Search Results (11)

The Zeta-Minimizer Theorem (ZMT) provides a complete deductive unification of statistical mechanics, number theory, helical geometry, thermodynamics, and electromagnetism from three primitive axioms alone. Starting with the non-proper Archimedean conical helix and the explicit covariant fugacity Hessian, the universal grand-partition function Z(s) is constructed via the integer-gear rule. This functorially invariant object yields gear occupations, Lyapunov exponents, and interaction parameters that govern all subsequent results. Interface matching and marginal stability λ_2,19 (x_2) = 0 trigger superconductivity at solid–fluid boundaries, while the categorical invariance of Z(s) produces exact magnetic and electric equilibrium curves. The Variational Reaction Rate Theorem then projects the framework onto dynamics, yielding Maxwell’s equations, demystified electrical units as helical torque quantities, and a complete classification of electronic phases. Phonons, Cooper pairing, the superconducting gap, and the full BCS correspondence follow without additional postulates. The same marginal-stability condition reproduces the Casimir effect, the Quantum Hall effect, and the entire 115-year experimental history of superconductivity. Generalization of interface matching to arbitrary solid–liquid pairs and introduction of Variational Anchor Cancellation (VAC) self-organizes a shielded superconducting layer. Finally, the first-principles engineering blueprint of the Radial Helical Gear Condenser (RHGC) delivers a modular, self-regulating device that engineers superconductivity at ambient or near-ambient temperature using only a radial pressure gradient and existing pipeline technology. All predictions are zero-parameter and fully deducible from the three axioms. Full article

The Zeta-Minimizer Theorem establishes that the Riemann zeta function $\zeta \left(s\right)$ and the primes arise variationally as unique minimizers of a phase functional defined on a symmetric measure space $\left(X,\mu ,G\right)$ equipped with helical operators. Three fundamental axioms—strict concave entropy maximization (Axiom 1), spectral Gibbs minima with non-vanishing ground states (Axiom 2), and irreducible bounded oscillations with flux conservation (Axiom 3)—allow for the selection of the non-proper Archimedean conical helix as the sole topology satisfying all constraints. Primes emerge as indivisible minimal cycles in the associated representation graph $\Gamma$ (via Hilbert irreducibility and Maschke’s theorem), while the Euler product is recovered through the spectral Dirichlet mapping of the helical eigenvalues. The partial zeta product, $Z\left(s\right)=\prod _j{\displaystyle \frac{1}{1-p_j^{-s}}},s\in \mathbb{R}\left\{0\right\},$ constitutes the exact grand partition function of any finite subsystem. Numerical inversion of this product directly recovers the mixture frequency $s$ from any experimental compressibility factor $Z_{\mathrm{m}\mathrm{i}\mathrm{x}}$. Mole fractions $x_i\left(s\right)$, interaction parameters $\Delta \left(x_i\right)$, and the Lyapunov spectrum $\lambda \left(x_i\right)$ then follow deductively via the helical transfer matrix and the closed-form linear ODE for $\Delta$. Occupation numbers $N\left(x_i\right)$ attain sharp maxima precisely at Fibonacci ratios $F_r/F_{r+1}$, leading to the molecular prime-ID rule. For twelve representative purely binary (irreducible) systems spanning atomic noble gases, simple diatomics, polar molecules, and an aromatic ring, the residuals satisfy $|Z\left(s\right)-Z_{\mathrm{m}\mathrm{i}\mathrm{x}}|<1.5\times {10}^{-8}$. The resulting $\lambda \left(x_i\right)$ curves accurately reproduce critical points, liquid ranges, and thermodynamic anomalies with zero adjustable parameters. The Riemann Hypothesis follows rigorously as a theorem: the unique fixed point of the duality functor $s\mapsto 1-s$ that preserves the orthogonality condition $\sum {\mathrm{c}\mathrm{o}\mathrm{s}}^2{\theta }^k=1$ is $\mathrm{R}\mathrm{e}\left(s\right)=1/2$, enforced by Axiom 1 concavity and Axiom 3 irreducibility. The framework is fully deductive and parameter-free and extends naturally to arbitrary mixtures and multiplicities through the helical representation graph. It provides a variational unification of analytic number theory, spectral geometry, thermodynamic phase behavior, and the Riemann Hypothesis from first principles. Full article

In this work, we develop a unified framework for Conformal Gravity and Noncommutative (Fuzzy) Gravity incorporating internal interactions. Our approach relies on two fundamental observations: first, the dimensions of a curved manifold and those of its tangent group need not coincide, and second, both gravitational models can be formulated as gauge theories. We begin with a discussion of the gauge-theoretic formulation of gravitational dynamics, emphasizing the role of diffeomorphism invariance. We then outline the constructions of Conformal Gravity and Fuzzy Gravity within this formalism. Building on an extension of the four-dimensional tangent group, we propose a scheme that unifies the two theories while naturally incorporating internal degrees of freedom. We further investigate the low-energy limits that emerge after appropriate spontaneous symmetry-breaking mechanisms, and we comment on potential observational signatures—particularly those associated with cosmic strings and their imprint on gravitational-wave spectra. Full article

One of the greatest quests in physics in current times is the search for a grand unified theory—to bring all the forces of nature into one coherent explanatory framework. Despite two centuries of progress, both in comprehending the individual forces and formulating mathematical constructs to explain the existence and operation of such forces, the final step to unify the localised atomic and subatomic forces with gravity has proven to be elusive. Whilst recognising that there are arguments for and against the unification of all the forces of nature, the pursuit for unity has been driving many physicists and mathematicians to explore increasingly extraordinary ideas, from string theory to various other options requiring multiple dimensions. Can process philosophy ride to the rescue? By changing our perspective, it might be possible to derive a provocative and compelling alternative way to understand basic (and advanced) physics. This process approach would see all matter objects, at whatever scale, as energetic systems (inherently dynamic). Through the use of game theory, there is a way to appreciate the combination of entropy together with all the apparent forces of nature, being gravity and the more localised forces, within a singular, metaphysically consistent, construct. The outcome, however, challenges our whole understanding of the universe and fundamentally changes our relationship with matter. Full article

We fit the three finestructure constants of the Standard Model, in which the first approximation of theoretically estimable parameters include (1) a “unified scale”, turning out not equal to the Planck scale and thus only estimable by a very speculative story, the second includes (2) a “number of layers” being a priori the number of families, and the third is (3) a unified coupling related to a critical coupling on a lattice. So formally, we postdict the three fine structure constants! In the philosophy of our model, there is a physical lattice theory with link variables taking values in a (or in the various) “small” representation(s) of the standard model Group. We argue for that these representations function in the first approximation based on the theory of a genuine $SU\left(5\right)$ theory. Next, we take into account fluctuation of the gauge fields in the lattice and obtain a correction to the a priori $SU\left(5\right)$ approximation, because of course the link fluctuations not corresponding to any standard model Lie algebra, but only to the SU(5), do not exist. The model is a development of our old anti-grand-unification model having as its genuine gauge group, close to fundamental scale, a cross-product of the standard model group $S\left(U\right(3)\times U(2\left)\right)$ with itself, with there being one Cartesian product factor for each family. In our old works, we included the hypothesis of the “multiple point criticallity principle”, which here effectively means the coupling constants are critical on the lattice. Counted relative to the Higgs scale, we suggest in our sense that the“unified scale” (where the deviations between the inverse fine structure constants deviate by quantum fluctuations being only from standard model groups, not SU(5)) makes up the 2/3rd power of the Planck scale relative to the Higgs scale or the topquarkmass scale. Full article

In the Standard Model, ad hoc hypotheses assume the existence of three generations of point-like leptons and quarks, which possess a point-like structure and follow the Dirac equation involving four anti-commutative matrices. In this work, we consider the sedenion hypercomplex algebra as an extension of the Standard Model and show its close link to SU(5), which is the underlying symmetry group for the grand unification theory (GUT). We first consider the direct-product quaternion model and the eight-element octonion algebra model. We show that neither the associative quaternion model nor the non-associative octonion model could generate three fermion generations. Instead, we show that the sedenion model, which contains three octonion sub-algebras, leads naturally to precisely three fermion generations. Moreover, we demonstrate the use of basis sedenion operators to construct twenty-four 5 × 5 generalized lambda matrices representing SU(5) generators, in analogy to the use of octonion basis operators to generate Gell-Mann’s eight 3 × 3 lambda-matrix generators for SU(3). Thus, we provide a link between the sedenion algebra and Georgi and Glashow’s SU(5) GUT model that unifies the electroweak and strong interactions for the Standard Model’s elementary particles, which obey SU(3)$\otimes$SU(2)$\otimes$U(1) symmetry. Full article

In this review article, we revisit the topic of baryogenesis, which is the physical process that generated the observed baryon asymmetry during the first stages of the primordial Universe. A viable theoretical explanation to understand and investigate the mechanisms underlying baryogenesis must always ensure that the Sakharov criteria are fulfilled. These essentially state the following: (i) baryon number violation; (ii) the violation of both C (charge conjugation symmetry) and CP (the composition of parity and C); (iii) and the departure from equilibrium. Throughout the years, various mechanisms have been proposed to address this issue, and here we review two of the most important, namely, electroweak baryogenesis (EWB) and Grand Unification Theories (GUTs) baryogenesis. Furthermore, we briefly explore how a change in the theory of gravity affects the EWB and GUT baryogenesis by considering Scalar–Tensor Theories (STT), where the inclusion of a scalar field mediates the gravitational interaction, in addition to the metric tensor field. We consider specific STT toy models and show that a modification of the underlying gravitational theory implies a change in the time–temperature relation of the evolving cosmological model, thus altering the conditions that govern the interplay between the rates of the interactions generating baryon asymmetry, and the expansion rate of the Universe. Therefore, the equilibrium of the former does not exactly occur as in the general relativistic standard model, and there are consequences for the baryogenesis mechanisms that have been devised. This is representative of the type of modifications of the baryogenesis processes that are to be found when considering extended theories of gravity. Full article

Grand unified theories (GUTs) may result in the $E_6$-inspired composite Higgs model (E${}_6$CHM) at low energies, almost stabilizing the electroweak scale. We consider an orbifold GUT in 6 dimensions in which the $E_6$-gauge group is broken to the gauge symmetry of the standard model (SM) while different multiplets of the SM fermions come from different 27-plets. The strongly coupled sector of the E${}_6$CHM is confined on the brane where $E_6$ is broken down to its $SU(6)$ subgroup. Near the scale of $f\gtrsim 5\mathrm{TeV}$, this approximate $SU(6)$ symmetry is expected to be further broken down to its $SU(5)$ subgroup, which contains the SM-gauge group. Such a breakdown leads to a set of pseudo-Nambu–Goldstone bosons (pNGBs) that includes an SM-like Higgs doublet. The approximate gauge coupling unification in the E${}_6$CHM takes place at high energies when the right-handed top quark is a composite fermion. To ensure anomaly cancellation, the weakly coupled sector of this model contains extra exotic matter beyond the SM. We discuss the mechanism of the generation of matter–antimatter asymmetry within the variant of the E${}_6$CHM in which the baryon number and CP invariance are violated. Full article

The tremendous phenomenological success of the Standard Model (SM) suggests that its flavor structure and gauge interactions may not be arbitrary but should have a fundamental first-principle explanation. In this work, we explore how the basic distinctive properties of the SM dynamically emerge from a unified New Physics framework tying together both flavor physics and Grand Unified Theory (GUT) concepts. This framework is suggested by a novel anomaly-free supersymmetric chiral ${\mathrm{E}}_6\times \mathrm{SU}{\left(2\right)}_{\mathrm{F}}\times \mathrm{U}{\left(1\right)}_{\mathrm{F}}$ GUT containing the SM. Among the most appealing emergent properties of this theory is the Higgs-matter unification with a highly-constrained massless chiral sector featuring two universal Yukawa couplings close to the GUT scale. At the electroweak scale, the minimal SM-like effective field theory limit of this GUT represents a specific flavored three-Higgs doublet model consistent with the observed large hierarchies in the quark mass spectra and mixing already at tree level. Full article

The Free Energy Principle (FEP) is currently one of the most promising frameworks with which to address a unified explanation of life-related phenomena. With powerful formalism that embeds a small set of assumptions, it purports to deal with complex adaptive dynamics ranging from barely unicellular organisms to complex cultural manifestations. The FEP has received increased attention in disciplines that study life, including some critique regarding its overall explanatory power and its true potential as a grand unifying theory (GUT). Recently, FEP theorists presented a contribution with the main tenets of their framework, together with possible philosophical interpretations, which lean towards so-called Markovian Monism (MM). The present paper assumes some of the abovementioned critiques, rejects the arguments advanced to invalidate the FEP’s potential to be a GUT, and overcomes criticism thereof by reviewing FEP theorists’ newly minted metaphysical commitment, namely MM. Specifically, it shows that this philosophical interpretation of the FEP argues circularly and only delivers what it initially assumes, i.e., a dual information geometry that allegedly explains epistemic access to the world based on prior dual assumptions. The origin of this circularity can be traced back to a physical description contingent on relative system-environment separation. However, the FEP itself is not committed to MM, and as a scientific theory it delivers more than what it assumes, serving as a heuristic unification principle that provides epistemic advancement for the life sciences. Full article

Local supersymmetry (SUSY) provides an attractive framework for the incorporation of gravity and unification of gauge interactions within Grand Unified Theories (GUTs). Its breakdown can lead to a variety of models with softly broken SUSY at low energies. In this review article, we focus on the SUSY extension of the Standard Model (SM) with an extra $U{\left(1\right)}_N$ gauge symmetry originating from a string-inspired $E_6$ GUTs. Only in this $U\left(1\right)$ extension of the minimal supersymmetric standard model (MSSM) can the right-handed neutrinos be superheavy, providing a mechanism for the baryon asymmetry generation. The particle content of this exceptional supersymmetric standard model (E ${}_6$ SSM) includes three 27 representations of the $E_6$ group, to ensure anomaly cancellation. In addition it also contains a pair of $SU{\left(2\right)}_W$ doublets as required for the unification of gauge couplings. Thus, E ${}_6$ SSM involves exotic matter beyond the MSSM. We consider symmetries that permit suppressing flavor changing processes and rapid proton decay, as well as gauge coupling unification, the gauge symmetry breaking and the spectrum of Higgs bosons in this model. The possible Large Hadron Collider (LHC) signatures caused by the presence of exotic states are also discussed. Full article