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Is the Quantum State Real in the Hilbert Space Formulation?

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Is the Quantum State Real in the Hilbert Space Formulation? Is the Quantum State Real in the Hilbert Space Formulation? Mani L. Bhaumik Department of Physics and Astronomy, University of California, Los Angeles, USA. E-mail: [email protected] Editors: Zvi Bern & Danko Georgiev Article history: Submitted on November 5, 2020; Accepted on December 18, 2020; Published on December 19, 2020. he persistent debate about the reality of a quan- 1 Introduction tum state has recently come under limelight be- Tcause of its importance to quantum informa- The debate about the reality of quantum states is as old tion and the quantum computing community. Almost as quantum physics itself. The objective reality underly- all of the deliberations are taking place using the ele- ing the manifestly bizarre behavior of quantum objects gant and powerful but abstract Hilbert space formal- is conspicuously at odds with our daily classical phys- ism of quantum mechanics developed with seminal ical reality. The scientific outlook of objective reality contributions from John von Neumann. Since it is commenced with the precepts of classical physics that rather difficult to get a direct perception of the events cemented our notion of reality for centuries. Discover- in an abstract vector space, it is hard to trace the ies starting in the last decade of the nineteenth century progress of a phenomenon. Among the multitude of revealing the uncanny quantum world in the microscopic recent attempts to show the reality of the quantum domain shook that perception. state in Hilbert space, the Pusey–Barrett–Rudolph With the particular exception of Einstein, who was the theory gets most recognition for their proof. But some lone supporter of his postulated wave-particle duality for of its assumptions have been criticized, which are still photons for about two decades, physicists continued to not considered to be entirely loophole free. A straight- think of the microscopic quantum world within the con- forward proof of the reality of the wave packet func- fines of the ingrained classical physics. Finally, with de tion of a single particle has been presented earlier Broglie’s proposed extension of the wave–particle dual- based on the currently recognized fundamental real- ity to matter particles like electrons and its experimental ity of the universal quantum fields. Quantum states verification, irrevocably opened the door ushering in the like the atomic energy levels comprising the wave bizarre new world of quantum physics. packets have been shown to be just as real. Here With some talented younger physicists like we show that an unambiguous proof of reality of the Schrodinger,¨ Heisenberg, Born, Dirac and others, quantum states gleaned from the reality of quantum the development of the quantum physics proceeded in a fields can also provide an explicit substantiation of break neck speed starting in early 1926. Although these the reality of quantum states in Hilbert space. efforts led to the most successful description of events in Quanta 2020; 9: 37–46. the atomic domain, the revelations of quantum physics were so weird that immediately a debate started about the significance of it all. This is an open access article distributed under the terms of the Creative Commons Attribution License CC-BY-3.0, which Soon the dispute came to a climax at the 1927 Solvay permits unrestricted use, distribution, and reproduction in any medium, Conference in Belgium with the famed Bohr–Einstein provided the original author and source are credited. debate. While Bohr insisting that there was no reality Quanta j DOI: 10.12743/quanta.v9i1.142 December 2020 j Volume 9 j Issue 1 j Page 37 before a quantum state is measured, Einstein maintained the Standard Model provides a remarkably uni- there must be a reality even before a quantum state is fied view of all types of matter and forces (ex- observed. Almost a century later the debate is surprisingly cept for gravitation) that we encounter in our still thriving. A conspicuous example is the substantial laboratories, in a set of equations that can fit account presented in the recent review article by Matthew on a single sheet of paper. We can be certain Leifer [1]. All of these contemporary considerations are that the Standard Model will appear as at least conducted using the abstract Hilbert space formulation of an approximate feature of any better future the- quantum mechanics initiated by John von Neumann. ory. [7] After John Bell’s epochal paper [2] presented Bell’s inequality and its numerous experimental substantiations, Thus, it would be cogent to consider the space filling the reality of the quantum state is now more acceptable in universal Quantum Fields as the primary ingredients of contrast to the conclusion of earlier Bohr–Einstein debate. physical reality uncovered by us so far. An abundant The most prominent recent theory of reality is presented proof of this can be encountered all around us in several by Matthew Pusey, Jonathan Barrett, and Terry Rudolph different ways. The most direct convincing evidence [3]. Other theories are also advanced by Lucien Hardy comes from the fact that elementary particles like an [4] as well as Roger Colbeck and Renato Renner [5]. electron has exactly the same properties, such as mass- However, none of these latest advances is considered to energy, charge, spin etc., irrespective of when or where in be entirely loophole free. Leifer’s considerably extensive the universe it comes into existence—in the big bang, in review [1] provides a distinct example of the difficulties of astrophysical processes throughout the eons or anywhere reaching a definitive conclusion using the circuitous way in a lab in the world. of deliberations in the abstract Hilbert space. Here we A manifestation of the fluctuations of the quantum present a rather straightforward way to prove the reality fields in a phenomenon like the electron anomalous g- of the quantum state. factor agrees up to an unprecedented twelve decimal In order to avoid any possible confusion, it would be places when the experimental results are compared to prudent to agree upon the definition of reality. In this the theoretical computation. Observed phenomena like regard, we rely upon the generally acknowledged conno- Lamb shift, Casimir effect further assert the existence of tation of reality. We consider something to be physically the fluctuations of the quantum fields. A very dramatic real if it is independently observed by several people confirmation of the indispensable effects of the quantum and they agree with each other that the result of their field fluctuations comes from the mass of the compos- observations is the same. Accordingly, one could rely on ite particles like protons and neutrons. The mass of the the following notions of the distinguished contemporary three valence quarks in a proton provided by the Higgs physicists for our understanding of reality. boson is only about 9 Mev while the total proton mass is Referring to the outstanding developments in the a whopping 938 Mev. This magical “mass without mass” cutting-edge quantum field theory or QFT in short, the ascends from the endowment of quantum fluctuations. distinguished Physics Nobel Laureate Frank Wilczek as- Perhaps the most spectacular graphic evidence is pro- serts vided by the observed anisotropy in the cosmic mi- crowave background radiation with their presumed origin the standard model is very successful in de- in the cosmic inflation in the early universe when the scribing reality—the reality we find ourselves quantum fluctuations of the reputed inflaton field enor- inhabiting. [6, p. 96] mously expanded from the very microscopic to macro- scopic dimensions providing seeds for galaxy formation Wilczek additionally enumerates afterwards. Any reasonable concept of physical reality The primary ingredient of physical reality, from should then owe its eventual origin to the fundamental re- which all else is formed, fills all space and time. ality of quantum fields and their characteristic attributes. Every fragment, each space-time element, has The elementary particles like electrons, one of the the same basic properties as every other frag- members of the initial act of material formation from ment. The primary ingredient of reality is alive the abstract but physical quantum fields, are quanta of the with quantum activity. Quantum activity has fields. Each of them can be rendered as a wave packet con- special characteristics. It is spontaneous and sisting of an admixture of the various fields. Accordingly, unpredictable. [6, p. 74] the wave packet function of the elementary particle ought to be considered as real as the primary quantum fields. Another esteemed Physics Nobel Laureate Steven Wein- More generally the fields whose quantization produces berg confirms the 24 other observed elementary particles in Nature, such Quanta j DOI: 10.12743/quanta.v9i1.142 December 2020 j Volume 9 j Issue 1 j Page 38 as the photons, W+, W−, Z0, quarks and gluons, embod- quently, the contribution of the different quantum fields ied in the Standard Model of particle physics should be to the single particle would comprise of irregular dis- just as real. Consequently so would be the composite turbances of the fields with energy off the mass shell, particles like protons and neutrons. We can then consider resulting in the electron ripple to be very highly distorted. the quantum states of atoms and molecules comprising It is well known that such a pulse, no matter how the elementary and composite particles real as well. deformed, can be expressed by a Fourier integral with This would empower us with confidence to extend the weighted linear combinations of simple periodic wave reality of the quantum states to those in Hilbert space forms like trigonometric functions [9]. The result would formalism including all its operations to be as real as the be a wave packet function to represent an electron that wave packet of a single quantum particle and the wave would embody a fundamental reality of the universe since functions of all quantum states of the Schrodinger¨ and all the amplitudes of the wave packet would consist of Heisenberg formulation.
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