Karl Svozil

Despite provable unknowables in recursion theory, indeterminism and randomness in physics is confined to conventions, subjective beliefs and preliminary evidence. The history of the issue is very briefly reviewed, and answers to five questions raised by Hector Zenil are presented.

arXiv:0905.0806•WORLD SCIENTIFIC eBooks•Feb 1, 2011•0 citations

Randomness in Physics: Five Questions, Some Answers

Karl Svozil

Despite provable unknowables in recursion theory, indeterminism and randomness in physics is confined to conventions, subjective beliefs and preliminary evidence. The history of the issue is very briefly reviewed, and answers to five questions raised by Zenil are presented.

•Jan 1, 2009•0 citations

Quantum physical systems as classical systems

Antonio Cassa

A physical system showing a classical (deterministic) behavior to an observer can appear to be a quantum system to another observer unable to distinguish between some distinct states.

arXiv:quant-ph/0111070•Journal of Mathematical Physics•Nov 1, 2001•3 citations

Thermalization of locally perturbed many-body quantum systems

Lennart Dabelow, Patrick Vorndamme, Peter Reimann

Deriving conditions under which a macroscopic system thermalizes directly from the underlying quantum many-body dynamics of its microscopic constituents is a long-standing challenge in theoretical physics. The well-known eigenstate thermalization hypothesis (ETH) is presumed to be a key mechanism, but has defied rigorous verification for generic systems thus far. A weaker variant (weak ETH), by contrast, is provably true for a large variety of systems, including even many integrable models, but its implications with respect to the problem of thermalization are still largely unexplored. Here we analytically demonstrate that systems satisfying the weak ETH exhibit thermalization for two very natural classes of far-from-equilibrium initial conditions: the overwhelming majority of all pure states with a preset nonequilibrium expectation value of some given local observable, and the Gibbs states of a Hamiltonian which subsequently is subject to a quantum quench in the form of a sudden change of some local system properties.

arXiv:2202.00271•Physical review. B./Physical review. B•Jan 28, 2022•12 citations
A variety of physical unknowables are discussed. Provable lack of physical omniscience, omnipredictability and omnipotence is derived by reduction to problems which are known to be recursively unsolvable. "Chaotic" symbolic dynamical systems are unstable with respect to variations of initial states. Quantum unknowables include the random occurrence of single events, complementarity and value indefiniteness.
As we know, there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns – the ones we don't know we don't know. –United States Secretary of Defense Donald H. Rumsfeld at a Department of Defense news briefing on February 12, 2002 Ei mihi, qui nescio saltem quid nesciam! (Alas for me, that I do not at least know the extent of my own ignorance!) –Aurelius Augustinus, 354–430, “Confessiones” (Book XI, chapter 25) Rise and Fall of Determinism In what follows, a variety of physical unknowables will be discussed. Provable lack of physical omniscience, omnipredictability and omnipotence is derived by reduction to problems that are known to be recursively unsolvable. “Chaotic” symbolic dynamical systems are unstable with respect to variations of initial states. Quantum unknowables include the random occurrence of single events, complementarity, and value indefiniteness. From antiquity onward, various waves of (in)determinism have influenced human thought. Regardless of whether they were shaped by some Zeitgeist , or whether, as Goethe's Faust puts it, “what you the Spirit of the Ages call, is nothing but the spirit of you all, wherein the Ages are reflected,” their proponents have sometimes vigorously defended their stance in irrational, unscientific, and ideologic ways.
Part I Embedded observers, reflexive perception and representation: Intrinsic and extrinsic observation mode -- Embedded observers and self-expression -- Reflexive measurement -- Intrinsic self-representation -- Part II Provable unknowns: On what is entirely hopeless -- Forecasting and unpredictability -- Induction by rule inference -- Other types of recursion theoretic unknowables -- What if there are no laws? Emergence of laws -- Part III Quantum unknowns: "Shut up and calculate" -- Evolution by permutation -- Quantum mechanics in a nutshell -- Quantum oracles -- Vacuum fluctuations -- Radioactive decay -- Part IV Exotic unknowns: Classical continua and infinities -- Classical (in)determinism -- Deterministic chaos -- Partition logics, finite automata and generalized urn models -- Part V Transcendence: Miracles -- Dualistic interfaces -- Part VI Executive summary: Executive summary -- Appendix A: Formal (in)computability and randomness -- B: Two particle correlations and expectations
Deriving conditions under which a macroscopic system thermalizes directly from the underlying quantum many-body dynamics of its microscopic constituents is a long-standing challenge in theoretical physics. The well-known eigenstate thermalization hypothesis (ETH) is presumed to be a key mechanism, but has defied rigorous verification for generic systems thus far. A weaker variant (weak ETH), by contrast, is provably true for a large variety of systems, including even many integrable models, but its implications with respect to the problem of thermalization are still largely unexplored. Here we analytically demonstrate that systems satisfying the weak ETH exhibit thermalization for two very natural classes of far-from-equilibrium initial conditions: the overwhelming majority of all pure states with a preset nonequilibrium expectation value of some given local observable, and the Gibbs states of a Hamiltonian which subsequently is subject to a quantum quench in the form of a sudden change of some local system properties.