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101.
Michael?HellerEmail author Leszek?Pysiak Wies?w?Sasin 《International Journal of Theoretical Physics》2005,44(6):619-628
We continue our program of unifying general relativity and quantum mechanics in terms of a noncommutative algebra А on a transformation groupoid Γ = E × G where E is the total space of a principal fibre bundle over spacetime, and G a suitable group acting on Γ . We show that every a ∊ А defines a random operator, and we study the dynamics of such operators. In the noncommutative regime, there is no usual time but, on the strength of the Tomita–Takesaki theorem, there exists a one-parameter group of automorphisms of the algebra А which can be used to define a state dependent dynamics; i.e., the pair (А, ϕ), where ϕ is a state on А, is a “dynamic object.” Only if certain additional conditions are satisfied, the Connes–Nikodym–Radon theorem can be applied and the dependence on ϕ disappears. In these cases, the usual unitary quantum mechanical evolution is recovered. We also notice that the same pair (А, ϕ) defines the so-called free probability calculus, as developed by Voiculescu and others, with the state ϕ playing the role of the noncommutative probability measure. This shows that in the noncommutative regime dynamics and probability are unified. This also explains probabilistic properties of the usual quantum mechanics. 相似文献
102.
Frank?ReiflerEmail author Randall?Morris 《International Journal of Theoretical Physics》2005,44(8):1307-1324
Defining a spin connection is necessary for formulating Dirac's bispinor equation in a curved space-time. Hestenes has shown
that a bispinor field is equivalent to an orthonormal tetrad of vector fields together with a complex scalar field. In this
paper, we show that using Hestenes' tetrad for the spin connection in a Riemannian space-time leads to a Yang-Mills formulation
of the Dirac Lagrangian in which the bispinor field Ψ is mapped to a set of SL(2,R)× U(1) gauge potentials FαK and a complex scalar field ρ. This result was previously proved for a Minkowski space-time using Fierz identities. As an
application we derive several different non-Riemannian spin connections found in the literature directly from an arbitrary
linear connection acting on the tensor fields (FαK, ρ). We also derive spin connections for which Dirac's bispinor equation is form invariant. Previous work has not considered
form invariance of the Dirac equation as a criterion for defining a general spin connection. 相似文献
103.
Carlos Castro 《Foundations of Physics》2005,35(6):971-1041
We construct the Extended Relativity Theory in Born-Clifford-Phase spaces with an upper R and lower length λ scales (infrared/ultraviolet cutoff). The invariance symmetry leads naturally to the real Clifford algebra Cl (2, 6, R) and complexified Clifford ClC (4) algebra related to Twistors. A unified theory of all Noncommutative branes in Clifford-spaces is developed based on the Moyal-Yang star product deformation quantization whose deformation parameter involves the lower/upper scale
. Previous work led us to show from first principles why the observed value of the vacuum energy density (cosmological constant) is given by a geometric mean relationship
, and can be obtained when the infrared scale R is set to be of the order of the present value of the Hubble radius. We proceed with an extensive review of Smith’s 8D model based on the Clifford algebra Cl (1, 7) that reproduces at low energies the physics of the Standard Model and Gravity, including the derivation of all the coupling constants, particle masses, mixing angles, ....with high precision. Geometric actions are presented like the Clifford-Space extension of Maxwell’s Electrodynamics, and Brandt’s action related to the 8D spacetime tangent-bundle involving coordinates and velocities (Finsler geometries). Finally we outline the reasons why a Clifford-Space Geometric Unification of all forces is a very reasonable avenue to consider and propose an Einstein-Hilbert type action in Clifford-Phase spaces (associated with the 8D Phase space) as a Unified Field theory action candidate that should reproduce the physics of the Standard Model plus Gravity in the low energy limit. 相似文献
104.
Relativistic Brownian Motion and Gravity as an Eikonal Approximation to a Quantum Evolution Equation
We solve the problem of formulating Brownian motion in a relativistically covariant framework in 3+1 dimensions. We obtain
covariant Fokker–Planck equations with (for the isotropic case) a differential operator of invariant d’Alembert form. Treating
the spacelike and timelike fluctuations separately in order to maintain the covariance property, we show that it is essential
to take into account the analytic continuation of “unphysical” fluctuations. 相似文献
105.
According to standard textbooks on compressible fluid dynamics, a shock wave is formed by an accumulation of compression waves. However, the process by which an accumulated compression wave grows into a shock wave has never been visualized. In the present paper, the authors tried to visualize this process using a model wedge with multiple steps. This model is useful for generating a series of compression waves and can simulate a compression process that occurs in a shock tube. By estimating the triple-point trajectory angle, we demonstrated visually that an accumulated compression wave grows into a shock wave. Further reflection experiments over a rough-surface wedge confirmed the tendency for the triple point trajectory angle to reach the asymptotic value
s in the end.This work was first presented at the Symposium on Shock Waves, Japan 2002 相似文献
106.
A Motorcycle Tire Model for Dynamic Simulations: Theoretical and Experimental Aspects 总被引:1,自引:0,他引:1
This paper describes a model for motorcycle tires based on a physical interpretation of experimental data. In this model the real shape of the tire carcass is accurately described and its deformability is taken into account. The actual position of the contact point, that is, the center of the contact patch, is calculated. The concept of instantaneous slip is defined by calculating the longitudinal slip and sideslip angles using the velocity of the actual contact point, which moves with respect to the rim. Tire forces and torques are applied on the actual contact point and calculated according to Pacejkas magic formula. The coupling of sliding properties with elastic ones and the use of the instantaneous slip concept make it possible to properly describe both steady state and transient behavior using the same relations, thus avoiding the use of any auxiliary equations. 相似文献
107.
I discuss the experiments of Joseph Weber (1919-2000) of the University of Maryland between
1960 and 1973 that were aimed at the detection of gravity waves. He used throughout a quadratic
detector to demodulate his antenna signal, which I analyze and compare to a linear detector.The
latter was used by all of the other groups that entered the field. Of these, Richard Garwin and I at
IBM were one of the first groups to publish, and I discuss in detail our experiments between 1973
and 1975. I then discuss the experiments that were carried out at Bell Labs-Rochester, Glasgow,
Munich-Frascati,Moscow, and Tokyo. I compare the results, all of which were negative, with Webers
claimed detection of large numbers of gravity-wave events, as many as seven per day. I conclude
that these were not in fact gravity waves, but artifacts of his extremely hands-on data-analysis procedures,
which I discuss in detail. Finally, I speculate on how this came about. 相似文献
108.
J. Ponce de Leon 《General Relativity and Gravitation》2004,36(5):923-948
We consider brane-world models embedded in a five-dimensional bulk spacetime with a large extra dimension and a cosmological constant. The cosmology in 5D possesses wave-like character in the sense that the metric coefficients in the bulk are assumed to have the form of plane waves propagating in the fifth dimension. We model the brane as the plane of collision of waves propagating in opposite directions along the extra dimension. This plane is a jump discontinuity which presents the usual Z
2 symmetry of brane models. The model reproduces the generalized Friedmann equation for the evolution on the brane, regardless of the specific details in 5D. Model solutions with spacelike extra coordinate show the usual big-bang behavior, while those with timelike extra dimension present a big bounce. This bounce is an genuine effect of a timelike extra dimension. We argue that, based on our current knowledge, models having a large timelike extra dimension cannot be dismissed as mathematical curiosities in non-physical solutions. The size of the extra dimension is small today, but it is increasing if the universe is expanding with acceleration. Also, the expansion rate of the fifth dimension can be expressed in a simple way through the four-dimensional deceleration and Hubble parameters as – q H. These predictions could have important observational implications, notably for the time variation of rest mass, electric charge and the gravitational constant. They hold for the three (k = 0, + 1, – 1) models with arbitrary cosmological constant, and are independent of the signature of the extra dimension. 相似文献
109.
We discuss boosts in a deformed Minkowski space, i.e., a four-dimensional spacetime with metric coefficients depending on nonmetric coordinates (in particular on the energy). The general form of a boost in an arbitrary direction is derived in the case of space anisotropy. Two maximal trivector velocities are mathematically possible, an isotropic and an anisotropic one. However, only the anisotropic velocity has physical meaning, being invariant indeed under deformed boosts. 相似文献
110.
Tomislav Ivezić 《Foundations of Physics》2003,33(9):1339-1347
In this paper it is exactly proved that the standard transformations of the three-dimensional (3D) vectors of the electric and magnetic fields E and B are not relativistically correct transformations. Thence the 3D vectors E and B are not well-defined quantities in the 4D space-time and, contrary to the general belief, the usual Maxwell equations with the 3D E and B are not in agreement with the special relativity. The 4-vectors E
a
and B
a
, as well-defined 4D quantities, are introduced instead of ill-defined 3D E and B. The proof is given in the tensor and the Clifford algebra formalisms. 相似文献