From Clock Synchronization to Dark Matter as a Relativistic Inertial Effect

Lusanna, Luca

doi:10.1007/978-3-319-00297-2_17

Cited by 2 publications

(13 citation statements)

References 57 publications

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“…To develop relativistic kinetic theory, one has to describe in this framework isolated systems of either free or interacting particles: this was done in [24][25][26][27][28]31] (see [8] for a review). In the 3 + 1 approach, each scalar positive-energy particle is described by radar three-coordinates η r i (τ) individuating the intersection of the world-line x µ i (τ), i= 1, ..., N, with the instantaneous three-space…”

Section: Classical Relativistic Mechanics In the Inertial Rest Frame mentioning

confidence: 99%

“…In the two-body case (see [8,24,25,[27][28][29] for the N-body case), a canonical transformation allows one to get the following collective (the notation η + , κ + = P ≈ 0 for the internal three-center of mass inside the Wigner three-space is used) and relative variables (m = m 1 + m 2 ):…”

Section: Classical Relativistic Mechanics In the Inertial Rest Frame mentioning

confidence: 99%

“…The ordinary and extended micro-canonical partition functions in the inertial rest frameZ (nr) (E , V, N) andZ (nr) (E , S, V, N) will be defined in Section 4.1 by using only the internal Galilei generators of the isolated system. In the non-relativistic setting, it is possible to reintroduce the dependence on the center of mass and to recover the original partition functions (8) and (12).…”

Section: The Relativistic Micro-canonical Ensemble In Inertial Rest Fmentioning

confidence: 99%

“…A relativistic one-particle distribution function in the inertial rest frame can be defined by considering a normalized density function for a relativistic Gibbs ensemble (assumed to transform like the relativistic micro-canonical distribution function to which it tends at equilibrium) of the type ρ ( η 1 , κ 1 , ..., η N , κ N , τ) with η i , κ i , i = 1, ..., N, being Wigner three-vectors in the Wigner three-spaces. Then, the natural definition for the one-particle distribution function in the Wigner three-spaces without a dependence on both the external and internal centers of mass is (see Equation (8) for χ(V)):…”

Section: The One-particle Distribution Function In the Relativistic Imentioning

confidence: 99%

“…After more than thirty years of efforts to solve these problems in 1965, Currie, Jordan and Sudarshan [6] demonstrated a no-interaction theorem according to which in the presence of a canonical realization of the Poincaré, group one can have q µ i (τ) = x µ i (τ) with these quantities being four-vectors only in the free case. In the next forty years, many different approaches trying to overcome the theorem were developed: see [7,8] for a review of all of these attempts.…”

Section: Introductionmentioning

confidence: 99%

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From Relativistic Mechanics towards Relativistic Statistical Mechanics

Lusanna¹

2017

Entropy

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Till now, kinetic theory and statistical mechanics of either free or interacting point particles were well defined only in non-relativistic inertial frames in the absence of the long-range inertial forces present in accelerated frames. As shown in the introductory review at the relativistic level, only a relativistic kinetic theory of "world-lines" in inertial frames was known till recently due to the problem of the elimination of the relative times. The recent Wigner-covariant formulation of relativistic classical and quantum mechanics of point particles required by the theory of relativistic bound states, with the elimination of the problem of relative times and with a clarification of the notion of the relativistic center of mass, allows one to give a definition of the distribution function of the relativistic micro-canonical ensemble in terms of the generators of the Poincaré algebra of a system of interacting particles both in inertial and in non-inertial rest frames. The non-relativistic limit allows one to get the ensemble in non-relativistic non-inertial frames. Assuming the existence of a relativistic Gibbs ensemble, also a "Lorentz-scalar micro-canonical temperature" can be defined. If the forces between the particles are short range in inertial frames, the notion of equilibrium can be extended from them to the non-inertial rest frames, and it is possible to go to the thermodynamic limit and to define a relativistic canonical temperature and a relativistic canonical ensemble. Finally, assuming that a Lorentz-scalar one-particle distribution function can be defined with a statistical average, an indication is given of which are the difficulties in solving the open problem of deriving the relativistic Boltzmann equation with the same methodology used in the non-relativistic case instead of postulating it as is usually done. There are also some comments on how it would be possible to have a hydrodynamical description of the relativistic kinetic theory of an isolated fluid in local equilibrium by means of an effective relativistic dissipative fluid described in the Wigner-covariant framework.

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Section: Classical Relativistic Mechanics In the Inertial Rest Frame mentioning

confidence: 99%

Section: Classical Relativistic Mechanics In the Inertial Rest Frame mentioning

confidence: 99%

Section: The Relativistic Micro-canonical Ensemble In Inertial Rest Fmentioning

confidence: 99%

Section: The One-particle Distribution Function In the Relativistic Imentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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From Relativistic Mechanics towards Relativistic Statistical Mechanics

Lusanna¹

2017

Entropy

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Non-inertial frames in Minkowski space-time, accelerated either mathematical or dynamical observers and comments on non-inertial relativistic quantum mechanics

Crater

Lusanna

2014

Int. J. Geom. Methods Mod. Phys.

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After a review of the existing theory of non-inertial frames and mathematical observers in Minkowski space-time we give the explicit expression of a family of such frames obtained from the inertial ones by means of point-dependent Lorentz transformations as suggested by the locality principle. These non-inertial frames have non-Euclidean 3-spaces and contain the differentially rotating ones in Euclidean 3-spaces as a subcase. Then we discuss how to replace mathematical accelerated observers with dynamical ones (their world-lines belong to interacting particles in an isolated system) and how to define Unruh-DeWitt detectors without using mathematical Rindler uniformly accelerated observers. Also some comments are done on the transition from relativistic classical mechanics to relativistic quantum mechanics in non-inertial frames.

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From Clock Synchronization to Dark Matter as a Relativistic Inertial Effect

Cited by 2 publications

References 57 publications

From Relativistic Mechanics towards Relativistic Statistical Mechanics

From Relativistic Mechanics towards Relativistic Statistical Mechanics

Non-inertial frames in Minkowski space-time, accelerated either mathematical or dynamical observers and comments on non-inertial relativistic quantum mechanics

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