Spacetime without reference frames: An application to the kinetic theory

Matolcsi, T.; Gruber, Thomas

doi:10.1007/bf02084958

Cited by 21 publications

(25 citation statements)

References 16 publications

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“…Still, unlike the theory of electromagnetism, the case of the gravitational interaction is significantly compounded by transformation of the tensor  and the given 4-velocity by Lorentz boost link. The Lorentz boost link was independently found by several authors [2], [3], [7] and we present it here in the form…”

Section: Theoretical Considerations Of Nonlinear Parallel Transportmentioning

confidence: 77%

“…Thus, it is expected that the field tensor which will be used to derive the equations of motion for the body with mass m to include the velocity (Ui). Analogously to the Lienard-Wiechert potentials in electromagnetism, let the relations among the elements of the tensor  be the following: (3) assuming that the gravitational interaction from the body with mass M at the space-time point (x*, y*, z*, ict*) arrives to the space-time point (x, y, z, ict), after time t  t*. …”

Section: Theoretical Considerations Of Nonlinear Parallel Transportmentioning

confidence: 99%

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On the Nordtvedt effect in Minkowski spacetime with nonlinear connection

Trenčevski

Celakoska

2017

IJAMR

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The Lunar Laser Ranging (LLR) experiment provided precise data which brought the possibility to make more stringent conclusions for the foundations of gravitational theories, i.e. the Equivalence Principles. Beside some effects of non -gravitational origin, the LLR data was fitted with the well-known gravitational effects such as the apsidal and geodetic precessions, the time delay, etc. The Nordtvedt effect in General Relativity (GR) vanishes, while the LLR experiment data of the Earth-Moon distance and the laboratory experiments with experimental bodies made of different chemical compositions measured a variation of distance in millimeters. According to the mathematical model of gravitation in Minkowski space endowed with a nonlinear connection we obtained a result closer to the experimental measurements. More precisely, we obtained a difference of 0.17 mm (or 0.28 mm, depending on the value of the scaling factor) from the LLR measurements of the variation of the Earth-Moon distance, while the corresponding result in GR makes a difference from the LLR measurements of 5.7 mm. The gravitational theory with nonlinear connection in Minkowski space gives the same results for the confirmed GR effects, nevertheless it yields some additional variations of the distance concerning the Nordtvedt effect.

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Section: Theoretical Considerations Of Nonlinear Parallel Transportmentioning

confidence: 77%

Section: Theoretical Considerations Of Nonlinear Parallel Transportmentioning

confidence: 99%

On the Nordtvedt effect in Minkowski spacetime with nonlinear connection

Trenčevski

Celakoska

2017

IJAMR

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“…Then, near one such end, quantum effects in the range of wavelengths that are much larger then the width of the wire as well as the size of this attached blob but smaller then the length of the wire may be well described by one of the "free particle on the half line" self-adjoint Hamiltonians, presumably different ones for different materials attached. 6 For a full theory of how physical dimensions can be formulated and treated mathematically -via one dimensional vector spaces and their tensorial products, quotients and powers -see [7].…”

Section: Free Particle On a Half Linementioning

confidence: 99%

Singular Potentials in Quantum Mechanics and Ambiguity in the Self-Adjoint Hamiltonian

Fülöp¹

2007

SIGMA

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Abstract. For a class of singular potentials, including the Coulomb potential (in three and less dimensions) and V (x) = g/x 2 with the coefficient g in a certain range (x being a space coordinate in one or more dimensions), the corresponding Schrödinger operator is not automatically self-adjoint on its natural domain. Such operators admit more than one self-adjoint domain, and the spectrum and all physical consequences depend seriously on the self-adjoint version chosen. The article discusses how the self-adjoint domains can be identified in terms of a boundary condition for the asymptotic behaviour of the wave functions around the singularity, and what physical differences emerge for different selfadjoint versions of the Hamiltonian. The paper reviews and interprets known results, with the intention to provide a practical guide for all those interested in how to approach these ambiguous situations.

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“…With the help of the Galilean relativistic space-time model one can show that the formal invariance (independency of the angular velocity of the rotating reference frame) is a wrong requirement, because reference frame independency is not always invariance, sometimes it requires that the characteristics of the relative motion appear in the transformation rules [44], as it is evident in case of Galilean transformations. Moreover, from a spacetime point of view the formulation of material frame indifference of Noll is self-contradictory [45].…”

Section: Introductionmentioning

confidence: 99%

Galilean relativistic fluid mechanics

Ván

2017

Continuum Mech. Thermodyn.

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Abstract. Single component nonrelativistic dissipative fluids are treated independently of reference frames and flow-frames. First the basic fields and their balances, then the related thermodynamic relations and the entropy production are calculated and the linear constitutive relations are given.The usual basic fields of mass, momentum, energy and their current densities, the heat flux, pressure tensor and diffusion flux are the time-and spacelike components of the third order mass-momentum-energy density-flux four-tensor. The corresponding Galilean transformation rules of the physical quantities are derived.It is proved, that the non-equilibrium thermodynamic frame theory, including the thermostatic Gibbs relation and extensivity condition and also the entropy production is independent of the reference frame and also the flow-frame of the fluid. The continuity-Fourier-Navier-Stokes equations are obtained almost in the traditional form if the flow of the fluid is fixed to the temperature. This choice of the flow-frame is the thermo-flow.A simple consequence of the theory is that the relation between the total, kinetic and internal energies is a Galilean transformation rule.

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Spacetime without reference frames: An application to the kinetic theory

Cited by 21 publications

References 16 publications

On the Nordtvedt effect in Minkowski spacetime with nonlinear connection

On the Nordtvedt effect in Minkowski spacetime with nonlinear connection

Singular Potentials in Quantum Mechanics and Ambiguity in the Self-Adjoint Hamiltonian

Galilean relativistic fluid mechanics

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