A clockwork universe?
Marco Iovino
Introduction and semantics
therefore inevitable and for the purpose of convenience, Âpre-determinedÊ in the title is to be effectively synonymous with determinism. 4
The western school of thought has been pondering the matter of determinism since the times of the Stoics. The answer to this metaphysical debate could potentially help give a profound insight as to whether we actually possess free will in our actions, and so we turn to physics in an attempt to gleam an objective conclusion to the debate. With the perspective gained with the established scientific method, material interpretations of the universe prior to the widespread acceptance of Isaac NewtonÊs Principia are seen to be largely rife with mysticism and thus can be ignored. James Cushing states that ÂAfter Newton, the material universe came to be seen as completely deterministic in principleÊ 1 . However, before we explore classical Newtonian mechanics and its potential shortcomings along with quantum mechanics and its implications, we must distinguish the meaning of philosophical terms used in these contexts. To quote Bertrand Russell ÂClearly our first problem must be to define the issue, since nothing is more prolific of fruitless controversy than an ambiguous questionÊ 2 . The variant of determinism explored in this essay shall be that of the most widely discussed in the physical sciences, expressed succinctly by John Earman as the ÂLaplacian variety of determinism according to which the instantaneous state of the world at any time uniquely determines the state at any other timeÊ 3 . In theory, this cause-event chain could be traced back to the inception of the universe. Since the future resulting state is 1 Cushing, James T. Philosophical Concepts in Physics , Cambridge: Cambridge University Press, 1998. p. 167. 2 Russell, Bertrand. Determinism and Physics . Durham: Armstrong College, 1936. 3 Earman, John. ÂDeterminism: what we have learned and what we still donÊt knowÊ, Freedom and determinism (2004): p. 21.
Determinism in the classical Newtonian system and the issue of chaos
Following the publication of NewtonÊs Principia , the universe was viewed as entirely deterministic. Given the initial velocity (v 0 ) and position (r 0 ) of a particle, its entire future trajectory can be determined as a function of time with F = ma as r ( t ). Therefore in theory, the same principle could be applied to every particle in the universe and there should be no deviance exhibited provided the arbitrary accuracy of the original values. This view was expressed by Laplace and has been commonly accepted among philosophers of science. 5 The main challenge that the Newtonian model faces is the issue of chaos, which is shown to manifest itself in nature. Dynamical chaos arises when non-linearity is present in an equation expressing position. Due to complications in interpreting such equations, Cushing opts for a more accessible solution of analysing discrete mapping problems. Using a logistic map, an iterative procedure is used for generating a 4 Despite some debate on whether determinism and pre-determinism should be used interchangeably, in the physical sciences it is commonly done. See for example Hooft, G, ÂHow does god play dice? Pre- determinism at the Planck scaleÊ . arXiv preprint hep- th/0104219. (2001). 5 That is until recently with John EarmanÊs A Primer on Determinism and other papers, though his view of the lack of provision for isotropy in the classical model is somewhat discredited by Mark Wilson stating in his essay Critical Notice: John EarmanÊs A Primer On Determinism: ÂThe inability of classical doctrines to accommodate isotropic possibilities coherently shouldn't legislate against either their correctness or their determinismÊ.
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