Publications (83)119.4 Total impact

[Show abstract] [Hide abstract]
ABSTRACT: An argument by Banks, Susskind and Peskin (BSP), according to which violation of unitarity would violate either locality or energymomentum conservation, is widely believed to be a strong argument against nonunitarity of Hawking radiation. We find that the whole BSP argument rests on the crucial assumption that the Hamiltonian is not highly degenerate, and point out that this assumption is not satisfied for systems with many degrees of freedom. Using Lindblad equation, we show that high degeneracy of the Hamiltonian allows local nonunitary evolution without violating energymomentum conservation. Moreover, since energymomentum is the source of gravity, we argue that energymomentum is necessarily conserved for a large class of nonunitary systems with gravity. Finally, we explicitly calculate the Lindblad operators for nonunitary Hawking radiation and show that they conserve energymomentum.Journal of Cosmology and Astroparticle Physics 04/2015; 2015(04):002002. DOI:10.1088/14757516/2015/04/002 · 5.88 Impact Factor 
[Show abstract] [Hide abstract]
ABSTRACT: An argument by Banks, Susskind and Peskin (BSP), according to which violation of unitarity would violate either locality or energymomentum conservation, is widely believed to be a strong argument against nonunitarity of Hawking radiation. We find that the whole BSP argument rests on the crucial assumption that the Hamiltonian is not highly degenerate, and point out that this assumption is wrong. Using Lindblad equation, we show that high degeneracy of the Hamiltonian allows local nonunitary evolution without violating energymomentum conservation. Moreover, since energymomentum is the source of gravity, we argue that energymomentum is necessarily conserved for a large class of nonunitary systems with gravity. Finally, we explicitly calculate the Lindblad operators for nonunitary Hawking radiation and show that they conserve energymomentum. 
[Show abstract] [Hide abstract]
ABSTRACT: In the usual formulation of quantum theory, time is a global classical evolution parameter, not a local quantum observable. On the other hand, both canonical quantum gravity (which lacks fundamental timeevolution parameter) and the principle of spacetime covariance (which insists that time should be treated on an equal footing with space) suggest that quantum theory should be slightly reformulated, in a manner that promotes time to a local observable. Such a reformulated quantum theory is unitary in a more general sense than the usual quantum theory. In particular, this promotes the nonunitary Hawking radiation to a unitary phenomenon, which avoids the blackhole information paradox.International Journal of Quantum Information 11/2014; 12(07n08):1560001. DOI:10.1142/S0219749915600011 · 0.99 Impact Factor 
[Show abstract] [Hide abstract]
ABSTRACT: In the literature one often finds the claim that there is no such thing as an energymomentum tensor for the gravitational field, and consequently, that the total energymomentum conservation can only be defined in terms of a gravitational energymomentum pseudotensor. I make a trivial observation that such a conclusion can be avoided by relaxing the assumption that gravitational energymomentum tensor should only depend on first derivatives of the metric. With such a relaxation, the Einstein equation directly leads to the result that gravitational energymomentum tensor is essentially the Einstein tensor. 
[Show abstract] [Hide abstract]
ABSTRACT: In the usual formulation of quantum theory, time is a global classical evolution parameter, not a local quantum observable. On the other hand, both canonical quantum gravity (which lacks fundamental timeevolution parameter) and the principle of spacetime covariance (which insists that time should be treated on an equal footing with space) suggest that quantum theory should be slightly reformulated, in a manner that promotes time to a local observable. Such a reformulated quantum theory is unitary in a more general sense than the usual quantum theory. In particular, this promotes the nonunitary Hawking radiation to a unitary phenomenon, which avoids the blackhole information paradox. 
[Show abstract] [Hide abstract]
ABSTRACT: The possibility of quantum interference of a composite object with many internal degrees of freedom is studied, such that the internal degrees play a role of an internal environment. In particular, if the internal degrees have a capacity for an irreversible record of whichpath information, then the internalenvironment induced decoherence prevents external experimentalists from observing interference. Interference can be observed only if the interfering object is sufficiently isolated from the external environment, so that the object cannot record whichpath information. Extrapolation to a hypothetical interference experiment with a conscious object implies that being a Schrodinger cat would be like being an ordinary cat living in a box without any information about the world external to the box. 
[Show abstract] [Hide abstract]
ABSTRACT: We present evidence that quantum Zeno effect, otherwise working only for microscopic systems, may also work for large black holes (BH's). The expectation that a BH geometry should behave classically at time intervals larger than the Planck time tPltPl indicates that the quantum process of measurement of classical degrees of freedom takes time of the order of tPltPl. Since BH has only a few classical degrees of freedom, such a fast measurement makes a macroscopic BH strongly susceptible to the quantum Zeno effect, which repeatedly collapses the quantum state to the initial one, the state before the creation of Hawking quanta. By this mechanism, Hawking radiation from a BH of mass M is strongly suppressed by a factor of the order of mPl/MmPl/M.Physics Letters B 06/2014; 733:6–10. DOI:10.1016/j.physletb.2014.04.017 · 6.02 Impact Factor 
[Show abstract] [Hide abstract]
ABSTRACT: In the textbook proofs of the Lorentz covariance of the Dirac equation, one treats the wave function as a spinor and gamma matrices as scalars, leading to a quite complicated formalism with several pedagogic drawbacks. As an alternative, I propose to teach the Dirac equation and its Lorentz covariance by using a much simpler, but physically equivalent formalism, in which these drawbacks do not appear. In this alternative formalism, the wave function transforms as a scalar and gamma matrices as components of a vector, such that the standard physically relevant bilinear combinations do not change their transformation properties. The alternative formalism allows also a natural construction of some additional nonstandard bilinear combinations with welldefined transformation properties.European Journal of Physics 03/2014; 35(3):035003. DOI:10.1088/01430807/35/3/035003 · 0.62 Impact Factor 
[Show abstract] [Hide abstract]
ABSTRACT: We present evidence that quantum Zeno effect, otherwise working only for microscopic systems, may also work for large black holes (BH's). The expectation that a BH geometry should behave classically at time intervals larger than the Planck time t_Pl indicates that the quantum process of measurement of classical degrees of freedom takes time of the order of t_Pl. Since BH has only a few classical degrees of freedom, such a fast measurement makes a macroscopic BH strongly susceptible to the quantum Zeno effect, which repeatedly collapses the quantum state to the initial one, the state before the creation of Hawking quanta. By this mechanism, Hawking radiation from a BH of mass M is strongly suppressed by a factor of the order of m_Pl/M. 
[Show abstract] [Hide abstract]
ABSTRACT: In the textbook proofs of Lorentz covariance of the Dirac equation, one treats the wave function as a spinor and gamma matrices as scalars, leading to a quite complicated formalism with several pedagogic drawbacks. As an alternative, I propose to teach Dirac equation and its Lorentz covariance by using a much simpler, but physically equivalent formalism, in which these drawbacks do not appear. In this alternative formalism, the wave function transforms as a scalar and gamma matrices as components of a vector, such that the standard physically relevant bilinear combinations do not change their transformation properties. The alternative formalism allows also a natural construction of some additional nonstandard bilinear combinations with welldefined transformation properties. 
[Show abstract] [Hide abstract]
ABSTRACT: Bohmian mechanics can be generalized to a relativistic theory without preferred foliation, with a price of introducing a puzzling concept of spacetime probability conserved in a scalar time. We explain how analogous concept appears naturally in classical statistical mechanics of relativistic particles, with scalar time being identified with the proper time along particle trajectories. The conceptual understanding of relativistic Bohmian mechanics is significantly enriched by this classical insight. In particular, the analogy between classical and Bohmian mechanics suggests the interpretation of Bohmian scalar time as a quantum proper time different from the classical one, the two being related by a nonlocal scale factor calculated from the wave function. In many cases of practical interest, including the macroscopic measuring apparatus, the fundamental spacetime probability explains the more familiar space probability as an emergent approximate description. Requiring that the quantum proper time in the classical limit should reduce to the classical proper time, we propose that only massive particles have Bohmian trajectories. An analysis of the macroscopic measuring apparatus made up of massive particles restores agreement with the predictions of standard quantum theory. 
Article: Solipsistic hidden variables
[Show abstract] [Hide abstract]
ABSTRACT: We argue that it is logically possible to have a sort of both reality and locality in quantum mechanics. To demonstrate this, we construct a new quantitative model of hidden variables (HV’s), dubbed solipsistic HV’s, that interpolates between the orthodox noHV interpretation and nonlocal Bohmian interpretation. In this model, the deterministic pointparticle trajectories are associated only with the essential degrees of freedom of the observer, and not with the observed objects. In contrast with Bohmian HV’s, nonlocality in solipsistic HV’s can be substantially reduced down to microscopic distances inside the observer. Even if such HV’s may look philosophically unappealing to many, the mere fact that they are logically possible deserves attention.International Journal of Quantum Information 12/2012; 10(8). DOI:10.1142/S021974991241016X · 0.99 Impact Factor 
[Show abstract] [Hide abstract]
ABSTRACT: It is often argued that measurable predictions of Bohmian mechanics cannot be distinguished from those of a theory with arbitrarily modified particle velocities satisfying the same equivariance equation. By considering the wave function of a closed system in a state with definite total energy, we argue that a distinction in measurable predictions is possible. Even though such a wave function is timeindependent, the conditional wave function for a subsystem depends on time through the timedependent particle trajectories not belonging to the subsystem. If these trajectories can be approximated by classical trajectories, then the conditional wave function can be approximated by a wave function which satisfies Schrodinger equation in a classical timedependent potential, which is in good agreement with observations. However, such an approximation cannot be justified for particle velocities significantly deviating from the Bohmian ones, implying that Bohmian velocities are observationally preferred. 
[Show abstract] [Hide abstract]
ABSTRACT: In 1930, Einstein argued against the consistency of the time–energy uncertainty relation by discussing a thought experiment involving a measurement of the mass of the box which emitted a photon. Bohr seemingly prevailed over Einstein by arguing that Einstein's own general theory of relativity saves the consistency of quantum mechanics. We revisit this thought experiment from a modern point of view at a level suitable for an undergraduate readership and find that neither Einstein nor Bohr was correct. Instead, this thought experiment should be thought of as an early example of a system demonstrating nonlocal 'EPR' quantum correlations, five years before the famous Einstein–Podolsky–Rosen paper.European Journal of Physics 06/2012; 33(5):1089. DOI:10.1088/01430807/33/5/1089 · 0.62 Impact Factor 
[Show abstract] [Hide abstract]
ABSTRACT: In classical relativistic mechanics, a "preferred" proper direction in spacetime for each particle is determined by the direction of its 4momentum. Analogously, for each quantum particle we find a local direction uniquely determined by the manyparticle wave function, which for each particle defines the proper foliation of spacetime. This can be used to formulate a relativisticcovariant version of Bohmian mechanics, with equivariant probability density on proper hypersurfaces. 
[Show abstract] [Hide abstract]
ABSTRACT: A general formulation of classical relativistic particle mechanics is presented, with an emphasis on the fact that superluminal velocities and nonlocal interactions are compatible with relativity. Then a manifestly relativisticcovariant formulation of relativistic quantum mechanics (QM) of fixed number of particles (with or without spin) is presented, based on manytime wave functions and the spacetime probabilistic interpretation. These results are used to formulate the Bohmian interpretation of relativistic QM in a manifestly relativisticcovariant form. The results are also generalized to quantum field theory (QFT), where quantum states are represented by wave functions depending on an infinite number of spacetime coordinates. The corresponding Bohmian interpretation of QFT describes an infinite number of particle trajectories. Even though the particle trajectories are continuous, the appearance of creation and destruction of a finite number of particles results from quantum theory of measurements describing entanglement with particle detectors. 
Article: Solipsistic hidden variables
[Show abstract] [Hide abstract]
ABSTRACT: We argue that it is logically possible to have a sort of both reality and locality in quantum mechanics. To demonstrate this, we construct a new quantitative model of hidden variables (HV's), dubbed solipsistic HV's, that interpolates between the orthodox noHV interpretation and nonlocal Bohmian interpretation. In this model, the deterministic pointparticle trajectories are associated only with the essential degrees of freedom of the observer, and not with the observed objects. In contrast with Bohmian HV's, nonlocality in solipsistic HV's can be substantially reduced down to microscopic distances inside the observer. Even if such HV's may look philosophically unappealing to many, the mere fact that they are logically possible deserves attention. 
Article: Hidden Variables with Nonlocal Time
[Show abstract] [Hide abstract]
ABSTRACT: To relax the apparent tension between nonlocal hidden variables and relativity, we propose that the observable proper time is not the same quantity as the usual propertime parameter appearing in local relativistic equations. Instead, the two proper times are related by a nonlocal rescaling parameter proportional to ψ2, so that they coincide in the classical limit. In this way particle trajectories may obey local relativistic equations of motion in a manner consistent with the appearance of nonlocal quantum correlations. To illustrate the main idea, we first present two simple toy models of local particle trajectories with nonlocal time, which reproduce some nonlocal quantum phenomena. After that, we present a realistic theory with a capacity to reproduce all predictions of quantum theory.Foundations of Physics 02/2011; 42(5). DOI:10.1007/s1070101296312 · 1.14 Impact Factor 
[Show abstract] [Hide abstract]
ABSTRACT: The fact that canonical quantum gravity does not possess a fundamental notion of time implies that the theory is unitary in a trivial sense. At the fundamental level, this trivial unitarity leaves no room for a blackhole information loss. Yet, a phenomenological loss of information may appear when some matter degrees of freedom are reinterpreted as a clocktime. This explains how both fundamental unitarity and phenomenological information loss may peacefully coexist, which offers a resolution of the blackhole information paradox. 
[Show abstract] [Hide abstract]
ABSTRACT: A simple relativistic quantum hiddenvariable theory of particle trajectories, similar to the Bohm theory but without nonlocal forces between the particles, is proposed. To provide compatibility with statistical predictions of quantum mechanics one needs to assume the initial probability density psi^2 of particle positions in spacetime, which is the only source of nonlocality in the theory. This demonstrates that the usual Bohm hiddenvariable theory contains much more nonlocality than required by the Bell theorem. Comment: 3 pages
Publication Stats
742  Citations  
119.40  Total Impact Points  
Top Journals
Institutions

2000–2014

Ruđer Bošković Institute
Zagrabia, Grad Zagreb, Croatia


2005–2006

Institute of Physics, Zagreb
Zagrabia, Grad Zagreb, Croatia


1999–2006

Ruder Boskovic Institute
Zagrabia, Grad Zagreb, Croatia
