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A Silk Road from Leibniz to Quantum Information

Rossella Lupacchini

Published Nov 24, 2016• 0 citations
Publisher

Abstract

At the roots of quantum physics we find two “specular” principles: a principle of distinguishability, which arranges the “uncertainty” of quantum \nmeasurement, and a principle of continuity, which drives the evolution of quantum systems. The vital link between the two principles was sharply \ncaptured by Leibniz. In his Theodicy, the issue of continuity (and indivisibles) is presented as one of “the two famous labyrinths” in which our \nreason can lose its way; the other concerns “the great question of freedom and necessity.” According to Leibniz, only geometry can provide a \nthread for the labyrinth of continuity. However, escaping from the labyrinth of Fate, Fortune, and Freedom requires a different perspective on nature. Leibniz’s perspective on the mechanism of nature is significantly different from Descartes’ or Newton’s. It reveals notable affinities with the Chinese correlative thinking. Surprisingly, the rationale behind these affinities may find a coherent setting in quantum information.

DOI
10.1142/9789813109032_0010

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At the roots of quantum physics we find two “specular” principles: a principle of distinguishability, which arranges the “uncertainty” of quantum \nmeasurement, and a principle of continuity, which drives the evolution of quantum systems. The vital link between the two principles was sharply \ncaptured by Leibniz. In his Theodicy, the issue of continuity (and indivisibles) is presented as one of “the two famous labyrinths” in which our \nreason can lose its way; the other concerns “the great question of freedom and necessity.” According to Leibniz, only geometry can provide a \nthread for the labyrinth of continuity. However, escaping from the labyrinth of Fate, Fortune, and Freedom requires a different perspective on nature. Leibniz’s perspective on the mechanism of nature is significantly different from Descartes’ or Newton’s. It reveals notable affinities with the Chinese correlative thinking. Surprisingly, the rationale behind these affinities may find a coherent setting in quantum information.
We systematically analyze the conceptual structure of modern physics, i.e., the theory of relativity and quantum mechanics and quantum field theory, from the perspective of Leibniz’s three basic principles of identity, sufficient reason and continuity. We find that Leibniz’s way of thinking can still provide insight into fundamental problems of physics, such as the nature of physical constants, the relation between physical invariances and covariant coordinate representations, the role of the Planck scale and quantum mechanical indeterminism and the measurement problem. Leibniz himself could not possess all those insights, simply because physics was not yet sufficiently developed then, but he had already forged some conceptual tools with which some fundamental problems of modern physics can be addressed.
Modern physics has achieved extraordinary empirical success while retaining much of the absolute, unobservable structure introduced by Newton, largely without questioning its necessity. We investigate how far this structure can be eliminated by adopting a relational ontology guided by Leibniz's principle of sufficient reason. Removing absolute position, orientation, time and, finally, scale leads naturally to a formulation of the gravitational NNN-body problem where only dimensionless ratios are physically meaningful. Within this framework, the scale-invariant variety VVV becomes a central quantity, providing a measure of structure, a natural ordering of shapes, and an emergent gravitational arrow of time. We argue that the resulting formulation unifies classes of Newtonian solutions previously regarded as distinct, uncovering a possible new symmetry, suggests a notion of explanation based on timeless spatial correlations rather than temporal evolution, and points towards a more economical ontology. Although developed in the context of Newtonian gravity, the principles proposed here may also offer a new perspective on general relativity and quantum mechanics.
The present article is written by a theoretical physicist who, for some time, has endeavored to trace the origin of the concepts and principles of quantum theory to an empirical background broader than that afforded by delicate optical and mechanical experiments on a microphysical scale involving the microconstant h. In particular he tried to reduce the dominant role of probability in modern physics to irrefutable evidence of a quite general nature. As long as quantum probability is deduced from experience with seemingly uncontrollable micro-mechanisms—think of radioactive disintegration as the most typical example—there will always be the objection that one day we still may find a hidden causality behind those small scale gambling devices called atoms, although one example of an exactly predictable atomic event would make present-day quantum theory untenable. In order to dislodge the remaining classicists from their fortress of doubt one may try to show that quantum probability is not an alibi for a temporary impotence of predicting microphysical events, but is a positive conclusion drawn from experience of a most general type, namely, from the principle of continuity, the basic tenet of the philosophy of Leibniz.
In his search for the ‘essence’ of continuity, Richard Dedekind (1872) discovered the notion of cut. Epistemologically speaking, a cut produces a separation of a simply infinite system into two parts (Stücke) such that all the elements of one part are screened off all the elements of the other. The distinct continuity of a two-state quantum system is encapsulated in the notion of qubit, the basic ‘unit’ of quantum information. A qubit secures an infinite amount of information, which, however, appears to be only penetrable through ‘sections’ of classical bits. Whereas Dedekind’s cuts dwell on the discrete of number theory, the theory of nature is primarily concerned with continuous transformations. In contrast with Dedekind’s line of thought, could the notion of information be derived from a ‘principle’ of continuity?
The philosophical Framework of modern physics puts forward a philosophical solution to the contradiction between relativity theory and quantum mechanics theory, aiming to break through the restriction of material philosophy on human thought and solve the artificial contradiction generated by material philosophy. This scheme is the physical principle of natural philosophy. Newton discovered the mathematical principles of natural philosophy, he expressed the principles of the universe’s natural philosophy through mathematics, discovering universal gravitation, the mutual perception and motion of material mass. This line of thought continued with the discovery of electromagnetism by Faraday and Maxwell, and quantum mechanics by Einstein, Planck, Born, Bohr, and Dirac many scientists. This represents the completion of the great natural theology of the universe, a credit to these great scientists. However, we have not recognized this as natural theology. Newton and Leibniz jointly discovered absolute space, but due to insufficient scientific information, we lost an opportunity. Today, modern physics has given us another chance; by combining scientific information with the Cosmic origin principles left by our ancestors, we can understand absolute space. Starting with an analysis of the “theoretical contradictions” in quantum mechanics and relativity, reflecting on the concept and essence of physics, and recognizing the Cosmic origin principle is the natural philosophy principle of physics.