Quaternion Algebra on 4D Superfluid Quantum Space-Time: Gravitomagnetism

Abstract

Gravitomagnetic equations result from applying quaternionic differential operators to the energy-momentum tensor. These equations are similar to the Maxwell's EM equations. Both sets of the equations are isomorphic after changing orientation of either the gravitomagnetic orbital force or the magnetic induction. The gravitomagnetic equations turn out to be parent equations generating the following set of equations: (a) the vorticity equation giving solutions of vortices with nonzero vortex cores and with infinite lifetime; (b) the Hamilton-Jacobi equation loaded by the quantum potential. This equation in pair with the continuity equation leads to getting the Schrödinger equation describing a state of the superfluid quantum medium (a modern version of the old ether); (c) gravitomagnetic wave equations loaded by forces acting on the outer space. These waves obey to the Planck's law of radiation.Keywords superfluid quantum vacuum · gravitomagnetic · electromagnetism · wave function · vorticity · vortex · cosmic microwave radiation 1 Introduction Roger Penrose in his earlier works [65,66] has proposed the formalism of twistor algebra where four parameters of the space-time, t, x, y, z, by amazing manner find accordance with spinor group SU(2). Twistor theory was originally proposed as a new geometric framework for physics that aims to unify general relativity and quantum mechanics [6]. An unexpected interconnection between

Quaternion Algebra on 4D Superfluid Quantum Space-Time: Can Dark Matter Be a Manifestation of the Superfluid Ether?

“…Finally, one can note that the superfluid BEC may be a source of plasmoids, ball lightning, that sometimes are observed in the fault zones of geological plates (in anomalous zones). Perhaps ancient civilizations such as the Egyptian one knew about this and could use such sources as perfect energy employing pyramids [138].…”

“…Here the leftmost v s is the velocity of superfluid carriers, while in the rightmost v s = (1/m)∇S the subscript s means an irrotational velocity [42]. From here it follows, that the superfluid carriers have only irrotational velocities.…”

“…Therefore, the quaternion algebra on 4D space-time can be viewed to be a lateral branch of Penrose's twister program. A general quaternion matrix representation has the following form [42,62,63]:…”

“…Hereṽ s is the irrotational velocity coming from gradient of the action function S [74] andṽ o is the orbital velocity [42] that is due to rotation of the carrier with mass m and charge e. Note that [∇ ×ṽ s ] = 0 while [∇ ×ṽ o ] = ω is not zero. The latter is called vorticity.…”

“…Now it is the superfluid quantum ether [34,40]. The space filled everywhere densely by the superfluid quantum medium named ether represents the superfluid quantum space-time [41,42].…”