Physics

This paper proposes a new approach to deriving a finite particle content, suitable for the construction of a gauge theory. Specifically, the outlined construction generates a finite set of irreducible gauge representations, which are interpreted as describing a full set of elementary particles. These representations are constructed from endofunctions between restricted representations of some symmetry group G acting on some space V . As a proof of concept, we show how a set of irreducible representations arise as endofunctions on the vector space V= C 8 equipped with the exceptional Lie group G= G 2 as its symmetry group. We discuss how the irreducible representations of our simple example compare to the various particle types of the Standard Model. The process through which the particle content is constructed yields adjoint, fundamental, and Higgs-like representations, thereby reproducing the essential types of particle transformations seen in the Standard Model. In particular we focus on the discrimination of gauge structures and the natural appearance of Higgs-like representations. Avenues to generalizing the construction are considered, and some inevitable consequences are discussed. We conclude by comparing our results to those of non-commutative geometry, commenting on key similarities and differences between the two approaches.

An approach to the quantization of gravity in the presence matter is examined which starts from the classical Einstein-Hilbert action and matter approximated by point particles minimally coupled to the metric. Upon quantization, the Hamilton constraint assumes the form of the Schrödinger equation: it contains the usual Wheeler-DeWitt term and the term with the time derivative of the wave function. In addition, the wave function also satisfies the Klein-Gordon equation, which arises as the quantum counterpart of the constraint among particles' momenta. Comparison of the novel approach with the usual one in which matter is represented by scalar fields is performed, and shown that those approaches do not exclude, but complement each other. In final discussion it is pointed out that the classical matter could consist of superparticles or spinning particles, described by the commuting and anticommuting Grassmann coordinates, in which case spinor fields would occur after quantization.

We propose the generalized uncertainty principle (GUP) with an additional term of quadratic momentum motivated by string theory and black hole physics as a quantum mechanical framework for the minimal length uncertainty at the Planck scale. We demonstrate that the GUP parameter, β 0 , could be best constrained by the the gravitational waves observations; GW170817 event. Also, we suggest another proposal based on the modified dispersion relations (MDRs) in order to calculate the difference between the group velocity of gravitons and that of photons. We conclude that the upper bound reads β 0 ≃ 10 60 . Utilizing features of the UV/IR correspondence and the obvious similarities between GUP (including non-gravitating and gravitating impacts on Heisenberg uncertainty principle) and the discrepancy between the theoretical and the observed cosmological constant Λ (apparently manifesting gravitational influences on the vacuum energy density), known as {\it catastrophe of non-gravitating vacuum}, we suggest a possible solution for this long-standing physical problem, Λ≃ 10 −47 GeV 4 / ℏ 3 c 3 .

The Bell Spaceship Paradox has promoted confusion and numerous resolutions since its first statement in 1959, including resolutions based on relativistic stress due to Lorentz contractions. The paradox is that two ships, starting from the same reference frame and subject to the same acceleration, would snap a string that connected them, even as their separation distance would not change as measured from the original reference frame. This paper uses a Simple Relativity approach to resolve the paradox and explain both why the string snaps, and how to adjust accelerations to avoid snapping the string. In doing so, an interesting parallel understanding of the Lorentz contraction is generated. The solution is applied to rotation to address the Ehrenfest paradox and orbital precession as well.

We give an exceptionally short derivation of Schroedinger's equation by replacing the idealization of a point particle by a density distribution.

The modified gravitational theory by Hajdukovic [arXiv:1210.7421], based on the idea that quantum vacuum contains virtual gravitational dipoles, predicts, among other things, anomalous secular precessions of the planets of the Solar System as large as ≃700−6,000 milliarceconds per century. We demonstrate that they are ruled out by several orders of magnitude by the existing bounds on any anomalous orbital secular rates obtained with the EPM and INPOP ephemerides.

In this study, we develop the generalized Dirac like four-momentum equation for rotating spin-half particles in four-dimensional quaternionic algebra. The generalized quaternionic Dirac equation consists the rotational energy and angular momentum of particle and anti-particle. Accordingly, we also discuss the four vector form of quaternionic relativistic mass, moment of inertia and rotational energy-momentum in Euclidean space-time. The quaternionic four angular momentum (i.e. the rotational analogy of four linear momentum) predicts the dual energy (rest mass energy and pure rotational energy) and dual momentum (linear like momentum and pure rotational momentum). Further, the solutions of quaternionic rotational Dirac energy-momentum are obtained by using one, two and four-component of quaternionic spinor. We also demonstrate the solutions of quaternionic plane wave equation which gives the rotational frequency and wave propagation vector of Dirac particles and anti-particles in terms of quaternionic form.

We reveal a duality in classical and quantum mechanics. Dual systems are related by duality transforms. All mechanical systems that are dual to each other form a duality family. In a duality family, once a system is solved, all other potentials are solved by the dual transform. That is, in a duality family, we only need to solve one system.

It is shown that there exists a duality among fields. If a field is dual to another field, the solution of the field can be obtained from the dual field by the duality transformation. We give a general result on the dual fields. Different fields may have different numbers of dual fields, e.g., the free field and the ϕ 4 -field are self-dual, the ϕ n -field has one dual field, a field with an n -term polynomial potential has n+1 dual fields, and a field with a nonpolynomial potential may have infinite number of dual fields. All fields which are dual to each other form a duality family. This implies that the field can be classified in the sense of duality, or, the duality family defines a duality class. Based on the duality relation, we can construct a high-efficiency approach for seeking the solution of field equations: solving one field in the duality family, all solutions of other fields in the family are obtained immediately by the duality transformation. As examples, we consider some ϕ n -fields, general polynomial-potential fields, and the sine-Gordon field.

A duality among scalar fields is revealed. If two fields are dual to each other, the solutions of their field equations are related by a duality transform. That is, once the solution of a field equation is known, the solution of the dual field can be obtained by the duality transform. A scalar field has a series of dual fields, forming a duality family. Once the solution of a field in the duality family is solved, the solutions of all other fields in the family are given by the duality transform. That is, a series of exactly solvable model can be constructed from one exactly solvable model. The dual field of the sine-Gordon field, the sinh-Gordon field, the power-introduction field, etc., are considered as examples.