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36 pages, 3212 KB  
Review
Bipolar Entropy vs. Entropy/Negentropy: From Quantum Emergence to Agentic AI&QI with Collectively Entangled Bipolar Strings ER ≥≥ EPR
by Wen-Ran Zhang and Hengyu Zhang
Quantum Rep. 2026, 8(2), 36; https://doi.org/10.3390/quantum8020036 - 20 Apr 2026
Viewed by 844
Abstract
While the quantum emergence of spacetime is becoming a major research topic in physics, the quantum emergence of intelligence has not been widely researched in quantum information science (QIS). Following causal-logical quantum gravity theory, bipolar entropy vs. entropy and negative entropy (or negentropy) [...] Read more.
While the quantum emergence of spacetime is becoming a major research topic in physics, the quantum emergence of intelligence has not been widely researched in quantum information science (QIS). Following causal-logical quantum gravity theory, bipolar entropy vs. entropy and negative entropy (or negentropy) are reviewed and distinguished for quantum emergence/submergence of quantum agent (QA) and quantum intelligence (QI) in algebraic terms. This work refers to QA as an entangled bipolar string/superstring in bipolar dynamic equilibrium (BDE) and QI being centered on logically definable causality in regularity, mind-light-matter unity, and brain-universe similarity. ER = EPR is extended to ER ≥≥ EPR for the mathematical scalability of bipolar strings and their collective entanglement. The extension leads to a number of conjectures, testable predictions, and theorems. The term equilibraton is proposed as a type of EPR or bipolar generic string to serve as an entropic stitch to collectively hold the universe together as a quantum entanglement in BDE with ubiquitous, regulated local emergence and submergence of QA&QI. Equilibraton leads to the concept of bipolar entropy square—a complete entropic solution to the background issue in quantum gravity. With complete background independence, energy/information conservational bipolar entropy, energy/information invariance, bipolar entropy non-additivity, and equilibrium-based plateau concavity are introduced. The nature of the one-dimensional arrow of time is conjectured. As a unification of order and disorder for equilibrium-based regulation, bipolar entropy bridges QA&QI to agentic AI, where quantum-bio-economics can be viewed as a topological intervention of a natural dynamic equilibrium in a social or natural world. Use cases are reviewed to illustrate the practical and theoretical aspects of bipolar entropy in business management, quantum-bio-economics, quantum cryptography, physics, and biology. Eddington–Einstein’s comments on entropy are revisited. It is expected that bipolar entropy will bring quantum emergence/submergence to agentic AI&QI for entangled machine thinking and imagination as a naturally scalable and testable foundation of real-world quantum gravity, quantum information science (QIS), quantum cognition, and quantum biology (QCQB) to enhance Large Language AI Models (LLMs) and machine intelligence. Full article
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11 pages, 1977 KB  
Article
Structural, Up-Conversion Luminescence, and Electron Paramagnetic Resonance Investigations of Yb3+/Er3+-Doped LiGdF4 Nanocrystals Dispersed in Silica Glassy Matrix
by Corina Secu, Cristian Radu, Arpad Rostas and Mihail Secu
Inorganics 2025, 13(11), 378; https://doi.org/10.3390/inorganics13110378 - 19 Nov 2025
Viewed by 764
Abstract
We have investigated the structural, morphological, magnetic, and up-conversion luminescence properties of the Yb3+/Er3+-doped LiGdF4 nanocrystals precipitated in the silica glassy matrix. Morphological analysis showed uniform distribution of LiGdF4 nanocrystals (tens of nm in size), embedded in [...] Read more.
We have investigated the structural, morphological, magnetic, and up-conversion luminescence properties of the Yb3+/Er3+-doped LiGdF4 nanocrystals precipitated in the silica glassy matrix. Morphological analysis showed uniform distribution of LiGdF4 nanocrystals (tens of nm in size), embedded in silica glass matrix. FTIR spectroscopy analysis showed trifluoracetates thermolysis with silica lattice formation and structural analysis by XRD is consistent with the LiGdF4 crystallization process, most likely through an autocatalytic reaction. The stress and crystalline lattice distortion are assigned to the doping and glass matrix environment where the growth process occurs. The EPR spectra associated with the Gd3+ ions have shown a well-defined spectrum in the xerogel, associated with the trifluoroacetate ligand environment. In the LiGdF4 nanocrystals, the broad and unresolved spectrum is due to an envelope of unresolved anisotropic fine structure and a high dipole–dipole interaction between the Gd3+/Yb3+/Er3+ paramagnetic ions. Under 980 nm laser light pumping, we observed the characteristic “blue”, “green” and “red” up-conversion luminescences of the Er3+ ions through Yb → Er energy transfer process, that imply three and two-photon process; near UV up-conversion luminescence of Gd3+ is observed at about 280–300 nm where Yb → Er and Er → Gd energy transfer is involved. The UC luminescence properties can be improved up to two times by additional Yttrium co-doping due to the induced crystal field distortion. Full article
(This article belongs to the Special Issue Feature Papers in Inorganic Solid-State Chemistry 2025)
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15 pages, 1489 KB  
Article
Comparative EPR Studies on the Influence of Genistein on Free Radicals in Non-Irradiated and UV-Irradiated MCF7, T47D and MDA-MB-231 Breast Cancer Cells
by Magdalena Jurzak, Paweł Ramos, Barbara Pilawa and Ilona Anna Bednarek
Biomedicines 2024, 12(3), 518; https://doi.org/10.3390/biomedicines12030518 - 26 Feb 2024
Cited by 5 | Viewed by 2384
Abstract
The antioxidant activity and the association of genistein with carcinogenesis are widely documented. Few studies directly measure the number of free radicals generated in cells, either during the action of factors stimulating their formation, e.g., ultraviolet (UV), or after exposure to antioxidants. The [...] Read more.
The antioxidant activity and the association of genistein with carcinogenesis are widely documented. Few studies directly measure the number of free radicals generated in cells, either during the action of factors stimulating their formation, e.g., ultraviolet (UV), or after exposure to antioxidants. The most suitable method for analysing free radicals is electron paramagnetic resonance (EPR) spectroscopy. The EPR method detects a paramagnetic centre with a single electron. Antioxidants neutralize free radicals, therefore, EPR analysis of antioxidant efficacy is as valuable and important as studying the paramagnetic centres of radicals. The aim of the study was to determine the influence of genistein on free radicals basal level and after UV exposure in breast cancer cell lines MCF7, T47D and MDA-MB-231 cell lines. The impact of genistein on cell viability was investigated at concentrations of 0.37 μM, 3.7 μM, 37 μM and 370 μM. Genistein at a concentration of 370 μM revealed a cytotoxic effect on the cells of all three tested breast cancer lines. Genistein at a concentration of 0.37 μM showed no significant effect on the cell viability of all tested breast cancer lines. Therefore, cell proliferation and antioxidant properties were examined using genistein at a concentration of 0.37 μM and 37 μM. X-band (9.3 GHz) EPR spectra of three different types of breast cancer cells (ER-positive, PR-positive and HER-2 negative: MCF7 and T47D and triple-negative MDA-MB-231) were compared. UV irradiation was used as a factor to generate free radicals in cells. The effect of free radical interactions with the antioxidant genistein was tested for non-UV-irradiated (corresponding to the basal level of free radicals in cells) and UV-irradiated cells. The levels of free radicals in the non-irradiated cells studied increased in the following order in breast cancer cells: T47D < MDA-MB-231 < MCF7 and UV-irradiated breast cancer cells: MDA-MB-231 < MCF7 < T47D. UV-irradiation altered free radical levels in all control and genistein-cultured cells tested. UV irradiation caused a slight decrease in the amount of free radicals in MCF7 cells. A strong decrease in the amount of free radicals was observed in UV-irradiated MDA-MB-231 breast cancer cells. The amount of free radicals in T47D cancer cells increased after UV irradiation. Genistein decreased the amount of free radicals in non-irradiated and UV-irradiated MCF7 cells, and only a weak effect of genistein concentrations was reported. Genistein greatly decreased the amount of free radicals in UV-irradiated T47D cancer cells cultured with genistein at a concentration of 3.7 μM. The effect of genistein was negligible in the other samples. Genistein at a concentration of 3.7 μM decreased the amount of free radicals in non-irradiated MDA-MB-231 cancer cells, but genistein at a concentration of 37 μM did not change the amount of free radicals in these cells. An increase in the amount of free radicals in UV-irradiated MDA-MB-231 cancer cells was observed with increasing genistein concentration. The antioxidant efficacy of genistein as a potential plant-derived agent supporting the treatment of various cancers may be determined by differences in signalling pathways that are characteristic of breast cancer cell line subtypes and differences in activation of oxidative stress response pathways. Full article
(This article belongs to the Special Issue Antioxidants and Oxidative Stress in Human Health and Diseases)
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14 pages, 5165 KB  
Article
The Role of Er3+ Content in the Luminescence Properties of Y3Al5O12 Single Crystals: Incorporation into the Lattice and Defect State Creation
by Maksym Buryi, Amayès Médhi Gaston-Bellegarde, Jan Pejchal, Fedor Levchenko, Zdeněk Remeš, Katarína Ridzoňová, Vladimir Babin and Sergii Chertopalov
Crystals 2023, 13(4), 562; https://doi.org/10.3390/cryst13040562 - 25 Mar 2023
Cited by 4 | Viewed by 2330
Abstract
Erbium-doped Y3Al5O12 (YAG) single crystals grown using the micro-pulling-down technique were investigated. Three Er concentrations were chosen: 0.1, 0.3 and 1 at%. Er3+ electron paramagnetic resonance (EPR) spectra were measured in the ground and first excited states. [...] Read more.
Erbium-doped Y3Al5O12 (YAG) single crystals grown using the micro-pulling-down technique were investigated. Three Er concentrations were chosen: 0.1, 0.3 and 1 at%. Er3+ electron paramagnetic resonance (EPR) spectra were measured in the ground and first excited states. The corresponding g tensors and 167Er hyperfine interaction were changing upon Er content indicating moderation of the Er-O bond length and/or Er local surrounding. Photoluminescence (PL) and radioluminescence (RL) spectra were complex, consisting of strongly overlapped typical Er3+ transitions. In addition, there were other broad PL band (3.1 eV) and RL band (3.95 eV) attributed to the F+ center and yttrium substituting for aluminum (YAl), respectively. The X-ray excited decay kinetics exhibited a decrease of the decay time of the YAl from hundreds of nanoseconds to nanoseconds upon Er doping level. This is discussed and explained considering EPR data. Full article
(This article belongs to the Special Issue Rare Earths-Doped Materials (Volume II))
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23 pages, 8382 KB  
Article
Cr-Containing Rare-Earth Substituted Yttrium Iron Garnet Ferrites: Catalytic Properties in the Ethylbenzene Oxidation
by José Vitor C. do Carmo, Rita de Cássia F. Bezerra, Y. Guerra, R. Peña-Garcia, Alcineia C. Oliveira, E. Padron-Hernandez, Gilberto D. Saraiva, João M. Soares, Antonio Joel R. Castro, Samuel Tehuacanaero-Cuapa, Elena Rodríguez-Aguado and Enrique Rodríguez-Castellón
Catalysts 2022, 12(9), 1033; https://doi.org/10.3390/catal12091033 - 11 Sep 2022
Cited by 14 | Viewed by 2990
Abstract
A series of the Cr-containing erbium substituted yttrium iron garnet ferrites (ECYIG) was synthesized with distinct Cr amounts, herein referred to as Y3(Er0.02Fe5Cr1−x)O12, where x refers to Cr amounts from 0 to 0.05. [...] Read more.
A series of the Cr-containing erbium substituted yttrium iron garnet ferrites (ECYIG) was synthesized with distinct Cr amounts, herein referred to as Y3(Er0.02Fe5Cr1−x)O12, where x refers to Cr amounts from 0 to 0.05. The catalytic performance of the solids was investigated in ethylbenzene oxidation in the presence of hydrogen peroxide to assess the role of Cr and Er present in the YIG garnet lattice for fine chemistry compound production. Raman spectroscopy, HRTEM, EPR and FTIR revealed that the insertion of Er (at a fixed amount of 2%) in dodecahedral sites had a great impact on the catalytic activity of the garnets. Both Er3+ and Y3+ in the lattice simultaneously provided structural stability to the garnet structure in any harsh environment. XPS and EPR indicated that the Cr3+ ions replaced those of Fe3+ located in both octahedral and tetrahedral sites of the YIG garnets. The Cr3+ ions acted as electronic promoter to increase the oxidation rate of the Fe3+ active species responsible for activating the EB molecule. SEM-EDS demonstrated that the solids having Cr amounts lower than 4% experienced the most severe deactivation due to the Cr leaching and strong carbon species adsorption on the surface of the catalysts, which decreased their efficiency in the reaction. Full article
(This article belongs to the Section Catalytic Materials)
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19 pages, 8227 KB  
Article
Erodibility of Nanocomposite-Improved Unsaturated Soil Using Genetic Programming, Artificial Neural Networks, and Evolutionary Polynomial Regression Techniques
by Kennedy C. Onyelowe, Ahmed M. Ebid, Uchenna Egwu, Michael E. Onyia, Hyginus N. Onah, Light I. Nwobia, Izuchukwu Onwughara and Ali Akbar Firoozi
Sustainability 2022, 14(12), 7403; https://doi.org/10.3390/su14127403 - 16 Jun 2022
Cited by 8 | Viewed by 3261
Abstract
Genetic programming (GP) of four levels of complexity, including artificial neural networks of the hyper-tanh activation function (ANN-Hyper-Tanh), artificial neural networks of the sigmoid activation function (ANN-Sigmoid), evolutionary polynomial regression (optimized with genetic algorithm) (EPR), and intelligent techniques have been used to predict [...] Read more.
Genetic programming (GP) of four levels of complexity, including artificial neural networks of the hyper-tanh activation function (ANN-Hyper-Tanh), artificial neural networks of the sigmoid activation function (ANN-Sigmoid), evolutionary polynomial regression (optimized with genetic algorithm) (EPR), and intelligent techniques have been used to predict the erodibility of lateritic soil collected from an erosion site and treated with hybrid cement. Southeastern Nigeria and specifically Abia State is being destroyed by gully erosion, the solution of which demands continuous laboratory examinations to determine the parameters needed to design sustainable solutions. Furthermore, complicated equipment setups are required to achieve reliable results. To overcome constant laboratory works and equipment needs, intelligent prediction becomes necessary. This present research work adopted four different metaheuristic techniques to predict the erodibility of the soil; classified as A-7-6, weak, unsaturated, highly plastic, high swelling and high clay content treated with HC utilized in the proportions of 0.1–12% at the rate of 0.1%. The results of the geotechnics aspect of the work shows that the HC, which is a cementitious composite formulated from blending nanotextured quarry fines (NQF) and hydrated lime activated nanotextured rice husk ash (HANRHA), improves the erodibility of the treated soil substantially and consistently. The outcome of the prediction models shows that EPR with SSE of 1.6% and R2 of 0.996 outclassed the other techniques, though all four techniques showed their robustness and ability to predict the target (Er) with high performance accuracy. Full article
(This article belongs to the Special Issue Sustainability in Pavement Materials and Design)
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25 pages, 1683 KB  
Article
The “ER = EPR” Conjecture and Generic Gravitational Properties: A Universal Topological Linking Model of the Correspondence between Tripartite Entanglement and Planck-Scale Wormholes
by Elias Zafiris and Albrecht von Müller
Universe 2022, 8(3), 189; https://doi.org/10.3390/universe8030189 - 18 Mar 2022
Cited by 1 | Viewed by 7827
Abstract
The “ER = EPR” conjecture, conceived by Maldacena and Susskind, is grounded on the notion that a gravitational theory in the bulk is dual to the corresponding quantum field theory on the boundary in accordance to the AdS/CFT correspondence. The conjecture pertains to [...] Read more.
The “ER = EPR” conjecture, conceived by Maldacena and Susskind, is grounded on the notion that a gravitational theory in the bulk is dual to the corresponding quantum field theory on the boundary in accordance to the AdS/CFT correspondence. The conjecture pertains to the idea that Einstein-Rosen (ER) spacetime bridges and Einstein-Podolsky-Rosen (EPR) quantum entanglement may be considered as dually equivalent. Since ER bridges refer to the connectivity between black holes, the “ER = EPR” conjecture implies that black holes connected by ER bridges are entangled, and conversely, that entangled black holes are connected by ER bridges. However, the instance of the maximally entangled tripartite (GHZ) quantum state points to the necessity of devising a model of non-classical Planck scale ER bridges going beyond the standard description of these bridges in spacetime. Based on the topological structure of the maximally entangled GHZ state, we propose that a universal topological link, called the Borromean rings, furnishes a particular linking structure that is able to unravel the equavalence between entanglement and wormholes, and thus, to address the validity of the “ER = EPR” conjecture beyond the initial context of the AdS/CFT correspondence. As a consequence, we propose the explicit construction of distinguishable extensions of the smooth classical spacetime manifold taking place in the transition to the quantum gravity regime according to a naturally induced physical criterion of gravitational generic properties following from this intrinsic topological qualification of the “ER = EPR” conjecture. Full article
(This article belongs to the Special Issue Recent Advances in Wormhole Physics)
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20 pages, 677 KB  
Review
Molecular Perspective of Nanoparticle Mediated Therapeutic Targeting in Breast Cancer: An Odyssey of Endoplasmic Reticulum Unfolded Protein Response (UPRER) and Beyond
by Safikur Rahman, Vijay Kumar, Anuj Kumar, Tasduq S. Abdullah, Irfan A. Rather and Arif Tasleem Jan
Biomedicines 2021, 9(6), 635; https://doi.org/10.3390/biomedicines9060635 - 2 Jun 2021
Cited by 13 | Viewed by 5059
Abstract
Breast cancer (BC) is the second most frequent cause of death among women. Representing a complex and heterogeneous type of cancer, its occurrence is attributed by both genetic (gene mutations, e.g., BRCA1, BRCA2) and non-genetic (race, ethnicity, etc.) risk factors. The effectiveness of [...] Read more.
Breast cancer (BC) is the second most frequent cause of death among women. Representing a complex and heterogeneous type of cancer, its occurrence is attributed by both genetic (gene mutations, e.g., BRCA1, BRCA2) and non-genetic (race, ethnicity, etc.) risk factors. The effectiveness of available treatment regimens (small molecules, cytotoxic agents, and inhibitors) decreased due to their poor penetration across biological barriers, limited targeting, and rapid body clearance along with their effect on normal resident cells of bone marrow, gastrointestinal tract, and hair follicles. This significantly reduced their clinical outcomes, which led to an unprecedented increase in the number of cases worldwide. Nanomedicine, a nano-formulation of therapeutics, emerged as a versatile delivering module for employment in achieving the effective and target specific delivery of pharmaceutical payloads. Adoption of nanotechnological approaches in delivering therapeutic molecules to target cells ensures not only reduced immune response and toxicity, but increases the stability of therapeutic entities in the systemic circulation that averts their degradation and as such increased extravasations and accumulation via enhanced permeation and the retention (EPR) effect in target tissues. Additionally, nanoparticle (NP)-induced ER stress, which enhances apoptosis and autophagy, has been utilized as a combative strategy in the treatment of cancerous cells. As nanoparticles-based avenues have been capitalized to achieve better efficacy of the new genera of therapeutics with enhanced specificity and safety, the present study is aimed at providing the fundamentals of BC, nanotechnological modules (organic, inorganic, and hybrid) employed in delivering different therapeutic molecules, and mechanistic insights of nano-ER stress induced apoptosis and autophagy with a perspective of exploring this avenue for use in the nano-toxicological studies. Furthermore, the current scenario of USA FDA approved nano-formulations and the future perspective of nanotechnological based interventions to overcome the existing challenges are also discussed. Full article
(This article belongs to the Special Issue Theranostic Drug Delivery: Prospects and Problems)
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40 pages, 17219 KB  
Review
Structures of Impurity Defects in Lithium Niobate and Tantalate Derived from Electron Paramagnetic and Electron Nuclear Double Resonance Data
by Valentin G. Grachev and Galina I. Malovichko
Crystals 2021, 11(4), 339; https://doi.org/10.3390/cryst11040339 - 27 Mar 2021
Cited by 21 | Viewed by 7204
Abstract
Point intrinsic and extrinsic defects, especially paramagnetic ions of transition metals and rare-earth elements, have essential influence on properties of lithium niobate, LN and tantalate, LT, and often determine their suitability for numerous applications. Discussions about structures of the defects in LN/LT have [...] Read more.
Point intrinsic and extrinsic defects, especially paramagnetic ions of transition metals and rare-earth elements, have essential influence on properties of lithium niobate, LN and tantalate, LT, and often determine their suitability for numerous applications. Discussions about structures of the defects in LN/LT have lasted for decades. Many experimental methods facilitate progress in determining the structures of impurity centers. This paper gives current bird’s eye view on contributions of Electron Paramagnetic Resonance (EPR), and Electron Nuclear Double Resonance (ENDOR) studies to the determination of impurity defect structures in LN and LT crystals for a broad audience of researchers and students. Symmetry and charge compensation considerations restrict a number of possible structures. Comparison of measured angular dependences of ENDOR frequencies with calculated ones for Li and Nb substitution using dipole–dipole approximation allows unambiguously to determine the exact location of paramagnetic impurities. Models with two lithium vacancies explain angular dependencies of EPR spectra for Me3+ ions substituting for Li+ like Cr, Er, Fe, Gd, Nd, and Yb. Self-compensation of excessive charges through equalization of concentrations of Me3+(Li+) and Me3+(Nb5+) and appearance of interstitial Li+ in the structural vacancy near Me3+(Nb5+) take place in stoichiometric LN/LT due to lack of intrinsic defects. Full article
(This article belongs to the Special Issue New Trends in Lithium Niobate: From Bulk to Nanocrystals)
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13 pages, 3469 KB  
Article
Cu-IM-5 as the Catalyst for Selective Catalytic Reduction of NOx with NH3: Role of Cu Species and Reaction Mechanism
by Guangying Fu, Junwen Chen, Yuqian Liang, Rui Li, Xiaobo Yang and Jiuxing Jiang
Catalysts 2021, 11(2), 221; https://doi.org/10.3390/catal11020221 - 7 Feb 2021
Cited by 13 | Viewed by 3563
Abstract
The role of Cu species in Cu ion-exchanged IM-5 zeolite (Cu-IM-5) regarding the performance in selective catalytic reduction (SCR) of NOx with NH3 (NH3-SCR) and the reaction mechanism was studied. Based on H2 temperature-programmed reduction (H2-TPR) [...] Read more.
The role of Cu species in Cu ion-exchanged IM-5 zeolite (Cu-IM-5) regarding the performance in selective catalytic reduction (SCR) of NOx with NH3 (NH3-SCR) and the reaction mechanism was studied. Based on H2 temperature-programmed reduction (H2-TPR) and electron paramagnetic resonance (EPR) results, Cu–O–Cu and isolated Cu species are suggested as main Cu species existing in Cu-IM-5 and are active for SCR reaction. Cu–O–Cu species show a good NH3-SCR activity at temperatures below 250 °C, whereas their NH3 oxidation activity at higher temperatures hinders the SCR performance. At low temperatures, NH4NO3 and NH4NO2 are key reaction intermediates. In situ diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) suggests a mixed Eley–Rideal (E–R) and Langmuir–Hinshelwood (L–H) mechanism over Cu-IM-5 at low temperatures. Full article
(This article belongs to the Special Issue Catalysis with Ordered Porous Materials)
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11 pages, 1247 KB  
Communication
Detection of Two Phenomena Opposite to the Expected Ones
by Boris I. Kochelaev
Condens. Matter 2020, 5(4), 56; https://doi.org/10.3390/condmat5040056 - 24 Sep 2020
Cited by 1 | Viewed by 2850
Abstract
Both phenomena mentioned in the title were revealed by the electron paramagnetic resonance (EPR) method. The first phenomenon was found in superconducting La metal with Er impurities—the spin relaxation rate of the erbium impurities was sharply decreasing after transition into the superconducting state [...] Read more.
Both phenomena mentioned in the title were revealed by the electron paramagnetic resonance (EPR) method. The first phenomenon was found in superconducting La metal with Er impurities—the spin relaxation rate of the erbium impurities was sharply decreasing after transition into the superconducting state instead of the expected, i.e., the well-known Hebel–Slichter peak. The second unexpected phenomenon was discovered in the YbRh2Si2 compound—an excellent EPR signal from the Yb ions was observed at temperatures below the Kondo temperature determined thermodynamically, while according to the existing belief the EPR signal should not be observed at these temperatures due to the Kondo effect. In this tribute to K. Alex Müller, I describe the nature of the detected phenomena. Full article
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14 pages, 292 KB  
Article
General Relativistic Wormhole Connections from Planck-Scales and the ER = EPR Conjecture
by Fabrizio Tamburini and Ignazio Licata
Entropy 2020, 22(1), 3; https://doi.org/10.3390/e22010003 - 18 Dec 2019
Cited by 17 | Viewed by 7365
Abstract
Einstein’s equations of general relativity (GR) can describe the connection between events within a given hypervolume of size L larger than the Planck length L P in terms of wormhole connections where metric fluctuations give rise to an indetermination relationship that involves the [...] Read more.
Einstein’s equations of general relativity (GR) can describe the connection between events within a given hypervolume of size L larger than the Planck length L P in terms of wormhole connections where metric fluctuations give rise to an indetermination relationship that involves the Riemann curvature tensor. At low energies (when L L P ), these connections behave like an exchange of a virtual graviton with wavelength λ G = L as if gravitation were an emergent physical property. Down to Planck scales, wormholes avoid the gravitational collapse and any superposition of events or space–times become indistinguishable. These properties of Einstein’s equations can find connections with the novel picture of quantum gravity (QG) known as the “Einstein–Rosen (ER) = Einstein–Podolski–Rosen (EPR)” (ER = EPR) conjecture proposed by Susskind and Maldacena in Anti-de-Sitter (AdS) space–times in their equivalence with conformal field theories (CFTs). In this scenario, non-traversable wormhole connections of two or more distant events in space–time through Einstein–Rosen (ER) wormholes that are solutions of the equations of GR, are supposed to be equivalent to events connected with non-local Einstein–Podolski–Rosen (EPR) entangled states that instead belong to the language of quantum mechanics. Our findings suggest that if the ER = EPR conjecture is valid, it can be extended to other different types of space–times and that gravity and space–time could be emergent physical quantities if the exchange of a virtual graviton between events can be considered connected by ER wormholes equivalent to entanglement connections. Full article
(This article belongs to the Special Issue Relativistic Quantum Information)
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