Tajron Juric - Academia.edu (original) (raw)

Papers by Tajron Juric

˜The œJournal of high energy physics/˜The œjournal of high energy physics, Jun 19, 2024

We use the framework of Hopf algebra and noncommutative differential geometry to build a noncommu... more We use the framework of Hopf algebra and noncommutative differential geometry to build a noncommutative (NC) theory of gravity in a bottom-up approach. Noncommutativity is introduced via deformed Hopf algebra of diffeomorphisms by means of a Drinfeld twist. The final result of the construction is a general formalism for obtaining NC corrections to the classical theory of gravity for a wide class of deformations and a general background. This also includes a novel proposal for noncommutative Einstein manifold. Moreover, the general construction is applied to the case of a linearized gravitational perturbation theory to describe a NC deformation of the metric perturbations. We specifically present an example for the Schwarzschild background and axial perturbations, which gives rise to a generalization of the work by Regge and Wheeler. All calculations are performed up to first order in perturbation of the metric and noncommutativity parameter. The main result is the noncommutative Regge-Wheeler potential. Finally, we comment on some differences in properties between the Regge-Wheeler potential and its noncommutative counterpart.

arXiv (Cornell University), Jul 19, 2021

We further develop the general theory of quantum time distributions introduced in [D. Jurman and ... more We further develop the general theory of quantum time distributions introduced in [D. Jurman and H. Nikolić, Phys. Lett. A 396, 127247 (2021)] and apply it to find the distribution of arrival times at the detector. Even though the Hamiltonian in the absence of detector is hermitian, the time evolution of the system before detection involves dealing with a non-hermitian operator obtained from the projection of the hermitian Hamiltonian onto the region in front of the detector. Such a formalism eventually gives rise to a simple and physically sensible analytical expression for the arrival time distribution, for arbitrary wave packet moving in one spatial dimension with negligible distortion.

Fortschritte der Physik, Jul 2, 2023

Classical measurements are passive, in the sense that they do not affect the physical properties ... more Classical measurements are passive, in the sense that they do not affect the physical properties of the measured system. Normally, quantum measurements are not passive in that sense. In the infinite dimensional Hilbert space, however, it is found that quantum projective measurement can be passive in a way which is impossible in finite dimensional Hilbert spaces. Specifically, it is found that expectation value of a hermitian Hamiltonian can have an imaginary part in the infinite dimensional Hilbert space and that such an imaginary part implies a possibility to avoid quantum Zeno effect, which can physically be realized in quantum arrival experiments. The avoidance of quantum Zeno effect can also be understood as avoidance of a quantum version of gambler's fallacy, leading to the notion of passive quantum measurement that updates information about the physical system without affecting its physical properties. The arrival time probability distribution of a particle is found to be given by the flux of the probability current. Possible negative fluxes correspond to regimes at which there is no arrival at all, physically understood as regimes at which the particle departs rather than arrives.

arXiv (Cornell University), Jul 4, 2023

We develop a new method for finding the quantum probability density of arrival at the detector. T... more We develop a new method for finding the quantum probability density of arrival at the detector. The evolution of the quantum state restricted to the region outside of the detector is described by a restricted Hamiltonian that contains a non-hermitian boundary term. The non-hermitian term is shown to be proportional to the flux of the probability current operator through the boundary, which implies that the arrival probability density is equal to the flux of the probability current.

Ovaj rad je izraden na Zavodu za teorijsku fiziku Instituta "Ruder Bošković" pod vodstvom dr. Stj... more Ovaj rad je izraden na Zavodu za teorijsku fiziku Instituta "Ruder Bošković" pod vodstvom dr. Stjepana Meljanca. Ovom prilikom zahvaljujem mentoru na iznimno brižnom i strpljivom vodenju kroz nastanak ovog rada, mnogim korisnim diskusijama i sugestijama. Takoder zahvaljujem svim kolegama (a posebno "ekipi s tavana": BK, AS i SD) s kojima sam gotovo svakodnevno raspravljao o fizici. Veliko hvala Beniju za njegova Predavanja, koja su bila jedna od ključnih u mom putu ka postajanju teorijski fizičar. Za kraj, posebno hvala mojoj majci Nini i mojoj djevojci Tamarišto su me podržavale sve ovo vrijeme te njima i posvećujem ovaj rad.

Universe, Feb 17, 2022

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

The European Physical Journal Plus

We apply the recently developed general theory of quantum time distributions [1] to find the dist... more We apply the recently developed general theory of quantum time distributions [1] to find the distribution of arrival times at the detector. Even though the Hamiltonian in the absence of detector is hermitian, the time evolution of the system before detection involves dealing with a non-hermitian operator obtained from the projection of the hermitian Hamiltonian onto the region in front of the detector. Such a formalism eventually gives rise to a simple and physically sensible analytical expression for the arrival time distribution, for arbitrary wave packet moving in one spatial dimension with negligible distortion.

arXiv (Cornell University), Sep 15, 2022

We study the noncommutative corrections to the entropy of the Reissner-Nordström black hole using... more We study the noncommutative corrections to the entropy of the Reissner-Nordström black hole using a κ-deformed scalar probe within the brick-wall framework. The noncommutativity is encoded in an Abelian Drinfeld twist constructed from the Killing vector fields of the Reissner-Nordström black hole. We show that the noncommutative effects naturally lead to a logarithmic correction to the Bekenstein-Hawking entropy even at the lowest order of the WKB approximation. In contrast, such logarithmic corrections in the commutative setup appear only after the quantum effects are included through higher order WKB corrections or through higher loop effects. Our analysis thus provides further evidence towards the hypothesis that the noncommutative framework is capable of encoding quantum effects in curved spacetime.

arXiv (Cornell University), Jul 19, 2022

Classical measurements are passive, in the sense that they do not affect the physical properties ... more Classical measurements are passive, in the sense that they do not affect the physical properties of the measured system. Normally, quantum measurements are not passive in that sense. In the infinite dimensional Hilbert space, however, we find that quantum projective measurement can be passive in a way which is impossible in finite dimensional Hilbert spaces. Specifically, we find that expectation value of a hermitian Hamiltonian can have an imaginary part in the infinite dimensional Hilbert space and that such an imaginary part implies a possibility to avoid quantum Zeno effect, which can physically be realized in quantum arrival experiments. The avoidance of quantum Zeno effect can also be understood as avoidance of a quantum version of gambler's fallacy, leading to the notion of passive quantum measurement that updates information about the physical system without affecting its physical properties. The arrival time probability distribution of a particle is found to be given by the flux of the probability current. Possible negative fluxes correspond to regimes at which there is no arrival at all, physically understood as regimes at which the particle departs rather than arrives.

Universe, 2022

We are focused on the idea that observables in quantum physics are a bit more then just hermitian... more We are focused on the idea that observables in quantum physics are a bit more then just hermitian operators and that this is, in general, a “tricky business”. The origin of this idea comes from the fact that there is a subtle difference between symmetric, hermitian, and self-adjoint operators which are of immense importance in formulating Quantum Mechanics. The theory of self-adjoint extensions is presented through several physical examples and some emphasis is given on the physical implications and applications.

Opis kvantne gravitacije zahtijeva ujedinjenje postulata opce teorije relativnosti i Heisenbergov... more Opis kvantne gravitacije zahtijeva ujedinjenje postulata opce teorije relativnosti i Heisenbergovog principa neodređenosti, sto vodi na neodređeno

arXiv: High Energy Physics - Theory, 2016

In this paper we perform a parallel analysis to the model proposed in [25]. By considering the ce... more In this paper we perform a parallel analysis to the model proposed in [25]. By considering the central co-tetrad (instead of the central metric) we investigate the modifications in the gravitational metrics coming from the noncommutative spacetime of the kappa\kappakappa-Minkowski type in four dimensions. The differential calculus corresponding to a class of Jordanian $ \kappa$-deformations provide metrics which lead either to cosmological constant or spatial-curvature type solutions of non-vacuum Einstein equations. Among vacuum solutions one finds pp-waves.

arXiv (Cornell University), Dec 13, 2022

Symmetry

Noncommutative geometry is an established potential candidate for including quantum phenomena in ... more Noncommutative geometry is an established potential candidate for including quantum phenomena in gravitation. We outlined the formalism of Hopf algebras and its connection to the algebra of infinitesimal diffeomorphisms. Using a Drinfeld twist, we deformed spacetime symmetries, algebra of vector fields and differential forms, leading to a formulation of noncommutative Einstein equations. We studied a concrete example of charged BTZ spacetime and deformations steaming from the so-called angular twist. The entropy of the noncommutative charged BTZ black hole was obtained using the brick-wall method. We used a charged scalar field as a probe and obtained its spectrum and density of states via WKB approximation. We provide the method used to calculate corrections to the Bekenstein–Hawking entropy in higher orders in WKB, but we present the final result in the lowest WKB order. The result is that, even in the lowest order in WKB, the entropy, in general, contains higher powers in ℏ, and ...

Journal of High Energy Physics, 2018

Motivated by the question whether quantum gravity can “smear out” the classical singularity we an... more Motivated by the question whether quantum gravity can “smear out” the classical singularity we analyze a certain quantum space and its quantum-mechanical completeness. Classical singularity is understood as a geodesic incompleteness, while quantum completeness requires a unique unitary time evolution for test fields propagating on an underlying background. Here the crucial point is that quantum completeness renders the Hamiltonian (or spatial part of the wave operator) to be essentially self-adjoint in order to generate a unique time evolution. We examine a model of quantum space which consists of a noncommutative BTZ black hole probed by a test scalar field. We show that the quantum gravity (noncommutative) effect is to enlarge the domain of BTZ parameters for which the relevant wave operator is essentially self-adjoint. This means that the corresponding quantum space is quantum complete for a larger range of BTZ parameters rendering the conclusion that in the quantum space one obs...

Journal of High Energy Physics

We study the noncommutative corrections to the entropy of the Reissner-Nordström black hole using... more We study the noncommutative corrections to the entropy of the Reissner-Nordström black hole using a κ-deformed scalar probe within the brick-wall framework. The noncommutativity is encoded in an Abelian Drinfeld twist constructed from the Killing vector fields of the Reissner-Nordström black hole. We show that the noncommutative effects naturally lead to a logarithmic correction to the Bekenstein-Hawking entropy even at the lowest order of the WKB approximation. In contrast, such logarithmic corrections in the commutative setup appear only after the quantum effects are included through higher order WKB corrections or through higher loop effects. Our analysis thus provides further evidence towards the hypothesis that the noncommutative framework is capable of encoding at least some quantum effects in curved spacetime, although additional contributions will appear when the NC effects are fully incorporated in a gravity theory.

Physical Review D

One of the long standing problems is a quest for regular black hole solutions, in which a resolut... more One of the long standing problems is a quest for regular black hole solutions, in which a resolution of the spacetime singularity has been achieved by some physically reasonable, classical field, before one resorts to the quantum gravity. The prospect of using nonlinear electromagnetic fields for this goal has been limited by the Bronnikov's no-go theorems, focused on Lagrangians depending on the electromagnetic invariant F ab F ab only. We extend Bronnikov's results by taking into account Lagrangians that depend on both electromagnetic invariants, F ab F ab and F ab F ab , and prove that the tension between the Lagrangian's Maxwellian weak field limit and boundedness of the curvature invariants persists in more general class of theories.

Physical Review D, 2022

We prove two theorems which imply that any stationary nonlinear electromagnetic field obeying a d... more We prove two theorems which imply that any stationary nonlinear electromagnetic field obeying a dominant energy condition in a strictly stationary, everywhere regular, asymptotically flat spacetime must be either trivial or a stealth field. The first theorem holds in static spacetimes and is independent of the gravitational part of the action, as long as the coupling of the electromagnetic field to the gravitational field is minimal. The second theorem assumes Einstein-Hilbert gravitational action and relies on the positive energy theorem, but does not assume that the spacetime metric is static. In addition, we discuss possible generalizations of these results, to theories with charged matter, as well as higher-dimensional nonlinear electromagnetic fields.

In this paper, we derive Lorentz force and Maxwell's equations on kappa-Minkowski space-time up t... more In this paper, we derive Lorentz force and Maxwell's equations on kappa-Minkowski space-time up to the first order in the deformation parameter. This is done by elevating the principle of minimal coupling to non-commutative space-time. We also show the equivalence of minimal coupling prescription and Feynman's approach. It is shown that the motion in kappa space-time can be interpreted as motion in a background gravitational field, which is induced by this non-commutativity. In the static limit, the effect of kappa deformation is to scale the electric charge. We also show that the laws of electrodynamics depend on the mass of the charged particle, in kappa space-time.

˜The œJournal of high energy physics/˜The œjournal of high energy physics, Jun 19, 2024

We use the framework of Hopf algebra and noncommutative differential geometry to build a noncommu... more We use the framework of Hopf algebra and noncommutative differential geometry to build a noncommutative (NC) theory of gravity in a bottom-up approach. Noncommutativity is introduced via deformed Hopf algebra of diffeomorphisms by means of a Drinfeld twist. The final result of the construction is a general formalism for obtaining NC corrections to the classical theory of gravity for a wide class of deformations and a general background. This also includes a novel proposal for noncommutative Einstein manifold. Moreover, the general construction is applied to the case of a linearized gravitational perturbation theory to describe a NC deformation of the metric perturbations. We specifically present an example for the Schwarzschild background and axial perturbations, which gives rise to a generalization of the work by Regge and Wheeler. All calculations are performed up to first order in perturbation of the metric and noncommutativity parameter. The main result is the noncommutative Regge-Wheeler potential. Finally, we comment on some differences in properties between the Regge-Wheeler potential and its noncommutative counterpart.

arXiv (Cornell University), Jul 19, 2021

We further develop the general theory of quantum time distributions introduced in [D. Jurman and ... more We further develop the general theory of quantum time distributions introduced in [D. Jurman and H. Nikolić, Phys. Lett. A 396, 127247 (2021)] and apply it to find the distribution of arrival times at the detector. Even though the Hamiltonian in the absence of detector is hermitian, the time evolution of the system before detection involves dealing with a non-hermitian operator obtained from the projection of the hermitian Hamiltonian onto the region in front of the detector. Such a formalism eventually gives rise to a simple and physically sensible analytical expression for the arrival time distribution, for arbitrary wave packet moving in one spatial dimension with negligible distortion.

Fortschritte der Physik, Jul 2, 2023

Classical measurements are passive, in the sense that they do not affect the physical properties ... more Classical measurements are passive, in the sense that they do not affect the physical properties of the measured system. Normally, quantum measurements are not passive in that sense. In the infinite dimensional Hilbert space, however, it is found that quantum projective measurement can be passive in a way which is impossible in finite dimensional Hilbert spaces. Specifically, it is found that expectation value of a hermitian Hamiltonian can have an imaginary part in the infinite dimensional Hilbert space and that such an imaginary part implies a possibility to avoid quantum Zeno effect, which can physically be realized in quantum arrival experiments. The avoidance of quantum Zeno effect can also be understood as avoidance of a quantum version of gambler's fallacy, leading to the notion of passive quantum measurement that updates information about the physical system without affecting its physical properties. The arrival time probability distribution of a particle is found to be given by the flux of the probability current. Possible negative fluxes correspond to regimes at which there is no arrival at all, physically understood as regimes at which the particle departs rather than arrives.

arXiv (Cornell University), Jul 4, 2023

We develop a new method for finding the quantum probability density of arrival at the detector. T... more We develop a new method for finding the quantum probability density of arrival at the detector. The evolution of the quantum state restricted to the region outside of the detector is described by a restricted Hamiltonian that contains a non-hermitian boundary term. The non-hermitian term is shown to be proportional to the flux of the probability current operator through the boundary, which implies that the arrival probability density is equal to the flux of the probability current.

Ovaj rad je izraden na Zavodu za teorijsku fiziku Instituta "Ruder Bošković" pod vodstvom dr. Stj... more Ovaj rad je izraden na Zavodu za teorijsku fiziku Instituta "Ruder Bošković" pod vodstvom dr. Stjepana Meljanca. Ovom prilikom zahvaljujem mentoru na iznimno brižnom i strpljivom vodenju kroz nastanak ovog rada, mnogim korisnim diskusijama i sugestijama. Takoder zahvaljujem svim kolegama (a posebno "ekipi s tavana": BK, AS i SD) s kojima sam gotovo svakodnevno raspravljao o fizici. Veliko hvala Beniju za njegova Predavanja, koja su bila jedna od ključnih u mom putu ka postajanju teorijski fizičar. Za kraj, posebno hvala mojoj majci Nini i mojoj djevojci Tamarišto su me podržavale sve ovo vrijeme te njima i posvećujem ovaj rad.

Universe, Feb 17, 2022

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

The European Physical Journal Plus

We apply the recently developed general theory of quantum time distributions [1] to find the dist... more We apply the recently developed general theory of quantum time distributions [1] to find the distribution of arrival times at the detector. Even though the Hamiltonian in the absence of detector is hermitian, the time evolution of the system before detection involves dealing with a non-hermitian operator obtained from the projection of the hermitian Hamiltonian onto the region in front of the detector. Such a formalism eventually gives rise to a simple and physically sensible analytical expression for the arrival time distribution, for arbitrary wave packet moving in one spatial dimension with negligible distortion.

arXiv (Cornell University), Sep 15, 2022

We study the noncommutative corrections to the entropy of the Reissner-Nordström black hole using... more We study the noncommutative corrections to the entropy of the Reissner-Nordström black hole using a κ-deformed scalar probe within the brick-wall framework. The noncommutativity is encoded in an Abelian Drinfeld twist constructed from the Killing vector fields of the Reissner-Nordström black hole. We show that the noncommutative effects naturally lead to a logarithmic correction to the Bekenstein-Hawking entropy even at the lowest order of the WKB approximation. In contrast, such logarithmic corrections in the commutative setup appear only after the quantum effects are included through higher order WKB corrections or through higher loop effects. Our analysis thus provides further evidence towards the hypothesis that the noncommutative framework is capable of encoding quantum effects in curved spacetime.

arXiv (Cornell University), Jul 19, 2022

Classical measurements are passive, in the sense that they do not affect the physical properties ... more Classical measurements are passive, in the sense that they do not affect the physical properties of the measured system. Normally, quantum measurements are not passive in that sense. In the infinite dimensional Hilbert space, however, we find that quantum projective measurement can be passive in a way which is impossible in finite dimensional Hilbert spaces. Specifically, we find that expectation value of a hermitian Hamiltonian can have an imaginary part in the infinite dimensional Hilbert space and that such an imaginary part implies a possibility to avoid quantum Zeno effect, which can physically be realized in quantum arrival experiments. The avoidance of quantum Zeno effect can also be understood as avoidance of a quantum version of gambler's fallacy, leading to the notion of passive quantum measurement that updates information about the physical system without affecting its physical properties. The arrival time probability distribution of a particle is found to be given by the flux of the probability current. Possible negative fluxes correspond to regimes at which there is no arrival at all, physically understood as regimes at which the particle departs rather than arrives.

Universe, 2022

We are focused on the idea that observables in quantum physics are a bit more then just hermitian... more We are focused on the idea that observables in quantum physics are a bit more then just hermitian operators and that this is, in general, a “tricky business”. The origin of this idea comes from the fact that there is a subtle difference between symmetric, hermitian, and self-adjoint operators which are of immense importance in formulating Quantum Mechanics. The theory of self-adjoint extensions is presented through several physical examples and some emphasis is given on the physical implications and applications.

Opis kvantne gravitacije zahtijeva ujedinjenje postulata opce teorije relativnosti i Heisenbergov... more Opis kvantne gravitacije zahtijeva ujedinjenje postulata opce teorije relativnosti i Heisenbergovog principa neodređenosti, sto vodi na neodređeno

arXiv: High Energy Physics - Theory, 2016

In this paper we perform a parallel analysis to the model proposed in [25]. By considering the ce... more In this paper we perform a parallel analysis to the model proposed in [25]. By considering the central co-tetrad (instead of the central metric) we investigate the modifications in the gravitational metrics coming from the noncommutative spacetime of the kappa\kappakappa-Minkowski type in four dimensions. The differential calculus corresponding to a class of Jordanian $ \kappa$-deformations provide metrics which lead either to cosmological constant or spatial-curvature type solutions of non-vacuum Einstein equations. Among vacuum solutions one finds pp-waves.

arXiv (Cornell University), Dec 13, 2022

Symmetry

Noncommutative geometry is an established potential candidate for including quantum phenomena in ... more Noncommutative geometry is an established potential candidate for including quantum phenomena in gravitation. We outlined the formalism of Hopf algebras and its connection to the algebra of infinitesimal diffeomorphisms. Using a Drinfeld twist, we deformed spacetime symmetries, algebra of vector fields and differential forms, leading to a formulation of noncommutative Einstein equations. We studied a concrete example of charged BTZ spacetime and deformations steaming from the so-called angular twist. The entropy of the noncommutative charged BTZ black hole was obtained using the brick-wall method. We used a charged scalar field as a probe and obtained its spectrum and density of states via WKB approximation. We provide the method used to calculate corrections to the Bekenstein–Hawking entropy in higher orders in WKB, but we present the final result in the lowest WKB order. The result is that, even in the lowest order in WKB, the entropy, in general, contains higher powers in ℏ, and ...

Journal of High Energy Physics, 2018

Motivated by the question whether quantum gravity can “smear out” the classical singularity we an... more Motivated by the question whether quantum gravity can “smear out” the classical singularity we analyze a certain quantum space and its quantum-mechanical completeness. Classical singularity is understood as a geodesic incompleteness, while quantum completeness requires a unique unitary time evolution for test fields propagating on an underlying background. Here the crucial point is that quantum completeness renders the Hamiltonian (or spatial part of the wave operator) to be essentially self-adjoint in order to generate a unique time evolution. We examine a model of quantum space which consists of a noncommutative BTZ black hole probed by a test scalar field. We show that the quantum gravity (noncommutative) effect is to enlarge the domain of BTZ parameters for which the relevant wave operator is essentially self-adjoint. This means that the corresponding quantum space is quantum complete for a larger range of BTZ parameters rendering the conclusion that in the quantum space one obs...

Journal of High Energy Physics

We study the noncommutative corrections to the entropy of the Reissner-Nordström black hole using... more We study the noncommutative corrections to the entropy of the Reissner-Nordström black hole using a κ-deformed scalar probe within the brick-wall framework. The noncommutativity is encoded in an Abelian Drinfeld twist constructed from the Killing vector fields of the Reissner-Nordström black hole. We show that the noncommutative effects naturally lead to a logarithmic correction to the Bekenstein-Hawking entropy even at the lowest order of the WKB approximation. In contrast, such logarithmic corrections in the commutative setup appear only after the quantum effects are included through higher order WKB corrections or through higher loop effects. Our analysis thus provides further evidence towards the hypothesis that the noncommutative framework is capable of encoding at least some quantum effects in curved spacetime, although additional contributions will appear when the NC effects are fully incorporated in a gravity theory.

Physical Review D

One of the long standing problems is a quest for regular black hole solutions, in which a resolut... more One of the long standing problems is a quest for regular black hole solutions, in which a resolution of the spacetime singularity has been achieved by some physically reasonable, classical field, before one resorts to the quantum gravity. The prospect of using nonlinear electromagnetic fields for this goal has been limited by the Bronnikov's no-go theorems, focused on Lagrangians depending on the electromagnetic invariant F ab F ab only. We extend Bronnikov's results by taking into account Lagrangians that depend on both electromagnetic invariants, F ab F ab and F ab F ab , and prove that the tension between the Lagrangian's Maxwellian weak field limit and boundedness of the curvature invariants persists in more general class of theories.

Physical Review D, 2022

We prove two theorems which imply that any stationary nonlinear electromagnetic field obeying a d... more We prove two theorems which imply that any stationary nonlinear electromagnetic field obeying a dominant energy condition in a strictly stationary, everywhere regular, asymptotically flat spacetime must be either trivial or a stealth field. The first theorem holds in static spacetimes and is independent of the gravitational part of the action, as long as the coupling of the electromagnetic field to the gravitational field is minimal. The second theorem assumes Einstein-Hilbert gravitational action and relies on the positive energy theorem, but does not assume that the spacetime metric is static. In addition, we discuss possible generalizations of these results, to theories with charged matter, as well as higher-dimensional nonlinear electromagnetic fields.

In this paper, we derive Lorentz force and Maxwell's equations on kappa-Minkowski space-time up t... more In this paper, we derive Lorentz force and Maxwell's equations on kappa-Minkowski space-time up to the first order in the deformation parameter. This is done by elevating the principle of minimal coupling to non-commutative space-time. We also show the equivalence of minimal coupling prescription and Feynman's approach. It is shown that the motion in kappa space-time can be interpreted as motion in a background gravitational field, which is induced by this non-commutativity. In the static limit, the effect of kappa deformation is to scale the electric charge. We also show that the laws of electrodynamics depend on the mass of the charged particle, in kappa space-time.