Physics

The application of the CPT theorem to an apple falling on Earth leads to the description of an anti-apple falling on anti-Earth (not on Earth). On the microscopic level, the Dirac equation in curved space-time simultaneously describes spin-1/2 particles and their antiparticles coupled to the same curved space-time metric (e.g., the metric describing the gravitational field of the Earth). On the macroscopic level, the electromagnetically and gravitationally coupled Dirac equation therefore describes apples and anti-apples, falling on Earth, simultaneously. A particle-to-antiparticle transformation of the gravitationally coupled Dirac equation therefore yields information on the behavior of "anti-apples on Earth". However, the problem is exacerbated by the fact that the operation of charge conjugation is much more complicated in curved as opposed to flat space-time. Our treatment is based on second-quantized field operators and uses the Lagrangian formalism. As an additional helpful result, prerequisite to our calculations, we establish the general form of the Dirac adjoint in curved space-time. On the basis of a theorem, we refute the existence of tiny, but potentially important, particle-antiparticle symmetry breaking terms whose possible existence has been investigated in the literature. Consequences for antimatter gravity experiments are discussed.

Through a Möbius transformation, we study aspects like topology, ligth cones, horizons, curvature singularity, lines of constant Schwarzschild coordinates r and t , null geodesics, and transformed metric, of the spacetime (SKS/2 ) ′ that results from: i) the antipode identification in the Schwarzschild-Kruskal-Szekeres ( SKS ) spacetime, and ii) the suppression of the consequent conical singularity. In particular, one obtains a non simply-connected topology: (SKS/2 ) ′ ≅ R 2∗ × S 2 and, as expected, bending light cones.

Identification of crack positions or anomalies in materials using the time reversal based nonlinear elastic wave spectroscopy (TR-NEWS) is an established method. We propose a system using transducers which emit forward propagating solitonic wave and time-reversed propagating solitonic wave produced by memristers placed on a side of a rectangle and scattered by cracks in the material and received by receivers which are placed on the opposite side of the rectangle. By minimizing the difference of the scattered forward propagating wave and the scattered TR wave, we get information of the position of the crack by using the neural network technique. Route of the solitons are expressed by 2 dimensional projective quaternion functions, and parameters for getting the optimal route from signals are expected to be reduced. We consider the wave is expressed by a soliton which is conformal, and discuss symmetry protected topological impurities and gravitational effects using the Atiyah-Patodi-Singer's index theorem.

The existing viscous and incompressible theory of isothermal sound propagation and attenuation in suspensions considers solid particles which are infinitely viscous. We extend the theory by applying the amended Coriolis flowmeter "bubble theory". Here, the drag force is a function of both the fluid and particle Stokes numbers and the particle-to-fluid ratio of the dynamic viscosity [V.Galindo and G.Gerbeth, A note on the force of an accelerating spherical drop at low-Reynolds number, Phys. Fluids A Vol. 5, 3290-3292 (1993)]. Aerosol and hydrosol examples are presented and differences between the original and extended theories are discussed.

The Bell inequality is thought to be a common constraint shared by all models of local hidden variables that aim to describe the entangled states of two qubits. Since the inequality is violated by the quantum mechanical description of these states, it purportedly allows distinguishing in an experimentally testable way the predictions of quantum mechanics from those of models of local hidden variables and, ultimately, ruling the latter out. In this paper, we show, however, that the models of local hidden variables constrained by the Bell inequality all share a subtle, though crucial, feature that is not required by fundamental physical principles and, hence, it might not be fulfilled in the actual experimental setup that tests the inequality. Indeed, the disputed feature neither can be properly implemented within the standard framework of quantum mechanics and it is even at odds with the fundamental principle of relativity. Namely, the proof of the inequality requires the existence of a preferred absolute frame of reference (supposedly provided by the lab) with respect to which the hidden properties of the entangled particles and the orientations of each one of the measurement devices that test them can be independently defined through a long sequence of realizations of the experiment. We notice, however, that while the relative orientation between the two measurement devices is a properly defined physical magnitude in every single realization of the experiment, their global rigid orientation with respect to a lab frame is a spurious gauge degree of freedom. Following this observation, we were able to explicitly build a model of local hidden variables that does not share the disputed feature and, hence, it is able to reproduce the predictions of quantum mechanics for the entangled states of two qubits.

Bell's theorem is supposed to exclude all local hidden-variable models of quantum correlations. However, an explicit counterexample shows that a new class of local realistic models, based on generalized arithmetic and calculus, can exactly reconstruct rotationally symmetric quantum probabilities typical of two-electron singlet states. Observable probabilities are consistent with the usual arithmetic employed by macroscopic observers, but counterfactual aspects of Bell's theorem are sensitive to the choice of hidden-variable arithmetic and calculus. The model is classical in the sense of Einstein, Podolsky, Rosen, and Bell: elements of reality exist and probabilities are modeled by integrals of hidden-variable probaility densities. Probability densities have a Clauser-Horne product form typical of local realistic theories. However, neither the product nor the integral nor the representation of rotations are the usual ones. The integral has all the standard properties but only with respect to the arithmetic that defines the product. Certain formal transformations of integral expressions one finds in the usual proofs à la Bell do not work, so standard Bell-type inequalities cannot be proved. The system we consider is deterministic, local-realistic, rotationally invariant, observers have free will, detectors are perfect, so is free of all the canonical loopholes discussed in the literature.

Strands are causal curves in spacetime with no distinct interior points, introduced to describe quantum nonlocality in a spacetime framework. We present a model where the standard model particles are bound states of strands that interact by exchanging strands. In strand spacetime, it is not just the positron whose existence is implied by the Dirac Lagrangian: we show that hidden within this simple Lagrangian are all the quarks, leptons, and gauge bosons, with their correct spin, electric charges, color charges, and, in the electroweak sector, stability. Also encoded in the combinatorics of the Dirac Lagrangian are all the trivalent electroweak interactions (involving both leptons and quarks), electroweak parity violation, as well as 16 independent mass orderings that all agree exactly with experiment. However, the model predicts the existence of massive gluons that are cousins of the W and Z bosons, but no other particles. Using the geometry of strands, we are able to derive many properties of quarks, such confinement, three color charges, and their allowable combinations into baryons and mesons. We also show that CPT invariance holds for all interactions, where C, P, and T each sit in a different connected component of the full Lorentz group. Finally, we introduce a quantum modification to Einstein's equation by reinterpreting the chiral decomposition of the Dirac Lagrangian.

The star product usually associated to the Snyder model of noncommutative geometry is nonassociative, and this property prevents the construction of a proper Hopf algebra. It is however possible to introduce a well-defined Hopf algebra by including the Lorentz generators and their conjugate momenta into the algebra. In this paper, we study the realizations of this extended Snyder spacetime, and obtain the coproduct and twist and the associative star product in a Weyl-ordered realization, to first order in the noncommutativity parameter. We then extend our results to the most general realizations of the extended Snyder spacetime, always up to first order.

Classical and quantum mechanical analysis have been carried out on harmonic like oscillator with asymmetric position dependent mass. Phase space analysis are performed both classically and quantum mechanically for a plausible understanding of the subject.

In this paper, we present a type D, non-vanishing cosmological constant, vacuum solution of the Einstein's field equations, extension of an axially symmetric, asymptotically flat vacuum metric with a curvature singularity. The space-time admits closed time-like curves (CTCs) that appear after a certain instant of time from an initial spacelike hypersurface, indicating it represents a time-machine space-time. We wish to discuss the physical properties and show that this solution can be interpreted as gravitational waves of Coulomb-type propagate on anti-de Sitter space backgrounds. Our treatment focuses on the analysis of the equation of geodesic deviation.