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The clockwork universe theory compares the motions of everything in the universe to the innards of a mechanical clock. This idealized clock continues ticking along, as would a perfect machine, with its gears governed by the laws of physics, making every single aspect of the device completely predictable. Since Newton unified the description of terrestrial and heavenly motion, scientists originally had good reason to believe that the universe was completely deterministic at least in principle.

This was not incompatible with the religious view that God the creator wound up the universe in the first place at the Big Bang; and from there the laws of science took hold and have governed every sequence of events since; aka Secondary Causation. But it did tend to undermine the notion that God's instant-by-instant attention was required for the universe to function as expressed in the theory of Occasionalism.

The clockwork universe was popular among deists during the Enlightenment, when scientists demonstrated that Newton's laws of motion, including the law of universal gravitation, could explain the behavior of falling objects on earth as well as the motion of the planets to within the limits of the observational accuracy of the day.

Opposition

Suggested arguments against the possibility of the universe being predictable via the laws of science include: the concept of free will acting through the agency of a soul not strictly governed by the laws of physics; the second law of thermodynamics in which the total entropy tends to increase over time; the axiomatic foundation of mathematics which underlies scientific inquiry;quantum physics with its probabilistic description of the wave function; and most recently modern Chaos Theory. The nuances of all such objections are fundamentally different in character.

Isaac Newton has been recognized as a prominent opponent of the clockwork universe theory, though the theory has often been wrongly attributed to him. Edward B. Davis has acknowledged Newton's belief that the clockwork universe theory wrongly reduces God's role in the universe, as reflected in the writings of Newton-supporter Samuel Clarke. Responding to Gottfried Leibniz, a prominent supporter of the theory, in the Leibniz–Clarke correspondence, Clarke wrote:

"The Notion of the World's being a great Machine, going on without the Interposition of God, as a Clock continues to go without the Assistance of a Clockmaker; is the Notion of Materialism and Fate, and tends, (under pretense of making God a Supra-mundane Intelligence,) to exclude Providence and God's Government in reality out of the World."

World-machine

A similar concept goes back, to John of Sacrobosco's early 13th-century introduction to astronomy: On the Sphere of the World. In this widely popular medieval text, Sacrobosco spoke of the universe as the machina mundi, the machine of the world, suggesting that the reported eclipse of the Sun at the crucifixion of Jesus was a disturbance of the order of that machine.

This conception of the universe consisted of a huge, regulated and uniform machine that operated according to natural laws in absolute time, space, and motion. God was the master-builder, who created the perfect machine and let it run. God was the Prime Mover, who brought into being the world in its lawfulness, regularity, and beauty. This view of God as the creator, who stood aside from his work and didn’t get involved directly with humanity, was called Deism (which predates Newton) and was accepted by many who supported the “new philosophy”.

Objections Due to Free Will

However, from the existence of a Creator of the universe it does not follow either determinism or indeterminism, since God has different descriptions by different people. While some argument can be made from the Bible about the existence of free will, God does not necessarily mean the God of the Bible.

Objections Due to Entropy

In the mid and late 19th century the concept of Entropy in Thermodynamics was first described by both Rudolph Clausius and William Thomson (Lord Kelvin) and was given mathematical rigor by Boltzmann, who had the pivotal equation inscribed on his gravestone. In this context and to the extent it is a correct formulation, it requires disorder in the universe taken as a whole to continually increase and thus demands the universe, or all multi-verses in total, have a begining. Because it is logically impossible for physical objects to spring into existence without a physical cause, many invoke a supernatural being, or God, as the creator of the universe from nothing “ex nihilo”. As such, this argument concerning entropy does not strictly bear on the current functioning of the universe, which is well described by the laws of thermodynamics, but rather on the origin of these laws and thus the possibility of a higher order than can be described by physics alone.

Objections Due to Quantum Mechanics

Quantum mechanics describes physical objects as wave functions whose amplitudes are smeared out to give only relative probabilities of being in different states rather than exact locations and velocities. In a sense this does not remove all determinism from physics because, if the initial state of a wave function could be known with absolute precision, its future evolution could be exactly predicted, at least in principle. But since the uncertainty principle declares the theoretical impossibility of a precise knowledge of initial conditions, this alone prevents absolute certainty as to a deterministic clock work universe even using wave functions.

The objection of quantum mechanics does not, however, depend on any lack of knowledge concerning the positions or velocities or states of microscopic particles but rather is fundamentally rooted in the mathematics itself. In principle even if we knew the initial conditions perfectly, the wave function, by describing a particle as existing in many different states at the same time, removes causality from individual events; notwithstanding the satisfyingly exact predictions of their relative probabilities in aggregate. Because we cannot say that state Z was caused by state A, but rather that state Z could also have been preceded by state B, or by state C, and so forth, more or less often, the best we can do is to replace causation with correlation. We are forced to such descriptions because all deterministic formulations, to include Newtonian dynamics, fail miserably for phenomena at the atomic level. They are, at best, collective approximations of the seething indeterminism of the wave function that governs an underlying and more fundamental behavior.

Quantum mechanics predicts, for instance, that when you leave for work in the morning, the now unobserved pendulum in your grandfather clock will suddenly assume multiple positions and velocities all at the same time to include jumping off its restraints to skewer your house cat, which in turn will not be killed outright but will exist uncomfortably in a state of being both alive and dead. And the result of this carnage will be not resolved until you return home in the evening to survey the damage. Fortunately for large tabbies like Schrödinger's cat, but not for atoms, the probability of common sense behavior is much the more likely

Indeed, the power of quantum mechanics is to start by assuming a lack of determinism and then to successfully calculate the consequences. To reiterate, not only is determinism not a required assumption but rather it is assumed not to be the case at all. Thus, to the extent that quantum mechanical equations reflect reality, rather than simply being a mathematical contrivance, then all of nature is at its very core unequivocally indeterministic.

A few early interpretations of quantum mechanics attempted to wish away this violation of common sense notions. But with theoretical advances to include the Schrödinger equation, the equivalency of the Heisenberg matrix formulation, the unification with special relativity under Dirac, the linear Hilbert space operators of von Neumann, the quantum field theories of Feynman and many others, the mathematics describing this inherent lack of determinism has become rigorous and undeniable. To the extent this remains an uncomfortable fact, some have suggested the possibility of replacing quantum mechanics with better, albeit as yet unknown, unformulated (without complete mathematical rigor), and untested theories which might be wholly, or in part, deterministic and calling these efforts “re-interpretations” of microscopic phenomena.

Driven by a life-long philosophical revulsion at the quantum mechanical violation of common sense sensibilities, and in undoubtedly the most famous attempt, Einstein championed the old world order against the upstart ideas of this newfangled indeterminism with the famous quip:

“God does not play dice with the universe.”

But more rigorously, even as the predictive success of quantum mechanics climbed to nearly unassailable heights, Einstein and a small cadre of supporters developed the now famous hidden variable conjecture. The idea was that there might be heretofore unknown aspects of an object which when measured could perhaps provide a deterministic description of atoms without resort to pesky probability waves. Note that this did not re-interpret quantum mechanics so much as criticize its “incompleteness” and suggest it should be replaced with something else entirely.

The problems in attempting to restore determinism to modern physics have been two fold, one practical and the other theoretical.

a) First and foremost, in literally millions of experiments and in many new venues, quantum mechanics with its intrinsic indeterminism has not had a single predictive failure.

b) The other more profound danger to determinism is the insight by Bell in Bell's theorem that there exists definitive experiments which would conclusively demonstrate whether real-world objects, actually exist indeterministically in many different states simultaneously until they are measured (against common sense); or are really deterministic after all and only appear otherwise because of our ignorance of unknown “hidden variables.”

The nature of Bell's insight was not in any way a new interpretation of existing theory but rather surprisingly a mathematical proof that such experiments are actually possible. And while difficult to perform, if successful these would provide definitive experimental verification of the basic indeterminacy of nature invalidating all possible deterministic theories to include hidden variables and variants. And while not all experimental difficulties have yet been removed, all Bell test experiments to date, indicate that the indeterminism of quantum particles is real and consequentially that “God does indeed play at dice."

Criticism of the claim that quantum mechanics supports indeterminism

However, the matter is far from being settled, e.g. some interpretations which were published after the publication of Bell's theorem from 1964, i.e. between 1970 and 1984, are either deterministic or agnostic in respect to determinism. So far, these interpretations have not been falsified. Gerard 't Hooft, a Nobel prizewinner in physics, supported in 2006 the case that the quantum mechanics is or should be deterministic. Till now, there is no scientific consensus on whether the quantum mechanics implies determinism or indeterminism. While quantum phenomena are described indeterministically, it is not known if in themselves they are deterministic or indeterministic.

Objections Due to Axiomatic Mathematics

All of geometry and mathematics is based on a few simple assumptions, or unprovable axioms, from which logical consequences are drawn to form a bewilderingly complex assembly of proofs and laws. While the initial assumptions of Euclid's Elements or the Peano Axioms have been chosen to be simple and "self-evident", there can be no assurance that they do not result in some subtle error far down the chain of reasonings.

Indeed one consequence of any axiomatic basis is Godel's Theorem which demonstrates there must be mathematical laws which are both true and logically impossible to prove. In this sense, any mathematical structures we could devise must always be an incomplete theory. And as Galileo opined:

"Philosophy is written in this grand book — I mean the universe — which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering about in a dark labyrinth."

Basically none of these considerations imply that mathematics or science is wrong but rather that there is no way to be absolutely certain of their results. Rather we prefer those theories that match all current observations and are simplest. Thus as our knowledge of the wonders of science improves, so does our appreciation of its limits.

Objections Due to Chaos Theory

Since the late 1960's with the rediscovery of Poincaré's proofs on the three body problem, difficulties with many non-periodic real world systems slipping into a chaotic state have been demonstrated. Amazingly, these systems were previously thought to be well described by Newton's classical laws of motion and theory of gravitation. Instabilities in predictions generally arise because of some non-linear aspect as well as an extreme sensitivity to initial conditions.

Another difficulty is that even for simple systems there seems to be a finite limit on any predictability. Even though an increasingly better knowledge of the initial state allows a prediction further into the future, the requirements on initial accuracy increase at a faster rate than the window of predictability improves. Thus even for classical systems, there is a finite window extending both into the past and the future beyond which no predictions are theoretically possible.

In 1969, Sir James Lighthill (l924-l998) was elected Lucasian Professor of Applied Mathematics at the University of Cambridge to succeed Physics Nobel Laureate, P.A.M. Dirac. As a firm believer of Newtonian mechanics, Sir James’ statement of public apology is an enlightenment to read:

“Here I have to pause, and to speak once again on behalf of the broad global fraternity of practitioners of mechanics. We are all deeply conscious today that the enthusiasm of our forebears for the marvelous achievements of Newtonian mechanics led them to make generalizations in this area of predictability which, indeed, we may have generally tended to believe before 1960, but which we now recognize were false. We collectively wish to apologize for having misled the general educated public by spreading ideas about the determinism of systems satisfying Newton’s laws of motion that, after 1960, were to be proved incorrect. In this lecture, I am trying to make belated amends by explaining both the very different picture that we now discern, and the reasons for it having been uncovered so late.”

The best current evidence seems to be that even for classical systems, the argument for a clockwork universe as a strict consequence of Newtonian dynamics is no longer logically valid. Since errors accumulate over time, perhaps exponentially, we cannot be certain of precise determinism even for short times, or even in principle, due to the finite accuracy of all physical measurements. Basically, nature seems to draw a curtain on predictions of mechanical motion that is forever beyond our ability to penetrate.

Criticism of the claim that Chaos Theory supports determinism

But this set limits to determinism only insofar it requires the capacity of humans to calculate (predict) future events, so it is about the limits of human knowledge, not about the fact that nature in itself would behave deterministically or indeterministically. No one assumes that a Lorentz system would in itself behave indeterministically, it is even clear to anyone who computes it that the Lorentz systems are wholly deterministic, but that small differences in initial conditions determine very different end results. Speaking of measuring such differences for real world systems, they could go below the measurement error and thus render humans unable to predict the end result of such system, without entailing that in itself the system would behave indeterministically. At best, we would be unable to tell whether it is deterministic or indeterministic through employing the scientific method. Therefore the claim that real world chaotic systems are in themselves completely indeterministic is a metaphysical claim which leads to no testable predictions.

Art

In 2009 artist Tim Wetherell created a large wall piece for Questacon (The National Science and Technology centre in Canberra, Australia) representing the concept of the clockwork universe. This steel artwork contains moving gears, a working clock, and a movie of the moon's terminator in action.

See also

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• Isaac Newton
• Isaac Newton's religious views
• Predestination

References

1. Davis, Edward B. 1991. "Newton's rejection of the "Newtonian world view" : the role of divine will in Newton's natural philosophy." Science and Christian Belief 3, no. 2: 103-117. Clarke quotation taken from article.
2. John of Sacrbosco, On the Sphere, quoted in Edward Grant, A Source Book in Medieval Science, (Cambridge: Harvard Univ. Pr., 1974), p. 465.
3. “Mr Tompkins in Paperback”, by George Gamow (Author), Roger Penrose, Canto Classics) Publication Date: March 26, 2012, ISBN-10: 1107604680, ISBN-13: 978-1107604681.
4. “Quantum Mechanics and Determinism: An Investigation into Gerard ‘t Hooft’s Recent Theories" by Andres M. Morey and Professor Antal Jevicki, December 20, 2002, Brown University, Providence, RI 02912
5. “Determinism beneath Quantum Mechanics" by Gerard 't Hooft, Spinoza Institute, Utrecht University, Conf. Proceedings, "Quo Vadis Quantum Mechanics", Philadelphia, (2002), Report number ITP-02/69, SPIN-2002/45.
6. "The mathematical basis for deterministic quantum mechanics", Gerard 't Hooft (2006) in Beyond the Quantum, World Scientific, Th. M. Nieuwenhuizen et al, ed., pp.3-19; ITP-UU-06/14, SPIN-06/12, quant-ph/0604008, at http://arxiv.org/abs/quant-ph/0604008].
7. “The Born-Einstein Letters", Bohn, Walker and Company, New York, (1971) (paraphrased).
8. “The Shaky Game: Science and Its Conceptual Foundations series", by Arthur Fine, University Of Chicago Press, (1996), ISBN-10: 0226249492; ISBN-13: 978-0226249490
9. "Can quantum-mechanical description of physical reality be considered complete?", Einstein, Podolsky, and Rosen, Phys. Rev. 47 777 (1935).
10. “On the Einstein–Poldolsky–Rosen paradox", Bell, Physics 1 195-200 (1964).
11. “The Fabric of the Cosmos", by Greene, Brian, (2005), Vintage Books, IBSN 0-375-72720-5, page 107.
12. “Experimental Bell tests using uncalibrated devices" from "Guaranteed violation of a Bell inequality without aligned reference frames or calibrated devices", Shadbolt, Vértesi, et. al, Scientific Reports, Vol 2, No. 470, June 2012.
13. “Revealing Bell’s nonlocality for unstable systems in high energy physics", Beatrix, Hiesmayr, et. al. The European Physical Journal C, 2012; 72 (1) DOI: 10.1140/epjc/s10052-012-1856-X
14. Gerard 't Hooft (2006) "The mathematical basis for deterministic quantum mechanics" in Beyond the Quantum, World Scientific, Th. M. Nieuwenhuizen et al, ed., pp.3-19; ITP-UU-06/14, SPIN-06/12, quant-ph/0604008, at http://arxiv.org/abs/quant-ph/0604008
15. "The Philosophy of the Sixteenth and Seventeenth Centuries", (1966) by Richard Henry Popkin, p. 65.
16. "Deterministic Nonperiodic Flow". Lorenz, (March 1963). Journal of the Atmospheric Sciences 20 (2): 130–141
17. “Sir James Lighthill and Modern Fluid Mechanics”, by Lokenath Debnath, The University of Texas-Pan American, US, Imperial College Press: ISBN-13 978-1-84816-113-9: ISBN-10 1-84816-113-1, Singapore, page 31. Online at http://cs5594.userapi.com/u11728334/docs/25eb2e1350a5/Lokenath_Debnath_Sir_James_Lighthill_and_mode.pdf

1. "A Short Scheme of the True Religion", manuscript quoted in Memoirs of the Life, Writings and Discoveries of Sir Isaac Newton by Sir David Brewster, Edinburgh, 1850; cited in; ibid, p. 65.
2. Webb, R.K. ed. Knud Haakonssen. "The Emergence of Rational Dissent." Enlightenment and Religion: Rational Dissent in Eighteenth-Century Britain. Cambridge University Press, Cambridge: 1996. p. 19.
3. Westfall, Richard S. Science and Religion in Seventeenth-Century England. p. 201.

Further reading

• Dolnick, Edward, The Clockwork Universe: Isaac Newton, the Royal Society, and the Birth of the Modern World, Harper Collins, 2011.

External links

• "The Clockwork Universe". The Physical World. Ed. John Bolton, Alan Durrant, Robert Lambourne, Joy Manners, Andrew Norton.

• History of physics
• Isaac Newton