The man who cannot occasionally imagine events and conditions of existence that are contrary to the causal principle as he knows it will never enrich his science by the addition of a new idea.
Max Planck

 
 

OPEN QUESTIONS IN QUANTUM THEORY

D. G. Chakalov1

 

Abstract

The major unresolved problem in quantum physics is the transition from a quantum realm, where cats may be 'both alive and dead', to the macro-world, where cats are either alive or dead. After a brief examination of the measurement problem in quantum mechanics and the cosmic coincidence problem in inflationary cosmology, it is suggested that their joint solution may require (i) an unknown selection mechanism in the quantum realm, which operates as a 'chooser' of one quantum propensity amongst others, and is not dependent on the Heisenberg Schnitt (cut) dividing the observer and the system being observed, and (ii) an unknown emergence mechanism securing an almost zero cosmological constant and background spacetime for the macro-world prior to the formation of that macro-world. The need for a new quantum theory explaining the nature of the quantum of action seems obvious.

The present paper is confined to identifying only the new tasks and challenges resulting from examining some long-standing problems of quantum mechanics and inflationary cosmology en block. A proposal for the two mechanisms above, expressed in purely phenomenological terms, and based on the selection mechanism in the human brain (Ulric Neisser's cognitive cycle), may be published by December 14, 2000.
 

Address: 35 Sutherland Street, London SW1V 4JU, UK.
Email dchakalov@email.com
 


 
 

1. Introduction
 

December 14, 1900 is considered the birthday of quantum mechanics: Max Planck launched an astonishing, counter-intuitive proposal for a new constant, elementares Wirkungsquantum (known later as Planck constant), with the main purpose to explain why the so-called ultraviolet catastrophe has never happened (Planck, 1900). Not surprisingly, his ideas were not embraced by the established physical community at that time (Jammer, 1966).

What if we try to explain why we never observe a quite different catastrophic event: tables and chairs being 'both here and there' and cats being 'both alive and dead' (Polkinghorne, 1990)? How come we never ever lose the definiteness of objects and events in our macro-world, thanks to which we can ascribe the notion of spacetime to it? According to our current interpretation of Heisenberg relations, we should not be able to enjoy this luxury. Statistically, the chance for obtaining a definite macro-world out of the quantum realm is practically zero, and so is the chance for setting up the initial condition of the Big Bang to match the Universed we live in -- the accuracy of pinpoiting our Universe is one part in 101230 (Penrose, 1997). On the other hand, we should not trust quantum theory entirely, at least because there is something quite suspicious in the way quantum mechanics was stated: it contains classical mechanics as a limiting case, yet at the same time requires this limiting case for its own formulation (Landau and Lifshitz, 1974).

It shouldn't be surprising that, despite the practical achievements of quantum mechanics (QM), a solution of the measurement problem is still out of sight (Anandan, 1999; Haag, 1998; Gittins, 1999; Measurement in quantum mechanics FAQ (1999); Measurement in quantum mechanics, Encyclopædia Britannica (1999); Incompatible observables, Encyclopædia Britannica (1999); Shimony, 1997; Polkinghorne, 1990). The crux of the problem is that QM permits the occurrence of all possible events, with definite probabilities, but in our consciousness there is only one world (Peres, 1997). Moreover, there are no time operators in QM, which has very important implications (Oppenheim et al., 1998; Time in microphysics, Encyclopædia Britannica (1999); Aharonov and Albert, 1984). With respect to our macro-world, nothing ever happens in QM "during" a unitary time evolution. If we want to manipulate quantum waves in real-time mode (e.g., to manipulate the entanglement locally (Virmani and Plenio, 1999), as in some hypothetical quantum computations), we need backward causation (Wharton, 1998). Changes in the phase of quantum waves cannot be registered as events (Haag, 1998). If we eliminate the imaginary unit in the phase of quantum waves, we get classical mechanics (Ni, 1998). Physically, we can't do that, unless we 'kill' everything and produce just one collapsed event which, however, cannot in any way be related to the chain of actual events in the macro-world. The state-vector reduction can not, even in principle, be construed as a normal dynamical process (Chris Isham, private communication, 13 March 1999). Schrödinger's equation characterizes the evolution of what is possible, not what is actual (Bub, 1999). This evolution of potentialities is not an evolution in time, as measured with physical clocks (Oppenheim et al., 1998; Time in microphysics, Encyclopædia Britannica (1999); Aharonov and Albert, 1984). The projection postulate introduced ad hoc is of no help -- we cannot use the temporal notions "before" and "after" the collapse, simply because we cannot logically relate things that do not exist: "before" the collapse there is no event, while "after" the collapse there is no quantum wave. (Besides, the very idea that something may acquire the probability unit, e.g.,  "after" the collapse, is not physical at all -- nothing can be absolutely certain.) The collapse may only give us a false impression that we have managed to 'project' something from the quantum realm on our macro-world, as if the latter were some sort of a 'filter' for one of the non-commuting observables: "Afterwards the system is in that particular eigenstate, selected from the original superposition, which corresponds to the eigenvalue actually obtained as the result of that measurement" (Polkinghorne, 1990; cf. also Bassi and Ghirardi, 1999). As Werner Heisenberg put it, "If we want to describe what happens in an atomic event, we have to realize that the word 'happens' can only apply to the observation, not to the state of affairs between two observations" (Heisenberg, 1958). We may be happy to see some traces triggered undoubtedly by particles, but what these traces really mean? Is it possible to map the unitary time evolution of quantum systems to some dynamical process from classical physics? Undoubtedly not. The gap between the quantum realm and our macro-world remains open. Mother Nature surely knows how to bridge this gap, for in the absence of an observer or measuring apparatus something must be happening in the quantum world 'out there' (Ashtekar, 1993). So, the solution is 'out there', we simply have to reveal it.

Pressed by these highly non-trivial challenges, I believe we first have to collect and examine all cases relevant to our task, to get a coherent and clear picture of the quantum of action, as operating both in the Small and in the Large (Penrose, 1997).

The plan of the paper is as follows. In the next section, I will examine briefly the measurement problem (Barrett, 1998) caused by the linearity of the unitary evolution or U process (Anandan, 1999). Section 3 deals with the cosmic coincidence problem, and Section 4 offers an old 'unsolved mystery' in QM to support the view of the author of these lines that we may never understand QM without a full-blown theory of quantum gravity. Conclusions are drawn in Section 5, along with a sketch of what may be the physics of the human brain (to be published by December 14, 2000): a new (quantum?) theory reconciling the principles of superposition and general covariance from the outset (Butterfield and Isham, 1999).
 

2. The measurement problem.

[To be continued.]
 

References and notes

Planck M. (1900) Zur Theorie des Gesetzes der Energieverteilung im Normalspectrum. Vehrandlungen der Deutschen Physikalischen Gesellschaft 2, 237-245 (quoted after [Jammer, 1966, Ch. 1, Ref. 90]).

Jammer M. (1966) The Conceptual Development of Quantum Mechanics. New York: McGraw-Hill.

Anandan J. (1999) Quantum Measurement Problem and the Possible Role of the Gravitational Field. Found. Phys. 29, 333-348.
http://xxx.lanl.gov/abs/gr-qc/9808033

Jeeva Anandan: "The simplest, though dramatic, statement of the measurement problem in quantum theory is that quantum theory does not explain the occurrence of events. So, quantum theory does not explain the first thing we observe about the world around us. (...) The U process is the linear unitary evolution which in the present day quantum theory is governed by Schrödinger's equation. But what causes the measurement problem is the linearity of the U process. The unitarity is really relevant to the R process. Unitarity ensures that the sum of the probabilities of the possible outcomes in any measurement, each of which is given by an R process remains constant during the U time evolution."

Gittins R. (1999) An Introduction to Quantum Theory,
http://www.sees.bangor.ac.uk/~andy/final_year_projects/
robert/Theory.htm

Measurement in quantum mechanics FAQ (1999),
http://www.mtnmath.com/faq/meas-qm.html

Measurement in quantum mechanics. Encyclopædia Britannica (1999),
http://www.britannica.com/bcom/eb/article/1/0,5716,119071+4,00.html

Incompatible observables. Encyclopædia Britannica (1999),
http://www.britannica.com/bcom/eb/article/0/0,5716,119070+15,00.html

Oppenheim J., Reznik B., Unruh W. G. (1998) Time as an Observable.
http://xxx.lanl.gov/abs/quant-ph/9807058

Bub J. (1999) Quantum Mechanics as a Principle Theory.
http://xxx.lanl.gov/abs/quant-ph/9910096

Shimony A. (1997). On Mentality, Quantum Mechanics and the Actualization of Potentialities. In: R. Penrose. The Large, the Small and the Human Mind. Cambridge: Cambridge University Press, pp. 144-160.

Polkinghorne J.C. (1990) The Quantum World. London: Penguin Books.

Heisenberg W. (1958) Physics and Philosophy. New York: Harper and Row.

Landau L., Lifshitz E. (1974) Quantum Mechanics. Oxford: Pergamon Press.

Penrose R. (1997) The Large, the Small and the Human Mind. Cambridge: Cambridge University Press.

Aharonov Y., Albert D.Z. (1984) Is the usual notion of time evolution adequate for quantum-mechanical systems? II. Relativistic considerations. Phys. Rev. D 29, 228.

Michael E. (1999) How physically plausible is the cosmological constant?
http://super.colorado.edu/~michaele/phys.html

Bassi A., Ghirardi G. (1999) About the Notion of Truth in the Decoherent Histories Approach: a reply to Griffiths.
http://xxx.lanl.gov/abs/quant-ph/9912065

Angelo Bassi and GianCarlo Ghirardi: "In Standard Quantum Mechanics, on the other hand, one cannot even think that systems possess physical properties prior to measurements: mathematically, this is reflected in the peculiar properties of the Hilbert space (with dimension greater than 2): the set of projection operators cannot be endowed with a Boolean structure, and it is not possible to attach consistently truth-values to them, as implied by the theorems of Gleason, Bell and Kochen and Specker."

Wharton W. (1998) Backward Causation and the EPR Paradox.
http://xxx.lanl.gov/abs/quant-ph/9810060

William R. Wharton: "Because there is no backward causation in the macroworld, there are no superposition of macroscopically different states. The superposition of different states is a propensity distribution. Propensities are outcomes, which are to be selectively chosen in the future through backward causation. Because there is no backward causation, these propensities do not exist in the macroworld and there is no macroscopic superposition, as for example a partially alive and dead Schrödinger cat (assuming the cat is in the macroworld)."

Ni G. (1998) To Enjoy the Morning Flower in the Evening -- Where is the Subtlety of Quantum Mechanics?
http://xxx.lanl.gov/abs/quant-ph/9804013



Isham C., Private communication, 13 March 1999:

Re: Request for explanation
Date: Sat, 13 Mar 1999 19:50:40 +0000
Message-ID: <4.1.19990313194613.0093b710@plato.tp.ph.ic.ac.uk>

"The 'non-unitary' refers to the fact (i) any genuine time-evolution in quantum theory that is determined by an actual physical process is implemented by a unitary operator (the exponential of itH where H is the associated Hamiltonian operator); (ii) the scalar product between a pair of vectors is maintained by a unitary transformation; and (iii) the transformation associated with state-vector reduction does *not* preserve scalar products. Hence the state-vector reduction process can not, even in principle, be construed as a normal dynamical process."

Virmani S., Plenio M. B. (1999) Ordering States with Entanglement Measures.
http://xxx.lanl.gov/abs/quant-ph/9911119
 

Haag R. (1998) Objects, Events and Localization. Expanded version of lecture given at the Max-Born-Symposium on Quantum Future, Przieka,
September 1997. Preprint ESI 541 (March 20, 1998),
ftp://ftp.esi.ac.at:/pub/Preprints/esi541.ps
http://www.esi.ac.at
 

Ashtekar A. (1993) Mathematical Problems of Non-perturbative Quantum General Relativity. Les Houches Summer School on Gravitation and 
Quantizations, Les Houches, France, July 5 - August 1, 1992.
http://xxx.lanl.gov/abs/gr-qc/9302024

Abhay Ashtekar: "At a fundamental level, since there is no background metric, there is no a priori notion of time either. What does dynamics and evolution even mean if there is no background space-time? How is time born in the framework? (...) The probabilities for an exhaustive set of mutually exclusive alternatives should add up to one. In quantum mechanics, this is generally ensured by using an instant of time to specify such alternatives. What is one to do when there is no time and no instants? These are fascinating issues."
 

Butterfield J. and Isham C.J. (1999). Spacetime and the Philosophical Challenge of Quantum Gravity. 
http://xxx.lanl.gov/abs/gr-qc/9903072

Jeremy Butterfield and Chris Isham: "4. Start ab initio with a radically new theory.

"The idea here is that both classical general relativity and standard quantum theory emerge from a theory that looks very different from both. Such a theory would indeed be radically new. (...) So the kind of theory envisaged here would somehow be still more radical than that; presumably by not being a quantum theory, even in a broad sense -- for example, in the sense of states giving amplitudes to the values of quantities, whose norms squared give probabilities."
 

Peres A. (1997) Interpreting the Quantum World.
http://xxx.lanl.gov/abs/quant-ph/9711003

Asher Peres: "In classical mechanics, a dynamical variable indeed has a definite value at each point of phase space. Specifying a point in phase space is the standard way of indicating the state of a physical system. However, in quantum  mechanics, a dynamical variable is represented by a Hermitian matrix (or, more generally, by a self-adjoint operator). It is manifestly pointless to attribute to it a numerical value. 

"Basically, the problem is whether quantum mechanics is a theory of physical reality, or one of our perception of the physical world. For the advocates of the realistic alternative, who wish to give a consistent dynamical description to the measuring process, the source of the difficulty is clear: the evolution that we know to write for the quantum mechanical wave function during a measurement does not correspond with what is actually seen happening in the real world.
...
"The fundamental conundrum in the quantum formalism is not there. It is that quantum mechanics permits the occurrence of all possible events (with definite probabilities), but in our consciousness there is only one world.
...
"To interpret quantum theory, to explain its meaning, to make it understandable, the way has been shown to us: we have to translate the abstract mathematical formalism in such a way that 'we can tell others what we have done and what we have learned and [this] must be expressed in unambiguous language with the terminology of classical physics.'"
 

Time in microphysics. Encyclopædia Britannica (1999),
http://www.britannica.com/bcom/eb/article/0/
0,5716,115440+10,00.html

 

Barrett J.A. (June 3, 1998). Everett's Relative-State Formulation of Quantum Mechanics. The Stanford Encyclopedia of Philosophy (Fall 1999 Edition), Edward N. Zalta (ed.). The Metaphysics Research Lab at the Center for the Study of Language and Information, Stanford University, Stanford, CA. ISSN 1095-5054.
http://plato.stanford.edu/entries/qm-everett/
 
 

January 20, 2000