Quantum mechanics and the local observer

A notion of local observer inspired by the work of Segal is introduced here in the Hilbert space theory of quantum mechanics. The local observer finds a mathematical place in the Hilbert space through local negation or complementation. A logicomathematical theory of local negation is presented and its implications for quantum logic and the problem of measurement are discussed. The setting is constructivist mathematics and the main result of the paper states that the introduction of a local observer implies the nonorthocomplementability of the whole Hilbert space even in the finite-dimensional case. Making a mathematical place for the observer (the “projector”) thus modifies the structure of the observables or the system of the projections, in accordance with a nonclassical theory of quantum-mechanical measurement.     

Irreversibility and quantum measurement—The observer’s role

The role of the observer in physical theories in the sense of the observer’s viewpoint determining prominent features of the observed phenomena is discussed with reference to the problem of irreversibility and quantum measurement, the latter being closely related to the problem of classical behaviour of quantum systems. A completely subjective interpretation of irreversibility is proposed. It is claimed that irreversibility belongs only to phenomena as observed by a restricted observer who must project all phenomena on a restricted subset of the set of all possible states. The possibility of a completely unrestricted observer who does not see irreversibility is discussed.     

Quantum Measurement and Extended Feynman Path Integral

Quantum measurement problem has existed many years and inspired a large of literature in both physics and philosophy, but there is still no conclusion and consensus on it. We show it can be subsumed into the quantum theory if we extend the Feynman path integral by considering the relativistic effect of Feynman paths. According to this extended theory, we deduce not only the Klein--Gordon equation, but also the wave-function-collapse equation. It is shown that the stochastic and instantaneous collapse of the quantum measurement is due to the “potential noise” of the apparatus or environment and “inner correlation” of wave function respectively. Therefore, the definite-status of the macroscopic matter is due to itself and this does not disobey the quantum mechanics. This work will give a new recognition for the measurement problem.     

Insufficiency of the quantum state for deducing observational probabilities

It is usually assumed that the quantum state is sufficient for deducing all probabilities for a system. This may be true when there is a single observer, but it is not true in a universe large enough that there are many copies of an observer. Then the probability of an observation cannot be deduced simply from the quantum state (say as the expectation value of the projection operator for the observation, as in traditional quantum theory). One needs additional rules to get the probabilities. What these rules are is not logically deducible from the quantum state, so the quantum state itself is insufficient for deducing observational probabilities. This is the measure problem of cosmology.     

The Observer Determination

Quantum measurement requires an observer to prepare a specific measuring device among alternatives where the prepared basis of states, representing the device, is the way the observer interprets quantum reality into his macroscopic word. We redefine that observer role through a new concept: The observer determination, that is, a selection between the measurement options facing the observer. Unlike the measurement itself that is rationalized as dictated by nature, the observer determination can neither be measured nor proven to be true or false. In this paper we propose a mathematical formalism demonstrating how to define the observer determination. Moreover, we present a scheme showing how the apparently subjective observer determination transform into a measurable quantity.     

No-Cloning Theorem,Kochen-Specker Theorem,and Quantum Measurement Theories

The usual no-cloning theorem implies that two quantum states are identical or orthogonal if we allow a cloning to be on the two quantum states. Here, we investigate a relation between the no-cloning theorem and the projective measurement theory that the results of measurements are either + 1 or − 1. We introduce the Kochen-Specker (KS) theorem with the projective measurement theory. We result in the fact that the two quantum states under consideration cannot be orthogonal if we avoid the KS contradiction. Thus the no-cloning theorem implies that the two quantum states under consideration are identical in that case. It turns out that the KS theorem with the projective measurement theory says a new version of the no-cloning theorem. Next, we investigate a relation between the no-cloning theorem and the measurement theory based on the truth values that the results of measurements are either + 1 or 0. We return to the usual no-cloning theorem that the two quantum states are identical or orthogonal in the case.

     

关于量子测量问题的一点思考

量子测量原理是量子力学的重要组成部分。具体的测量实验是否构成量子测量,是有商榷的余地的。并不是所有可观测量的本征值都具有实在的意义。量子测量原理中论及的经典—量子世界分界处之扰动的作用,可改述为量子测量需要加入统计原理的考量,这其实正印证了“统计原则高于量子原则”的现实。类似双缝干涉和Stern—Gerlach实验这样的宏观实验同量子测量原理是相融洽的,可能反映的恰是量子测量原理建立的历史背景和心理基础。本文的目的在于引起对量子测量问题的关注,并深信对该问题严肃、深入的讨论是有意义的。     

The Madelung Picture as a Foundation of Geometric Quantum Theory

Despite its age, quantum theory still suffers from serious conceptual difficulties. To create clarity, mathematical physicists have been attempting to formulate quantum theory geometrically and to find a rigorous method of quantization, but this has not resolved the problem. In this article we argue that a quantum theory recursing to quantization algorithms is necessarily incomplete. To provide an alternative approach, we show that the Schrödinger equation is a consequence of three partial differential equations governing the time evolution of a given probability density. These equations, discovered by Madelung, naturally ground the Schrödinger theory in Newtonian mechanics and Kolmogorovian probability theory. A variety of far-reaching consequences for the projection postulate, the correspondence principle, the measurement problem, the uncertainty principle, and the modeling of particle creation and annihilation are immediate. We also give a speculative interpretation of the equations following Bohm, Vigier and Tsekov, by claiming that quantum mechanical behavior is possibly caused by gravitational background noise.     

Explaining the Unobserved—Why Quantum Mechanics Ain’t Only About Information

A remarkable theorem by Clifton et al [Found Phys. 33(11), 1561–1591 (2003)] (CBH) characterizes quantum theory in terms of information-theoretic principles. According to Bub [Stud. Hist. Phil. Mod. Phys. 35 B, 241–266 (2004); Found. Phys. 35(4), 541–560 (2005)] the philosophical significance of the theorem is that quantum theory should be regarded as a “principle” theory about (quantum) information rather than a “constructive” theory about the dynamics of quantum systems. Here we criticize Bub’s principle approach arguing that if the mathematical formalism of quantum mechanics remains intact then there is no escape route from solving the measurement problem by constructive theories. We further propose a (Wigner-type) thought experiment that we argue demonstrates that quantum mechanics on the information-theoretic approach is incomplete.     

The self-contradictory foundations of formalistic quantum measurement theories

One school of thought in quantum measurement theory adopts as its aim the derivation of a certain mixed statistical operator to characterize the ensemble of global objectapparatus systems subsequent to the measurement interaction. This paper demonstrates that even if that goal were achieved, the consequent theory of measurement would be self-contradictory; hence the measurement problem is improperly formulated. The epistemological root of the difficulty is discussed briefly. A logical resolution is offered in terms of quantum axiomatics by emphasizing the actual relationship of quantum theory to experimental and observational data.Work supported by a grant from Research Corporation.     

Undecidable Classical Properties of Observers

A property of a system is called actual, if the observation of the outcome of the test that pertains to that property yields an affirmation with certainty. We formalize the act of observation by assuming the outcome itself is an actual property of the state of the observer after the act of observation and correlates with the state of the system. For an actual property this correlation needs to be perfect. A property is called classical if either the property or its negation is actual. We show by a diagonal argument that there exist classical properties of an observer that he cannot observe perfectly. Because states are identified with the collection of properties that are actual for that state, it follows no observer can perfectly observe his own state. Implications for the quantum measurement problem are briefly discussed. PACS: 02.10-v, 03.65.Ta     

Experimental simulation of the Unruh effect on an NMR quantum simulator

The Unruh effect is one of the most fundamental manifestations of the fact that the particle content of a field theory is observer dependent. However, there has been so far no experimental verification of this effect, as the associated temperatures lie far below any observable threshold. Recently, physical phenomena, which are of great experimental challenge, have been investigated by quantum simulations in various fields. Here we perform a proof-of-principle simulation of the evolution of fermionic modes under the Unruh effect with a nuclear magnetic resonance(NMR) quantum simulator. By the quantum simulator, we experimentally demonstrate the behavior of Unruh temperature with acceleration, and we further investigate the quantum correlations quantified by quantum discord between two fermionic modes as seen by two relatively accelerated observers. It is shown that the quantum correlations can be created by the Unruh effect from the classically correlated states. Our work may provide a promising way to explore the quantum physics of accelerated systems.     

Mind,matter, and physicists

Some aspects of the problem of measurement in quantum theory are treated. We stress that the problem is both physical and conceptual, that the physical problem has been solved and the conceptual one is inherent in quantum theory. We also deal with some remarks made by Wigner concerning physics and the explanation of life, and present alternative positions on the mind-matter relationship within a deterministic framework, as we see them.     

Quantum vacuum noise in physics and cosmology

The concept of the vacuum in quantum field theory is a subtle one. Vacuum states have a rich and complex set of properties that produce distinctive, though usually exceedingly small, physical effects. Quantum vacuum noise is familiar in optical and electronic devices, but in this paper I wish to consider extending the discussion to systems in which gravitation, or large accelerations, are important. This leads to the prediction of vacuum friction: The quantum vacuum can act in a manner reminiscent of a viscous fluid. One result is that rapidly changing gravitational fields can create particles from the vacuum, and in turn the backreaction on the gravitational dynamics operates like a damping force. I consider such effects in early universe cosmology and the theory of quantum black holes, including the possibility that the large-scale structure of the universe might be produced by quantum vacuum noise in an early inflationary phase. I also discuss the curious phenomenon that an observer who accelerates through a quantum vacuum perceives a bath of thermal radiation closely analogous to Hawking radiation from black holes, even though an inertial observer registers no particles. The effects predicted raise very deep and unresolved issues about the nature of quantum particles, the role of the observer, and the relationship between the quantum vacuum and the concepts of information and entropy. (c) 2001 American Institute of Physics.