Editing Determinism (section)

=== Other interpretations ===

Bell's theorem only applies to [[Principle of locality|local]] hidden variables. Quantum mechanics can be formulated with non-local hidden variables to achieve a deterministic theory that is in agreement with experiment.<ref>{{cite journal |last1=Jabs |first1=Arthur |year=2016 |title=A conjecture concerning determinism, reduction, and measurement in quantum mechanics |journal=Quantum Studies: Mathematics and Foundations |volume=3 |issue=4 |pages=279–292 |arxiv=1204.0614 |doi=10.1007/s40509-016-0077-7 |bibcode=2016QSMF....3..279J |s2cid=32523066}}</ref> An example is the [[De Broglie–Bohm theory|Bohm interpretation]] of quantum mechanics. Bohm's Interpretation, though, violates special relativity and it is highly controversial whether or not it can be reconciled without giving up on determinism.

The [[Many worlds]] interpretation focuses on the deterministic nature of the [[Schrodinger's equation]]. For any closed system, including the entire universe, the wavefunction solutions to this equation evolve deterministically. The apparent randomness of observations corresponds to branching of the wavefunction, with one world for each possible outcome.<ref>{{Cite web |last=Vaidman |first=Lev |date=2021 |editor-last=Zalta |editor-first=Edward N. |title=Many-Worlds Interpretation of Quantum Mechanics |url=https://plato.stanford.edu/entries/qm-manyworlds/ |access-date=2025-03-03 |publisher=Metaphysics Research Lab, Stanford University}}</ref> 

Another foundational assumption to quantum mechanics is that of [[free will]],<ref>{{Cite book |last=Zeilinger |first=Anton |title=Dance of the Photons: From Einstein to Quantum Teleportation |publisher=Farrar, Straus and Giroux |year=2010 |isbn=978-0-374-23966-4 |edition= |location=New York |page=261 |quote=A new picture of the world must encompass three properties that evidently seem to play a significant role in quantum experiments[...]The second important property of the world that we always implicitly assume is the freedom of the individual experimentalist. This is the assumption of free will. It is a free decision what measurement one wants to perform.}}</ref> which has been argued to be foundational to the scientific method as a whole.<ref>{{Cite book |last=Gisin |first=Nicolas |title=Quantum Chance: Nonlocality, Teleportation and Other Quantum Marvels |publisher=Sringer International Publishing |year=2014 |isbn=978-3-319-05472-8 |location=Switzerland |page=90 |quote=not only does free will exist, but it is a prerequisite for science, philosophy, and our very ability to think rationally in a meaningful way. Without free will, there could be no rational thought. As a consequence, it is quite simply impossible for science and philosophy to deny free will.}}</ref> Bell acknowledged that abandoning this assumption would both allow for the maintenance of determinism as well as locality.<ref>BBC Radio interview with Paul Davies, 1985: "''There is a way to escape the inference of superluminal speeds and spooky action at a distance. But it involves absolute determinism in the universe, the complete absence of free will. Suppose the world is super-deterministic, with not just inanimate nature running on behind-the-scenes clockwork, but with our behavior, including our belief that we are free to choose to do one experiment rather than another, absolutely predetermined, including the 'decision' by the experimenter to carry out one set of measurements rather than another, the difficulty disappears."''

</ref>{{Citation needed|date=March 2025}} This perspective is known as [[superdeterminism]], and is defended by some physicists such as [[Sabine Hossenfelder]] and [[Tim Palmer (physicist)|Tim Palmer]].<ref>{{Cite journal|last1=Hossenfelder|first1=Sabine|last2=Palmer|first2=Tim|date=2020|title=Rethinking Superdeterminism|journal=Frontiers in Physics|volume=8|page=139|language=English|doi=10.3389/fphy.2020.00139|arxiv=1912.06462|bibcode=2020FrP.....8..139P|issn=2296-424X|doi-access=free}}</ref>

More advanced variations on these arguments include [[quantum contextuality]], by Bell, [[Simon B. Kochen]] and [[Ernst Specker]], which argues that hidden variable theories cannot be "sensible", meaning that the values of the hidden variables inherently depend on the devices used to measure them.

This debate is relevant because there are possibly specific situations in which the arrival of an electron at a screen at a certain point and time would trigger one event, whereas its arrival at another point would trigger an entirely different event (e.g. see [[Schrödinger's cat]]—a thought experiment used as part of a deeper debate).

In his 1939 address "The Relation between Mathematics and Physics",<ref>{{Cite journal |last=Dirac |first=P. A. M. |date=1940 |title=XI.—The Relation between Mathematics and Physics |url=https://www.cambridge.org/core/product/identifier/S0370164600012207/type/journal_article |journal=Proceedings of the Royal Society of Edinburgh |language=en |volume=59 |pages=122–129 |doi=10.1017/S0370164600012207 |issn=0370-1646}}</ref> [[Paul Dirac]] pointed out that purely deterministic classical mechanics cannot explain the cosmological origins of the universe; today the early universe is modeled quantum mechanically.<ref>{{Cite journal |last=Lehners |first=Jean-Luc |date=June 2023 |title=Review of the no-boundary wave function |url=https://linkinghub.elsevier.com/retrieve/pii/S0370157323001904 |journal=Physics Reports |language=en |volume=1022 |pages=1–82 |doi=10.1016/j.physrep.2023.06.002|arxiv=2303.08802 |bibcode=2023PhR..1022....1L }}</ref>

Nevertheless, the question of determinism in modern physics remains debated. On one hand, [[Albert Einstein]]'s [[theory of relativity]], which represents an advancement over Newtonian mechanics, is based on a deterministic framework. On the other hand, Einstein himself resisted the indeterministic view of quantum mechanics, as evidenced by his famous debates with [[Niels Bohr]], which continued until his death.<ref>{{cite book |last1=Bishop |first1=Robert C. |title=The Oxford Handbook of Free Will |publisher=Oxford University Press |year=2011 |isbn=978-0195399691 |editor1-last=Kane |editor1-first=Robert |edition=2nd |location=Oxford & New York |page=90 |chapter=Chaos, Indeterminism, and Free Will |oclc=653483691 |quote= |chapter-url=https://books.google.com/books?id=kzcFDsWg0GEC&pg=PA90}}</ref><ref>{{cite book |last1=Baggott |first1=Jim E. |title=Beyond Measure: Modern Physics, Philosophy, and the Meaning of Quantum Theory |publisher=Oxford University Press |year=2004 |isbn=978-0-19-852536-3 |location=Oxford & New York |page=203 |chapter=Complementarity and Entanglement |oclc=52486237 |quote= |chapter-url=https://books.google.com/books?id=uVdjwsqrgz8C&q=scientific+consensus+determinism+bell+theorem&pg=PA203}}</ref>

Moreover, [[chaos theory]] highlights that even within a deterministic framework, the ability to precisely predict the evolution of a system is often limited. A deterministic system may appear random: two apparently identical starting points can result in vastly different results. Such [[dynamical systems]] are sensitive to [[initial conditions]].<ref>{{Cite book |last=Lorenz |first=Edward N. |title=The Essence of Chaos |date=2008 |publisher=Univ. of Washington Press |isbn=978-0-295-97514-6 |edition=Nachdr. |series=The Jessie and John Danz Lectures |location=Seattle}}</ref>{{rp|8}} Even if the universe followed a strict deterministic order, the human capacity to predict every event and comprehend all underlying causes would still be constrained this kind of sensitivity.<ref>{{Cite book |last=Lorenzo |first=Edward |url=https://www.worldcat.org/title/ocm46653646 |title=The chaos avant-garde: memories of the early days of chaos theory |date=2000 |publisher=World Scientific |isbn=978-981-02-4404-0 |editor-last=Abraham |editor-first=Ralph |series=World Scientific series on nonlinear science. Series A |location=Singapore ; River Edge, NJ |chapter=The butterfly effect |oclc=ocm46653646 |editor-last2=Ueda |editor-first2=Yoshisuke}}</ref>{{rp|91}}

Adequate determinism (see [[#Varieties|Varieties]], above) is the reason that Stephen Hawking called [[Libertarianism (metaphysics)|libertarian free will]] "just an illusion".<ref name="GDesign"/>