arXiv subjects

Andrzej Góźdź

Publications and source records attributed to Andrzej Góźdź.

15 recordsLinked to original sources

arXiv2026

Delayed Choice Phenomena in the Projection Evolution Model

In the Schrödinger evolution of a quantum state time enters as a real parameter representing the coordinate. In a more consistent approach time should be defined as a quantum observable, with the evolution taking place in a four-dimensional spacetime. This is possible in the projection evolution model in which the wave function is defined in both space and time. This allows to construct the time operator and discuss the temporal structure of quantum processes. In this paper we discuss a photon travelling through a Mach-Zehnder interferometer, focusing the description on the temporal profile of the wave function. We show that in this approach the delayed-choice experiments can be explained by the temporal overlap of the photon and the devices in the interferometer.

quant-ph↗

arXiv2025

Semiclassical causal geodesics: Minkowski spacetime case

We use an integral quantization model based on the Heisenberg-Weyl group to describe the motion of a spinless particle in the Minkowski background spacetime. This work is a sequel to a previous paper, devoted to mathematical aspects of our model: construction of the space of coherent states and properties of elementary observables. We compute transition amplitudes corresponding to a free motion of a particle between two coherent states. These amplitudes are then used to model quantum random walks of free relativistic particles. Our quantization scheme allows us to recover interference patterns occurring in a standard double-slit experiment, known from the classical approach. This result is obtained by modeling the slits in terms of eigenstates of the position operator and computing transition amplitudes between position and coherent states. We design our model in a way which allows for a future generalization to a semi-classical quantization of the geodesic motion in curved spacetimes.

gr-qc↗

arXiv2025

Integral quantization based on the Heisenberg-Weyl group

We develop a relativistic framework of integral quantization applied to the motion of spinless particles in the four-dimensional Minkowski spacetime. The proposed scheme is based on coherent states generated by the action of the Heisenberg-Weyl group and has been motivated by the Hamiltonian description of the geodesic motion in General Relativity. We believe that this formulation should also allow for a generalization to the motion of test particles in curved spacetimes. A key element in our construction is the use of suitably defined positive operator-valued measures. We show that this approach can be used to quantize the one-dimensional nonrelativistic harmonic oscillator, recovering the standard Hamiltonian as obtained by the canonical quantization. A direct application of our model, including a computation of transition amplitudes between states characterized by fixed positions and momenta, is postponed to a forthcoming article.

gr-qc↗

arXiv2023

Quantum clock in the projection evolution formalism

Using the projection evolution (PEv) approach, time can be included in the quantum mechanics as an observable. Having the time operator, it is possible to explore the temporal structure of various quantum events. In the present paper we discuss the possibility of constructing a quantum clock, which advances in time during its quantum evolution, in each step having some probability to localize itself on the time axis in the new position. We propose a working two-state model as the simplest example of such a clock.

quant-ph↗

arXiv2023

Projection evolution and quantum spacetime

We discuss the problem of time in quantum mechanics. In the traditional formulation time enters the model as a~parameter, not an observable. In our model time is a quantum observable as any other quantum quantity and it is also a component of the spacetime position operator. In this case, instead of the unitary time evolution, other operators, usually projection or POVM operators which map the space of initial states into the space of final states at each step of the evolution can be used. The quantum evolution itself is a stochastic process. This allows to treat time as a quantum observable in a consistent, observer independent way, which is a very important feature to resolve some quantum paradoxes and the time problem in cosmology. An idea of construction of a quantum spacetime as a special set of the allowed states is presented. An example of a structureless quantum Minkowski-like spacetime is also considered. We present the projection evolution model and show how the traditional Schroedinger evolution and relativistic equations can be obtained from it, in the flat structureless spacetime. We propose the form of the time operator which satisfies the energy-time uncertainty relation based on the same inequality as the space position and spatial momenta observables. The sign of the temporal component of the four-momentum operator defines the basic arrow of time in spacetime.

quant-ph↗

arXiv2023

Quantum dynamics of gravitational massive shell

The quantum dynamics of a self-gravitating thin matter shell in vacuum has been considered. Quantum Hamiltonian of the system is positive definite. Within chosen set of parameters, the quantum shell bounces above the horizon. Considered quantum system does not collapse to the gravitational singularity of the corresponding classical system.

gr-qc↗

arXiv2023

Quantum dynamics corresponding to chaotic BKL scenario

We quantize the solution to the Belinski-Khalatnikov-Lifshitz (BKL) scenario using the integral quantization method. Quantization smears the gravitational singularity avoiding its localization in the configuration space. The latter is defined in terms of spatial and temporal coordinates, which are treated on the same footing that enables respecting covariance of general relativity. The relative quantum perturbations grow as the system evolves towards the gravitational singularity. The quantum randomness amplifies the deterministic classical chaos of the BKL scenario. Additionally, our results suggest that the generic singularity of general relativity can be avoided at quantum level giving support to the expectation that quantum gravity has good chance to be a regular theory.

gr-qc↗

arXiv2022

Ascribing quantum system to Schwarzschild spacetime with naked singularity

We quantize the Schwarzschild spacetime with naked singularity using the affine coherent states quantization method. The novelty of our approach is quantization of both temporal and spatial coordinates. Quantization smears the gravitational singularity indicated by the Kretschmann invariant avoiding its localization in the configuration space. This way we resolve the singularity problem of considered spacetime at quantum level.

gr-qc↗

arXiv2021

Hunting for gravitational quantum spikes

We present the result of our examination of quantum structures called quantum spikes. The classical spikes, that are known in gravitational systems, occur in the evolution of the inhomogeneous spacetimes. Different kind of spikes, which we name strange spikes, can be seen in the dynamics of the homogeneous sector of the Belinski-Khalatnikov-Lifshitz scenario. They can be made visible if the so-called inhomogeneous initial data are used. The question to be explored is whether the strange spikes may survive quantization. The answer is in the affirmative. However, this is rather a subtle effect that needs further examination using sophisticated analytical and numerical tools. The spikes seem to be of fundamental importance, both at classical and quantum levels, as they may serve as seeds of real structures in the universe.

gr-qc↗

arXiv2020

Dependence of the affine coherent states quantization on the parametrization of the affine group

The affine coherent states quantization is a promising integral quantization of Hamiltonian systems when the phase space includes at least one conjugate pair of variables which takes values from a half-plane. Such a situation is common for gravitational systems which include singularities. The construction of the quantization map includes a one-to-one mapping of the half-plane onto the affine group. Particular cases of this mapping define specific parametrizations of the group. Our aim is showing that different such parametrizations lead to unitarily inequivalent quantum theories. Depending on the Hamiltonian system under consideration, this dependence could potentially be used constructively.

math-ph↗

arXiv2020

Temporal interference of relativistic bosons

In quantum mechanics, time is introduced as a non-measurable quantity, as there is no possibility to build a hermitian operator canonically conjugated to the Hamiltonian. We cannot have, therefore, the time operator, which means that the temporal structure of the evolution of quantum systems is ill-defined. We present an extension to the model, in which the time evolution is based on the projection postulate rather than the unitary operator. This approach is in agreement with all other aspects of quantum mechanics and allows to discuss time as an observable. Using this framework we present a description of the temporal double-slit experiment in which a~single particle interferes with itself from a different instant of time. Such behaviour has already been observed experimentally but lacked a consistent theoretical explanation.

quant-ph↗

arXiv2020

Robustness of the quantum BKL scenario

Quantum Belinski-Khalatnikov-Lifshitz scenario presents an unitary evolution of the system. However, the affine coherent states quantization applied to the quantization of the underlying classical scenario depends on the choice of the group parametrization. Using two simplest parameterizations of the affine group, we show that qualitative features of our quantum system do not depend on the choice. It means that the quantum bounce replacing singular classical scenario is expected to be a generic feature of considered system. This paper complements our recent article [1].

gr-qc↗

arXiv2019

Quantum Belinski-Khalatnikov-Lifshitz scenario

We present the quantum model of the asymptotic dynamics underlying the Belinski-Khalatnikov-Lifshitz (BKL) scenario. The symmetry of the physical phase space enables making use of the affine coherent states quantization. Our results show that quantum dynamics is regular in the sense that during quantum evolution the expectation values of all considered observables are finite. The classical singularity of the BKL scenario is replaced by the quantum bounce that presents a unitary evolution of considered gravitational system. Our results suggest that quantum general relativity is free from singularities.

gr-qc↗

arXiv2017

Dynamical structures specific to strong gravitational field: Quantum formalism

The dynamics of the general Bianchi IX spacetime, near the gravitational singularity, underlies the Belinskii, Khalatnikov and Lifshitz scenario. Asymptotically, near the singularity, the oscillations of the directional scale factors (defining the spacetime metric) are freezed so the evolution of the Bianchi IX model is devoid of chaotic features. However, it includes special structures, that we call the wiggles, which change their properties in the asymptotic regime. We propose the formalism, based on an affine quantization scheme, to examine the fate of the wiggles at the quantum level. We present the way of comparing the classical wiggles with their quantum counterparts. We expect that our work may contribute towards understanding some quantum aspects of the BKL scenario.

gr-qc↗

arXiv2013

On particle oscillations

It has been firmly established, that neutrinos change their flavour during propagation. This feature is attributed to the fact, that each flavour eigenstate is a superposition of three mass eigenstates, which propagate with different frequencies. This picture, although widely accepted, is wrong in the simplest approach and requires quite sophisticated treatment based on the wave-packet description within quantum field theory. In this communication we present a novel, much simpler explanation and show, that oscillations among massive particles can be obtained in a natural way. We use the framework of quantum mechanics with time being a physical observable, not just a parameter.

quant-ph↗