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7 Wave Functions: Mathematics Is Reality

H. Chris Ransford

Published Mar 20, 2015• 0 citations
Publisher

Abstract

Wave Functions: Mathematics Is RealityIf the ultimate reality of anything is mathematical, it ensues that there must be some kind of 'personal' mathematical 'object', or property, or 'signature', attached to everything and anything, i.e. to any object or person or any definable, correlated collection or assembly of things -in brief, to every conceivable thing, object, or correlated collection of things in the universe.Indeed, that mathematical object must be, in some sense, more real than the object itself, because it must describe and determine that object across the range of all its possible realities, both actualized and potential, within any applicable dimensionality.

DOI
10.2478/9783110440287.7

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Wave Functions: Mathematics Is RealityIf the ultimate reality of anything is mathematical, it ensues that there must be some kind of 'personal' mathematical 'object', or property, or 'signature', attached to everything and anything, i.e. to any object or person or any definable, correlated collection or assembly of things -in brief, to every conceivable thing, object, or correlated collection of things in the universe.Indeed, that mathematical object must be, in some sense, more real than the object itself, because it must describe and determine that object across the range of all its possible realities, both actualized and potential, within any applicable dimensionality.
Reality is the conjectured state of things as they actually exist, rather than as they may appear or might beimagined. [1] In a wider definition, reality includes everything that is and has been, whether or not it is observable orcomprehensible. A still broader definition includes everything that has existed, exists, or will exist. Philosophers,mathematicians, and other ancient and modern thinkers, such as Aristotle, Plato, Frege, Wittgenstein, and Russell,have made a distinction between thought corresponding to reality, coherent abstractions (thoughts of things that areimaginable but not real), and that which cannot even be rationally thought. By contrast existence is often restrictedsolely to that which has physical existence or has a direct basis in it in the way that thoughts do The full paper: http://www.iiste.org/PDFshare/APTA-PAGENO-362446-366609.pdf
Understanding the nature of reality has been a central theme in philosophy for centuries. Classical science presented a well-defined, deterministic view of reality as objects are governed by clear laws. However, quantum mechanics introduced a radically different perspective that suggests a “quantum reality” where particles exhibit wave-like behavior and defy classical intuitions. This chapter delves into the evolution of reality, exploring its characteristics in classical physics and its transformation in the face of quantum mechanics. One key aspect of quantum reality is the wave function, as in whether the wave function is of reality. The Copenhagen interpretation posits that the wave function is a probabilistic tool, rather than a description of the real state of microscopic particles. However, the fundamental principles of quantum control and the very objects it manipulates challenge this view. By directly or indirectly influencing the wave function, quantum control techniques provide compelling evidence for its quantum reality. The PBR theorem suggests that the wave function reflects a real physical state, not merely a mathematical tool. This chapter argues that the wave function is of the “reality of relative entity-structure”. In addition, the “quantum Cheshire cat” experiment further highlights the unusual nature of quantum reality, which shares some connections with the concept of “Tao” in Chinese Taoism that suggests that everything arises from a fundamental nothingness that itself is real. Quantum technology brings forth a “quantum technological reality” characterized by new properties and applications.
Physicists usually admit a rather naive concept of physical reality: it is the object they are investigating using experiments understood as actions in the real world.in theoretical physics, the object of investigation is not the real world itself but its mathematical description which is considered as describing physical reality as exactly as possible.i present arguments from philosophy of science and from recent work in the theory of gravitational physics which indicate a possibility to defend also antirealistic views, and clarify in which sense both standpoints can be viable.
Based on a thought experiment the Einstein-Podolsky-Rosen paper’s authors concluded that in quantum mechanics the mathematical objects called wave functions fail to describe the physical reality and consequently quantum theory is incomplete. They left open the question of whether or not a complete description of the physical reality exists, but expressed their belief that such a complete theory is possible. In this paper I show that indeed a theory that gives a complete description of the physical reality exists.
The most puzzling issue in the foundations of quantum mechanics is perhaps that of the status of the wave function of a system in a quantum universe. Is the wave function objective or subjective? Does it represent the physical state of the system or merely our information about the system? If the former, does it provide a complete or partial description of the system ? We address these questions mainly from a Bohmian perspective and argue that part of the difficulty in ascertaining the status of the wave function arises from the fact that there are two different sorts of wave functions involved. The most fundamental wave function is that of the universe, which, we argue, has a law-like character. From the wave function of the universe together with its configuration one can define the wave function of a subsystem of the universe. This, although objective, has a strong informational/subjective aspect.
This essay extends the argument begun in "Why Quantum Mechanics Makes Sense," exploring the conditions under which a physical world can define and communicate information. I argue that like the structure of quantum physics, the principles of Special and General Relativity can be understood as reflecting the requirements of a universe in which things are observable and measurable. I interpret the peculiar hyperbolic structure of spacetime not as the static, four-dimensional geometry of an unobservable "block universe", but as the background metric of an evolving web of communicated information that we, along with all our measuring instruments and recording devices, actually experience in our local "here and now." Our relativistic universe is conceived as a parallel distributed processing system, in which a common objective reality is constantly being woven out of many kinds of facts determined separately in countless local measurement-contexts.