A Haptic Model of Entanglement, Gauge Symmetries and Minimal Interaction Based on Knot Theory

The Heegaard splitting of S U ( 2 ) is a particularly useful representation for quantum phases of spin j-representation arising in the mapping S 1 → S 3, which can be related to ( 2 j , 2 ) torus knots in Hilbert space. We show that transitions to homotopically equivalent knots can be associated with gauge invariance, and that the same mechanism is at the heart of quantum entanglement. In other words, (minimal) interaction causes entanglement. Particle creation is related to cuts in the knot structure. We show that inner twists can be associated with operations with the quaternions ( I , J , K ), which are crucial to understand the Hopf mapping S 3 → S 2. We discuss the relationship between observables on the Bloch sphere S 2, and knots with inner twists in Hilbert space. As applications, we discuss selection rules in atomic physics, and the status of virtual particles arising in Feynman diagrams. Using a simple paper strip model revealing the knot structure of quantum phases in Hilbert space including inner twists, a h a p t i c model of entanglement and gauge symmetries is proposed, which may also be valid for physics education.

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A Haptic Model for the Quantum Phase of Fermions and Bosons in Hilbert Space Based on Knot Theory

Symmetry ◽

10.3390/sym11030426 ◽

2019 ◽

Vol 11 (3) ◽

pp. 426 ◽

Cited By ~ 1

Author(s):

Stefan Heusler ◽

Malte Ubben

Keyword(s):

Hilbert Space ◽

Braid Group ◽

Knot Theory ◽

Arbitrary Spin ◽

Paper Strip ◽

Spin States ◽

Quantum Phases ◽

Before And After ◽

Jones Polynomials ◽

Knots And Links

A generalization of the famous Dirac belt trick opens up the way to a haptic model for quantum phases of fermions and bosons in Hilbert space based on knot theory. We introduce a simple paper strip model as an aid for visualization of the quantum phases before and after Hopf-mapping, which can be extended to arbitrary spin states with almost no mathematical formalism. Knot theory arises naturally, leading to the Jones polynomials derived from Artin’s braid group for fermionic knots and for bosonic links. The paper strip model explicitly illuminates the relation between these knots and links within the S U ( 2 ) -representation of spin-jstates in C 2 j + 1 before Hopf-mapping and the number p = 2 j of nodes in the stellar representation in C P 1 after Hopf mapping.

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REVIEW OF TRENDS IN PHYSICS EDUCATION RESEARCH USING TOPIC MODELING

Journal of Baltic Science Education ◽

10.33225/jbse/20.19.388 ◽

2020 ◽

Vol 19 (3) ◽

pp. 388-400 ◽

Cited By ~ 2

Author(s):

Eunjeong Yun

Keyword(s):

Education Research ◽

Physics Education ◽

Topic Modeling ◽

Introductory Physics ◽

Research Trend ◽

Physics Education Research ◽

Pedagogical Content ◽

Future Studies ◽

The Status ◽

And Gender

For both physicists who teach students in university and physics educators, how physics should be taught is a vital question. This study reviewed the trends of research in the field of physics education to identify the status of physics education research and help researchers in future studies. 2,959 articles were collected from the American Journal of Physics (AJP) and 745 articles from the Physics Review Physics Education Research (PRPER). Abstracts of the collected articles were used for the study. After preprocessing the texts of the abstracts, topics were extracted from the texts using topic modeling. The Late Dirichlet Allocation (LDA) model of Mallet was used for topic modeling. A total of 13 topics were extracted from the two journals. In recent years, “pedagogical content of knowledge (PCK),” “assessment” of achievement and “gender” of student have been topics of increasing interest; “teacher education” and “students’ reasoning process” have been topics with continuous high interest, and “introductory physics” and “problem solving” in physics have been topics with decreasing interest. Keywords: physics education research, physics education, research trend, topic modeling.

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The Information Loss Problem: An Analogue Gravity Perspective

Entropy ◽

10.3390/e21100940 ◽

2019 ◽

Vol 21 (10) ◽

pp. 940 ◽

Cited By ~ 3

Author(s):

Stefano Liberati ◽

Giovanni Tricella ◽

Andrea Trombettoni

Keyword(s):

Hilbert Space ◽

Black Hole ◽

Degrees Of Freedom ◽

Particle Creation ◽

Information Loss ◽

Quantum Evolution ◽

Unitary Evolution ◽

Black Hole Evaporation ◽

Analogue Gravity ◽

Information Loss Problem

Analogue gravity can be used to reproduce the phenomenology of quantum field theory in curved spacetime and in particular phenomena such as cosmological particle creation and Hawking radiation. In black hole physics, taking into account the backreaction of such effects on the metric requires an extension to semiclassical gravity and leads to an apparent inconsistency in the theory: the black hole evaporation induces a breakdown of the unitary quantum evolution leading to the so-called information loss problem. Here, we show that analogue gravity can provide an interesting perspective on the resolution of this problem, albeit the backreaction in analogue systems is not described by semiclassical Einstein equations. In particular, by looking at the simpler problem of cosmological particle creation, we show, in the context of Bose–Einstein condensates analogue gravity, that the emerging analogue geometry and quasi-particles have correlations due to the quantum nature of the atomic degrees of freedom underlying the emergent spacetime. The quantum evolution is, of course, always unitary, but on the whole Hilbert space, which cannot be exactly factorized a posteriori in geometry and quasi-particle components. In analogy, in a black hole evaporation one should expect a continuous process creating correlations between the Hawking quanta and the microscopic quantum degrees of freedom of spacetime, implying that only a full quantum gravity treatment would be able to resolve the information loss problem by proving the unitary evolution on the full Hilbert space.

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The status of Galileo’s law of free-fall and its implications for physics education

American Journal of Physics ◽

10.1119/1.3096643 ◽

2009 ◽

Vol 77 (5) ◽

pp. 417-423 ◽

Cited By ~ 11

Author(s):

Yaron Lehavi ◽

Igal Galili

Keyword(s):

Physics Education ◽

Free Fall ◽

The Status

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The study of interfacial reactions of nickel thin films on GaAs

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100074616 ◽

1983 ◽

Vol 41 ◽

pp. 156-157

Author(s):

L.J. Chen ◽

Y.F. Hsieh

Keyword(s):

Thin Films ◽

Integrated Circuits ◽

Interfacial Reactions ◽

Metal Contacts ◽

Nickel Thin Films ◽

Thin Foils ◽

The Status ◽

Si Doped ◽

Electron Microscopes

One measure of the maturity of a device technology is the ease and reliability of applying contact metallurgy. Compared to metal contact of silicon, the status of GaAs metallization is still at its primitive stage. With the advent of GaAs MESFET and integrated circuits, very stringent requirements were placed on their metal contacts. During the past few years, extensive researches have been conducted in the area of Au-Ge-Ni in order to lower contact resistances and improve uniformity. In this paper, we report the results of TEM study of interfacial reactions between Ni and GaAs as part of the attempt to understand the role of nickel in Au-Ge-Ni contact of GaAs.N-type, Si-doped, (001) oriented GaAs wafers, 15 mil in thickness, were grown by gradient-freeze method. Nickel thin films, 300Å in thickness, were e-gun deposited on GaAs wafers. The samples were then annealed in dry N2 in a 3-zone diffusion furnace at temperatures 200°C - 600°C for 5-180 minutes. Thin foils for TEM examinations were prepared by chemical polishing from the GaA.s side. TEM investigations were performed with JE0L- 100B and JE0L-200CX electron microscopes.

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Fate of sperm membrane in fertilized ova

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100146047 ◽

1993 ◽

Vol 51 ◽

pp. 40-41

Author(s):

Frank J. Longo

Keyword(s):

Electron Microscopy ◽

Electrical Activity ◽

Sea Urchins ◽

Morphological Changes ◽

Integrated System ◽

Electrophysiological Recording ◽

Experimental Conditions ◽

The Status ◽

Sperm Membrane ◽

Temporal And Spatial

Measurement of the egg's electrical activity, the fertilization potential or the activation current (in voltage clamped eggs), provides a means of detecting the earliest perceivable response of the egg to the fertilizing sperm. By using the electrical physiological record as a “real time” indicator of the instant of electrical continuity between the gametes, eggs can be inseminated with sperm at lower, more physiological densities, thereby assuring that only one sperm interacts with the egg. Integrating techniques of intracellular electrophysiological recording, video-imaging, and electron microscopy, we are able to identify the fertilizing sperm precisely and correlate the status of gamete organelles with the first indication (fertilization potential/activation current) of the egg's response to the attached sperm. Hence, this integrated system provides improved temporal and spatial resolution of morphological changes at the site of gamete interaction, under a variety of experimental conditions. Using these integrated techniques, we have investigated when sperm-egg plasma membrane fusion occurs in sea urchins with respect to the onset of the egg's change in electrical activity.

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