A multidimensional Monster in a pre-big bang scenario: when the Multiple precedes the One
The Monster group, the biggest of the sporadic groups, is equipped with the highest known number of dimensions and symmetries. Taking into account variants of the Borsuk-Ulam theorem and a novel topological approach cast in a physical fashion that has the potential to be operationalized, the Universe can be conceived as a lower-dimensional manifold encompassed in the Monster group. Our Universe might arise from spontaneous dimension decrease and symmetry breaking that occur inside the very structure of the Monster Module. We elucidate how the energetic loss caused by projection from higher to lower dimensions and by the Monster group’s non-abelian features is correlated with the present-day asymmetry in thermodynamic arrow. By linking the Monster Module to theoretical physical counterparts, we are allowed to calculate its enthalpy and Lie group trajectories. Our approach also reveals how a symmetry break might lead to a Universe based on multi-dimensional string theories and CFT/AdS correspondence.
Non-commutative unification of relativity and quantum dynamics: Connes comes into play
Tozzi, A.; Peters, J.F.. Unification of Commutative Relativity and Noncommutative Quantum Dynamics Via Cyclic Groupoids and Spacetime Fusion Categories. Preprints 2018, 2018090021 (doi: 10.20944/preprints201809.0021.v1).
The unexploited unification of general relativity and quantum physics is a painstaking issue that prevents physicists to properly understanding the whole of Nature. Here we propose a pure mathematical approach that introduces the problem in terms of group theory. Indeed, we build a cyclic groupoid (a nonempty set with a binary operation defined on it) that encompasses both the theories as subsets, making it possible to join together two of their most dissimilar experimental results, i.e., the commutativity detectable in our macroscopic relativistic world and the noncommutativity detectable in the quantum, microscopic world. This approach, combined with the Connes fusion operator, leads to a mathematical framework useful in the investigation of relativity/quantum mechanics relationships.
From Avicenna’s Active Intellect to Quantum dynamics on hyperbolic manifolds
Tozzi A. 2022. Informational Approaches Lead to Formulations of Quantum Mechanics on Poincaré Disks. Proceedings, 81(1), 20; https://doi.org/10.3390/proceedings2022081020.
A novel methodological approach requires the observer to investigate the information accessible outside the object under scrutiny. The object becomes an “hole” devoid of information, surrounded by a container that is no longer a passive structure. We use this container-framed attitude for a mathematical attempt to take a step towards the unexploited unification of general relativity and quantum mechanics. We show that the tenets of quantum mechanics, i.e., the observable A, the autostates ψa, and the Schrodinger equation for the temporal evolution of states, can be described in terms of oscillatory paths taking place on negative-curvature Poincaré disks.
Quantum entanglement can be solved in 4D
A quantum entanglement’s composite system does not display separable states and a single constituent cannot be fully described without considering the other states. We introduce quantum entanglement on a hypersphere - which is a 4D space undetectable by observers living in a 3D world -, derived from signals originating on the surface of an ordinary 3D sphere. From the far-flung branch of algebraic topology, the Borsuk-Ulam theorem states that, when a pair of opposite (antipodal) points on a hypersphereare projected onto the surface of 3D sphere, the projections have matching description. In touch with this theorem, we show that a separable state can be achieved for each of the entangled particles, just by embedding them in a higher dimensional space. We view quantum entanglement as the simultaneous activation of signals in a 3D space mapped into a hypersphere. By showing that the particles are entangled at the 3D level and un-entangled at the 4D hypersphere level, we achieved a composite system in which each local constituent is equipped with a pure state. We anticipate this new view of quantum entanglement leading to what are known as qubit information systems. PDF
Heidegger’s Being & quantum vacuum: physical operationalization of the ancient Being, Essence, Existence, and so on
A dialogue between Martin Heidegger and a theoretical physicist, namely Richie, unveils the striking relationships between the Eastern and Western philosophical concepts of Being and the experimentally detectable quantum vacuum. We provide an account of long-standing theoretical issues, such Being, Entity, Existence and the unique role of the human Thoughts in the world, and expound their possible physical counterparts. PDF
Quantum computer in 4D: how to build a multidimensional computer through Quantum Hall effect
Relationships among near set theory, shape maps and recent accounts of the Quantum Hall effect pave the way to quantum computations performed in higher dimensions. We illustrate the operational procedure to build a quantum computer able to detect, assess and quantify a fourth spatial dimension. We show how, starting from two-dimensional shapes embedded in a 2D topological charge pump, it is feasible to achieve the corresponding four-dimensional shapes, which encompass a larger amount of information. This novel, relatively straightforward architecture not only permits to increase the amount of available qbits in a fixed volume, but also converges towards a solution to the problem of optical computers, that are not allowed to tackle quantum entanglement through their canonical superposition of electromagnetic waves.
An atomic geometric model encompassing also quantum mechanics' dictates
Here we provide a novel atomic, paraxial model in which a single belt of electrons surrounds the nucleus. The electronic belt is depicted in terms of broken lines and split wavy trajectories that intersect an axis, giving rise to small angles that can be accurately calculated. We demonstrate that the probabilistic electronic cloud of the atom described by quantum mechanics can be depicted in terms of an electronic belt, because its sizes closely match the descriptions given by de Broglie and Heisenberg. In touch with the claims of the two latter Authors, the wavy trajectories around the nucleus come back to a starting point, so that their orbits are stationary. PDF
Black holes horizons: unnoticed correlations with the Borsuk-Ulam theorem and the Mobius strip
The Möbius strip spacetime topology and the entangled antipodal points on black hole surfaces, recently described by ‘t Hooft, display an unnoticed relationship with the Borsuk-Ulam theorem from algebraic topology. Considering this observation and other recent claims which suggest that quantum entanglement takes place on the antipodal points of a S3 hypersphere, a novel topological framework can be developed: a feature encompassed in an S2 unentangled state gives rise, when projected one dimension higher, to two entangled particles. This allows us to achieve a mathematical description of the holographic principle occurring in S2. Furthermore, our observations let us to hypothesize that a) quantum entanglement might occur in a four-dimensional spacetime, while disentanglement might be achieved on a motionless, three-dimensional manifold; b) a negative mass might exist on the surface of a black hole. PDF
The geometry of black holes in terms of random walks
The Universe, rather than being homogeneous, displays an almost infinite topological genus, because it is punctured with a countless number of gravitational vortexes, i.e., black holes. Starting from this view, we aim to show that the occurrence of black holes is constrained by geometric random walks taking place during cosmic inflationary expansion. At first, we introduce a visual model, based on the Pascal’s triangle and linear and nonlinear arithmetic octahedrons, which describes three-dimensional cosmic random walks. In case of nonlinear 3D paths, trajectories in an expanding Universe can be depicted as the operation of filling the numbers of the octahedrons in the form of “islands of numbers”: this leads to separate cosmic structures (standing for matter/energy), spaced out by empty areas (constituted by black holes and dark matter). These procedures allow us to describe the topology of an universe of infinite genus, to assess black hole formation in terms of infinite Betti numbers, to highlight how non-linear random walks might provoke gravitational effects also in absence of mass/energy, and to propose a novel interpretation of Beckenstein-Hawking entropy: it is proportional to the surface, rather than the volume, of a black hole, because the latter does not contain information.
Observer horizon & relational quantum dynamics: when entropy and information become subjective
We describe cosmic expansion as correlated with the standpoints of local observers’ co-moving horizons. In keeping with relational quantum mechanics, which claims that quantum systems are only meaningful in the context of measurements, we suggest that information gets ergodically “diluted” in our isotropic and homogeneous expanding Universe, so that an observer detects just a limited amount of the total cosmic bits. The reduced bit perception is due the decreased density of information inside the expanding cosmic volume in which the observer resides. Further, we show that the second law of thermodynamics can be correlated with cosmic expansion through a relational mechanism, because the decrease in information detected by a local observer in an expanding Universe is concomitant with an increase in perceived cosmic thermodynamic entropy, via the Bekenstein bound and the Laudauer principle. Reversing the classical scheme from thermodynamic entropy to information, we suggest that the cosmological constant of the quantum vacuum, which is believed to provoke the current cosmic expansion, could be one of the sources of the perceived increases in thermodynamic entropy. We conclude that entropies, including the entangled entropy of the recently developed framework of quantum computational spacetime, might not describe independent properties, but rather relations among systems and observers.