Abstract:
Although experiments carried out by Jain et al. showed that the Cooper pairs obey the strong equivalence principle, The measurement of the Cooper pairs inertial mass by Tate et al. revealed an anomalous excess of mass. In the present paper we interpret these experimental results in the framework of an electromagnetic model of dark energy for the superconductors' vacuum. We argue that this physical vacuum is associated with a preferred frame. Ultimately from the conservation of energy for Cooper pairs we derive a model for a variable vacuum speed of light in the superconductors physical vacuum in relation with a possible breaking of the weak equivalence principle for Cooper pairs.

Abstract:
The presence of a non-zero cosmological term in Einstein field equations can be interpreted as the physical possibility for preferred reference frames without breaking of general covariance. This possibility is used in the process of linearizing Einstein field equations in a de Sitter background, and in formulating the resulting equations in the framework of gravitoelectromagnetism. It is proposed that this set of equations only applies to the physical vacuum and not to baryonic (normal) matter.

Abstract:
Non classical rotational inertia observed in rotating supersolid $He^4$ can be accounted for by a gravitomagnetic London moment similar to the one recently reported in rotating superconductive rings.

Abstract:
In 1989 Cabrera and Tate reported an anomalous excess of mass of the Cooper pairs in rotating thin Niobium rings. So far, this experimental result never received a proper theoretical explanation in the context of superconductor's physics. In the present work we argue that what Cabrera and Tate interpreted as an anomalous excess of mass can also be associated with a deviation from the classical gravitomagnetic Larmor theorem due to the presence of dark energy in the superconductor, as well as with the discrete structure of the area of the superconducting Niobium ring as predicted by Loop Quantum Gravity. From Cabrera and Tate measurements we deduce that the quantization of spacetime in superconducting circular rings occurs at the Planck-Einstein scale $l_{PE} = (\hbar G/c^3 \Lambda)^{1/4}\sim 3.77\times 10 ^{-5} m$, instead of the Planck scale $l_{P} =(\hbar G / c^3)^{1/2}=1.61 \times 10 ^{-35} m$, with an Immirzi parameter which depends on the specific critical temperature of the superconducting material and on the area of the ring. The stephan-Boltzmann law for quantized areas delimited by superconducting rings is predicted, and an experimental concept based on the electromagnetic black-body radiation emitted by this surfaces, is proposed to test loop quantum gravity and electromagnetic dark energy in superconductors.

Abstract:
In the present paper we argue that timing irregularities in pulsars, like glitches and timing noise, could be associated with the violation of the weak equivalence principle for vortices in the superfluid core of rotating neutron stars.

Abstract:
The attractive gravitational force between two electrons in superconductors is deduced from the Eddington-Dirac large number relation, together with Beck and Mackey electromagnetic model of vacuum energy in superconductors. This force is estimated to be weaker than the gravitational attraction between two electrons in the vacuum.

Abstract:
The phenomenological nature of a new gravitational type interaction between two different bodies derived from Verlinde's entropic approach to gravitation in combination with Sorkin's definition of Universe's quantum information content, is investigated. Assuming that the energy stored in this entropic gravitational field is dissipated under the form of gravitational waves and that the Heisenberg principle holds for this system, one calculates a possible value for an absolute minimum time scale in nature $\tau=15/16 \frac{\Lambda^{1/2}\hbar G}{c^4}\sim9.27\times10^{-105}$ seconds, which is much smaller than the Planck time $t_{P}=(\hbar G/c^5)^{1/2}\sim 5.38\times10^{-44}$ seconds. This appears together with an absolute possible maximum value for Newtonian gravitational forces generated by matter $F_g=32/30\frac{c^7}{\Lambda \hbar G^2}\sim 3.84\times 10^{165}$ Newtons, which is much higher than the gravitational field between two Planck masses separated by the Planck length $F_{gP}=c^4/G\sim1.21\times10^{44}$ Newtons.

Abstract:
Verlinde recently developed a theoretical account of gravitation in terms of an entropic force. The central element in Verlinde's derivation is information and its relation with entropy through the holographic principle. The application of this approach to the case of superconductors requires to take into account that information associated with superconductor's quantum vacuum energy is not stored on Planck size surface elements, but in four volume cells with Planck-Einstein size. This has profound consequences on the type of gravitational force generated by the quantum vacuum condensate in superconductors, which is closely related with the cosmological repulsive acceleration responsible for the accelerated expansion of the Universe. Remarkably this new gravitational type force depends on the level of breaking of the weak equivalence principle for cooper pairs in a given superconducting material, which was previously derived by the author starting from similar principles. It is also shown that this new gravitational force can be interpreted as a surface force. The experimental detection of this new repulsive gravitational-type force appears to be challenging.

Abstract:
A gravitomagnetic analogue of the London moment in superconductors can explain the anomalous Cooper pair mass excess reported by Janet Tate. Ultimately the gravitomagnetic London moment is attributed to the breaking of the principle of general covariance in superconductors. This naturally implies non-conservation of classical energy-momentum. Possible relation with the manifestation of dark energy in superconductors is questioned.

Abstract:
The propagation of the wave function of a particle is characterised by a group and a phase velocity. The group velocity is associated with the particle's classical velocity, which is always smaller than the speed of light, and the phase velocity is associated with the propagation speed of the wave function phase and is treated as being unphysical, since its value is always greater than the speed of light. Here we show, using Sciama's Machian formulation of rest mass energy, that this physical interpretation, for the group and the phase velocity of the wave function, is only valid if the weak equivalence principle strictly holds for the propagating particle, except for the photon. In case this constraint is released the phase velocity of the wave function could acquire a physical meaning in quantum condensates.