Principles of Quantum General Relativity

Born-Kothari Condensation for Fermions

“…Interestingly enough, this point was nicely demonstrated with several examples (including the deviation from standard Planck's distribution law) by Born that the correction due to reciprocity principle (although very small) makes sense only at extremely high energy (or equivalent temperature) [12]. An estimation of the aforesaid energy scale following Born is given by k B Θ 0 1.41 × 10 8 eV, which in terms of temperature corresponds to Θ 0 1.63 × 10 12 degrees (See Equation (37) of Reference [12]). Since in the last twenty years there are experimental data reporting that electrons may reach 200 GeV [47], it suggests that any modification in the density of states due to reciprocity principle may only appear at energies 1 TeV (see also Discussion Section 6).…”

“…With the advent of renormalization theory and Higg's mechanism in the last seventy years [32][33][34][35], both in theory as well as in experiments, it has also been suggested that Born's reciprocity may be the underlying physical reason for the T-duality symmetry in string theory [25,35,36], and may be of relevance in developing a quantum geometry [37,38].…”

“…It is also possible to account for a Bardeen-Cooper-Schrieffer (BCS)-like condensation incorporating Grassmann variables, which calls for a separate discussion [66][67][68][69]. Here, instead, we invoke the seldom used but reasonable basis for the possible existence of a condensed phase for the FD gas [14] that is based on the hypothesis of reciprocity principle [12,13,17,21,40,41,43,[104][105][106], which is considered one of the cornerstones for the development of the theory of elementary particles [16,18,20,[22][23][24]42] and other related fields [25,[35][36][37][38]. As evident filling up a Fermi sea of real particles at an energy scale of MeV or even more is not only difficult but hardly imaginable.…”

A Short-Range Force

“…Let us apply equation (4) to equation (1), keeping in mind equation (5). We then get, considering only the order of magnitude, which is what interests us here, after some manipulation…”

“…We can ask whether such a consideration can be applied to elementary particles, if in fact they can be considered in the context of General Relativity. It may be mentioned that apart from Quantum Gravity, there have been three different approaches for studying elementary particles via General Relativity [4,5,6] and references therein. We will now show that it is possible to extend the Gravitomagnetic and Gravitoelectric formulations to elementary particles within the framework of the theory developed in [6].…”