Clockwork Universe Theory - Objections Due To Quantum Mechanics

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 clockwork universe even one consisting of 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 precise predictions of their relative probabilities in aggregate. 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. Or in the opposite direction, we observe that identical particles in identical states, at least to all outward appearences, can decay along many different paths, again more or less often. It seems 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 apparently 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 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-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 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 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 and none provide the means to calculate all or even most quantum behavior so far observed.

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 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 ; 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 real-world 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."

Indeed, as the technical difficulties with tests of Bell's theorem are resolved, perhaps the last remaining loophole for determinism lies in the future development of "non-local" theories, q.v. nonlocality, which would unfortunately violate Einsteins's well tested Special theory of relativity and would require effects to precede causes.