arXiv subjects

Petr Hajicek

Publications and source records attributed to Petr Hajicek.

At least 19 recordsLinked to original sources

arXiv2016

Realism-Completeness-Universality interpretation of quantum mechanics

The paper reviews and discusses four ideas scattered in previous papers of the author. First, objective properties of quantum systems are not associated with observables but are defined by preparations. Second, measurable results of classical theories are not sharp. All such results can be obtained as high-entropy limits of quantum mechanics. Third, a careful study of exchange symmetry requires a modification of the theory of measurement. Fourth, screens and detectors are closely associated with state reduction. A new, rather improved understanding of quantum mechanics is achieved without any deep changes of the theory itself. In the framework of a model approach to the philosophy of science, the RCU interpretation is developed step by step by adding specific supplementary hypotheses to the Minimum Interpretation of quantum mechanics.

quant-ph↗

arXiv2016

The phenomenon of state reduction

A theory of quantum measurement was introduced some time ago that was based on the notion of the so-called separation status. This separation status had a spatial, local character, so that the theory worked only in special cases. Nevertheless, it enabled a description of state reduction process that was specific in where, when and under which objective conditions the process occurs and that preserved the unitary transformation symmetry of quantum mechanics. Now, in an accompanying paper (arxiv:1411.5524), a completely general mathematical definition of the status is given and analyzed. The present paper reformulates the theory of state reduction accordingly. A general mathematical form of the process is postulated and illustrated by examples of Stern-Gerlach experiment and of screening.

quant-ph↗

arXiv2016

Incompleteness of measurement apparatuses

A complete apparatus is defined as reacting to every state of the measured system. Standard quantum mechanics of indistinguishable particles is shown to imply that apparatuses must be incomplete or else they would be drowned out by noise. Each quantum observable is then an abstract representation of many measurement apparatuses, each incomplete in a different way. Moreover, a measured system must be prepared in a state that is orthogonal to the states of all particles of the same type in the environment. This is the main purpose of preparations. A system so prepared is said to have a "separation status". A new, more satisfactory definition of separation status than the spatial one proposed in previous papers then results. Conditions are specified under which the particles in the environment may be ignored as is usually done in the theory of measurement.

quant-ph↗

arXiv2015

Quantum models of classical systems

Quantum statistical methods that are commonly used for the derivation of classical thermodynamic properties are extended to classical mechanical properties. The usual assumption that every real motion of a classical mechanical system is represented by a sharp trajectory is not testable and is replaced by a class of fuzzy models, the so-called maximum entropy (ME) packets. The fuzzier are the compared classical and quantum ME packets, the better seems to be the match between their dynamical trajectories. Classical and quantum models of a stiff rod will be constructed to illustrate the resulting unified quantum theory of thermodynamic and mechanical properties.

quant-ph↗

arXiv2013

On the theory of quantum measurement

The notion of state reduction employed by the standard quantum theory of measurement is difficult to accept for two reasons: It leaves open where and when the reduction takes place and it does not give any objective conditions under which the reduction occurs. Some recently published ideas on this problem are developed an improved. The disturbance of measurement due to identical particles in the environment is shown to make any POV measure non-measurable. Truncated POV (TPOV) measures are introduced that can be measurable if object systems satisfy the additional requirement of having separation status. The separation status is generalised from domain of space to domain of phase space. Starting from the previously introduced distinction between ancillas and detectors, further study of experiments suggests that a thermodynamic mixing within a detector and the consequent loss of separation status is the objective condition for the occurrence of the state reduction. The conjecture is simple, specific and testable. The theory is illustrated by a model of a real measurement.

quant-ph↗

arXiv2013

Realist model approach to quantum mechanics

The paper proves that quantum mechanics is compatible with the constructive realism of modern philosophy of science. The proof is based on the observation that properties of quantum systems that are uniquely determined by their preparations can be assumed objective without the difficulties that are encountered by the same assumption about values of observables. The resulting realist interpretation of quantum mechanics is made rigorous by studying the space of quantum states---the convex set of state operators. Prepared states are classified according to their statistical structure into indecomposable and decomposable instead of pure and mixed. Simple objective properties are defined and showed to form a Boolean lattice.

quant-ph↗

arXiv2013

Quantum models of classical world

This paper is a review of our recent work on three notorious problems of non-relativistic quantum mechanics: realist interpretation, quantum theory of classical properties and the problem of quantum measurement. A considerable progress has been achieved, based on four distinct new ideas. First, objective properties are associated with states rather than with values of observables. Second, all classical properties are selected properties of certain high entropy quantum states of macroscopic systems. Third, registration of a quantum system is strongly disturbed by systems of the same type in the environment. Fourth, detectors must be distinguished from ancillas and the states of registered systems are partially dissipated and lost in the detectors. The paper has two aims: a clear explanation of all new results and a coherent and contradiction-free account of the whole quantum mechanics including all necessary changes of its current textbook version.

quant-ph↗

arXiv2012

Changes of separation status during registration and scattering

In our previous work, a new approach to the notorious problem of quantum measurement was proposed. Existing treatments of the problem were incorrect because they ignored the disturbance of measurement by identical particles and standard quantum mechanics had to be modified to obey the cluster separability principle. The key tool was the notion of separation status. Changes of separation status occur during preparations, registrations and scattering on macroscopic targets. Standard quantum mechanics does not provide any correct rules that would govern these changes. This gives us the possibility to add new rules to quantum mechanics that would satisfy the objectification requirement. The method of the present paper is to start from the standard unitary evolution and then introduce minimal corrections. Several representative examples of registration and particle scattering on macroscopic targets are analysed case by case in order to see their common features. The resulting general Rule of Separation Status Changes is stated in the Conclusion.

quant-ph↗

arXiv2012

Emergence of classical theories from quantum mechanics

Three problems stand in the way of deriving classical theories from quantum mechanics: those of realist interpretation, of classical properties and of quantum measurement. Recently, we have identified some tacit assumptions that lie at the roots of these problems. Thus, a realist interpretation is hindered by the assumption that the only properties of quantum systems are values of observables. If one simply postulates the properties to be objective that are uniquely defined by preparation then all difficulties disappear. As for classical properties, the wrong assumption is that there are arbitrarily sharp classical trajectories. It turns out that fuzzy classical trajectories can be obtained from quantum mechanics by taking the limit of high entropy. Finally, standard quantum mechanics implies that any registration on a quantum system is disturbed by all quantum systems of the same kind existing somewhere in the universe. If one works out systematically how quantum mechanics must be corrected so that there is no such disturbance, one finds a new interpretation of von Neumann's "first kind of dynamics", and so a new way to a solution of the quantum measurement problem. The present paper gives a very short review of this work.

quant-ph↗

arXiv2011

A new approach to quantum measurement problem: cluster separability

The paper describes a solution to the problem of quantum measurement that has been proposed recently. The literal understanding of the basic rule of quantum mechanics on identical particles violates the cluster separation principle and so leads to difficulties. A proposal due to Peres of how such difficulties could be removed is reformulated and extended. Cluster separability leads to a locality requirement on observables and to the key notion of separation status. Separation status of a microsystem is shown to change in preparation and registration processes. The indispensability of detectors plays an important role. Changes of separation status are alterations of kinematic description rather than some parts of dynamical trajectories and so more radical than 'collapse of the wave function'. Textbook quantum mechanics does not provide any information of how separation status changes run, hence new rules must be formulated. This enables to satisfy the objectification requirement for registrations. To show how the ideas work, a simplified model of registration apparatus is constructed.

quant-ph↗

arXiv2011

Quantum measurement problem and cluster separability

A modified Beltrametti-Cassinelli-Lahti model of measurement apparatus that satisfies both the probability reproducibility condition and the objectification requirement is constructed. Only measurements on microsystems are considered. The cluster separability forms a basis for the first working hypothesis: the current version of quantum mechanics leaves open what happens to systems when they change their separation status. New rules that close this gap can therefore be added without disturbing the logic of quantum mechanics. The second working hypothesis is that registration apparatuses for microsystems must contain detectors and that their readings are signals from detectors. This implies that separation status of a microsystem changes during both preparation and registration. A new rule that specifies what happens at these changes and that guarantees the objectification is formulated and discussed. A part of our result has certain similarity with 'collapse of the wave function'.

quant-ph↗

arXiv2011

Survey of an approach to quantum measurement, classical properties and realist interpretation problems

The paper gives a systematic review of the basic ideas of (non-relativistic) quantum mechanics including all changes that result from previous work of the authors. This shows that the new theory is self-consistent and (in certain sense) complete. The most important changes are: 1) A new realist interpretation of quantum mechanics based on the observation that there are enough objective properties of quantum systems if one looks for them elsewhere than among values of observables. This enables us to introduce the notion of quantum object. 2) Classical systems are defined as macroscopic quantum objects in states close to maximum entropy. For classical mechanics, new states of such kind are introduced, the so-called maximum-entropy packets, and shown to approximate classical dynamics better than Gaussian wave packets. 3) A new solution of quantum measurement problem is proposed for measurements that are performed on microsystems. First, it is assumed that readings of registration apparatuses are always signals from detectors. This implies restrictions on what is observable. Second, an application of the cluster separability principle leads to the key notion of the paper: the separation status of microsystems. The processes of preparation and registration include changes of separation status. A crucial observation is that standard quantum mechanics does not prescribe the evolution during such changes. This gap can be filled by new rules without contradicting the rest of quantum mechanics. As an example of such a new rule, Beltrametti-Cassinelli-Lahti model of measurement is modified and shown then to satisfy both the probability-reproducibility and the objectification requirements.

quant-ph↗

arXiv2010

Cluster separability, indispensability of detectors and quantum measurement problem

Careful analysis of cluster separability opens a way to a completely new understanding of preparation and registration procedures for microsystems: they are changes of separation status. An important observation is that quantum mechanics does not specify what happens to systems when they change their separation status. New rules that close this gap can therefore be added without disturbing the logic of quantum mechanics. Another important observation is that registration apparatuses for microsystems must contain detectors and that their readings are signals from detectors. This leads to further restrictions on measurability of observables, especially for macroscopic quantum systems. Beltrametti-Cassinelli-Lahti model is used to show how this approach leads to solution of the measurement problem.

quant-ph↗

arXiv2008

Freedom in Nature

The paper starts with the proposal that the cause of the apparent insolubility of the free-will problem are several popular but strongly metaphysical notions and hypotheses. To reduce the metaphysics, some ideas are borrowed from physics. A concept of event causality is discussed. The importance of Hume's Principle of Causality is stressed and his Principle of Causation is weakened. The key concept of the paper, the so-called relative freedom, is also suggested by physics. It is a kind of freedom that can be observed everywhere in nature. Turning to biology, incomplete knowledge is defined for all organisms. They cope with the problem by Popper's trial and error processes. One source of their success is the relative freedom of choice from the basic option ranges: mutations, motions and neural connections. Finally, the conjecture is adopted that communicability can be used as a criterion of consciousness and free will is defined as a conscious version of relative freedom. The resulting notion is logically self-consistent and it describes an observable phenomenon that agrees with our experience.

physics.hist-ph↗

arXiv2006

Liberties in Nature. On Photons, Bugs and Chess Players

Free will is an old philosophical enigma that has been recently revived by neuropsychology. We restrict ourselves to the problem that determinism seems to allow only an illusion of freedom but random decissions do not contain any freedom either. We show that this is a problem of natural sciences, not philosophy. Physics motivates replacing determinism by the principle of weak causality and introducing the concept of liberty. Its empirical basis remains untouched, but the theoretical interpretations of the state space in Newton theory and of the space-time in general relativity are changed. The emerging understanding of time agrees with the idea suggested once by Popper. In biology, the most important liberties are those of mutation, of motion and of the portable neural representation. We distinguish freedom and liberty. Each freedom is associated with some liberty and is defined as the ability to perform three processes called realization, selection and use of memory. This makes freedom accessible to experimental study. The freedom of will is explained by giving account of the underlying specific liberty and processes. While the realization has an ample space for randomness, the selection is mostly causal. Thus, determinism can be rejected without forcing decissions to be random. The experiments of Libet and the role of consciousness are discussed.

physics.class-ph↗

arXiv2006

Can differently prepared mixed states be distinguished?

A measurement has been proposed by B. d'Espagnat that would distinguish from one another some ensembles that are differently prepared but correspond to the same density matrix. Here, the idea is modified so that it becomes applicable to much more general situations. The method is illustrated in simple examples. Some matter of concern might then be that information could be transmitted by methods based on our idea in the EPR kind of experiments. A simple proof is given that this is impossible.

quant-ph↗

arXiv2003

Gauge-invariant Hamiltonian dynamics of cylindrical gravitational waves

The model of cylindrical gravitational waves is employed to work out and check a recent proposal in Ref. [11] how a diffeomorphism-invariant Hamiltonian dynamics is to be constructed. The starting point is the action by Ashtekar and Pierri because it contains the boundary term that makes it differentiable for non-trivial variations at infinity. With the help of parametrization at infinity, the notion of gauge transformation is clearly separated from that of asymptotic symmetry. The symplectic geometry of asymptotic symmetries and asymptotic time is described and the role of the asymptotic structures in defining a zero-motion frame for the Hamiltonian dynamics of Dirac observables is explained. Complete sets of Dirac observables associated with the asymptotic fields are found and the action of the asymptotic symmetries on them is calculated. The construction of the corresponding quantum theory is sketched: the Fock space, operators of asymptotic fields, the Hamiltonian and the scattering matrix are determined.

gr-qc↗

arXiv2003

Canonical theory of spherically symmetric spacetimes with cross-streaming null dusts

The Hamiltonian dynamics of two-component spherically symmetric null dust is studied with regard to the quantum theory of gravitational collapse. The components--the ingoing and outgoing dusts--are assumed to interact only through gravitation. Different kinds of singularities, naked or "clothed", that can form during collapse processes are described. The general canonical formulation of the one-component null-dust dynamics by Bicak and Kuchar is restricted to the spherically symmetric case and used to construct an action for the two components. The transformation from a metric variable to the quasilocal mass is shown to simplify the mathematics. The action is reduced by a choice of gauge and the corresponding true Hamiltonian is written down. Asymptotic coordinates and energy densities of dust shells are shown to form a complete set of Dirac observables. The action of the asymptotic time translation on the observables is defined but it has been calculated explicitly only in the case of one-component dust (Vaidya metric).

gr-qc↗