From Heisenberg to Gödel via Chaitin

In 1927 Heisenberg discovered that the “more precisely the position is determined, the less precisely the momentum is known in this instant, and vice versa.” Four years later Gödel showed that a finitely specified, consistent formal system which is large enough to include arithmetic is incomplete. As both results express some kind of impossibility it is natural to ask whether there is any relation between them, and, indeed, this question has been repeatedly asked for a long time. The main interest seems to have been in possible implications of incompleteness to physics. In this note we will take interest in the converse implication and will offer a positive answer to the question: Does uncertainty imply incompleteness? We will show that algorithmic randomness is equivalent to a “formal uncertainty principle” which implies Chaitin’s information-theoretic incompleteness. We also show that the derived uncertainty relation, for many computers, is physical. In fact, the formal uncertainty principle applies to all systems governed by the wave equation, not just quantum waves. This fact supports the conjecture that uncertainty implies algorithmic randomness not only in mathematics, but also in physics.     

Solutions to Nonlocal Integrable Discrete Nonlinear Schr?dinger Equations via Reduction

Solutions to local and nonlocal integrable discrete nonlinear Schr?dinger(IDNLS) equations are studied via reduction on the bilinear form. It is shown that these solutions to IDNLS equations can be expressed in terms of the single Casorati determinant under different constraint conditions.     

Erratum to: Consistent LDA’ + DMFT—an Unambiguous Way to Avoid Double Counting Problem: NiO Test

JETP Letters - The name of the second author should read N. S. Pavlov     

From quantum chemistry to dissociation kinetics: what we need to know †

The relationship between rate constants for dissociation and the reverse association reactions and their potential energy surfaces is illustrated. The reaction systems e^? + SF₆ ? SF₆ ^? →SF₅ ^? + F, H + CH₃ ?CH₄, 2 CF₂ ? C₂F₄, H + O₂ →HO₂, HO + O ?HO₂ ? H + O₂, and C + HO →CHO are chosen as representative examples. The necessity to know precise thermochemical data is emphasised. The interplay between attractive and anisotropic components of the potentials influences the rate constants. Spin–orbit and electronic–rotational coupling in reactions between electronic open-shell radicals so far generally has been neglected, but is shown to have a marked influence on low temperature rate constants.     

Synchronized pendula: From Huygens’ clocks to chimera states

This topical issue collects contribution exemplifying the recent scientific progress in understanding the dynamics of coupled pendula. The individual papers focus on different questions of present day interest in theory and applications of systems of coupled oscillators. Both theoretical and experimental studies are presented.     

From the melt via mesomorphic and granular crystalline layers to lamellar crystallites: A major route followed in polymer crystallization?

Based on broad and detailed evidence from a large variety of experiments on several polymer systems carried out by other authors and ourselves, a novel concept for understanding the crystallization of polymers from the melt is developed. The experiments generally indicate that the formation and growth of the lamellar crystallites is a multi-step process passing over intermediate states. We suggest a specific route which is compatible with the observations. It is proposed that the initial step is always the creation of a mesomorphic layer which spontaneously thickens, up to a critical value, where it solidifies through a cooperative structural transition. The transition produces a granular crystalline layer, which transforms in the last step into homogeneous lamellar crystallites. The model leads to predictions about the temperature dependencies of the crystal thickness and the growth rate which are at variance with conventional views but in agreement with findings in recent experiments. Received 17 February 2000 and Received in final form 30 March 2000     

Einstein, Wigner and Feynman: From E=mc 2 to Feynman’s decoherence via Wigner’s little groups

The 20th-century physics starts with Einstein and ends with Feynman. Einstein introduced the Lorentz-covariant world with E=mc ². Feynman observed that fast-moving hadrons consist of partons which interact incoherently with external signals. If quarks and partons are the same entities observed in different Lorentz frames, the question then is why partons are incoherent while quarks are coherent. This is the most puzzling question Feynman left for us to solve. In this report, we discuss Wigner’s role in settling this question. Einstein’s E=mc ², which takes the form $E = \sqrt {m^2 + p^2 } $ , unifies the energy-momentum relations for massive and massless particles, but it does not take into account internal space-time structure of relativistic particles. It is pointed out Wigner’s 1939 paper on the inhomogeneous Lorentz group defines particle spin and gauge degrees of freedom in the Lorentz-covariant world. Within the Wigner framework, it is shown possible to construct the internal space-time structure for hadrons in the quark model. It is then shown that the quark model and the parton model are two different manifestations of the same covariant entity. It is shown therefore that the lack of coherence in Feynman’s parton picture is an effect of the Lorentz covariance.     

A Maple Package to Compute Lie Symmetry Groups and Symmetry Reductions of （1＋1）-Dimensional Nonlinear Systems

Armed with the computer algebra system Maple, using a direct algebraic substitution method, we obtain Lie point symmetries, Lie symmetry groups and the corresponding symmetry reductions of one component nonlinear integrable and nonintegrable equations only by clicking the ‘Enter＇ key. Abundant （1＋1）-dimensional nonlinear mathematical physical systems are analysed effectively by using a Maple package LieSYMGRP proposed by us.     

Consistent LDA’ + DMFT—an unambiguous way to avoid double counting problem: NiO test

We present a consistent way of treating a double counting problem unavoidably arising within the LDA + DMFT combined approach to realistic calculations of electronic structure of strongly correlated systems. The main obstacle here is the absence of systematic (e.g., diagrammatic) way to express LDA (local density approximation) contribution to exchange correlation energy appearing in the density functional theory. It is not clear then, which part of interaction entering DMFT (dynamical mean-field theory) is already taken into account through LDA calculations. Because of that, up to now there is no accepted unique expression for the double counting correction in LDA + DMFT. To avoid this problem we propose here the consistent LDA’ + DMFT approach, where LDA exchange correlation contribution is explicitly excluded for correlated states (bands) during self-consistent band structure calculations. What is left out of Coulomb interaction for those strongly correlated states (bands) is its non-local part, which is not included in DMFT, and the local Hartreelike contribution. Then the double counting correction is uniquely reduced to the local Hartree contribution. Correlations for strongly correlated states are then directly accounted for via the standard DMFT. We further test the consistent LDA’ + DMFT scheme and compare it with conventional LDA + DMFT calculating the electronic structure of NiO. Opposite to the conventional LDA + DMFT our consistent LDA’ + DMFT approach unambiguously produces the insulating band structure in agreement with experiments.     

Theory and nonlinearity of thermoacoustics:Ⅱ. Nonlinear sound waves in thermoacoustic tubes

1IntroductionImPort8Dtprogresshasbeenmade,inrecelltyears,inthermoacoustics,boththeondicallyandpractically,duetoitspotelitialaPplic8tionsinrefrigerationandcryogeulcs[1-3]-Assi~catthermoacousticeffectsareproducedonlyinhighintensitysoundfield,whosenoIilinariyplaysanhoport8Dtroleinthehighperformanceofthethermoacousticsystem-ThetheoreticalandexPerAneatalstudiesonnonlinearproPagationofhighilltensitysoundwavshavearousedgreatinterestofinvestigatorsI41.Manpaticularlyconcernthepropagationinthermoaco…     

From Desire to Data: How JLab’s Experimental Program Evolved

This is the first in a three-part article describing the development of the experimental program at the Thomas Jefferson National Accelerator Facility, from the first dreams of incisive electromagnetic probes into the structure of the nucleus through the era in which equipment was designed and constructed and a program crafted so that the long-desired experiments could begin. Part 1, which is presented here, focuses on how the scientific and technical work of previous decades inspired physicists in the 1970s to develop and launch plans for the necessary accelerators and experimental equipment for such probes. This effort required devising an initial wish list of experiments and working with the Department of Energy (DOE) and expert advisory committees to choose the best accelerator plan so that a laboratory design report could be produced in 1986. DOE approval of this report then opened the way for the construction of a 4 GeV continuous wave, superconducting radiofrequency accelerator at a new laboratory in Newport News, Virginia. Along the way those struggling to make experimental dreams come true faced many challenges, including the rise of the more bureaucratic New Big Science and the intellectual revolution that resulted from new understanding about quark-level physics.     

Cognition versus Constitution of Objects: From Kant to Modern Physics

Classical mechanics in phase space as well as quantum mechanics in Hilbert space lead to states and observables but not to objects that may be considered as carriers of observable quantities. However, in both cases objects can be constituted as new entities by means of invariance properties of the theories in question. We show, that this way of reasoning has a long history in physics and philosophy and that it can be traced back to the transcendental arguments in Kant’s critique of pure reason.     

From Voice Clinic to Operating Room: Are We Out of Tune?

Introduction: To determine the consistency and accuracy of preoperative diagnosis in the voice clinic with intraoperative diagnosis and to suggest a standardized laryngeal examination protocol in the UK that is supported by evidence-based findings.Method: From January 2011-September 2014, 164 patients were referred to the Multidisciplinary Team voice clinic and diagnosed with laryngeal pathology that required phonosurgery. The visualization (videostrobolaryngoscopy) in clinic was performed using either rigid laryngoscope or a video-naso-laryngoscope. Intraoperatively, laryngeal visualization and surgical procedure was conducted using Storz Aida HD system, 10-mm rigid laryngoscope 0° or 5-mm rigid laryngoscope 0°/30° and a Zeiss S7 microscope.Results: Of the 164 patients seen in the multidisciplinary voice clinic, 86 clinic diagnoses were confirmed intraoperatively (52.4%), 15 patients had the diagnosis confirmed intraoperatively with additional lesion found (9.1%). The clinic diagnosis changed intraoperatively in 63 cases (38.4%). 61 (37.2%) patients seen in the voice clinic were diagnosed with cyst, in 39.3% the diagnosis was confirmed intraoperatively with 5 cases (8.2%) having an additional diagnosis. Twenty (12.2%) patients were diagnosed with polyps, with 80% confirmation intraoperatively; 3 patients (10%) had an additional diagnosis.Conclusion: Videolaryngostroboscopy imaging of the larynx provides an outpatient tool for accurately diagnosing more than 50% of laryngeal pathologies when interpreted by multidisciplinary voice clinicians. However direct laryngeal examination under general anesthesia remains the gold standard when obtaining accurate diagnoses of laryngeal pathology. Patients diagnosed with nonorganic voice disorders should be considered for direct laryngoscopy under general anesthetic should they fail to respond to conservative management.     

John Tyndall’s Vertical Physics: From Rock Quarries to Icy Peaks

I analyze, through the work of the Irish physicist John Tyndall (1820–1893), the close relationship formed in the mid-nineteenth century between advances in the physical sciences and the rise of mountaineering as a sport. Along with groundbreaking experimental research in the physical sciences, Tyndall worked throughout his career to define and popularize the study of physics. He also was a pioneering mountaineer during the golden age of mountaineering. As he practiced his science, from rock quarries to the study of the blue sky, Tyndall’s interests in the fundamental forces of Nature brought him to the summits of mountains. His sojourns to the mountains, in turn, affected the manner in which he approached his researches. His science and mountaineering were tellingly mixed, and worked in unison to shape public perceptions of what physicists did during a period of increasing specialization and popularization of the field.