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Siberian Journal of Philosophy

The philosophical foundations of quantum computer modeling

Anna Yu. Storozhuk

Published Jan 1, 2019• 0 citations
Publisher

Abstract

The source of some problems of the quantum mechanics is the observer’s influence on the system. In particular, such problems include the reduction wave function, which forces physicists to talk about “hidden parameters” and the incompleteness of quantum mechanics. Measurements of a quantum system violate its internal state and make it impossible to obtain information about its other parameters (Heisenberg’s uncertainty principle). In 1980 there appeared the thesis that since modeling the behavior of a quantum system on a classical computer cannot provide sufficient accuracy for reproducing all its parameters, there is a need for a quantum computer. The question arises: to what degree can a quantum computer help to solve traditional epistemological problems of quantum mechanics? Can modelling the behavior of elementary particles on a quantum computer “bypass” the problem of the observer’s influence on the system? In other words, is it possible to obtain information about the behavior of a quantum system without observation? Will the internal state of the simulated system be preserved?

DOI
10.25205/2541-7517-2019-17-4-85-92

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The source of some problems of the quantum mechanics is the observer’s influence on the system. In particular, such problems include the reduction wave function, which forces physicists to talk about “hidden parameters” and the incompleteness of quantum mechanics. Measurements of a quantum system violate its internal state and make it impossible to obtain information about its other parameters (Heisenberg’s uncertainty principle). In 1980 there appeared the thesis that since modeling the behavior of a quantum system on a classical computer cannot provide sufficient accuracy for reproducing all its parameters, there is a need for a quantum computer. The question arises: to what degree can a quantum computer help to solve traditional epistemological problems of quantum mechanics? Can modelling the behavior of elementary particles on a quantum computer “bypass” the problem of the observer’s influence on the system? In other words, is it possible to obtain information about the behavior of a quantum system without observation? Will the internal state of the simulated system be preserved?
When investigating various interpretations of quantum mechanics one notices that each interpretation contains an element which escapes a complete and full description. This element is always associated with the stochasticity of the individual event in the quantum measurement process. It appears that the implications of this limit to any description of the world has not been sufficiently appreciated with notable exceptions of, for example, Heisenberg, Pauli and Wheeler. If we assume that a deeper foundation of quantum mechanics is possible, the question arises which features such a philosophical foundation might have. It is suggested that the objective randomness of the individual quantum event is a necessity of a description of the world in view of the significant influence the observer in quantum mechanics has. It is also suggested that the austerity of the Copenhagen interpretation should serve as a guiding principle in a search for deeper understanding. In recent years, a significant increase of interest in the foundations of quantum mechanics can be observed. This increase is certainly related to the immense progress made during the last two decades in experiments with individual quantum systems. This technological progress has made it possible to really perform more and more of the famous gedanken experiments which were so important in the early days of the theory. Not only did these experiments confirm the theory in every detail, they also opened up avenues for new experimental directions which might even lead some day to new technology. While such applications are certainly still far away, areas like quantum cryptography[1], quantum computation[2] and interaction-free measurement[3], just to name a few examples, certainly deserve the attention they receive. All this activity has also drawn more attention to the problems of understanding and interpreting quantum mechanics. It seems that there, a definitive consensus has not yet been reached. As witnesses quote authorities like Feynman as saying[4]: I think can safely say that nobody today understands quantum mechanics, whereby he apparently included himself, or like Roger Penrose[5], who describes his opinion remarking that while the theory agrees incredibly well with experiment and while it is of profound mathematical beauty, it makes absolutely no sense. Why did even physicists who have contributed so significantly to quantum theory Feynman was even rewarded the Nobel Prize for one of its mathematical formulations choose such emphatic and strong formulations? Why is it that the average physicist hears very little about such problems during his/her education? Why is the comprehension of the theory very often focused on formalism while questions that probe for deeper meaning are usually not tackled? To take a closer look at the situation, let us turn to a brief analysis of the interpretation of quantum mechanics. We note that there are at least two levels of interpreting a formalism, a physical theory. The first, basic, level supplies the rules that determine which element of the formalism corresponds to which measurable quantity or to which observable fact in a concrete experimental situation. Theses rules are a large, mostly not explicated but only implicit, set of instructions. These instructions concern the manner of working with the statements of the theory in order to obtain predictions for future experiments or events, and they concern the instructions on how to proceed in experiment in order to demonstrate or test a theoretical
From the very beginning, Quantum Mechanics has been accompanied by crucial foundational questions: the possibility of visualizing physical processes, the limits of measurement epitomized by the Heisenberg uncertainty principle, the existence of a deeper underlying reality with additional degrees of freedom, the role of measurements, and the status of locality. Long regarded as philosophical speculations, these issues were progressively reformulated into precise mathematical statements and ultimately subjected to experimental verification. The trajectory proved unpredictable: questions once dismissed as metaphysical gave rise to experimental platforms, which in turn matured into devices and technologies powering quantum computation, communication, and sensing. Yet this development is not unidirectional: advances in technology also feed back into foundations, enabling tests of principles that were previously out of reach, for example, whether quantum superposition persists at larger and larger scales and whether reality, gravity included, is fundamentally quantum. In this way, the dialogue between foundational inquiry and technological progress continues to shape both our theoretical understanding and the practical realization of quantum phenomena.
We present a historical-epistemological analysis of the foundations of quantum mechanics, highlighting the relationships between quantum mechanics and scientific realism, as well as the influence of the neo-positivist philosophy of the first decades of the 20th century. The great significance of the measurement process in the context of quantum mechanics is underlined as an essential element in providing a coherent description of reality, moving from micro to macrocosm, as well as the role that the measurement apparatus and the consciousness of the observer assume during the act of measurement, the related ontological problems, the question of the objectification of the wave function, and that of the definition of discernibility. We consider also an overview of the most important alternative proposals to the standard interpretation of quantum mechanics (Copenhagen interpretation), with particular reference to hidden variable theories and other alternatives to standard quantum mechanics philosophical approach, that are modifying the vision of reality, such as the Everett’s many-worlds theory, the QBism and unified holistic approaches, such as the Primordial Dynamic Space.
This work proposes that the physical dynamics observed in 3+1 dimensions are not a fundamental property, but rather the operational result of a measurement process ( coarse-graining ) on an extended space with internal degrees of freedom . It is argued that the observing apparatus and the environment integrate the internal degrees , generating a reduced state that retains only observables robust to decoherence ("pointer states"). Within this framework, Heisenberg's Uncertainty Principle emerges structurally due to the impossibility of the 4D observer accessing complete information about the system, which introduces minimal diffusive terms into the effective dynamics. Similarly, the wave-particle duality of light is reinterpreted as a projection artifact: the wave-like behavior manifests the unresolved dynamics in the 4D space , while the particle-like aspect arises from the collapse into observable space. The paper concludes that standard physics (QFT) recovers in the scale-separation regime, where the effects of [unclear] are suppressed. Furthermore, the narrative allegory of "MultiCine DQ" is included to conceptually illustrate the relationship between extended phase space and the limitations of observable projection.
Quantum mechanics occupies a unique position in the history of science. It has survived all experimental tests to date, culminating with the most precise comparison of any measurement to any theory – a 1987 measurement of the electron's magnetic moment, or gyromagnetic ratio g e = 2.002 319 304 39 (Van Dyck et al. 1987), agreeing with QED theory to 12 digits. Despite this and other dramatic successes of quantum mechanics, its foundations are often questioned, owing to the glaring difficulties in reconciling quantum physics with the classical laws of physics that govern macroscopic bodies. If quantum mechanics is indeed a complete theory of nature, why does it not apply to everyday life? Even Richard Feynman (1982), a fierce defender of quantum mechanics, memorably stated that: We have always had a great deal of difficulty in understanding the world view that quantum mechanics represents … Okay, I still get nervous with it … It has not yet become obvious to me that there is no real problem. I cannot define the real problem, therefore I suspect there's no real problem, but I'm not sure there's no real problem. In the dawn of the twenty-first century, John A. Wheeler's big question “Why the quantum?” has returned to the forefront of physics with full steam. Advances in experimental physics are beginning to realize the same thought-experiments that proved helpful to Einstein, Bohr, Heisenberg, Schrödinger, and the other founders of quantum mechanics.
An interpretation of Quantum Mechanics published at the International Journal of Quantum Foundations. Abstract: A new interpretation of quantum mechanics is presented in which there is one hidden variable. This could be described as “partial realism” where sometimes quantum variables have real values before we measure and sometimes they don’t. While one hidden variable is insufficient to explain Bell nonlocality, it is allowed by Bell’s inequality. This can help solve the measurement problem and may, in principle, be testable. In addition, a theory of nonlocality emerges directly from this assumption. From the perspective of an outside observer, not correlated with an observed system, we treat all interactions within the system as unitary. However, from the perspective of an “observer” inside the system, we treat all new entanglements as “micromeasurements”, as a projection onto some basis of measurement. One particle can act as a measurement device on another and give the other particle a defined value on one possible measurement axis from an inside perspective. This means that the wave function, from the outside view, will at times describe an objective, fundamentally stochastic uncertainty, at other times a subjective uncertainty that reflects only our lack of knowledge, and at yet other times a combination of both. The standard wave function describes the total uncertainty, the minimal uncertainty that is present for any observer outside of the system, whereas for an “observer” inside the system, only the objective, fundamentally stochastic part of the uncertainty remains, and this can be described by an inner wave function. The hidden variable is invisible to the outside observer.