Browsing by Author "Marchal,C."

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The Energy probability distribution of quantum levels of a particle imprisoned in a three dimensional box
(IOP Publishing Ltd, 2022) Yarman,T.; Akkus,B.; Arik,M.; Marchal,C.; Cokcoskun,S.; Kholmetskii,A.; Özaydin,F.
This work was trigerred by the earlier achivements of Yarman et al, aiming to bridge themordynamics and quantum mechanics, whence, Planck constant came to replace Boltzmann constant, and "average quantum level number"came to replace "temperature". This evoked that the classical Maxwell energy probability distribution p(E) with respect to energy E of gas molecules might be taken care of, by the "energy probability distribution of the quantum levels"of a particle imprisoned in a given volume, assuming that in the case we have many particles, following Pauli exclusion principle, no pair of particles can sit at the same level. Thereby, the energy probability distribution of the quantum levels of a particle imprisoned in three dimensions, will be the subject of this essay. Such an outlook becomes interesting from several angles: i) It looks indeed very much like a classical Maxwellian distribution. ii) In the case we have as many free particles in the box as the number of levels depicted by the number of quantum levels in between the predetermined lower bound energy level and the upperbound energy level, all the while assuming that the Pauli principle holds, the distribution we disclose becomes the energy probability distribution of the ensemble of particles imprisoned in the given box. iii) It can even be guessed that, if elastic collisions between the free particles were allowed, and still assuming quantization and the Pauli principle, the outcome we disclose should be about the same as that of the energy probability distribution, molecules in a room would display in equilibrium. iv) The quantized energy being proportional to the sum of three squared integers associated with respectively, each of the spatial dimensions; the property we reveal certainly becomes remarkable from the point of view of mathematics of integer numbers. All the more, we further disclose that, to the probability distribution outlook remains the same, be this qualitatively for higher dimensions than 3. © Published under licence by IOP Publishing Ltd.
Citation Count: 2
The Eötvös experiment, GTR, and differing gravitational and inertial masses Proposition for a crucial test of metric theories
(Institute of Physics Publishing, 2019) Yarman,T.; Kholmetskii,A.L.; Marchal,C.; Yarman,O.; Arik,M.
The Eötvös experiment has been taken as basis for metric theories of gravity and particularly for the general theory of relativity (GTR), which assumes that gravitational and inertial masses are identical. We highlight the fact that, unlike the long lasting and reigning belief, the setup by Eötvös experiments and its follow-ups serve to demonstrate no more than a mere linear proportionality between said masses, and not ineludibly their exclusive equality. So much so that, as one distinct framework, Yarman-Arik-Kholmetskii (YARK) gravitation theory, where a purely metric approach is not aimed, makes the identity between inertial and gravitational masses no longer imperative while still remaining in full conformance with the result of the Eötvös experiment, as well as that of free fall experiments. It is further shown that Eötvös experiment deprives us of any knowledge concerning the determination of the proportionality coefficient coming into play. Henceforward, the Eötvös experiment and its follow-ups cannot be taken as a rigorous foundation for GTR. In this respect, we suggest a crucial test of the equality of gravitational and inertial masses via the comparison of the oscillation periods of two pendulums with different arm lengths, where the deviation of the predictions by GTR and by YARK theory represents a measurable value. © Published under licence by IOP Publishing Ltd.