Law without law: from observer states to physics via algorithmic information theory

Markus P. Müller

Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria
Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5, Canada

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

According to our current conception of physics, any valid physical theory is supposed to describe the objective evolution of a unique external world. However, this condition is challenged by quantum theory, which suggests that physical systems should not always be understood as having objective properties which are simply revealed by measurement. Furthermore, as argued below, several other conceptual puzzles in the foundations of physics and related fields point to limitations of our current perspective and motivate the exploration of an alternative: to start with the first-person (the observer) rather than the third-person perspective (the world).
In this work, I propose a rigorous approach of this kind on the basis of algorithmic information theory. It is based on a single postulate: that $\textit{universal induction}$ determines the chances of what any observer sees next. That is, instead of a world or physical laws, it is the local state of the observer alone that determines those probabilities. Surprisingly, despite its solipsistic foundation, I show that the resulting theory recovers many features of our established physical worldview: it predicts that it appears to observers $\textit{as if there was an external world}$ that evolves according to simple, computable, probabilistic laws. In contrast to the standard view, objective reality is not assumed on this approach but rather provably emerges as an asymptotic statistical phenomenon. The resulting theory dissolves puzzles like cosmology's Boltzmann brain problem, makes concrete predictions for thought experiments like the computer simulation of agents, and suggests novel phenomena such as ``probabilistic zombies'' governed by observer-dependent probabilistic chances. It also suggests that some basic phenomena of quantum theory (Bell inequality violation and no-signalling) might be understood as consequences of this framework.

► BibTeX data

► References

[1] A. Aguirre and M. Tegmark, Born in an Infinite Universe: a Cosmological Interpretation of Quantum Mechanics, Phys. Rev. D 84, 105002 (2011).
https:/​/​doi.org/​10.1103/​PhysRevD.84.105002

[2] A. Linde and M. Noorbala, Measure problem for eternal and non-eternal inflation, J. Cosmol. Astropart. Phys. 1009 (2010).
https:/​/​doi.org/​10.1088/​1475-7516/​2010/​09/​008

[3] A. Albrecht, Cosmic Inflation and the Arrow of Time, in J. D. Barrow, P. C. W. Davies, and C. L. Harper (eds.), Science and Ultimate Reality: Quantum Theory, Cosmology, and Complexity, Cambridge University Press, 2004.
https:/​/​doi.org/​10.1017/​CBO9780511814990

[4] A. Albrecht and L. Sorbo, Can the universe afford inflation?, Phys. Rev. D 70, 063528 (2004).
https:/​/​doi.org/​10.1103/​PhysRevD.70.063528

[5] Y. Nomura, Physical theories, eternal inflation, and the quantum universe, J. High Energ. Phys. 11, 063 (2011).
https:/​/​doi.org/​10.1007/​JHEP11(2011)063

[6] A. Peres, Unperformed experiments have no results, Am. J. Phys. 46, 745–747 (1978).
https:/​/​doi.org/​10.1119/​1.11393

[7] C. A. Fuchs and R. Schack, Quantum-Bayesian coherence, Rev. Mod. Phys. 85, 1693–1715 (2013).
https:/​/​doi.org/​10.1103/​RevModPhys.85.1693

[8] C. Fuchs, Quantum Foundations in the Light of Quantum Information, in A. Gonis and P. E. A. Turchi, Decoherence and its Implications in Quantum Computation and Information Transfer: Proceedings of the NATO Advanced Research Workshop, Mykonos, Greece, June 25–30, 2000, IOS Press, Amsterdam, arXiv:quant-ph/​0106166.
arXiv:quant-ph/0106166

[9] Č. Brukner, A no-go theorem for observer-independent facts, Entropy 20, 350 (2018).
https:/​/​doi.org/​10.3390/​e20050350

[10] K.-W. Bong, A. Utreras-Alarcón, F. Ghafari, Y.-C. Liang, N. Tischler, E. G. Cavalcanti, G. F. Pryde, and H. M. Wiseman, Testing the reality of Wigner's friend's observations, arXiv:1907.05607.
arXiv:1907.05607

[11] N. Bostrom, Are You Living In a Computer Simulation?, Philosophical Quarterly 53(211), 243–255 (2003).
https:/​/​doi.org/​10.1111/​1467-9213.00309

[12] D. R. Hofstadter and D. C. Dennett, The Mind's I — Fantasies and Reflections on Self and Soul, Basic Books, 1981.

[13] D. Parfit, Reasons and Persons, Clarendon Press, Oxford, 1984.
https:/​/​doi.org/​10.1093/​019824908X.001.0001

[14] C. Rovelli, Relational Quantum Mechanics, Int. J. Theor. Phys. 35(8), 1637–1678 (1996).
https:/​/​doi.org/​10.1007/​BF02302261

[15] J. A. Wheeler, Information, physics, quantum: the search for links, Proceedings of the 3rd International Symposium on Quantum Mechanics, 354–368, Tokyo, 1989.

[16] J. S. Bell, On the Einstein Podolsky Rosen Paradox, Physics 1(3), 195–200 (1964).
https:/​/​doi.org/​10.1103/​PhysicsPhysiqueFizika.1.195

[17] J. S. Bell, On the problem of hidden variables in quantum mechanics, Rev. Mod. Phys. 38(3), 447–452 (1966).
https:/​/​doi.org/​10.1142/​9789812795854_0071

[18] D. Deutsch, Quantum theory, the Church-Turing principle and the universal quantum computer, Proceedings of the Royal Society of London A 400, pp. 97-117 (1985).
https:/​/​doi.org/​10.1098/​rspa.1985.0070

[19] L. Hardy, Quantum Theory From Five Reasonable Axioms, arXiv:quant-ph/​0101012.
arXiv:quant-ph/0101012

[20] B. Dakić and Č. Brukner, Quantum Theory and Beyond: Is Entanglement Special?, in H. Halvorson (ed.), ``Deep Beauty: Understanding the Quantum World through Mathematical Innovation'', Cambridge University Press, 2011.
https:/​/​doi.org/​10.1017/​CBO9780511976971

[21] Ll. Masanes and M. P. Müller, A derivation of quantum theory from physical requirements, New J. Phys. 13, 063001 (2011).
https:/​/​doi.org/​10.1088/​1367-2630/​13/​6/​063001

[22] G. Chiribella, G. M. D'Ariano, and P. Perinotti, Informational derivation of quantum theory, Phys. Rev. A 84, 012311 (2011).
https:/​/​doi.org/​10.1103/​PhysRevA.84.012311

[23] L. Hardy, Reformulating and Reconstructing Quantum Theory, arXiv:1104.2066.
arXiv:1104.2066

[24] Ll. Masanes, M. P. Müller, R. Augusiak, and D. Pérez-García, Existence of an information unit as a postulate of quantum theory, Proc. Natl. Acad. Sci. USA 110(41), 16373 (2013).
https:/​/​doi.org/​10.1073/​pnas.1304884110

[25] H. Barnum, M. P. Müller, and C. Ududec, Higher-order interference and single-system postulates characterizing quantum theory, New J. Phys. 16, 123029 (2014).
https:/​/​doi.org/​10.1088/​1367-2630/​16/​12/​123029

[26] P. A. Höhn, Quantum theory from rules on information acquisition, Entropy 19(3), 98 (2017).
https:/​/​doi.org/​10.3390/​e19030098

[27] P. A. Höhn and C. S. P. Wever, Quantum theory from questions, Phys. Rev. A 95, 012102 (2017).
https:/​/​doi.org/​10.1103/​PhysRevA.95.012102

[28] A. Wilce, A Royal Road to Quantum Theory (or Thereabouts), Entropy 20(4), 227 (2018).
https:/​/​doi.org/​10.3390/​e20040227

[29] A. Peres, Quantum Theory: Concepts and Methods, Kluwer Academic Publishers, 2002.
https:/​/​doi.org/​10.1007/​0-306-47120-5

[30] W. Myrvold, Beyond Chance and Credence, unpublished manuscript (2017).

[31] M. Hutter, Universal Artificial Intelligence – Sequential Decisions Based on Algorithmic Probability, Springer, 2005.
https:/​/​doi.org/​10.1007/​b138233

[32] R. Kirk, Zombies, The Stanford Encyclopedia of Philosophy, E. N. Zalta (ed.), URL=http:/​/​plato.stanford.edu/​archives/​win2012/​entries/​zombies (2011).
http:/​/​plato.stanford.edu/​archives/​win2012/​entries/​zombies

[33] J. A. Wheeler, Law Without Law, in J. A. Wheeler and W. H. Zurek (eds.), ``Quantum Theory and Measurement'', Princeton Series in Physics, Princeton University Press, 1983.
https:/​/​doi.org/​10.1515/​9781400854554

[34] A. M. Turing, On computable numbers, with an application to the Entscheidungsproblem, Proc. London Maths. Soc. Ser. 2 42, 230–265 (1936).
https:/​/​doi.org/​10.1112/​plms/​s2-42.1.230

[35] S. B. Cooper, Computability Theory, Chapman & Hall/​CRC, 2004.
https:/​/​doi.org/​10.1201/​9781315275789

[36] S. Wolfram, A New Kind of Science, Champaign, Illinois, 2002.

[37] R. Gandy, Church's thesis and principles for mechanisms, in J. Barwise, H. Jerome Keisler, and K. Kunen (eds.), The Kleene Symposium, North Holland Publishing, Amsterdam, 1980.
https:/​/​doi.org/​10.1016/​S0049-237X(08)71257-6

[38] P. Arrighi and G. Dowek, The physical Church-Turing thesis and the principles of quantum theory, Int. J. Found. Comput. S. 23(5), 1131–1145 (2012).
https:/​/​doi.org/​10.1142/​S0129054112500153

[39] D. R. Hofstadter, Gödel, Escher, Bach: an eternal golden braid, Basic Books, New York, 1979.

[40] G. Piccinini, Computationalism, The Church-Turing Thesis, and the Church-Turing Fallacy, Synthese 154(1), 97–120 (2007).
https:/​/​doi.org/​10.1007/​s11229-005-0194-z

[41] M. Davis, Why there is no such discipline as hypercomputation, Appl. Math. Comput. 178, 4–7 (2006).
https:/​/​doi.org/​10.1016/​j.amc.2005.09.066

[42] M. Tegmark, Does the universe in fact contain almost no information?, Found. Phys. Lett. 9 25-42 (1996).
https:/​/​doi.org/​10.1007/​BF02186207

[43] R. W. Spekkens, Evidence for the epistemic view of quantum states: A toy theory, Phys. Rev. A 75, 032110 (2007).
https:/​/​doi.org/​10.1103/​PhysRevA.75.032110

[44] H. Everett, The Theory of the Universal Wave Function, in B. S. Dewitt and N. Graham (eds.), The Many Worlds Interpretation of Quantum Mechanics, Princeton University Press, 1973.
https:/​/​doi.org/​10.1515/​9781400868056

[45] B. Marchal, Mechanism and personal identity, in Proceedings of the 1st World Conference on the Fundamentals of Artificial Intelligence (WOCFAI'91), 461–475, Paris, 1991.

[46] I. Wood, P. Sunehag, and M. Hutter, (Non-)Equivalence of Universal Priors, in D. L. Dowe (ed.), Algorithmic Probability and Friends – Bayesian Prediction and Artificial Intelligence, Springer Lecture Notes in Artificial Intelligence, 2013.
https:/​/​doi.org/​10.1007/​978-3-642-44958-1

[47] M. Li and P. Vitányi, An Introduction to Kolmogorov Complexity and Its Applications, Springer, 1997.
https:/​/​doi.org/​10.1007/​978-3-030-11298-1

[48] G. J. Chaitin, Algorithmic Information Theory, Cambridge University Press, Cambridge, 1987.
https:/​/​doi.org/​10.1017/​CBO9780511608858

[49] T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd edition, John Wiley & Sons, 2006.
https:/​/​doi.org/​10.1002/​047174882X

[50] M. Hutter, Open Problems in Universal Induction & Intelligence, Algorithms 2(3), 879–906 (2009).
https:/​/​doi.org/​10.3390/​a2030879

[51] R. Schack, Algorithmic information and simplicity in statistical physics, Int. J. Theor. Phys. 36(1), 209–226 (1997).
https:/​/​doi.org/​10.1007/​BF02435782

[52] M. Müller, Stationary algorithmic probability, Theoretical Computer Science 411, 113–130 (2010).
https:/​/​doi.org/​10.1016/​j.tcs.2009.09.017

[53] P. Walley, Statistical Reasoning with Imprecise Probabilities, Monographs on Statistics and Applied Probability, Springer Science and Business Media, 1991.

[54] R. Lima, Equivalence of ensembles in quantum lattice systems, Annales de l'I.H.P. 15(1), 61–68 (1971).

[55] R. Lima, Equivalence of ensembles in quantum lattice systems: states, Commun. Math. Phys. 24, 180–192 (1972).
https:/​/​doi.org/​10.1007/​BF01877711

[56] M. P. Müller, E. Adlam, Ll. Masanes, and N. Wiebe, Thermalization and canonical typicality in translation-invariant quantum lattice systems, Commun. Math. Phys. 340(2), 499–561 (2015).
https:/​/​doi.org/​10.1007/​s00220-015-2473-y

[57] R. Colbeck, Quantum And Relativistic Protocols For Secure Multi-Party Computation, PhD Thesis, University of Cambridge (2006), arXiv:0911.3814.
arXiv:0911.3814

[58] S. Pironio, A. Acín, S. Massar, A. Boyer de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, Random numbers certified by Bell's theorem, Nature 464, 1021 (2010).
https:/​/​doi.org/​10.1038/​nature09008

[59] A. K. Zvonkin and L. A. Levin, The complexity of finite objects and the development of the concepts of information and randomness by means of the theory of algorithms, Russian Math. Surveys 25(6), 83–124 (1970).
https:/​/​doi.org/​10.1070/​RM1970v025n06ABEH001269

[60] A. A. Brudno, Entropy and the complexity of the trajectories of a dynamical system, Trans. Moscow Math. Sec. 2, 127–151 (1983).

[61] M. Hutter, On universal prediction and Bayesian confirmation, Theoret. Comput. Sci. 384, 33–48 (2007).
https:/​/​doi.org/​10.1016/​j.tcs.2007.05.016

[62] M. Hutter and A. Muchnik, On semimeasures predicting Martin-Löf random sequences, Theor. Comput. Sci. 382(3), 247–261 (2007).
https:/​/​doi.org/​10.1016/​j.tcs.2007.03.040

[63] J. M. Bernardo and A. F. M. Smith, Bayesian theory, Wiley Series in Probability and Statistics, Toronto, 1993.
https:/​/​doi.org/​10.1002/​9780470316870

[64] C. Glymour, Why I am not a Bayesian, in H. Arló-Costa, V. F. Hendricks, and J. van Benthem (eds.), Readings in Formal Epistemology, Springer Graduate Texts in Philosophy, Springer, 2016.
https:/​/​doi.org/​10.1007/​978-3-319-20451-2

[65] B. Eva and S. Hartmann, On the Origins of Old Evidence, Australas. J. Philos. 1–14 (2019).
https:/​/​doi.org/​10.1080/​00048402.2019.1658210

[66] N. Goodman, Fact, Fiction, and Forecast, Harvard University Press, Cambridge, MA, 1955.

[67] T. F. Sterkenburg, A Generalized Characterization of Algorithmic Probability, Theory Comput. Syst. 1–16 (2017).
https:/​/​doi.org/​10.1007/​s00224-017-9774-9

[68] T. F. Sterkenburg, Universal Prediction – A Philosophical Investigation, PhD thesis, University of Groningen, 2018.
https:/​/​ir.cwi.nl/​pub/​27326

[69] S. Wolf, Second Thoughts on the Second Law, in H. J. Böckenhauer, D. Komm, and W. Unger (eds.), Adventures Between Lower Bounds and Higher Altitudes, Lecture Notes in Computer Science, Springer, Cham, 2018.
https:/​/​doi.org/​10.1007/​978-3-319-98355-4

[70] T. Zeugmann and S. Zilles, Learning recursive functions: A survey, Theor. Comput. Sci. 397, 4–56 (2008).
https:/​/​doi.org/​10.1016/​j.tcs.2008.02.021

[71] N. Harrigan and R. W. Spekkens, Einstein, Incompleteness, and the Epistemic View of Quantum States, Found. Phys. 40(2), 125–157 (2010).
https:/​/​doi.org/​10.1007/​s10701-009-9347-0

[72] R. W. Spekkens, Contextuality for Preparations, Transformations, and Unsharp Measurements, Phys. Rev. A 71, 052108 (2005).
https:/​/​doi.org/​10.1103/​PhysRevA.71.052108

[73] G. Piccinini, Computation in Physical Systems, The Stanford Encyclopedia of Philosophy, Edward N. Zalta (ed.), URL =https:/​/​plato.stanford.edu/​archives/​sum2017/​entries/​computation-physicalsystems/​ (2017).
https:/​/​plato.stanford.edu/​archives/​sum2017/​entries/​computation-physicalsystems/​

[74] K. Zuse, Rechnender Raum, Friedrich Vieweg u. Sohn, Wiesbaden, 1969.
https:/​/​doi.org/​10.1007/​978-3-663-02723-2

[75] J. Schmidhuber, Algorithmic Theories of Everything, Instituto Dalle Molle Di Studi Sull Intelligenza Artificiale (2000), arXiv:quant-ph/​0011122.
arXiv:quant-ph/0011122

[76] G. 't Hooft, Quantum Mechanics and Determinism, in P. Frampton and J. Ng (eds.), Proceedings of the Eighth International Conference on Particles, Strings and Cosmology, Univ. of North Carolina, Chapel Hill, 275–285, 2001.

[77] S. Lloyd, Programming the Universe: A Quantum Computer Scientist Takes on the Cosmos, Random House, New York, 2006.

[78] M. Hutter, A Complete Theory of Everything (will be subjective), Algorithms 3(4), 329–350 (2010).
https:/​/​doi.org/​10.3390/​a3040329

[79] P. Diaconis and D. Freedman, On the consistency of Bayes estimates, Ann. Statist. 14, 1–26 (1986).
https:/​/​doi.org/​10.1214/​aos/​1176349830

[80] H. Moravec, The Doomsday Device, in Mind Children: The Future of Robot and Human Intelligence, Harvard University Press, London, 1988.

[81] B. Marchal, Informatique théorique et philosophie de l'esprit, in Acte du 3ème colloque international Cognition et Connaissance, 193–227, Toulouse, 1988.

[82] M. Tegmark, The Interpretation of Quantum Mechanics: Many Worlds or Many Words?.
https:/​/​doi.org/​10.1002/​(SICI)1521-3978(199811)46:6/​8<855::AID-PROP855>3.0.CO;2-Q

[83] A. Linde, Inflationary Cosmology, in M. Lemoine, J. Martin, and P. Peter (eds), Inflationary Cosmology, Lecture Notes in Physics 738, Springer, Berlin/​Heidelberg, 2008.
https:/​/​doi.org/​10.1007/​978-3-540-74353-8

[84] D. N. Page, Cosmological Measures without Volume Weighting, J. Cosmol. Astropart. P. 10, (2008).
https:/​/​doi.org/​10.1088/​1475-7516/​2008/​10/​025

[85] D. N. Page, Is our Universe likely to decay within 20 billion years?, Phys. Rev. D 78, 063535 (2008).
https:/​/​doi.org/​10.1103/​PhysRevD.78.063535

[86] L. Dyson, M. Kleban, and L. Susskind, Disturbing Implications of a Cosmological Constant, JHEP 0210 (2002).
https:/​/​doi.org/​10.1088/​1126-6708/​2002/​10/​011

[87] W. H. Zurek, Thermodynamic cost of computation, algorithmic complexity and the information metric, Nature 341, 119–124 (1989).
https:/​/​doi.org/​10.1038/​341119a0

[88] F. Benatti, T. Krüger, M. Müller, Ra. Siegmund-Schultze, and A. Skoła, Entropy and quantum Kolmogorov complexity: a quantum Brudno's theorem, Commun. Math. Phys. 265(2), 437–461 (2006).
https:/​/​doi.org/​10.1007/​s00220-006-0027-z

[89] Č. Brukner, On the quantum measurement problem, in R. Bertlmann and A. Zeilinger (eds.), Quantum (Un)Speakables II — Half a Century of Bell's Theorem, Springer International Publishing Switzerland, 2017.
https:/​/​doi.org/​10.1007/​978-3-319-38987-5

[90] A. Zeilinger, A Foundational Principle for Quantum Mechanics, Found. Phys. 29(4), 631–643 (1999).
https:/​/​doi.org/​10.1023/​A:1018820410908

[91] C. A. Fuchs and A. Peres, Quantum Theory Needs No 'Interpretation', Phys. Today 53(3), 70 (2000).
https:/​/​doi.org/​10.1063/​1.883004

[92] C. A. Fuchs, Quantum Bayesianism at the Perimeter, Physics in Canada 66(2), 77–82 (2010).

[93] C. Timpson, Quantum information theory & the Foundations of Quantum Mechanics, Oxford University Press, Oxford, 2013.
https:/​/​doi.org/​10.1093/​acprof:oso/​9780199296460.001.0001

[94] D. N. Page and W. K. Wootters, Evolution without evolution: Dynamics described by stationary observables, Phys. Rev. D 27(12), 2885–2892 (1983).
https:/​/​doi.org/​10.1103/​PhysRevD.27.2885

[95] D. M. Appleby, Concerning Dice and Divinity, AIP Conference Proceedings 889, 30 (2007).
https:/​/​doi.org/​10.1063/​1.2713444

[96] C. J. Wood and R. W. Spekkens, The lesson of causal discovery algorithms for quantum correlations: causal explanations of Bell-inequality violations require fine-tuning, New J. Phys. 17, 033002 (2015).
https:/​/​doi.org/​10.1088/​1367-2630/​17/​3/​033002

[97] E. Schrödinger, Discussion of Probability Relations between Separated Systems, Proc. Camb. Phil. Soc. 31, 555 (1935).
https:/​/​doi.org/​10.1017/​S0305004100013554

[98] J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Proposed experiment to test local hidden-variable theories, Phys. Rev. Lett. 23, 880 (1969).
https:/​/​doi.org/​10.1103/​PhysRevLett.23.880

[99] C. H. Bennett and G. Brassard, Quantum cryptography: Public key distribution and coin tossing, in Proceedings of IEEE International Conference on Computers, Systems and Signal Processing, IEEE, New York, 1984.
https:/​/​doi.org/​10.1016/​j.tcs.2014.05.025

[100] J. Barrett, L. Hardy, and A. Kent, No Signaling and Quantum Key Distribution, Phys. Rev. Lett. 95, 010503 (2005).
https:/​/​doi.org/​10.1103/​PhysRevLett.95.010503

[101] M. Giustina, M. A. M. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer, K. Phelan, F. Steinlechner, J. Kofler, J.-Å. Larsson, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, J. Beyer, T. Gerrits, A. E. Lita, L. K. Shalm, S. W. Nam, T. Scheidl, R. Ursin, B. Wittmann, and A. Zeilinger, Significant-loophole-free test of Bell's theorem with entangled photons, Phys. Rev. Lett. 115, 250401 (2015).
https:/​/​doi.org/​10.1103/​PhysRevLett.115.250401

[102] R. Colbeck and R. Renner, A system's wave function is uniquely determined by its underlying physical state, New J. Phys. 19, 013016 (2017).
https:/​/​doi.org/​10.1088/​1367-2630/​aa515c

[103] R. Colbeck and R. Renner, A short note on the concept of free choice, arXiv:1302.4446.
arXiv:1302.4446

[104] M. Navascués, Y. Guryanova, M. J. Hoban, and A. Acín, Almost quantum correlations, Nat. Comm. 6, 6288 (2015).
https:/​/​doi.org/​10.1038/​ncomms7288

[105] L. A. Khalfin and B. S. Tsirelson, Quantum and quasi-classical analogs of Bell inequalities, in P. Lahti and P. Mittelstaedt (eds.), Symposium on the Foundations of Modern Physics, World Scientific, Singapore, 1985.

[106] B. S. Tsirelson, Some results and problems on quantum Bell-type inequalities, Hadronic J. Suppl. 8, 329 (1993).

[107] S. Popescu and D. Rohrlich, Quantum Nonlocality as an Axiom, Found. Phys. 24(3), 379–385 (1994).
https:/​/​doi.org/​10.1007/​BF02058098

[108] J. Barrett, N. Linden, S. Massar, S. Pironio, S. Popescu, and D. Roberts, Nonlocal correlations as an information-theoretic resource, Phys. Rev. A 71, 022101 (2005).
https:/​/​doi.org/​10.1103/​PhysRevA.71.022101

[109] A. Garg and N. D. Mermin, Detector inefficiencies in the Einstein-Podolsky-Rosen experiment, Phys. Rev. D 35(12), 3831 (1987).
https:/​/​doi.org/​10.1103/​PhysRevD.35.3831

[110] C. Branciard, Detection loophole in Bell experiments: How postselection modifies the requirements to observe nonlocality, Phys. Rev. A 83, 032123 (2011).
https:/​/​doi.org/​10.1103/​PhysRevA.83.032123

[111] P. M. Pearle, Hidden-Variable Example Based upon Data Rejection, Phys. Rev. D 2(8), 1418–1425 (1970).
https:/​/​doi.org/​10.1103/​PhysRevD.2.1418

[112] J. Berkson, Limitations of the Application of Fourfold Table Analysis to Hospital Data, Biometrics Bulletin 2(3), 47–53 (1946).
https:/​/​doi.org/​10.1093/​ije/​dyu022

[113] J.-P. W. MacLean, K. Ried, R. W. Spekkens, and K. Resch, Quantum-coherent mixtures of causal relations, Nat. Comm. 8, 15149 (2017).
https:/​/​doi.org/​10.1038/​ncomms15149

[114] G. Brassard and R. Raymond-Robichaud, Can Free Will Emerge from Determinism in Quantum Theory?, in A. Suarez and P. Adams (eds.), Is Science Compatible with Free Will? Exploring Free Will and Consciousness in the Light of Quantum Physics and Neuroscience, Springer, 2013; arXiv:1204.2128.
https:/​/​doi.org/​10.1007/​978-1-4614-5212-6
arXiv:1204.2128

[115] G. Brassard and P. Raymond-Robichaud, Parallel Lives: A local realistic interpretation of ``nonlocal'' boxes, poster (2015), available at http:/​/​www.thepoxbox.com/​tests/​poster_revsmall.jpg.
http:/​/​www.thepoxbox.com/​tests/​poster_revsmall.jpg

[116] G. Brassard and P. Raymond-Robichaud, Parallel lives: A local-realistic interpretation of ``nonlocal'' boxes, Entropy 21(1), 87 (2019).
https:/​/​doi.org/​10.3390/​e21010087

[117] W. van Dam, Implausible consequences of superstrong nonlocality, Natural Computing 12(1), 9–12 (2013).
https:/​/​doi.org/​10.1007/​s11047-012-9353-6

[118] G. Brassard, H. Buhrman, N. Linden, A. A. Méthot, A. Tapp, and F. Unger, Limit on Nonlocality in Any World in Which Communication Complexity Is Not Trivial, Phys. Rev. Lett. 96, 250401 (2006).
https:/​/​doi.org/​10.1103/​PhysRevLett.96.250401

[119] M. Pawlowski, T. Paterek, D. Kaszlikowski, V. Scarani, A. Winter, and M. Zukowski, Information causality as a physical principle, Nature 461, 1101–1104 (2009).
https:/​/​doi.org/​10.1038/​nature08400

[120] M. Navascués and H. Wunderlich, A glance beyond the quantum model, Proc. R. Soc. A 466, 881–890 (2009).
https:/​/​doi.org/​10.1098/​rspa.2009.0453

[121] A. Cabello, Simple Explanation of the Quantum Violation of a Fundamental Inequality, Phys. Rev. Lett. 110, 060402 (2013).
https:/​/​doi.org/​10.1103/​PhysRevLett.110.060402

[122] A. Cabello, Quantum correlations from simple assumptions, Phys. Rev. A 100, 032120 (2019).
https:/​/​doi.org/​10.1103/​PhysRevA.100.032120

[123] G. Chiribella, A. Cabello, M. Kleinmann, and M. P. Müller, General Bayesian theories and the emergence of the exclusivity principle, arXiv:1901.11412.
arXiv:1901.11412

[124] S. Armstrong, A. Sandberg, and N. Bostrom, Thinking inside the box: using and controlling an Oracle AI, Minds and Machines 22(4), 299–324 (2012).
https:/​/​doi.org/​10.1007/​s11023-012-9282-2

[125] N. Bostrom, Superintelligence: Paths, Dangers, Strategies, Oxford University Press, Oxford, 2014.

[126] N. Bostrom and A. Salamon, The Intelligence Explosion (extended abstract), retrieved April 2015 from http:/​/​singularityhypothesis.blogspot.com.es/​2011/​01/​intelligence-explosion-extended.html (2011).
http:/​/​singularityhypothesis.blogspot.com.es/​2011/​01/​intelligence-explosion-extended.html

[127] D. C. Dennett, Freedom evolves, Viking Books, 2003.

[128] S. Wolfram, Cellular automata as models of complexity, Nature 311, 419–424 (1984).
https:/​/​doi.org/​10.1038/​311419a0

[129] S. Wolfram, Undecidability and Intractability in Theoretical Physics, Phys. Rev. Lett. 54, 735–738 (1985).
https:/​/​doi.org/​10.1103/​PhysRevLett.54.735

[130] N. Israeli and N. Goldenfeld, Computational Irreducibility and the Predictability of Complex Physical Systems, Phys. Rev. Lett. 92, 074105 (2004).
https:/​/​doi.org/​10.1103/​PhysRevLett.92.074105

[131] E. Bernstein and U. Vazirani, Quantum Complexity Theory, SIAM J. Comput. 26(5), 1411–1473 (1997).
https:/​/​doi.org/​10.1137/​S0097539796300921

[132] M. Müller, Strongly Universal Quantum Turing Machines and Invariance of Kolmogorov Complexity, IEEE Trans. Inf. Th. 54(2), 763–780 (2008).
https:/​/​doi.org/​10.1109/​TIT.2007.913263

Cited by

[1] Artemy Kolchinsky and David H. Wolpert, "Thermodynamic costs of Turing machines", Physical Review Research 2 3, 033312 (2020).

[2] Gordana Dodig-Crnkovic, "Natural Morphological Computation as Foundation of Learning to Learn in Humans, Other Living Organisms, and Intelligent Machines", Philosophies 5 3, 17 (2020).

[3] Augustin Vanrietvelde, Philipp A Hoehn, Flaminia Giacomini, and Esteban Castro-Ruiz, "A change of perspective: switching quantum reference frames via a perspective-neutral framework", arXiv:1809.00556.

[4] Arne Hansen and Stefan Wolf, "The Measurement Problem Is the "Measurement" Problem", arXiv:1810.04573.

[5] Markus P. Mueller, "Mind before matter: reversing the arrow of fundamentality", arXiv:1812.08594.

[6] John Realpe-Gómez, "Modeling observers as physical systems representing the world from within: Quantum theory as a physical and self-referential theory of inference", arXiv:1705.04307.

[7] Arne Hansen and Stefan Wolf, "Wigner's Isolated Friend", arXiv:1912.03248.

[8] Rodolfo Gambini and Jorge Pullin, "The Montevideo Interpretation: How the inclusion of a Quantum Gravitational Notion of Time Solves the Measurement Problem", arXiv:2010.14519.

[9] İnanç Şahin, "Can parallel lives provide a solution to Hardy's paradox?", arXiv:2009.07633.

[10] John Realpe-Gomez, "Embodied observations from an intrinsic perspective can entail quantum dynamics", arXiv:2005.03653.

[11] Ali Barzegar, "QBism Is Not So Simply Dismissed", Foundations of Physics 50 7, 693 (2020).

[12] Philippe Allard Guérin, Veronika Baumann, Flavio Del Santo, and Časlav Brukner, "A no-go theorem for the persistent reality of Wigner's friend's perception", arXiv:2009.09499.

[13] Ian T. Durham, "Why is the universe comprehensible?", arXiv:2011.06672.

The above citations are from Crossref's cited-by service (last updated successfully 2020-11-25 15:52:17) and SAO/NASA ADS (last updated successfully 2020-11-25 15:52:18). The list may be incomplete as not all publishers provide suitable and complete citation data.