Editing Determinism (section)

== Modern scientific perspective ==
=== Generative processes ===
{{Main|Emergence}}

Although it was once thought by scientists that any indeterminism in quantum mechanics occurred at too small a scale to influence biological or neurological systems, there is indication that [[nervous system]]s are influenced by quantum indeterminism due to [[chaos theory]].<ref>{{Cite journal |last1=Lewis |first1=Edwin R. |last2=Macgregor |first2=Ronald J. |date=2006-06-01 |title=On indeterminism, chaos, and small number particle systems in the brain |url=https://www.worldscientific.com/doi/abs/10.1142/S0219635206001112 |journal=Journal of Integrative Neuroscience |volume=05 |issue=2 |pages=223–247 |doi=10.1142/S0219635206001112 |pmid=16783870 |issn=0219-6352|url-access=subscription }}</ref> It is unclear what implications this has for the problem of [[free will]] given various possible reactions to the problem in the first place.<ref>{{cite journal | doi=10.1142/S0219635206001112 | last=Lewis | first=E.R. |author2=MacGregor, R.J. | year=2006 | title=On Indeterminism, Chaos, and Small Number Particle Systems in the Brain | journal=[[Journal of Integrative Neuroscience]] | volume=5 | issue=2 | pages=223–247 |url=http://www.eecs.berkeley.edu/~lewis/LewisMacGregor.pdf |archive-url=https://web.archive.org/web/20110608034826/http://www.eecs.berkeley.edu/~lewis/LewisMacGregor.pdf |archive-date=2011-06-08 |url-status=live | citeseerx=10.1.1.361.7065 | pmid=16783870 }}</ref> Many biologists do not grant determinism: [[Christof Koch]], for instance, argues against it, and in favour of [[Libertarianism (metaphysics)|libertarian free will]], by making arguments based on generative processes ([[emergence]]).<ref name=Koch>{{cite book |last1=Koch |first1=Christof |author-link1=Christof Koch |editor1-first=Nancy|editor1-last=Murphy |editor2-first=George |editor2-last=Ellis |editor3-first=Timothy|editor3-last=O'Connor |title=Downward Causation and the Neurobiology of Free Will |year=2009 |publisher=[[Springer Science+Business Media|Springer]] |location=New York|isbn=978-3-642-03204-2 |chapter=Free Will, Physics, Biology and the Brain|bibcode=2009dcnf.book.....M }}</ref> Other proponents of emergentist or [[Generative science|generative philosophy]], [[cognitive science]]s, and [[evolutionary psychology]], argue that a certain form of determinism (not necessarily causal) is true.<ref name="Kenrick">{{cite journal | last1 = Kenrick | first1 = D. T. | last2 = Li | first2 = N. P. | last3 = Butner | first3 = J. | year = 2003 | title = Dynamical evolutionary psychology: Individual decision rules and emergent social norms | url = http://www.mysmu.edu/faculty/normanli/KenrickLiButner2003.pdf| journal = Psychological Review | volume = 110 | issue = 1| pages = 3–28 | doi=10.1037/0033-295x.110.1.3 | pmid=12529056| citeseerx = 10.1.1.526.5218 | s2cid = 43306158 }}</ref><ref name="Nowak">Nowak A., Vallacher R.R., Tesser A., Borkowski W., (2000) "Society of Self: The emergence of collective properties in self-structure", Psychological Review 107.</ref><ref name="Axtell">{{Cite book |last1=Epstein |first1=Joshua M. |title=Growing Artificial Societies: Social Science from the Bottom Up |last2=Axtell |first2=Robert |date=1996 |publisher=Brookings Institution Press |isbn=9780262272360 |location=Washington, D.C. |language=en |oclc=42854515}}</ref><ref name="Epstein">Epstein J.M. (1999) "Agent Based Models and Generative Social Science". ''Complexity'', IV (5)</ref> They suggest instead that an illusion of free will is experienced due to the generation of infinite behaviour from the interaction of finite-deterministic set of rules and [[parameter]]s. Thus the unpredictability of the emerging behaviour from deterministic processes leads to a perception of free will, even though free will as an [[Ontology|ontological]] entity does not exist.<ref name= "Kenrick"/><ref name= "Nowak"/><ref name= "Axtell"/><ref name= "Epstein"/>

[[File:Gospers glider gun.gif|thumb|right|120px|An animation of [[Conway's Game of Life]], where the interaction of just four simple rules creates patterns that seem somehow "alive".]]

As an illustration, the strategy board-games [[chess]] and [[Go (game)|Go]] have rigorous rules in which no information (such as cards' face-values) is hidden from either player and no [[randomness|random]] events (such as dice-rolling) happen within the game. Yet, chess and especially Go with its extremely simple deterministic rules, can still have an extremely large number of unpredictable moves. When chess is simplified to 7 or fewer pieces, however, endgame tables are available that dictate which moves to play to achieve a perfect game. This implies that, given a less complex environment (with the original 32 pieces reduced to 7 or fewer pieces), a perfectly predictable game of chess is possible. In this scenario, the winning player can announce that a checkmate will happen within a given number of moves, assuming a perfect defense by the losing player, or fewer moves if the defending player chooses sub-optimal moves as the game progresses into its inevitable, predicted conclusion. By this analogy, it is suggested, the experience of free will emerges from the interaction of finite rules and deterministic parameters that generate nearly infinite and practically unpredictable behavioural responses. In theory, if all these events could be accounted for, and there were a known way to evaluate these events, the seemingly unpredictable behaviour would become predictable.<ref name= "Kenrick"/><ref name= "Nowak"/><ref name= "Axtell"/><ref name= "Epstein"/> Another hands-on example of generative processes is [[John Horton Conway]]'s playable [[Conway's Game of Life|Game of Life]].<ref>{{cite web| url = http://www.bitstorm.org/gameoflife/| title = John Conway's Game of Life}}</ref> [[Nassim Nicholas Taleb|Nassim Taleb]] is wary of such models, and coined the term "[[ludic fallacy]]."

=== Compatibility with the existence of science ===
Certain [[philosophy of science|philosophers of science]] argue that, while causal determinism (in which everything including the brain/mind is subject to the laws of causality) is compatible with minds capable of science, fatalism and predestination is not. These philosophers make the distinction that causal determinism means that each step is determined by the step before and therefore allows sensory input from observational data to determine what conclusions the [[brain]] reaches, while fatalism in which the steps between do not connect an initial cause to the results would make it impossible for observational data to correct false hypotheses. This is often combined with the argument that if the brain had fixed views and the arguments were mere after-constructs with no causal effect on the conclusions, science would have been impossible and the use of arguments would have been a meaningless waste of energy with no persuasive effect on brains with fixed views.<ref>Karl Popper: ''Conjectures and rRefutations''{{page needed|date=August 2021}}</ref>

=== Mathematical models ===
Many [[mathematical model]]s of physical systems are deterministic. This is true of most models involving [[differential equation]]s (notably, those measuring rate of change over time). Mathematical models that are not deterministic because they involve randomness are called [[stochastic]]. Because of [[Butterfly effect|sensitive dependence on initial conditions]], some deterministic models may appear to behave non-deterministically; in such cases, a deterministic interpretation of the model may not be useful due to [[Numerical stability|numerical instability]] and a finite amount of [[accuracy and precision|precision]] in measurement. Such considerations can motivate the consideration of a stochastic model even though the underlying system is governed by deterministic equations.<ref>{{cite journal | last1 = Werndl | first1 = Charlotte | year = 2009 | title = Are Deterministic Descriptions and Indeterministic Descriptions Observationally Equivalent? | doi = 10.1016/j.shpsb.2009.06.004 | journal = Studies in History and Philosophy of Modern Physics | volume = 40 | issue = 3| pages = 232–242 | bibcode = 2009SHPMP..40..232W | arxiv = 1310.1615 | s2cid = 11515304 }}</ref><ref>Werndl, Charlotte (2009). ''[http://philsci-archive.pitt.edu/archive/00004775/ Deterministic Versus Indeterministic Descriptions: Not That Different After All?]''. In: A. Hieke and H. Leitgeb (eds), "Reduction, Abstraction, Analysis", ''Proceedings of the 31st International Ludwig Wittgenstein-Symposium''. Ontos, 63–78.</ref><ref>J. Glimm, D. Sharp, ''Stochastic Differential Equations: Selected Applications in Continuum Physics'', in: R.A. Carmona, B. Rozovskii (ed.) ''Stochastic Partial Differential Equations: Six Perspectives'', American Mathematical Society (1998) {{ISBN|0-8218-0806-0}}{{page needed|date=August 2021}}</ref>

=== Quantum and classical mechanics ===
==== Classical theories ====
{{Further|Macroscopic quantum phenomena}}

Since the beginning of the 20th century, quantum mechanics—the physics of the extremely small—has revealed previously concealed aspects of [[Phenomenon|event]]s. Before that, [[classical mechanics|Newtonian physics]]—the physics of everyday life—dominated. Taken in isolation (rather than as an [[approximation]] to quantum mechanics), Newtonian physics depicts a universe in which objects move in perfectly determined ways. At the scale where humans exist and interact with the universe, Newtonian mechanics remain useful, and make relatively accurate predictions (e.g. calculating the trajectory of a bullet). But whereas in theory, [[Universality (philosophy)|absolute knowledge]] of the forces accelerating a bullet would produce an absolutely accurate prediction of its path, modern quantum mechanics casts reasonable doubt on this main thesis of determinism.

This doubt takes radically different forms. The observed results of quantum mechanics are random but various [[interpretations of quantum mechanics]] make different assumptions about determinism which cannot be distinguished experimentally. The standard interpretation widely used by physicists is not deterministic, but the other interpretations have been devised which are deterministic.<ref>{{Cite web |last=Hoefer |first=Carl |date=2024 |editor-last=Zalta |editor-first=Edward N. |editor2-last=Nodelman |editor2-first=Uri |title=Causal Determinism |url=https://plato.stanford.edu/entries/determinism-causal/ |access-date=2025-03-03 |publisher=Metaphysics Research Lab, Stanford University}}</ref> 

==== Standard quantum mechanics ====
[[File:Feynman paths.png|thumb|These are five of the infinitely many paths available for a particle to move from point A at time t to point B at time t’(>t).]]

Quantum mechanics is the product of a careful application of the [[scientific method]], [[logic]] and [[empiricism]]. Through a large number of careful experiments physicists developed a rather unintuitive mental model: A particle's path cannot be specified in from its quantum description. "Path" is a classical, practical attribute in everyday life, but one that quantum particles do not possess. Quantum mechanics attributes probability to all possible paths and asserts the only one outcome will be observed. 

The randomness in quantum mechanics derives from the quantum aspect of the model. Different experimental results are obtained for each individual quanta. Only the probability can predicted.<ref name="Peres-2002">{{Cite book |last=Asher |first=Peres |url=http://link.springer.com/10.1007/0-306-47120-5 |title=Quantum Theory: Concepts and Methods |date=2002 |publisher=Springer Netherlands |isbn=978-0-7923-3632-7 |editor-last=Peres |editor-first=Asher |location=Dordrecht |language=en |doi=10.1007/0-306-47120-5|bibcode=2002qtcm.book.....P }}</ref>{{rp|7}}
As [[Stephen Hawking]] explains, the result is not traditional determinism, but rather determined probabilities.<ref name="GDesign">{{Cite book |last1=Hawking |first1=Stephen |title=The Grand Design |last2=Mlodinow |first2=Leonard |publisher=[[Bantam Books]] |year=2010 |isbn=978-0-553-80537-6 |editor-link=Stephen Hawking |location=New York |page=32 |oclc=654183639}}</ref> As far as the thesis of determinism is concerned, these probabilities, at least, are quite determined. 

[[File:Double-slit experiment results Tanamura 2.jpg|thumb|right|Although it is not possible to predict the arrival position or time for any particle, probabilities of arrival predict the final pattern of events.]]

On the topic of predictable probabilities, the [[double-slit experiment]]s are a popular example. [[Photon]]s are fired one-by-one through a double-slit apparatus at a distant screen. They do not arrive at any single point, nor even the two points lined up with the slits (the way it might be expected of bullets fired by a fixed gun at a distant target). Instead, the photons arrive in varying concentrations and times across the screen, and only the final distribution of photons can be predicted. In that sense the behavior of light in this apparatus is predictable, but there is no way to predict where or when in the resulting [[Wave interference|interference]] pattern any single [[photon]] will make its contribution.

Some (including [[Albert Einstein]]) have argued that the inability to predict any more than probabilities is simply due to ignorance.<ref>[[Albert Einstein]] insisted that, "I am convinced God does not play dice" in a private letter to [[Max Born]], 4 December 1926, [http://www.alberteinstein.info/db/ViewDetails.do?DocumentID=38009 Albert Einstein Archives] {{Webarchive|url=https://web.archive.org/web/20100819045822/http://www.alberteinstein.info/db/ViewDetails.do?DocumentID=38009 |date=19 August 2010 }} reel 8, item 180</ref> The idea is that, beyond the conditions and laws can be observed or deduced, there are also hidden factors or "[[Hidden-variable theory|hidden variables]]" that determine ''absolutely'' in which order photons reach the detector screen. They argue that the course of the universe is absolutely determined, but that humans are screened from knowledge of the determinative factors. So, they say, it only ''appears'' that things proceed in a probabilistically way. 

[[John Stewart Bell|John S. Bell]] analyzed Einstein's work in his famous [[Bell's theorem]], which demonstrates that quantum mechanics can makes statistical predictions that would be violated if local hidden variables really existed. Many experiments have verified the quantum predictions.<ref name="Markoff">{{cite news |last=Markoff |first=Jack |title=Sorry, Einstein. Quantum Study Suggests 'Spooky Action' Is Real. |url=https://www.nytimes.com/2015/10/22/science/quantum-theory-experiment-said-to-prove-spooky-interactions.html |date=21 October 2015 |work=[[New York Times]] |accessdate=21 October 2015 }}</ref><ref name="Hensen et al.">{{cite journal|last1=Hensen|title=Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres|journal=Nature|volume=526|issue=7575|pages=682–686|doi=10.1038/nature15759|display-authors=etal|bibcode = 2015Natur.526..682H|pmid=26503041|year=2015|arxiv=1508.05949|s2cid=205246446 }}</ref>

=== 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|url-access=subscription }}</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"/>