Publications (13)46.35 Total impact
 [Show abstract] [Hide abstract]
ABSTRACT: It has been suggested in the literature that spatial coherence of the wave function can be dynamically suppressed by fluctuations in the gravity of spacetime. These fluctuations represent the minimal uncertainty that is present when one probes spacetime geometry with a quantum probe. Two similar models have been proposed, one by Di\'osi [Dmodel] and one by Karolyhazy and collaborators [Kmodel], based on apparently unrelated minimal spacetime bounds. The two models arrive at somewhat different expressions for the dependence of the localization coherence length on the mass and size of the quantum object. In the present article we compare and contrast the two models. We show that under certain conditions the minimal spacetime bounds in the two models can be derived one from the other. We also derive the twopoint correlation for the fluctuation potential in the Kmodel, and show that it is nonwhite noise, unlike in the Dmodel, where the corresponding correlation is white noise in time. This seems to be the origin of the different results in the two models. We derive the nonMarkovian master equation for the Kmodel. We argue that the minimal spacetime bound cannot predict the noise correlation uniquely, and additional criteria are necessary to accurately determine the effects of gravitationally induced decoherence.08/2014;  [Show abstract] [Hide abstract]
ABSTRACT: The inflationary paradigm provides a mechanism to generate the primordial perturbations needed to explain the observed large scale structures in the universe. Inflation traces back all the inhomogeneities to quantum fluctuations although the structures look classical today. Squeezing of primordial quantum fluctuations along with the mechanism of decoherence accounts for many aspects of this quantum to classical transition, although it remains a matter of debate as to whether this is sufficient to explain the issue of realization of a single outcome (i.e. the issue of macroobjectification) from a quantum ensemble given that the universe is a closed system. A similar question of emergence of classical behavior of macroscopic objects exists also for laboratory systems and apart from decoherence there have been attempts to resolve this issue through Continuous Spontaneous Localization (CSL), which is a stochastic nonlinear modification of the nonrelativistic Schr\"{o}dinger equation. Recently, Martin {\it et al.} have investigated whether a CSLlike mechanism with a constant strength parameter, when the MukhanovSasaki variable is taken as the "collapseoperator", can explain how the primordial quantum perturbations generated during inflation become classical. Within the scope of their assumptions they essentially come to a negative conclusion. In the present work, we generalize their analysis by allowing the CSL strength parameter to depend on physical scales so as to capture the CSL amplification mechanism. We show that such a generalization provides a mechanism for macroobjectification (i.e. classicalization) of the inflationary quantum perturbations, while also preserving scale invariance of the power spectrum and phase coherence of superhorizon perturbation modes in a particular class of these models.Physical review D: Particles and fields 04/2013; 88(8).  [Show abstract] [Hide abstract]
ABSTRACT: Continuous Spontaneous Localization (CSL) model of Quantum Mechanics modifies Schr\"{o}dinger equation by adding nonlinear stochastic terms due to which the total energy of a system increases with a constant rate which is proportional to the collapse rate $\lambda$. Thus applying CSL model to cosmological scenarios can change the thermal behaviour of the particles during evolution and we will put constraints on $\lambda$ by considering several cosmological scenarios.02/2013;  [Show abstract] [Hide abstract]
ABSTRACT: This brief article reviews stochastic processes as relevant to dynamical models of wavefunction collapse, and is supplemental material for the review article arXiv:1204.432512/2012;  [Show abstract] [Hide abstract]
ABSTRACT: We attempt to calculate the point separated Noise Kernel for self similar Tolman Bondi metric, using a method similar to that developed by Hu et. al for ultrastatic metrics referring to work by Page. In case of formation of a naked singularity, the noise kernel thus obtained is found to be regular except on the Cauchy horizon, where it diverges. The behaviour of the noise in case of the formation of a covered singularity is found to be regular.Physical review D: Particles and fields 10/2012; 87(8).  [Show abstract] [Hide abstract]
ABSTRACT: Models of spontaneous wave function collapse modify the linear Schrödinger equation of standard quantum mechanics by adding stochastic nonlinear terms to it. The aim of such models is to describe the quantum (linear) nature of microsystems along with the classical nature (violation of superposition principle) of macroscopic ones. The addition of such nonlinear terms in the Schrödinger equation leads to nonconservation of energy of the system under consideration. Thus, a striking feature of collapse models is to heat nonrelativistic particles with a constant rate. If such a process is physical, then it has the ability to perturb the wellunderstood thermal history of the universe. In this article we will try to investigate the impacts of such heating terms, according to the continuous spontaneous localization model, on the standard evolution of nonrelativistic matter and on the formation of cosmic microwave background radiation. We will also put constraints on the continuous spontaneous localization collapse rate λ by considering that the standard evolution of nonrelativistic matter is not hampered and the observed precise blackbody spectrum of cosmic microwave background radiation would not get distorted (in the form of μtype and ytype distortions) so as to violate the observed bounds.Physical review D: Particles and fields 09/2012; 86(6).  [Show abstract] [Hide abstract]
ABSTRACT: In this paper we discuss the entropy of quantum black holes in the LQG formalism when the number of punctures on the horizon is treated as a quantum hair, that is we compute the black hole entropy in the grand canonical (area) ensemble. The entropy is a function of both the average area and the average number of punctures and bears little resemblance to the BekensteinHawking entropy. In the thermodynamic limit, both the "temperature" and the chemical potential can be shown to be functions only of the average area per puncture. At a fixed temperature, the average number of punctures becomes proportional to the average area and we recover the BekensteinHawking areaentropy law to leading order provided that the BarberoImmirzi parameter, $\gamma$, is appropriately fixed. This also relates the chemical potential to $\gamma$. We obtain a subleading correction, which differs in signature from that obtained in the microcanonical and canonical ensembles in its sign but agrees with earlier results in the grand canonical ensemble.Physical review D: Particles and fields 05/2012; 86(4).  [Show abstract] [Hide abstract]
ABSTRACT: We extend previous results on the reflection and transmission of selfgravitating dust shells across the apparent horizon during quantum dust collapse to nonmarginallybound dust collapse in arbitrary dimensions with a negative cosmological constant. We show that the Hawking temperature is independent of the energy function and that the wave functional describing the collapse is well behaved at the HawkingPage transition point. Thermal radiation from the apparent horizon appears as a generic result of nonmarginal collapse in AdS spacetime owing to the singular structure of the Hamiltonian constraint at the apparent horizon.Physical review D: Particles and fields 04/2012; 87(2).  [Show abstract] [Hide abstract]
ABSTRACT: Quantum mechanics is an extremely successful theory that agrees with every experiment. However, the principle of linear superposition, a central tenet of the theory, apparently contradicts a commonplace observation: macroscopic objects are never found in a linear superposition of position states. Moreover, the theory does not really explain as to why during a quantum measurement, deterministic evolution is replaced by probabilistic evolution, whose random outcomes obey the Born probability rule. In this article we review an experimentally falsifiable phenomenological proposal, known as Continuous Spontaneous Collapse: a stochastic nonlinear modification of the Schr\"{o}dinger equation, which resolves these problems, while giving the same experimental results as quantum theory in the microscopic regime. Two underlying theories for this phenomenology are reviewed: Trace Dynamics, and gravity induced collapse. As one approaches the macroscopic scale, the predictions of this proposal begin to differ appreciably from those of quantum theory, and are being confronted by ongoing laboratory experiments that include molecular interferometry and optomechanics. These experiments, which essentially test the validity of linear superposition for large systems, are reviewed here, and their technical challenges, current results, and future prospects summarized. We conclude that it is likely that over the next two decades or so, these experiments can verify or rule out the proposed stochastic modification of quantum theory.Review of Modern Physics 04/2012; 85(2). · 42.86 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: There ought to exist a description of quantum field theory which does not depend on an external classical time. To achieve this goal, in a recent paper we have proposed a noncommutative special relativity in which spacetime and matter degrees of freedom are treated as classical matrices with arbitrary commutation relations, and a spacetime line element is defined using a trace. In the present paper, following the theory of Trace Dynamics, we construct a statistical thermodynamics for the noncommutative special relativity, and show that one arrives at a generalized quantum dynamics in which space and time are nonclassical and have an operator status. In a future work, we will show how standard quantum theory on a classical spacetime background is recovered from here.Foundations of Physics 03/2012; 42(12). · 1.14 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We compute the canonical partition for quantum black holes in the approach of Loop Quantum Gravity (LQG). We argue that any quantum theory of gravity in which the horizon area is built of noninteracting constituents cannot yield qualitative corrections to the BekensteinHawking (BH) area law, but corrections to the area law can arise as a consequence additional constraints inducing interactions between the constituents. In LQG this is implemented by requiring spherical horizons. The canonical approach for LQG favours a logarithmic correction to the BH law with a coefficient of 1/2, independently of the area spectrum. Our initial calculation of the partition function uses certain approximations that, we show, do not qualitatively affect the expression for the black hole entropy. We later discuss the quantitative corrections to these results when the simplifying approximations are relaxed and the full LQG spectrum is dealt with. We show how these corrections can be recovered to all orders in perturbation theory. However, the convergence properties of the perturbative series remains unknown.Physical review D: Particles and fields 02/2012; 85(10).  [Show abstract] [Hide abstract]
ABSTRACT: Trace Dynamics is a classical dynamical theory of noncommuting matrices in which cyclic permutation inside a trace is used to define the derivative with respect to an operator. We use the methods of Trace Dynamics to construct a noncommutative special relativity. We define a lineelement using the Trace over space–time coordinates which are assumed to be operators. The lineelement is shown to be invariant under standard Lorentz transformations, and is used to construct a noncommutative relativistic dynamics. The eventual motivation for constructing such a noncommutative relativity is to relate the statistical thermodynamics of this classical theory to quantum mechanics.Physics Letters A 10/2011; 375(43):37473750. · 1.63 Impact Factor 
Article: Nonlinear quantum mechanics, the superposition principle, and the quantum measurement problem
[Show abstract] [Hide abstract]
ABSTRACT: There are four reasons why our present knowledge and understanding of quantum mechanics could be regarded as incomplete. Firstly, the principle of linear superposition has not been experimentally tested for position eigenstates of objects having more than about a thousand atoms. Secondly, there is no universally agreed upon explanation for the process of quantum measurement. Thirdly, there is no universally agreed upon explanation for the observed fact that macroscopic objects are not found in superposition of position eigenstates. Fourthly, and perhaps most importantly, the concept of time is classical and hence external to quantum mechanics : there should exist an equivalent reformulation of the theory which does not refer to an external classical time. In this paper we argue that such a reformulation is the limiting case of a nonlinear quantum theory, with the nonlinearity becoming important at the Planck mass scale. Such a nonlinearity can provide insights into the problems mentioned above. We use a physically motivated model for a nonlinear Schrodinger equation to show that nonlinearity can help in understanding quantum measurement. We also show that while the principle of linear superposition holds to a very high accuracy for atomic systems, the lifetime of a quantum superposition becomes progressively smaller, as one goes from microscopic to macroscopic objects. This can explain the observed absence of position superpositions in macroscopic objects [lifetime is too small]. It also suggests that ongoing laboratory experiments maybe able to detect the finite superposition lifetime for mesoscopic objects, in the foreseeable future. Comment: Minor revision in Introduction. 23 pages. To appear in Pramana J. PhysPramana 12/2009; 76(1). · 0.72 Impact Factor
Publication Stats
42  Citations  
46.35  Total Impact Points  
Top Journals
Institutions

2009–2012

Tata Institute of Fundamental Research
Mumbai, Mahārāshtra, India
