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Oxford University Press eBooks

What is a Quantum Superposition?

Gershon Kurizki, Goren Gordon

Published Apr 16, 2020• 0 citations
Publisher

Abstract

Henry has successfully tested the Split button of his quantum suit that enables a quantum object to be in several places at the same time. This bizarre phenomenon is explained by the superposition principle, which reflects Henry’s wavelike properties. Yet Henry remains a single entity as he splits into two superposed versions. In order to understand such behavior, the emergence of the relevant concepts, from classical wave theory, through the quanta hypothesis and the subsequent development of QM, are reviewed. The possibility of such momentous changes in human thinking as the QM scientific revolution is disconcerting if one seeks the truth of the world through physics. A retrospective of the views on the rapport of physics with reality and its roots in mythical or symbolic pictures of the world suggests that the QM revolution eludes straightforward explanation. The QM superposition principle is mathematically formulated in the appendix to this chapter.

DOI
10.1093/oso/9780198787464.003.0002

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International Journal of Modern Physics B•Feb 20, 2004•2 citations
Henry has successfully tested the Split button of his quantum suit that enables a quantum object to be in several places at the same time. This bizarre phenomenon is explained by the superposition principle, which reflects Henry’s wavelike properties. Yet Henry remains a single entity as he splits into two superposed versions. In order to understand such behavior, the emergence of the relevant concepts, from classical wave theory, through the quanta hypothesis and the subsequent development of QM, are reviewed. The possibility of such momentous changes in human thinking as the QM scientific revolution is disconcerting if one seeks the truth of the world through physics. A retrospective of the views on the rapport of physics with reality and its roots in mythical or symbolic pictures of the world suggests that the QM revolution eludes straightforward explanation. The QM superposition principle is mathematically formulated in the appendix to this chapter.
Henry Bar is about to become the first quantum superhero, having discovered the incredible yet true principle that all things, large and small, are subject to the laws of quantum physics. He finds out that it may be possible, albeit extremely challenging, even for us humans to manifest “quantumness”. This principle underlies Henry’s implementation of his quantum suit that allows him to act as a quantum object. In order to understand this principle, the historical route from early atomism to the emergence of quantum mechanics (QM) as a revolutionary theory of radiation and matter is presented. The inception of QM was a landmark in the age-old quest for answers to the question: is reality, in its complexity, reducible to simple constituents? Alternative questions include: How far up the complexity ladder can QM be pushed as a framework for explaining reality? The appendix to this chapter introduces mathematical notations for QM phenomena.
Chapter 4 introduces a great QM mystery: the notion of quantum measurements. Henry is in a superposition of versions localized in several places, but when Eve measures Henry’s position she (as a classical observer) either sees Henry or she does not. Physical reality is made of such measurements. Eve’s measurement projects or collapses Henry’s superposition state to a single location. The meaning of quantum-state or wavefunction “collapse” and the role of the observer have been at the heart of the historical debate concerning the interpretation of QM. Whereas Von Neumann and Wigner stressed the inseparability of the observed (measured) world from the human mind, alternative “observer-free” views were suggested, such as Everett’s many-world interpretation or Zurek’s quantum Darwinism that replaces the observer by the environment. In the appendix to this chapter the notion of probability amplitudes is elucidated, new notations for operators are introduced and projection operators are presented.
The early twentieth century was a revolutionary time in the history of physics. People often think of Einstein's special theory of relativity of 1905, which changed our conceptions of time and space. But among physicists, quantum mechanics is usually regarded as an even more radical change in our thinking about the physical world. Quantum mechanics, which was developed between 1900 and 1926, began as a theory of atoms and light but has now become the framework in terms of which all basic physical theories are expected to be cast. We need quantum ideas not only to understand atoms, molecules, and elementary particles, but also to understand the electronic properties of solids and even certain astronomical phenomena such as the stability of white dwarf stars. The theory was radical in part because it introduced probabilistic behavior as a fundamental aspect of the world, but even more because it seems to allow mutually exclusive situations to exist simultaneously in a “quantum superposition.” We will see later that the possibility of quantum superposition is largely responsible for a quantum computer's distinctive advantage over an ordinary computer. The present chapter is devoted to introducing the basic principles of quantum mechanics. There are essentially four components of the mathematical structure of quantum mechanics. We need to know how to represent (i) states, (ii) measurements, (iii) reversible transformations, and (iv) composite systems. We will develop the first three in stages, starting with a very simple case – linear polarization of photons – and working toward the most general case.
This chapter introduces quantum mechanics through the experimental discoveries that revealed the limits of classical physics. Beginning with the historical debate over whether light is a wave or a particle, it examines Young’s double-slit experiment and its modern single-particle versions, which demonstrate that quantum objects can exist in superpositions of mutually exclusive states. The chapter explains how interference arises when alternative possibilities are not measured and how interaction with the environment suppresses these effects through decoherence, giving rise to classical behavior at macroscopic scales. A sequence of thought experiments involving interferometers and Stern–Gerlach devices highlights the counterintuitive structure of quantum measurement and the incompatibility of certain physical properties, as captured by the uncertainty principle. The chapter emphasizes that quantum mechanics does not describe particles taking multiple paths simultaneously in a classical sense but rather requires a new framework for probability based on amplitudes and interference. Finally, the discussion connects these foundational ideas to emerging technologies such as quantum computing, showing how superposition and entanglement can be harnessed to perform computations that have no classical analogue.
The measurement problem in quantum mechanics has been a cause of much puzzlement over the years. The very idea of having two different versions of reality for the same system has been a cause for much debate. Often quantum mechanics textbooks follow the ‘shut up and calculate’ paradigm. This denies the opportunity for the common student to understand the consequence of one of the most elegant and beautiful aspects of science. The state of the art textbooks give a purely algebraic, perfunctory and monotonous approach where the real consequence of the system is not fully appreciated. A good reason for this is the considerable deviation of the quantum mechanical process from the commonsensical idea of truth, reality and reason. We tend to look at the world in a materialistic, deterministic, causal and objectivistic way. We tend not to accept a world of contradictions. A quantum measurement is essentially an amalgamation of contradictions, mystery and duality. It encompasses an implicit dependence on subjectivity and contradicts with causality as we know it. We look at the world as in the present. But a quantum mechanical measurement is a prediction of the future influenced by the observer or the measurer. This offers a philosophical and pedagogical conundrum. It poses a challenge on not just how our perception of the world might change in addition to providing a big challenge on how to make it compatible with the other successful theories of physics. The most common text book interpretation of quantum mechanics has been the Copenhagen Interpretation suggests the ‘collapse of the wave function’ as a mechanism of transition between duality. But a more bizarre yet elegant theory, extending quantum formalism to the classical domain, called the Many Worlds Interpretation has been catching up very quickly; it stands for the split of the universe when we make a quantum mechanical measurement. Consequently, reality as we is redefined as a universal wave function which is a superposition of several outcomes, which is incompatible with many of the successful concepts of physics and has several problems like the correct idea about probability or basis. We adapt the idea of the universal wave function, but instead suggest a continuum interpretation of quantum mechanics where the universal wave function represents the entire singular universe and the concept of atoms or electrons as conceptually a continuous part of it rather than a distinct separate entity. Such an interpretation could be compatible with other continuum theories like the Superfluid vacuum theory or the Higgs Field.
In spite of the recent extraordinary progresses of experimental techniques it does not seem that, after more than seventy years from the birth of quantum mechanics, a unanimous consensus has been reached in the physicist's community on how to understand the "strange" properties of quantons, the wavelike/particlelike objects of the quantum world. In the first paragraph I will briefly recall some results on the problem of decoherence in large quantum systems, which at the same time may be viewed as an attempt of providing a "realistic" physical interpretation of the standard mathematical formulation of the theory. In the following ones I will present a derivation from first principles of the Wigner representation of quantum mechanics in phase space which eliminates altogether from the theory the Schrödinger waves and their questionable properties. This approach leads to the conclusion that the wave/particle duality has nothing to do with "probability waves", but is simply the manifestation of two complementary aspects (continuity vs. discontinuity) of an intrinsically nonlocal physical entity (the quantum field) which objectively exists in ordinary three dimensional space.