Cosmology with cosmic microwave background anisotropy

Measurements of CMB anisotropy and, more recently, polarization have played a very important role in allowing precise determination of various parameters of the ‘standard’ cosmological model. The expectation of the paradigm of inflation and the generic prediction of the simplest realization of inflationary scenario in the early Universe have also been established — ‘acausally’ correlated initial perturbations in a flat, statistically isotropic Universe, adiabatic nature of primordial density perturbations. Direct evidence for gravitational instability mechanism for structure formation from primordial perturbations has been established. In the next decade, future experiments promise to strengthen these deductions and uncover the remaining crucial signature of inflation — the primordial gravitational wave background.     

Continuity of a Quantum Stochastic Process

We investigate a quantum counterpart of the classical notion of a stochastic process continuous with probability one, and prove that the L ²-limit of quantum martingales ‘continuous with probability one’ is a quantum martingale ‘continuous with probability one’. Applications of this result to a number of concrete situations is presented.     

The Possibilist Transactional Interpretation and Relativity

A recent ontological variant of Cramer’s Transactional Interpretation, called “Possibilist Transactional Interpretation” or PTI, is extended to the relativistic domain. The present interpretation clarifies the concept of ‘absorption,’ which plays a crucial role in TI (and in PTI). In particular, in the relativistic domain, coupling amplitudes between fields are interpreted as amplitudes for the generation of confirmation waves (CW) by a potential absorber in response to offer waves (OW), whereas in the nonrelativistic context CW are taken as generated with certainty. It is pointed out that solving the measurement problem requires venturing into the relativistic domain in which emissions and absorptions take place; nonrelativistic quantum mechanics only applies to quanta considered as ‘already in existence’ (i.e., ‘free quanta’), and therefore cannot fully account for the phenomenon of measurement, in which quanta are tied to sources and sinks.     

Non-Violation of Energy Conditions in the Future Accelerated Universe Due to Quantum Effects

Here, an accelerated phantom model for the late universe is explored, which is free from future singularity. It is interesting to see that this model exhibits strong curvature for all time in future, unlike models with ‘big-rip singularity’ showing high curvature near singularity time only. So, quantum gravity effects grow dominant as time increases in late universe too. More importantly, it is demonstrated that quantum corrections to FRW equations lead to non-violation of ‘cosmic energy conditions’ of general relativity, which are violated for accelerating universe without these corrections.     

On the Orthocomplementation of State–Property–Systems of Contextual Systems

We adopt an operational approach to quantum mechanics in which a physical system is defined by the mathematical structure of its set of states and properties. We present a model in which the maximal change of state of the system due to interaction with the measurement context is controlled by a parameter which corresponds with the number N of possible outcomes in an experiment. In the case N=2 the system reduces to a model for the spin measurements on a quantum spin-1/2 particle. In the limit N→∞ the system is classical, i.e. the experiments are deterministic and its set of properties is a Boolean lattice. For intermediate situations the change of state due to measurement is neither ‘maximal’ (i.e. quantum) nor ‘zero’ (i.e. classical). We show that two of the axioms used in Piron’s representation theorem for quantum mechanics are violated, namely the covering law and weak modularity. Next, we discuss a modified version of the model for which it is even impossible to define an orthocomplementation on the set of properties. Another interesting feature for the intermediate situations of this model is that the probability of a state transition in general not only depends on the two states involved, but also on the measurement context which induces the state transition.     

Observability of the effects of curl-free magnetic vector potential on the macroscale and the nature of the ‘transition amplitude wave’

We discuss here the prediction, based on a formalism by the author, on the observable effects of a curl-free magnetic vector potential on the macroscale as against the microscale of the Aharonov-Bohm effect. A new quantum concept — the ‘transition amplitude wave’ — postulated in the formalism has already been shown to exhibit matter wave manifestations in the form of one-dimensional interference effects on the macroscale. It was predicted by the formalism that the same entity would lead to the detection of a curl-free magnetic vector potential on the macroscale. We describe here the manner of generation of this quantum entity in an inelastic scattering episode and work out an algorithm to observe this radically new phenomenon, the detection of a curl-free magnetic vector potential on the macroscale. We determine the various characteristic features of such an observation which can then be looked for experimentally so as to verify the predicted effect, establishing thereby the physical reality of the new quantum entity, and to fully validate the formalism predicting it. It is also shown that this ‘transition amplitude wave’ can be regarded as a novel kind of ‘quasiparticle’ excited in the charged particle trajectory as a consequence of the scattering episode.     

de Broglie-Bohm formulation of quantum mechanics, quantum chaos and breaking of time-reversal invariance

A recently developed unified theory of classical and quantum chaos, based on the de Broglie-Bohm (Hamilton-Jacobi) formulation of quantum mechanics is presented and its consequences are discussed. The quantum dynamics is rigorously defined to be chaotic if the Lyapunov number, associated with the quantum trajectories in de Broglie-Bohm phase space, is positive definite. This definition of quantum chaos which under classical conditions goes over to the well-known definition of classical chaos in terms of positivity of Lyapunov numbers, provides a rigorous unified definition of chaos on the same footing for both the dynamics. A demonstration of the existence of positive Lyapunov numbers in a simple quantum system is given analytically, proving the existence of quantum chaos. Breaking of the time-reversal symmetry in the corresponding quantum dynamics under chaotic evolution is demonstrated. It is shown that the rigorous deterministic quantum chaos provides an intrinsic mechanism towards irreversibility of the Schrodinger evolution of the wave function, without invoking ‘wave function collapse’ or ‘measurements’     

The Phase Transition of the Quantum Ising Model is Sharp

An analysis is presented of the phase transition of the quantum Ising model with transverse field on the d-dimensional hypercubic lattice. It is shown that there is a unique sharp transition. The value of the critical point is calculated rigorously in one dimension. The first step is to express the quantum Ising model in terms of a (continuous) classical Ising model in d+1 dimensions. A so-called ‘random-parity’ representation is developed for the latter model, similar to the random-current representation for the classical Ising model on a discrete lattice. Certain differential inequalities are proved. Integration of these inequalities yields the sharpness of the phase transition, and also a number of other facts concerning the critical and near-critical behaviour of the model under study.     

The Klein-Gordon Equation in Machian Model

The non-local Machian model is regarded as an alternative theory of gravitation which states that all particles in the Universe as a ‘gravitationally entangled’ statistical ensemble. It is shown that the Klein-Gordon equation can be derived within this Machian model of the universe. The crucial point of the derivation is the activity of the Machian energy background field which causing a fluctuation about the average momentum of a particle, the non-locality problem in quantum theory is addressed in this framework.     

What is Erased in the Quantum Erasure?

In this paper, we re-examine a series of gedanken welcher Weg (WW) experiments introduced by Scully, Englert and Walther that contain the essential ideas underlying the quantum eraser. For this purpose we use the Bohm model which gives a sharp picture of the behaviour of the atoms involved in these experiments. This model supports the thesis that interference disappears in such WW experiments, even though the centre of mass wave function remains coherent throughout the experiment. It also shows exactly what it means to say ‘that the interference can be restored by manipulating the WW detectors long after the atoms have passed’. It does not support Wheeler’s notion that ‘the past is undefined and undefinable without the observation (in the present)’.     

Lorentz cobordism. II

It is shown that ‘changes of topology’ (of spacelike sections) in the spacetime of classical general relativity are consistent with the following requirements: (i) stable causality, (ii) future causal geodesic completeness, and (iii) finite, positive energy density. This amounts to showing that the framework of classical general relativity encompasses ‘changes of topology’.     

Contextuality and Nonlocality in ‘No Signaling’ Theories

We define a family of ‘no signaling’ bipartite boxes with arbitrary inputs and binary outputs, and with a range of marginal probabilities. The defining correlations are motivated by the Klyachko version of the Kochen-Specker theorem, so we call these boxes Kochen-Specker-Klyachko boxes or, briefly, KS-boxes. The marginals cover a variety of cases, from those that can be simulated classically to the superquantum correlations that saturate the Clauser-Horne-Shimony-Holt inequality, when the KS-box is a generalized PR-box (hence a vertex of the ‘no signaling’ polytope). We show that for certain marginal probabilities a KS-box is classical with respect to nonlocality as measured by the Clauser-Horne-Shimony-Holt correlation, i.e., no better than shared randomness as a resource in simulating a PR-box, even though such KS-boxes cannot be perfectly simulated by classical or quantum resources for all inputs. We comment on the significance of these results for contextuality and nonlocality in ‘no signaling’ theories.     

The crossover from classical to quantum behavior in Duffing oscillator based on quantum state diffusion

The classical Duffing oscillator is a dissipative chaotic system, and so there is not a definite Hamiltonian. We quantize the Duffing oscillator on the basis of quantum state diffusion (QSD) which is a formulation for open quantum systems and a useful tool for analyzing nonlinear problems and classical limits. We can define a ‘Lyapunov exponent’, which corresponds to the classical one in the proper limit, and investigate the behavior of the system by varying the Planck constant effectively. We show that there exists a critical stage, where the behavior of the system crosses over from classical to quantum one.     

Quantum Probability’s Algebraic Origin

Max Born’s statistical interpretation made probabilities play a major role in quantum theory. Here we show that these quantum probabilities and the classical probabilities have very different origins. Although the latter always result from an assumed probability measure, the first include transition probabilities with a purely algebraic origin. Moreover, the general definition of transition probability introduced here comprises not only the well-known quantum mechanical transition probabilities between pure states or wave functions, but further physically meaningful and experimentally verifiable novel cases. A transition probability that differs from 0 and 1 manifests the typical quantum indeterminacy in a similar way as Heisenberg’s and others’ uncertainty relations and, furthermore, rules out deterministic states in the same way as the Bell-Kochen-Specker theorem. However, the transition probability defined here achieves a lot more beyond that: it demonstrates that the algebraic structure of the Hilbert space quantum logic dictates the precise values of certain probabilities and it provides an unexpected access to these quantum probabilities that does not rely on states or wave functions.     

Computational Power of Infinite Quantum Parallelism

Recent works have independently suggested that quantum mechanics might permit procedures that fundamentally transcend the power of Turing Machines as well as of ‘standard’ Quantum Computers. These approaches rely on and indicate that quantum mechanics seems to support some infinite variant of classical parallel computing. We compare this new one with other attempts towards hypercomputation by separating (1) its %principal computing capabilities from (2) realizability issues. The first are shown to coincide with recursive enumerability; the second are considered in analogy to ‘existence’ in mathematical logic. PACS (2003): 03.67. Supported by DFG project Zi1009/1-1.     

Quantum Experimental Data in Psychology and Economics

We prove a theorem which shows that a collection of experimental data of probabilistic weights related to decisions with respect to situations and their disjunction cannot be modeled within a classical probabilistic weight structure in case the experimental data contain the effect referred to as the ‘disjunction effect’ in psychology. We identify different experimental situations in psychology, more specifically in concept theory and in decision theory, and in economics (namely situations where Savage’s Sure-Thing Principle is violated) where the disjunction effect appears and we point out the common nature of the effect. We analyze how our theorem constitutes a no-go theorem for classical probabilistic weight structures for common experimental data when the disjunction effect is affecting the values of these data. We put forward a simple geometric criterion that reveals the non classicality of the considered probabilistic weights and we illustrate our geometrical criterion by means of experimentally measured membership weights of items with respect to pairs of concepts and their disjunctions. The violation of the classical probabilistic weight structure is very analogous to the violation of the well-known Bell inequalities studied in quantum mechanics. The no-go theorem we prove in the present article with respect to the collection of experimental data we consider has a status analogous to the well known no-go theorems for hidden variable theories in quantum mechanics with respect to experimental data obtained in quantum laboratories. Our analysis puts forward a strong argument in favor of the validity of using the quantum formalism for modeling the considered psychological experimental data as considered in this paper.     

Quantum space-times in the year 2002

We review certain emergent notions on the nature of space-time from noncommutative geometry and their radical implications. These ideas of space-time are suggested from developments in fuzzy physics, string theory, and deformation quantization. The review focuses on the ideas coming from fuzzy physics. We find models of quantum space-time like fuzzy S ⁴ on which states cannot be localized, but which fluctuate into other manifolds like CP³. New uncertainty principles concerning such lack of localizability on quantum space-times are formulated. Such investigations show the possibility of formulating and answering questions like the probability of finding a point of a quantum manifold in a state localized on another one. Additional striking possibilities indicated by these developments is the (generic) failure of CPT theorem and the conventional spin-statistics connection. They even suggest that Planck’s ‘constant’ may not be a constant, but an operator which does not commute with all observables. All these novel possibilities arise within the rules of conventional quantum physics, and with no serious input from gravity physics.     

Quantum Isometry Groups: Examples and Computations

In this follow-up of [4], where the quantum isometry group of a noncommutative manifold has been defined, we explicitly compute such quantum groups for a number of classical as well as noncommutative manifolds including the spheres and the tori. It is also proved that the quantum isometry group of an isospectral deformation of a (classical or noncommutative) manifold is a suitable deformation of the quantum isometry group of the original (undeformed) manifold. The support from National Board of Higher Mathematics, India, is gratefully acknowledged. Partially supported by the project ‘Noncommutative Geometry and QuantumGroups’ funded by the Indian National Science Academy.     

Noncommutative gravity, a ‘no strings attached’ quantum-classical duality, and the cosmological constant puzzle

There ought to exist a reformulation of quantum mechanics which does not refer to an external classical spacetime manifold. Such a reformulation can be achieved using the language of noncommutative differential geometry. A consequence which follows is that the ‘weakly quantum, strongly gravitational’ dynamics of a relativistic particle whose mass is much greater than Planck mass is dual to the ‘strongly quantum, weakly gravitational’ dynamics of another particle whose mass is much less than Planck mass. The masses of the two particles are inversely related to each other, and the product of their masses is equal to the square of Planck mass. This duality explains the observed value of the cosmological constant, and also why this value is nonzero but extremely small in Planck units. Second Award in the 2008 Essay Competition of the Gravity Research Foundation.     

An Introduction to Many Worlds in Quantum Computation

The interpretation of quantum mechanics is an area of increasing interest to many working physicists. In particular, interest has come from those involved in quantum computing and information theory, as there has always been a strong foundational element in this field. This paper introduces one interpretation of quantum mechanics, a modern ‘many-worlds’ theory, from the perspective of quantum computation. Reasons for seeking to interpret quantum mechanics are discussed, then the specific ‘neo-Everettian’ theory is introduced and its claim as the best available interpretation defended. The main objections to the interpretation, including the so-called “problem of probability” are shown to fail. The local nature of the interpretation is demonstrated, and the implications of this both for the interpretation and for quantum mechanics more generally are discussed. Finally, the consequences of the theory for quantum computation are investigated, and common objections to using many worlds to describe quantum computing are answered. We find that using this particular many-worlds theory as a physical foundation for quantum computation gives several distinct advantages over other interpretations, and over not interpreting quantum theory at all.