[Show abstract][Hide abstract] ABSTRACT: We propose a new non-holographic formulation of AdS/CFT correspondence,
according to which quantum gravity on AdS and its dual non-gravitational field
theory both live in the same number D of dimensions. The field theory, however,
appears (D-1)-dimensional because the interactions do not propagate in one of
the dimensions. The D-dimensional action for the field theory can be identified
with the sum over (D-1)-dimensional actions with all possible values $\Lambda$
of the UV cutoff, so that the extra hidden dimension can be identified with
$\Lambda$. Since there are no interactions in the extra dimension, most of the
practical results of standard holographic AdS/CFT correspondence transcribe to
non-holographic AdS/CFT without any changes. However, the implications on
black-hole entropy change significantly. The maximal black-hole entropy now
scales with volume, while the Bekenstein-Hawking entropy is interpreted as the
minimal possible black-hole entropy. In this way, the non-holographic AdS/CFT
correspondence offers a simple resolution of the black-hole information
paradox, consistent with a recently proposed gravitational crystal.
[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 which-path information, then the internal-environment 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 which-path information. Extrapolation to a hypothetical interference experiment with a conscious object implies that being a Schrödinger cat would be like being an ordinary cat living in a box without any information about the world external to the box.
European Journal of Physics 07/2015; 36(4). DOI:10.1088/0143-0807/36/4/045003 · 0.63 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 energy-momentum conservation, is widely believed to be a strong argument against non-unitarity 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 non-unitary evolution without violating energy-momentum conservation. Moreover, since energy-momentum is the source of gravity, we argue that energy-momentum is necessarily conserved for a large class of non-unitary systems with gravity. Finally, we explicitly calculate the Lindblad operators for non-unitary Hawking radiation and show that they conserve energy-momentum.
Journal of Cosmology and Astroparticle Physics 04/2015; 2015(04):002-002. DOI:10.1088/1475-7516/2015/04/002 · 5.81 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 energy-momentum conservation, is
widely believed to be a strong argument against non-unitarity 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 non-unitary evolution without violating
energy-momentum conservation. Moreover, since energy-momentum is the source of
gravity, we argue that energy-momentum is necessarily conserved for a large
class of non-unitary systems with gravity. Finally, we explicitly calculate the
Lindblad operators for non-unitary Hawking radiation and show that they
conserve energy-momentum.
[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 time-evolution 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 non-unitary Hawking radiation to a unitary phenomenon, which avoids the black-hole information paradox.
International Journal of Quantum Information 11/2014; 12(07n08):1560001. DOI:10.1142/S0219749915600011 · 0.88 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: In the literature one often finds the claim that there is no such thing as an
energy-momentum tensor for the gravitational field, and consequently, that the
total energy-momentum conservation can only be defined in terms of a
gravitational energy-momentum pseudo-tensor. I make a trivial observation that
such a conclusion can be avoided by relaxing the assumption that gravitational
energy-momentum tensor should only depend on first derivatives of the metric.
With such a relaxation, the Einstein equation directly leads to the result that
gravitational energy-momentum 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 time-evolution 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 non-unitary Hawking
radiation to a unitary phenomenon, which avoids the black-hole 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 which-path information, then the
internal-environment 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 which-path 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 · 6.13 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 non-standard bilinear combinations with well-defined transformation properties.
European Journal of Physics 03/2014; 35(3):035003. DOI:10.1088/0143-0807/35/3/035003 · 0.63 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 non-standard bilinear combinations with
well-defined 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.
[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 no-HV interpretation and nonlocal Bohmian interpretation. In this model, the deterministic point-particle 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 · 0.88 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 time-independent, the conditional wave function for a
subsystem depends on time through the time-dependent 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
time-dependent 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:10.1088/0143-0807/33/5/1089 · 0.63 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 4-momentum.
Analogously, for each quantum particle we find a local direction uniquely
determined by the many-particle wave function, which for each particle defines
the proper foliation of spacetime. This can be used to formulate a
relativistic-covariant 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
relativistic-covariant formulation of relativistic quantum mechanics (QM) of
fixed number of particles (with or without spin) is presented, based on
many-time wave functions and the spacetime probabilistic interpretation. These
results are used to formulate the Bohmian interpretation of relativistic QM in
a manifestly relativistic-covariant 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.
[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 no-HV interpretation and nonlocal Bohmian
interpretation. In this model, the deterministic point-particle 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.
[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 proper-time parameter appearing in local relativistic equations. Instead, the two proper times are related by a nonlocal rescaling parameter proportional to |ψ|2, 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/s10701-012-9631-2 · 1.03 Impact Factor