Quantum Universe Research Articles

A vector quantization approach to universal noiseless coding and quantization

A two-stage code is a block code in which each block of data is coded in two stages: the first stage codes the identity of a block code among a collection of codes, and the second stage codes the data using the identified code. The collection of codes may be noiseless codes, fixed-rate quantizers, or variable-rate quantizers. We take a vector quantization approach to two-stage coding, in which the first stage code can be regarded as a vector quantizer that quantizes the input data of length n to one of a fixed collection of block codes. We apply the generalized Lloyd algorithm to the first-stage quantizer, using induced measures of rate and distortion, to design locally optimal two-stage codes. On a source of medical images, two-stage variable-rate vector quantizers designed in this way outperform standard (one-stage) fixed-rate vector quantizers by over 9 dB. The tail of the operational distortion-rate function of the first-stage quantizer determines the optimal rate of convergence of the redundancy of a universal sequence of two-stage codes. We show that there exist two-stage universal noiseless codes, fixed-rate quantizers, and variable-rate quantizers whose per-letter rate and distortion redundancies converge to zero as (k/2)n/sup -1/ log n, when the universe of sources has finite dimension k. This extends the achievability part of Rissanen's theorem from universal noiseless codes to universal quantizers. Further, we show that the redundancies converge as O(n/sup -1/) when the universe of sources is countable, and as O(n/sup -1+/spl epsiv//) when the universe of sources is infinite-dimensional, under appropriate conditions.

On the cost of finite block length in quantizing unbounded memoryless sources

The problem of fixed-rate block quantization of an unbounded real memoryless source is studied. It is proved that if the source has a finite sixth moment, then there exists a sequence of quantizers Q/sub n/ of increasing dimension n and fixed rate R such that the mean squared distortion /spl Delta/(Q/sub n/) is bounded as /spl Delta/(Q/sub n/)/spl les/D(R)+O(/spl radic/(log n/n)), where D(R) is the distortion-rate function of the source. Applications of this result include the evaluation of the distortion redundancy of fixed-rate universal quantizers, and the generalization to the non-Gaussian case of a result of Wyner on the transmission of a quantized Gaussian source over a memoryless channel.

The rate loss in the Wyner-Ziv problem

The rate-distortion function for source coding with side information at the decoder (the "Wyner-Ziv problem") is given in terms of an auxiliary random variable, which forms a Markov chain with the source and the side information. This Markov chain structure, typical to the solution of multiterminal source coding problems, corresponds to a loss in coding rate with respect to the conditional rate-distortion function, i.e., to the case where the encoder is fully informed. We show that for difference (or balanced) distortion measures, this loss is bounded by a universal constant, which is the minimax capacity of a suitable additive-noise channel. Furthermore, in the worst case, this loss is equal to the maximin redundancy over the rate-distortion function of the additive noise "test" channel. For example, the loss in the Wyner-Ziv problem is less than 0.5 bit/sample in the squared-error distortion case, and it is less than 0.22 bit for a binary source with Hamming distance. These results have implications also in universal quantization with side information, and in more general multiterminal source coding problems.

Dimensional reduction in a quantum universe from the viewpoint of a minisuperspace model

We solve the Wheeler-DeWitt equation of a minisuperspace model for the wave function of the Universe as expansions in powers of the Planck mass, in several ways. It is shown that, within a minisuperspace approximation, the wave functions in low order in our expansions are a good approximation for every small radius (0<a≪1), wherea is the cosmic-scale factor. This may mean that a «new phase» (the dynamical system described by the three-dimensional quantum Einstein gravity) exists at the very early stage of the evolution of the Universe.

The properties of neurognosis

An important concept in biogenetic structural theory is neurogenesis. It refers to the initial, inherited organization of neural models from which more developed models grow. The world of experience and knowledge, termed the cognized environment, develops from neurognostic structures in the brain. The development of models must address Piaget's two requirements of conservation and adaptation. The brain is the premier organ of “exaptation” in Gould's sense. Neurogenesis is thus an evolutionary process realized in ontogenesis. It explains universal patterns found in cross-cultural behavior, and provides the primitive realism that is found in knowledge systems of people everywhere. This primitive realism includes knowledge of the structure of the quantum universe, which is represented in the symbolism of traditional cosmologies.

The time surface term in quantum gravity

The role of the time surface term in the ADM Hamiltonian formulation of general relativity is investigated. We show that the variable contained in the time surface term (the scale factor) plays the role of a time-like variable. The conjugated variable represents the energy density in the reduced phase space, where the Schrödinger-like equation for a wave function is derived. The contribution from the surface term to the phase of the wave function allows us to define the phase time of the quantum Universe so that it coincides with the proper time as an invariant interval for the classical dust filled Universe. The quantum scenario of the evolution of the Universe filled in by the Weinberg-Salam fields is considered. The wave function of the early Universe as the functional from the Higgs fields and scale factor realizes the unitary irreducible representation of the SO(4, 1) group. The elementary particle masses are determined by the angles of the scale-scalar field mixing.

Preferred basis in quantum theory and the problem of classicalization of the quantum Universe.

We revive an old proposal of Zeh for the preferred basis in the many-worlds interpretation of quantum mechanics. The algorithm for the basis reduces to the eigenvalue problems for density matrices of subsystems forming the whole system under consideration. We generalize this procedure to the case of degenerate eigenvalues of reduced density matrices. A semiclassical calculational method for these eigenvalues is developed and applied to some model problems. The classical properties of elements of the preferred basis are investigated. It is shown that classicality exists only in some part of many-worlds branches. Moreover, it depends crucially on the initial conditions and Hamiltonians and under some circumstances turns out to be a temporary phenomenon. Applications of the preferred-basis proposal to quantum cosmology are discussed. The relation between the preferred-basis approach and quantum-histories approach is discussed.

Gaugeless reduction of gravity and the evolution of the Universe.

The physical phase space of Einstein gravity with the Dirac-Arnowitt-Deser-Misner metric is constructed without using a gauge-fixing condition by explicitly resolving the constraints for nonphysical fields. As a result, from the reduced Einstein action we get a new energy-momentum tensor for independent dynamical fields. The corresponding energy and time are in direct analogy with the ``spectral energy'' and ``observable time'' for a relativistic particle. We discuss the photon and graviton excitations in the reduced theory and the ``spectral history'' of the evolution of the quantum Universe from inflation until the classical Friedman stage.

Fixed-rate universal lossy source coding and rates of convergence for memoryless sources

A fixed-rate universal lossy coding scheme is introduced for independent and identically distributed (i.i.d.) sources. It is shown for finite alphabet sources and arbitrary single letter distortion measures that as the sample size n grows the expected distortion obtained using this universal scheme converges to Shannon's distortion rate function D(R) at a rate O(log n/n). The scheme can be extended to universal quantization of real i.i.d sources subject to a squared error criterion. It is shown in this case that the per-letter distortion converges to D(R) at a rate O(/spl radic/(log n/n)) both in expectation and almost surely for any real-valued bounded i.i.d. source.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Arrow of time in a recollapsing quantum universe.

We argue that the Wheeler-DeWitt equation with a consistent boundary condition is only compatible with an arrow of time that formally reverses in a recollapsing universe. To recover a classically recollapsing universe in terms of wave packets, we impose the usual boundary condition of excluding exponentially increasing wave functions for large scale factors. Consistency of these opposite arrows is then facilitated by quantum effects in the region of the classical turning point. We also discuss in this context the meaning of the time-asymmetric expression used in the definition of ``consistent histories.'' Since gravitational time dilation diverges at horizons, one has to conclude that collapsing matter must start reexpanding ``anticausally'' (controlled by the reversed arrow) in this scenario before horizons or singularities can form. There would then also be no mass inflation nor any information loss paradox.

Quantum Hall states of Cooper pairs and vortices in Josephson arrays

We consider regular two-dimensional arrays of small Josephson junctions ( E C ∼ E J) in a transverse magnetic field. The dynamics of this system can be described in terms of interacting quantum particles-charges (for small E J) or vortices (for large E J). We show that at low concentrations of the particles, n ⪡ Λ -2, i.e. in the limit when the range Λ of the interaction is short, the system is equivalent to a Bose gas with weak contact repulsive interaction. The ground state in a strong magnetic field is described by the Laughlin type wave function with even powers. We present numerical results for the largest plateau in the particle density at v = 1 2 and also a toy model that enables us to develop the picture of all plateaus. The Hall conductance σ xy of the array shows the universal quantization at least at the values (2 e) 2/2 mh for small E J and at the values 2 m(2 e) 2/ h for large E J .

Literature and Science

List of illustrations List of contributors Acknowledgements Frontispiece Editor's introduction: The Sphinx and the Muses: the third culture Part I. Literature and Science: 1. Literary Chinese as a scientific language. A selection from the concluding volume of Science and Civilisation in China. With illustrations Joseph Needham and Kenneth Robinson 2. 'The names of things not generally known ...': scientists, translators and terminology in the age of Newton L. G. Kelly 3. The poet's senses: G. B. Marino's epic poem L'Adone and the new science Maurice Slawinski 4. Science and supernaturalism: Sir David Brewster and Sir Walter Scott. With illustrations Frederick Burwick 5. Helmholtz, Tyndall, Gerard Manley Hopkins: leaps of the prepared imagination Gillian Beer 6. The hermeneutics of extinction: denial and discovery in scientific literature Joel Black 7. Beckett and science: Watt and the quantum universe Angela Montgomery Part II. Literature and Translation: 8. L'Experience de traduire: Verlaine's Femmes/Hombres Alistair Elliot 9. Notes on the Theory of Literary History Translated with an introduction by Ian Fairley Gyoergy Lukacs Part III. Essay Reviews: 10. Bacon among the literati: science and language Brian Vickers 11. A new discipline? Essays in 'literature and science' Roy Porter Bibliographies: Books and periodicals received Andrew Milne Bibliography of Comparative Literature in Britain and Ireland 1988 Joseph Th. Leerssen Special bibliography: Technical translation in England, 1640-1800 L. G. Kelly.

Fiction in the Quantum Universe

Fiction in the Quantum Universe

Fiction in the Quantum Universe.

Fiction in the Quantum Universe.

Donald Barthleme: An Exhibition , and: Dissident Postmodernists: Barthleme, Coover, Pynchon , and: Fiction in the Quantum Universe , and: Marginal Forces/Cultural Centers: Tolson, Pynchon, and the Politics of the Canon (review)

Reviewed by: Donald Barthleme: An Exhibition, and: Dissident Postmodernists: Barthleme, Coover, Pynchon, and: Fiction in the Quantum Universe, and: Marginal Forces/Cultural Centers: Tolson, Pynchon, and the Politics of the Canon Alan Nadel Jerome Klinkowitz . Donald Barthleme: An Exhibition. Durham: Duke UP, 1991. 157 pp. No price given. Paul Maltby . Dissident Postmodernists: Barthleme, Coover, Pynchon. Philadelphia: U of Pennsylvania P, 1991. 215 pp. No price given. Susan Strehle . Fiction in the Quantum Universe. Chapel Hill: U of North Carolina P, 1992. 293 pp. $45.00 cloth, $15.00 paper. Michael Bérubé . Marginal Forces/Cultural Centers: Toison, Pynchon, and the Politics of the Canon. Ithaca: Cornell UP, 1992. 362 pp. No price given. When the late William Stafford first asked me to review books for Modern Fiction Studies, he explained the policy at the time: that the reviews, always covering two or more books, were to be essays organized around a central theme. "If you can't find a rationale," he added, "make one up." This bit of meta-commentary about MFS reviews comes to mind because the four books at hand are most united by the question of what constitutes a rationale for commentary. To some degree, all four books question the role of writing, the status of books, the power of language. They do so in several ways: by trying to delimit, privilege, or thematize specific aspects of postmodernism; by trying to shape the canons of specific postmodern writers, or by trying to canonize the shaping of these writers; by trying to privilege the politics of the writers' canons or deprivilege the politics of canonicity. As a group, these books contain many interesting insights and telling details. What each lacks, however, is exactly what its tries to provide for the authors it discusses: a sustained, coherent approach. If a single-authored book should have a central argument, advanced by each chapter, an argument that aims to persuade the reader and that justifies its size and scope, then each of these books falls somewhat short, while displaying other notable merits. Donald Barthleme: An Exhibition is perhaps the most comprehensive discussion of Barthleme to date, and its author, Jerome Klinkowitz, knows as much about Barthleme—and perhaps about contemporary fiction—as anyone in America. Despite (or perhaps because of) this knowledge, the book lacks a central thesis, it's only unifying idea being that The Dead Father ("an artistically complete yet radically postmodern novel") is Barthleme's [End Page 384] masterpiece, against which his other work can be gauged. So dominant is this idea that in the 124 pages of text not directly devoted to discussing The Dead Father, it is mentioned over 40 times—or an average of once every three pages—often to tell us that the story being discussed in one way or another is like or unlike it. The discussion of The Dead Father reverses the process. In Snow White, for example, what was fragmented in the The Dead Father is "focused on a clear simple action concerning a central character so dominant that his very presence is a signal of what needs to be done. As a tale, The Dead Father is virtually prototypical in form." Klinkowitz likes the fact that in The Dead Father Barthleme "uses commentary not as a reflection of the novel's action but as a device to make that action all the more integral. His central character only has to be in order for the narrative to get under way and take shape." Thus Klinkowitz moves through the Barthelme canon, more or less chronologically, providing insights of a comparable order. A common feature of the stories in Unspeakable Practices, Unnatural Acts, he tells us, "is their performative exuberance"; they also have "a decided note of impending exhaustion." City Life, Sadness, and Guilty Pleasures are collections in which the "narratives are sustained, not by technique or theme alone . . . but with an integral combination of the two." The mannerist detail in the novel Paradise "remains postmodern thanks to Barthleme's ability to weave these elements as a texture of signs rather than just references." Nevertheless, that novel is "a narrative fated to deconstruct itself." Barthleme's short fiction in the fourteen years...

Fiction in the quantum universe

In this outstanding book Susan Strehle argues that a new fiction has developed from the influence of modern physics. She calls this new fiction actualism, and within that framework she offers a critical analysis of major novels by Thomas Pynchon, Robert Coover, William Gaddis, John Barth, Margaret Atwood, and Donald Barthelme. According to Strehle, the actualists balance attention to questions of art with an engaged meditation on the external, actual world. While these actualist novels diverge markedly from realistic practice, Strehle claims that they do so in order to reflect more acutely what we now understand as real. Reality is no longer realistic; in the new physical or quantum universe, reality is discontinuous, energetic, relative, statistical, subjectively seen, and uncertainly known -- all terms taken from new physics. Actualist fiction is characterized by incompletions, indeterminacy, and open endings unsatisfying to the readerly wish for fulfilled promises and completed patterns. Gravity's Rainbow , for example, ends not with a period but with a dash. Strehle argues that such innovations in narrative reflect on twentieth-century history, politics, science, and discourse.

On universal quantization by randomized uniform/lattice quantizers

Uniform quantization with dither, or lattice quantization with dither in the vector case, followed by a universal lossless source encoder (entropy coder), is a simple procedure for universal coding with distortion of a source that may take continuously many values. The rate of this universal coding scheme is examined, and a general expression is derived for it. An upper bound for the redundancy of this scheme, defined as the difference between its rate and the minimal possible rate, given by the rate distortion function of the source, is derived. This bound holds for all distortion levels. Furthermore, a composite upper bound on the redundancy as a function of the quantizer resolution that leads to a tighter bound in the high rate (low distortion) case is presented. >

Momentum of ϕ Field and Inflation11The project supported by National Natural Science Foundation of China.

With quantum mechanical method, we discuss the metastable states of the quantum universe, and give two eigenstates corresponding to nonzero and zero conjugate momenta Pϕ under the assumption of p = -5, where p is the ordering factor. Analyses for their classical evolution are made, and there comes a conclusion: The momentum of the scalar field of quantum state has very little effect on its later classical evolution. This gives a favourable support to the classical theory of inflation.

The self-measurement of the universe and the concept of time in quantum cosmology

The dynamics of the quantum universe under self-measurement is investigated in the framework of the path-integral approach to quantum theory of continuous measurements. The corresponding amplitude (propagator) is evaluated explicitly for a simple superspace model. It is shown that the picture of time evolution of the quantum universe naturally emerges as a result of its self-measurement. The Wheeler-DeWitt dynamics holds for small times when the effect of measurement can be neglected and time dependence disappears.

Holomorphic wave function of the Universe.

The quantum behavior of the vacuum Bianchi type-IX universe with the cosmological constant is investigated in terms of the Ashtekar variables. An exact solution to the quantum Hamiltonian constraint in the holomorphic representation is given. This solution reduces to the Hartle-Hawking wave function in the spatially isotropic sector and extends in the triad representation to the classically forbidden region where the determinant of the spatial metric becomes negative. The analysis of the quantum Robertson-Walker universe indicates that if the superspace is extended to such a classically forbidden region, the holomorphic representation picks up some restricted class of solutions in general. This observation leads to a new ansatz on the boundary condition of the Universe. In particular, the behavior of the Lorentzian and Euclidean WKB orbits corresponding to the solution suggests a new picture on the semiclassical behavior of the quantum Universe: that the Universe is created from an ensemble of Euclidean mother spacetimes. Further it is pointed out that the solution is a restriction to the spatially homogeneous sector of an almost exact solution to all the quantum constraints in the holomorphic representation for generic vacuum spacetime with the cosmological constant. The latter generic solution has a WKB structure for which the phase is proportional to the Chern-Simons functional.