Gravitation interactions

Neutron and quark stars are natural laboratories to investigate the interplay of strong, electro-weak and gravitational interaction. Many theoretically determined properties of these astrophysical objects were tested by the observed properties of pulsars, and detailed calculations exist for these stars[ 1 —4. ... 

GRA.3. I. Prigogine and G. Severne, Nonequilibrium Statistical Mechanics and gravitational interactions, Bull. Astronomique 3, 273-287 (1968). 

To conclude this contribution to the special issue of Advances in Chemical Physics, I would only recall that this question of the statistical mechanics of systems with gravitational interaction remained of interest to Professor Prigogine until the very end of his life, as it was the topic of an interesting and lively discussion between the two of us in June 2001 at a scientific meeting at Les Treilles in Southern France. 

M. L. Chabanol, F. Corson, and Y. Pomeau Statistical mechanics of point particles with a gravitational interaction, Europhys. Lett. 50, 148 (2000). 

Consider tlie mutual approach of two noble gas atoms. At infinite separation, there is no interaction between them, and this defines die zero of potential energy. The isolated atoms are spherically symmetric, lacking any electric multipole moments. In a classical world (ignoring the chemically irrelevant gravitational interaction) there is no attractive force between them as they approach one another. When tliere are no dissipative forces, the relationship between force F in a given coordinate direction q and potential energy U is... 

We note several very general formulations of the problem. A striking example of this is Ya.B. s 1967 paper [14 ], in which he considers the possibility of a theory in which the bare photon field is absent, while the observed electromagnetic field is created entirely by quantum fluctuations of a vacuum. This bold idea, which extends to electrodynamics an earlier idea about gravitational interaction (in part, under the influence of Ya.B. s papers on the cosmological constant), has not yet been either proved or disproved. However, both ideas have elicited lively discussion in the scientific literature. 

The extension of a Klein-Gordon-like equation, see Eqs. (65)-(73), to include gravitational interactions is quite straightforward in our present theory. Since general relativity associates gravity with tensor fields, we need to incorporate the operator and their conjugate counterparts simultaneously. To accomplish the first part of the conjugate pair formulation, we will attach to our previous model in the basis m,m), the interaction... 

This corresponds to a damped oscillator, which was expected since the tensor modes correspond to gravitational waves. These can propagate even in the absence of matter. In addition to these equations, one also has to specify the equations governing the evolution of matter, that is the matter conservation and the Euler equations. In the absence of gravitational interactions, they read... 

On small scales, these sources of pressure determine the evolution of perturbations. Consider once again Eq. 10.10. When the wavenumber k > kj, or conversely when the wavelength is smaller than the Jeans length, pressure dominates over gravity and the fluid oscillates with angular frequency u csk. The detailed solution actually involves Bessel functions when expansion is correctly taken into account, and there are additional complications due to gravitational interactions with any pressureless component such as CDM which can continue to collapse. 

Much current theoretical work is devoted to finding a more fundamental and general underlying theory from which the standard model of particle physics could be deduced as the low energy limit. String theory and the inclusion of the gravitational interaction are central viewpoints, and in such theories particles may have structure and the CPT theorem may be violated. 

We will now extend the present model to include gravitational interactions by augmenting the model presented in the previous section with a general scalar interaction as follows in the basis m, rn) ... 

Let us now consider the case with pr — 0 implying that the particle (and similarly for the antiparticle) either orbits the system M or is so far away from the large system that there is no "gravitational" interaction between m and M. In this situation, we realize, see Eqs. (52) and (53) further below, that the kinematical interaction p/c equals irac(r) for a given value of r or... 

The present model is quite surprising in its simplicity and yet the interpretation is very different compared to classical and quantum mechanical pictures. The ansatz Eq. (2) implies that every fundamental quantum particle will occupy one of two quantum states. When the choice is made the associated antiparticle will be indirectly recognized through the kinematical interaction v and the appearance of the length- and time-scale contractions. We do not, therefore, directly experience mirror- (anti-)particles, unless they are bodily excited. Within the present description, we have proposed a generalized quantum description, which transcends classical features as the contraction of scales mentioned above, including also a dynamical formulation of gravitational interactions. 

The runaway, oligarchic, and early post-oligarchic stages of planet formation take place while gas is present in the disk. Gravitational interactions between a planet and... 

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