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In the history of science, the concept of a clockwork universe compares the operation of the entire universe to the inner workings of a mechanical clock. As a metaphor for the inherent orderliness of nature, this idealized machine continues ticking along with its precision gears, governed only by a few simple yet elegant laws of physics, which make every aspect of the device completely predictable. Isaac Newton was a strong proponent, believing that phenomena of any kind should be explained in terms of mechanics.

The paradigm undermines the notion that God's instant-by-instant attention was the sole motivation for the functioning of the universe as expressed in the religious philosophy of Occasionalism. The observation of regular order and consistency in the clockwork universe also tended to discredit the assumption of a Pantheon of Deities with ever changing and contradictory moods and motivations.

The clockwork universe was especially popular among deists, who made a break with traditional religious organizations during the Enlightenment, when scientists first demonstrated that Newton's laws of motion and his law of universal gravitation, could predict the trajectories of falling objects on earth as well as the motion of the planets. Deism was rooted in the Judeo-Christian tradition in accepting the existence of God the creator of the universe but then rejected all ecclesiastical authority, especially state sponsored religion, by denying any subsequent Divine influence or intervention.

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.

World-machine

A nearly identical concept was earlier described in a 13th-century introduction to astronomy by Johannes de Sacrobosco : 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, and waxed poetic suggesting that a reported eclipse of the Sun at the crucifixion of Jesus might have been a disturbance in the order of that machine.

As in a clockwork mechanism, the machina mundi consisted of a huge, regulated, and uniform machine that operated according to natural laws in absolute time,space, and motion. This concept became a tenet of many christian traditions. Christians would, however, insist that both God and man have the potentiality to inject random non-physical perturbations into the world through the exercise of free will.

Opposition

Objections to the possibility of the universe being completely 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 of the universe tends to increase over time; the axiomatic foundation of mathematics which underlies scientific inquiry; especially modern Chaos Theory; and finally quantum physics with its dependence on the probabilistic wave function. The nuances of all such objections are fundamentally different in character as described in succeeding sections.

Even though the presumption of a clockwork universe was rooted in no little part in the momentous discoveries of Isaac Newton, he was neither the inventor of nor a proponent for the concept. Indeed, Newton warned against viewing the universe as a mere machine, specifically as something similar to a great clock.

"Gravity explains the motions of the planets, but it cannot explain who set the planets in motion. God governs all things and knows all that is or can be done.”

Throughout his life, Newton noted the inherent harmony between natural law and religion and claimed in his master work, the Principia:

“This most beautiful system of the sun, planets and comets, could only proceed from the counsel and dominion of an intelligent and powerful Being.”

Also as Edward B. Davis notes in recounting the writings of Newton-supporter Samuel Clarke, Newton's belief was that an overzealous and overreaching attachment to the clockwork universe paradigm wrongly reduced God's role in the universe. Responding to Gottfried Leibniz, who was a prominent supporter of the clockwork proposal, Clarke wrote, echoing the beliefs of Newton, (in the Leibniz–Clarke correspondence):

"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."

Considerations Due to Free Will

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Most arguments for free will are rooted in the sense that it is self evident and a natural outgrowth of our consciousness or soul. Supporting evidence includes a common sensibility of right and wrong independent of culture and often contrary to individual interest (ethics), a common regard for altruistic acts to include self-sacrifice for unrelated strangers (altruism), a common curiosity as to origins and purpose, and a human ability to conceptualize such varied things as absolute ideals and non-physical number sets; none of which are easily explained by the mechanisms of Darwinian selection pressures. These features do however suggest a spiritual component, which would be indeterministic by definition since operating in a realm outside of nature and natural laws necessarily implies a lack of predictability based on those laws. The religious argument is thus that any conscious being, either God or man made in His image, has the potential to introduce random uncertainties into the physical clockwork universe.

Indeed, so firmly ensconced is the popular belief in an individual’s freedom of choice as to generate an inordinate societal effort in the development of law and of religion to regulate behavior. Of course if the physical universe was strictly predictable and in this sense deterministic, free will would not be free but an illusion, responsibility would be meaningless, and there would be no logical foundation for ubiquitous social norms to include rewards and punishment for children, the treatment of one's neighbors, and especially for any criminal justice system; making all such efforts pointless at the core because nothing could be otherwise than what was destined to evolve through the natural laws of physics. The question is ancient and society and science continue to grapple with the question.

Another consideration is that science lacks the tools to investigate, much less explain, how a clockwork mechanism consisting of electrons bouncing off neurons could give rise to the self-awareness needed to host free will. The assertion is that the axioms of mathematics and science limit their applicability in the most fundamental sense to predictions of atomic locations and motions and can only correlate these in the most general way to physical sensations which do not easily explain the sense of being a free agent. Given these considerations, many assume the existence of a supernatural soul, not strictly governed by the laws of physics, which is thus the simplest explanation for the phenomenon.

The primary argument against free will is then, that while advances in neuroscience at the macroscopic level would not be determinative, a simulation of a living brain at the microscopic level, might conclusively demonstrate whether an individual’s choice was predictable or not. Whether this pivotal calculation is even theoretically possible using Newtonian dynamics, or not given the likely evolution into chaotic complexity, is somewhat moot since the resources required would almost certainly be beyond any means. That is not to say that model simulations cannot provide meaningful representations of and valuable insights into neural structures; but rather that a conclusive demonstration of predictability would require an intimate and precise comparison to the real time chemistry of a living brain, which would be more difficult.

At the most fundamental level, the question of whether the chemical activity of the brain is hidden behind the probabilistic veil of quantum mechanics continues to generate discussion as more and more biological processes that do exhibit quantum behavior are discovered. Generally, while most chemical reactions and diffusions active in biology are too large to be more than slightly random in a quantum sense, a few are not. And while large cascading events and their timing, often have smaller and more subtle triggers, most of the brain's functions seem to operate classically.

Considerations Due to Entropy

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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. As perhaps the most fundamental law of nature, the Second Law of Thermodynamics requires disorder to continually increase and thus demands the universe have a beginning. Our best scientific thinking is thus that the universe did not always exist. Questions related to the origin of natural law bear on considerations of a clockwork universe by raising the possibility of a hidden and higher order of things than can be described by physics alone.

That is not to say that much fundamental work in theoretical physics has not been done in attempting to describe the evolution of the very early universe, once the initial seeds came into existance by other erstwhile means, and from a variety of perspectives.

Recent work in string theory suggests the universe exists in 10 or perhaps 26 dimensions most of which are so tightly curled up that one circles back to the starting point after traversing only a microscopic distance along any one of these. But they do provide an elegant, but unfortunately unverifiable, framework for the possible collision of multidimensional surfaces enclosing higher dimensional spaces, or branes, which might give rise to a succession of big bang events creating a string of multiverses. Working out the mathematical details, however, verifies that from an entropic, as well as a quantum mechanical, perspective that such a progression could not have continued indefinitely; and thus still does not remove the necessity of a beginning of everything at some point in the past.

Another suggestion as to the evolution of the big bang at earliest times postulates an instanton, one variant of which was proposed by Hawking and Turok. Assuming the pre-existence of such an object of infinite or very large curvature, a quantum fluctuation could then have given rise to the extremely rapid inflation of the early universe. Because of the point-like localization of this quantum state one might suggest that it was almost nothing initially; but of course this does nothing to explain its own origin in the first place. Nor does it account for the pre-existence of other physical phenomena which must already have been in place, or as Turok says:

"Our instanton is a sort of self-lighting fuse that ignites inflation. To have our instanton, you have to have gravity, matter, space and time. Take any one ingredient away, and our instanton doesn't exist."

But all other considerations aside, the fundamental assumptions of natural law stipulate that it is logically impossible for physical objects to spring into existence without a physical cause or pre-existing physical basis of some sort such as gravity or space or time or zero point energy or some such. And since our well tested theory of entropy requires that there must have been a beginning, physics is confronted with a logical inconsistency. As a result, many invoke the simple notion of supernatural agency, or God, for creation of the universe necessarily in this view from nothing or ex nihilo.

That the universe must have had a beginning initiated by a prime mover was logically developed by Thomas Aquinas based on the earlier works of Augustine, who in making a rational argument that time itself must have started at creation, made a significant departure from the widely accepted Aristotelian philosophy of the time, but was well in agreement with modern considerations of entropy. This served to provide a theological framework for the later religious views of Sir Issac Newton. Interestingly, and at the other extreme, atheism, which rejects a creation event, requires a leap of faith in the eternal existence of the universe and a consequent lack of a beginning.

Considerations Due to Axiomatic Mathematics

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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 system is Godel's Theorem which demonstrates there must be mathematical statments which are both true and at the same time impossible to prove as well as statements which are false and yet impossible to refute. In this sense, any mathematics we could devise must always be incomplete. 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."

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. Simply speaking, we tend to prefer those theories that currently match all observations and are simplest.

As a case in point, a central underpinning of the clockwork universe was Newton’s law of gravitation which fostered the sense that nature was precisely predictable in the heavens as well as on earth. Newton’s putative gravitational fields were apparently pervasive and conclusive. Trajectories of cannon balls and planetary orbits were predicted with spectacular success. It was only much later that a deviation from Newtonian dynamics of roughly 43 arc seconds per century was detected in the position of the planet Mercury. This is an amount only discernible with telescopes and precision instruments and demands a leap of faith in your grandfather’s unwavering attention to astronomical detail. But the consequences were profound.

Newton’s gravitational fields are now recognized to be a complete illusion. And at no little increase in complexity, we now prefer to believe instead that the inertia of moving bodies carries them along straight lines through a space warped by massive objects in an unseen dimension. Whether this reflects reality any more than Newton’s inverse square law is problematical because Einstein’s General Relativity is not compatible with quantum theory and therefore known to be somehow fundamentally in error as well.

In addition, while a Theory of everything , may be possible, a true theory of everything is not logically possible. An oft quoted demonstration, in addition to those given above, is that one might always ask “Why that particular theory and not another?”

The inevitable trend seems to be, especially over the last century, that as science advances, so in like proportion has there been a sharpened understanding of the fundamental limits of logic and of the inherent limits of science itself.

Considerations 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 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.

That the evolution of a few seemingly simple differential equations in a Lorenz system model was inherently unpredictable in any possible computer simulation came as a real surprise in the early 1960's. But since then most real world systems, having complex relationships much beyond the early models of Lorenz, have been shown to be chaotic. In 1969, Sir James Lighthill (1924–1998) was elected Lucasian Professor of Mathematics to succeed Physics Nobel Laureate, P.A.M. Dirac. This is the chair at the University of Cambridge previously held by Sir Issac Newton. 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 thinking 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 both complexity and errors accumulate over time, perhaps exponentially, we cannot be certain of determinism even for short times, or even in principle, or even for classical systems. Chaos theory thus seems to demonstrate that nature draws a curtain on predictions of mechanical motion in a clockwork universe that is forever beyond any ability to penetrate.

Considerations Due to Quantum Mechanics

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Quantum mechanics describes physical objects in terms of 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 clockwork universe even one consisting of wave functions.

The objection of quantum mechanics does not, however, depend on any lack of knowledge concerning positions or velocities 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 precise predictions of their relative probabilities in aggregate. For instance, identical particles in identical states, at least to all outward appearances, are observed to decay into different fragments along many different paths and at different times. In the other direction we cannot say that state Z was caused by state A, but rather that state Z could also have been immediately preceded by state A, or by state B, or by state C, and so forth, again more or less often. Nor do the states A, B, C, etc. always result in state Z. It seems the best we can do to make sense of this nonsense, is to replace causation with correlation. We are forced to such descriptions because all deterministic formulations, to include Newtonian dynamics, fail miserably in describing phenomena at the atomic level. They are, at best, collective approximations of the seething indeterminism of the wave function that apparently governs an underlying and more fundamental reality.

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 core unequivocally indeterministic.

Driven by a life-long philosophical revulsion at this 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-formulate or re-interpret quantum mechanics so much as criticize its “incompleteness” and suggest it should be replaced with something else entirely.

A few early interpretations of quantum mechanics attempted to wish away the violation of common sense notions by manipulating the basic equations. But with theoretical advances to include theSchrödinger 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 to include Bohm, `t Hooft, and others, have suggested the possibility of replacing quantum mechanics with better, albeit as yet incomplete, theories or “re-interpretations” of microscopic phenomena. To date, none of these attempts founded entirely on deterministic principles are mathematically rigorous; none provide the means to calculate all or even most quantum behavior so far observed; and finally none have any experimental verification.

The problems in attempting to restore determinism to modern physics have been twofold, 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 second more profound reason to reject determinism is the theoretical insight by Bell in Bell's theorem that there are experiments which can actually measure whether all microscopic objects in the real-world are indeterministic as described by the wavefunction of quantum mechanics; or instead are deterministic as described by any conceivable hidden variable formulation, or indeed by any classical deterministic theory. The deciding criteria is Bell’s inequality which must be satisfied if reality follows the determinism of classical physics and must be violated if reality follows the indeterminism of the wavefunction.

The nature of Bell's insight was not in any way a new interpretation of existing theory but rather surprisingly a mathematical proof that experiments, able to measure this most basic aspect of reality, are actually possible. And the net result of every single one of the Bell test experiments to date, indicate that the indeterminism of quantum particles is real and consequentially that “God does indeed play at dice" as the formulae of quantum mechanics have always stipulated.

Indeed, perhaps the last loopholes providing any hope of determinism are limited to the following possibilities:

a) The glaring assumption of Bell’s work is the validity of Einstein's well tested Special theory of relativity. Thus determinism might be rescued from the clutches of Bell by the future development of "non-local" theories, q.v. nonlocality, which would unfortunately require superluminal signaling, i.e. faster than light, and which would also require physical effects to occur before their causes. In any event and in the strictest sense, all Bell test results to date thus only require that either determinism or special relativity be wrong. Because there is an overwhelming preponderance of evidence that traveling faster than light is not possible and a great difficulty in explaining how effects might come before causes, indeterminism seems to be the indicated result.

b) Critics cite technical difficulties in the experiments measuring quantities in Bell’s inequality to include not detecting enough events for statistical confidence. But as each new generation of Bell test experiments definitively eliminates more and more loopholes in more and more combinations, these objections are becoming less and less viable . And this is especially true as each and every test measurement has supported the finding of indeterminism, at whatever confidence level, and never the opposite.

c) Entirely new theories might be invented in the future which would supersede quantum mechanics, with its inherent indeterminism, based on novel assumptions or principles of which we cannot now imagine. Unfortunately we currently lack any such complete replacement formulation for quantum mechanics despite more than a century of determined effort.

See also

Template:Misplaced Pages books

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

References

1. John of Sacrbosco, On the Sphere, quoted in Edward Grant, A Source Book in Medieval Science, (Cambridge: Harvard Univ. Pr., 1974), p. 465.
2. "Teaching the Tradition" by Piderit, Melanie M. Morey, Oxford University Press, (2012), page 371.
3. Tiner, J.H. (1975). Isaac Newton: Inventor, Scientist and Teacher. Milford, Michigan, U.S.: Mott Media. ISBN 0-915134-95-0.
4. The Principia: Mathematical Principles of Natural Philosophy, by Issac Newton, translated by B. Cohen and A. Whitman (trans.), Berkeley: University of California Press (1999).
5. 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.
6. "Experimental Philosophy and the Problem of Free Will" by Shaun Nichols, Science, 18 March 2011: Vol. 331 no. 6023 pp. 1401-1403.
7. “The Blackwell Companion to Consciousness”, by Velmans and Schneider (editors), Wiley-Blackwell (2007), ISBN: 978-1-4051-2019-7.
8. ”A Large Scale Model of the Functioning Brain”, Eliasmith, Stewart, et al., Science Magazine, Vol. 338, page 1202 (2012).
9. NIH Center for Macromolecular Modeling & Bioinformatics University of Illinois at Urbana-Champaign, Theoretical and Computational Research Group.
10. "Quantum mechanics in the brain" by Christof Koch and Klaus Hepp, Nature, Vol. 440(30), page 611, (2006).
11. “The Beginning of Time” lecture by S. Hawking, online at http://www.hawking.org.uk/the-beginning-of-time.html
12. “Relativity, Thermodynamics, and Cosmology” by Tolman, Oxford University Press, Oxford, UK, (1934), .
13. “A Larger Estimate of the Entropy of the Universe,” Egan and Lineweaver, Astrophysical Journal Volume 710 (2010), page 1825.
14. “Inflationary Spacetimes Are Incomplete in Past Directions”, Borde, Guth, and Vilenkin, Phys. Rev. Lett. 90, 151301 (2003).
15. “Open Inflation Without False Vacua”, Hawking and Turok, Phys.Lett. B425 (1998) pages 25-30.
16. “Singular Instantons and Creation of Open Universe”, Vilenkin, Phys. Rev. D Volume 57 (1998), pages 7069-7070.
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18. “Stephen Hawking: An Unfettered Mind” by Kitty Ferguson, Macmillan, New York, NY, (2012) page 194; ISBN 978-0-230-34060-2.
19. “Why physicists can't avoid a creation event” by Lisa Grossman, New Scientist, Issue 2847, 11 January 2012.
20. "The Philosophy of the Sixteenth and Seventeenth Centuries", (1966) by Richard Henry Popkin, p. 65.
21. “The Attraction of Gravitation: New Studies in the History of General Relativity (Einstein Studies)”, by John Earman, Michel Janssen, and John D. Norton, Birkhäuser. (1993); ISBN 0817636242 : ISBN 978-0817636241.
22. “Human Knowledge: Its Scope and Limits” by Bertrand Russell, Routledge Classics (2009) ISBN 0415474442
23. “Logic and Knowledge: Essays 1901-1950” by Bertrand Russell, Spokesman Books, (2007) ISBN 0851247342
24. ”Formal Logic: Its Scope And Limits” by Richard Jeffrey (Author), John P. Burgess (Editor) (2006) ISBN 0872208133
25. "Deterministic Nonperiodic Flow". Lorenz, (March 1963). Journal of the Atmospheric Sciences 20 (2): 130–141
26. “Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas?“, Edward N. Lorenz, American Association for the Advancement of Science (AAAS), December 29, 1972.
27. “Sir James Lighthill and Modern Fluid Mechanics”, by Lokenath Debnath, The University of Texas-Pan American, US, Imperial College Press: ISBN 978-1-84816-113-9: ISBN 1-84816-113-1, Singapore, page 31. Online athttp://cs5594.userapi.com/u11728334/docs/25eb2e1350a5/Lokenath_Debnath_Sir_James_Lighthill_and_mode.pdf
28. “Nonlinear Dynamical Systems and Control: A Lyapunov-Based Approach” by Haddad, and Chellaboina, Princeton University Press, (2011).
29. “Chaos and Nonlinear Dynamics”, by Hilborn, (2001). ISBN-10: 0198507232.
30. “Chaos, Scattering and Statistical Mechanics” by Gaspard, Cambridge Nonlinear Science Series, (2005), ISBN-10: 0521018250.
31. “Mr. Tompkins in Paperback”, by George Gamow (Author), Roger Penrose, Canto Classics) Publication Date: March 26, 2012, ISBN 1107604680, ISBN 978-1107604681.
32. “The Born-Einstein Letters", Bohn, Walker and Company, New York, (1971) (paraphrased).
33. “The Shaky Game: Science and Its Conceptual Foundations series", by Arthur Fine, University Of Chicago Press, (1996), ISBN 0226249492; ISBN 978-0226249490
34. "Can quantum-mechanical description of physical reality be considered complete?", Einstein, Podolsky, and Rosen, Phys. Rev. 47 777 (1935).
35. “Causality and Chance in Modern Physics” by David Bohm (1957) Routledge & Kegan Paul and D. Van Nostrand, (1957) ISBN 0-8122-1002-6.
36. “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
37. “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.
38. 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
39. “On the Einstein–Poldolsky–Rosen paradox", Bell, Physics 1 195-200 (1964).
40. “The Fabric of the Cosmos", by Greene, Brian, (2005), Vintage Books, IBSN 0-375-72720-5, page 107.
41. “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.
42. “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

Further reading

• Dolnick, Edward, The Clockwork Universe: Isaac Newton, the Royal Society, and the Birth of the Modern World, Harper Collins, 2011.
• "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.
• 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.
• Westfall, Richard S. Science and Religion in Seventeenth-Century England. p. 201.

External links

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

• History of physics
• Isaac Newton