Is the Quantum State Real in the Hilbert Space Formulation Mani L. Bhaumik

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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: bhaumik@physics.ucla.edu

Editors: Zvi Bern &Danko Georgiev

Article history: Submitted on November 5, 2020; Accepted on December 18, 2020; Published on December 19, 2020.

The persistent debate about the reality of a quan-

tum state has recently come under limelight be-

cause of its importance to quantum informa-

tion and the quantum computing community. Almost

all of the deliberations are taking place using the ele-

gant and powerful but abstract Hilbert space formal-

ism of quantum mechanics developed with seminal

contributions from John von Neumann. Since it is

rather diﬃcult to get a direct perception of the events

in an abstract vector space, it is hard to trace the

progress of a phenomenon. Among the multitude of

recent attempts to show the reality of the quantum

state in Hilbert space, the Pusey–Barrett–Rudolph

theory gets most recognition for their proof. But some

of its assumptions have been criticized, which are still

not considered to be entirely loophole free. A straight-

forward proof of the reality of the wave packet func-

tion of a single particle has been presented earlier

based on the currently recognized fundamental real-

ity of the universal quantum ﬁelds. Quantum states

like the atomic energy levels comprising the wave

packets have been shown to be just as real. Here

we show that an unambiguous proof of reality of the

quantum states gleaned from the reality of quantum

ﬁelds can also provide an explicit substantiation of

the reality of quantum states in Hilbert space.

Quanta 2020; 9: 37–46.

This is an open access article distributed under the terms

of the Creative Commons Attribution License CC-BY-3.0, which

permits unrestricted use, distribution, and reproduction in any medium,

provided the original author and source are credited.

1 Introduction

The debate about the reality of quantum states is as old

as quantum physics itself. The objective reality underly-

ing the manifestly bizarre behavior of quantum objects

is conspicuously at odds with our daily classical phys-

ical reality. The scientiﬁc outlook of objective reality

commenced with the precepts of classical physics that

cemented our notion of reality for centuries. Discover-

ies starting in the last decade of the nineteenth century

revealing the uncanny quantum world in the microscopic

domain shook that perception.

With the particular exception of Einstein, who was the

lone supporter of his postulated wave-particle duality for

photons for about two decades, physicists continued to

think of the microscopic quantum world within the con-

ﬁnes of the ingrained classical physics. Finally, with de

Broglie’s proposed extension of the wave–particle dual-

ity to matter particles like electrons and its experimental

veriﬁcation, irrevocably opened the door ushering in the

bizarre new world of quantum physics.

With some talented younger physicists like

Schr

odinger, Heisenberg, Born, Dirac and others,

the development of the quantum physics proceeded in a

break neck speed starting in early 1926. Although these

eﬀorts led to the most successful description of events in

the atomic domain, the revelations of quantum physics

were so weird that immediately a debate started about the

signiﬁcance of it all.

Soon the dispute came to a climax at the 1927 Solvay

Conference in Belgium with the famed Bohr–Einstein

debate. While Bohr insisting that there was no reality

Quanta |DOI: 10.12743/quanta.v9i1.142 December 2020 |Volume 9 |Issue 1 |Page 37

arXiv:2210.13973v1 [physics.pop-ph] 21 Oct 2022

before a quantum state is measured, Einstein maintained

there must be a reality even before a quantum state is

observed. Almost a century later the debate is surprisingly

still thriving. A conspicuous example is the substantial

account presented in the recent review article by Matthew

Leifer [1]. All of these contemporary considerations are

conducted using the abstract Hilbert space formulation of

quantum mechanics initiated by John von Neumann.

After John Bell’s epochal paper [2] presented Bell’s

inequality and its numerous experimental substantiations,

the reality of the quantum state is now more acceptable in

contrast to the conclusion of earlier Bohr–Einstein debate.

The most prominent recent theory of reality is presented

by Matthew Pusey, Jonathan Barrett, and Terry Rudolph

[3]. Other theories are also advanced by Lucien Hardy

[4] as well as Roger Colbeck and Renato Renner [5].

However, none of these latest advances is considered to

be entirely loophole free. Leifer’s considerably extensive

review [1] provides a distinct example of the diﬃculties of

reaching a deﬁnitive conclusion using the circuitous way

of deliberations in the abstract Hilbert space. Here we

present a rather straightforward way to prove the reality

of the quantum state.

In order to avoid any possible confusion, it would be

prudent to agree upon the deﬁnition of reality. In this

regard, we rely upon the generally acknowledged conno-

tation of reality. We consider something to be physically

real if it is independently observed by several people

and they agree with each other that the result of their

observations is the same. Accordingly, one could rely on

the following notions of the distinguished contemporary

physicists for our understanding of reality.

Referring to the outstanding developments in the

cutting-edge quantum ﬁeld theory or QFT in short, the

distinguished Physics Nobel Laureate Frank Wilczek as-

serts

the standard model is very successful in de-

scribing reality—the reality we ﬁnd ourselves

inhabiting. [6, p. 96]

Wilczek additionally enumerates

The primary ingredient of physical reality, from

which all else is formed, ﬁlls all space and time.

Every fragment, each space-time element, has

the same basic properties as every other frag-

ment. The primary ingredient of reality is alive

with quantum activity. Quantum activity has

special characteristics. It is spontaneous and

unpredictable. [6, p. 74]

Another esteemed Physics Nobel Laureate Steven Wein-

berg conﬁrms

the Standard Model provides a remarkably uni-

ﬁed view of all types of matter and forces (ex-

cept for gravitation) that we encounter in our

laboratories, in a set of equations that can ﬁt

on a single sheet of paper. We can be certain

that the Standard Model will appear as at least

an approximate feature of any better future the-

ory. [7]

Thus, it would be cogent to consider the space ﬁlling

universal Quantum Fields as the primary ingredients of

physical reality uncovered by us so far. An abundant

proof of this can be encountered all around us in several

diﬀerent ways. The most direct convincing evidence

comes from the fact that elementary particles like an

electron has exactly the same properties, such as mass-

energy, charge, spin etc., irrespective of when or where in

the universe it comes into existence—in the big bang, in

astrophysical processes throughout the eons or anywhere

in a lab in the world.

A manifestation of the ﬂuctuations of the quantum

ﬁelds in a phenomenon like the electron anomalous

factor agrees up to an unprecedented twelve decimal

places when the experimental results are compared to

the theoretical computation. Observed phenomena like

Lamb shift, Casimir eﬀect further assert the existence of

the ﬂuctuations of the quantum ﬁelds. A very dramatic

conﬁrmation of the indispensable eﬀects of the quantum

ﬁeld ﬂuctuations comes from the mass of the compos-

ite particles like protons and neutrons. The mass of the

three valence quarks in a proton provided by the Higgs

boson is only about 9 Mev while the total proton mass is

a whopping 938 Mev. This magical “mass without mass”

ascends from the endowment of quantum ﬂuctuations.

Perhaps the most spectacular graphic evidence is pro-

vided by the observed anisotropy in the cosmic mi-

crowave background radiation with their presumed origin

in the cosmic inﬂation in the early universe when the

quantum ﬂuctuations of the reputed inﬂaton ﬁeld enor-

mously expanded from the very microscopic to macro-

scopic dimensions providing seeds for galaxy formation

afterwards. Any reasonable concept of physical reality

should then owe its eventual origin to the fundamental re-

ality of quantum ﬁelds and their characteristic attributes.

The elementary particles like electrons, one of the

members of the initial act of material formation from

the abstract but physical quantum ﬁelds, are quanta of the

ﬁelds. Each of them can be rendered as a wave packet con-

sisting of an admixture of the various ﬁelds. Accordingly,

the wave packet function of the elementary particle ought

to be considered as real as the primary quantum ﬁelds.

More generally the ﬁelds whose quantization produces

the 24 other observed elementary particles in Nature, such

Quanta |DOI: 10.12743/quanta.v9i1.142 December 2020 |Volume 9 |Issue 1 |Page 38

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IstheQuantumStateRealintheHilbertSpaceFormulation?ManiL.BhaumikDepartmentofPhysicsandAstronomy,UniversityofCalifornia,LosAngeles,USA.E-mail:bhaumik@physics.ucla.eduEditors:ZviBern&DankoGeorgievArticlehistory:SubmittedonNovember5,2020;AcceptedonDecember18,2020;PublishedonDecember19,2020.Thepersistent...

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