Superfluid Quantum Space as the Unified Field Theory

The novelty of 21st-century physics is the development of the “superfluid quantum vacuum” model, also named “superfluid quantum space” SQS. This SQS is replacing space-time as the fundamental arena of the universe. It also represents the model that has the potential of unifying four fundamental forces of the universe. SQS in this article is represented as the time-invariant fundamental field of the universe where time is merely the duration of material changes.


Introduction
Valeriy Sbitnev suggests that superfluid quantum vacuum also named superfluid quantum space (SQS) is the physical origin of the universal space [1,2]. In this article I developed a model of the time-invariant n-dimensional complex universal space which offers the new solution for Einstein's dream of a "Unified Field Model". In Einstein's Relativity the universal space is understood as a 4-D reality with tree spatial dimensions and one temporal dimension. Bezuglav also suggested that the superfluid quantum vacuum, which is the physical origin of the universal space, is four-dimensional [3]. In experimental physics, time is duration of material change, i.e. motion in space. Taking this in account I developed the model of timeinvariant n-dimensional complex universal space.
The measured value of cosmological constant Λ = 5.96 · 10 -27 kg/m 3 [4] is different from its calculated value following the Planck metrics for the magnitude of 10 123 ; this discrepancy is an unsolved subject of physics for decades [5]. Regarding the suggested energy density of space proposed in this article, I'm defending my proposal by the fact that the gravitational constant G is obtained by measurement and is expressed by the Planck energy density and the Planck time t P as [6]: (1).
This means that the Planck energy density reflects the real energy density of a 4-D universal space. In the absence of stellar objects, the energy density of the universal space has a value of Planck energy density which is = 4.64 • 10 113 −3 [6].
Meis has developed another formula for calculating the gravitational constant G: where e is the elementary charge constant and ξ is the vector potential amplitude of the electromagnetic field to a single photon state (ξ = 1.747 · 10 -25 V m -1 s 2 ) [7].
We can replace in Eq. (2) the term c 2 with the electric permittivity ε 0 and the magnetic permeability μ 0 obtaining: Eq. (3) confirms that the 4-D SQS electromagnetic properties are defining the gravitational constant.

SQS as the unified field model
Superfluid quantum space(SQS) has a general n-dimensional complex structure ℂ n ; every point of it has complex coordinates: (x i , y i ) (i = 1, ... , n) is an ordered n-uple of real numbers ((x i , y i )∈ℝ n ); for the purpose of this paper we consider its subset ℂ 4 where all elementary particles are different structures of ℂ 4-SQS and have four complex dimensions z i . In ℂ n -SQS the elapsed time of a given material change, i.e. motion is the sum of Planck times t P : where is the energy density of SQS far away of a stellar object in the interstellar space and V is its volume [6]. By Eq. (6) we can calculate the minimal energy density of space in the centre of a given physical object: Eq. (7) holds from the proton scale to black holes scale. Going away from the centre of a given physical object, the energy density of space is increasing by the following equation where r is the radius of the physical object and d is the distance from its centre. When d tends to the infinite, tends to ( Figure 2).  I will use this Eq. (7) to calculate the energy density of space in the centre of different stellar objects, considering that these objects are non-rotating. In Table 1 there is the comparation of the energy densities of space in the centre of the black hole with the mass of the Sun, in the centre of the proton, in the centre of the Moon, Earth, and Sun: The energy density of space in the proton centre is lower than in the centre of Sun, Earth and Moon because these stellar objects are made out of atoms where there is a vast empty space between the nucleus and electrons orbits. Proton's mass is very small compared with the mass of the Sun, but it diminishes the energy density of an extremely small area of space compared with that of Sun, that diminishes the energy density of an extremely big area of universal space; that's why the gravity force of the Sun has such a long-range. kg is the mass of proton and neutron, and 0.87 · 10 -15 m is their radius. We see that the energy density of ℂ 4 -SQS in the proton centre is higher for the rate of 10 2 than the correspondent energy density in the centre of the black hole. This shows that proton cannot be a mini black hole as suggested by Stephen Hawking [10]; Voyager did not find these primordial black holes suggested by him [11].
From the macro to the microscale it holds that a given physical object is interacting with the ℂ 4 -SQS in which it exists and the result of this interaction are the inertial mass m i and the gravitational mass m g : The rest mass m 0 of the proton is not its inertial mass m i , but is related to the amount of ℂ 4 -SQS energy E which is incorporated in the proton, as per Eq. (9): The mass m i of any elementary particle i can be expressed using Eq. (13): with |μ i | = μ B for the electron and |μ i | = (2α / n i ) for other particles, with n i an integer and α the fine structure constant [7].
In Meis model, as well in ℂ 4 -SQS model, elementary particles are different energy structures of the ℂ 4 -SQS energy. This is also the view of Erwin Schrödinger who used to say: "What we observe as material bodies and forces are nothing but shapes and variations in the structure of space" [12]. This is expressed in Einstein formula E = mc 2 ; E is the ℂ 4 -SQS energy which is incorporated in a given physical object, m is the mass of the object.
Relativistic particles are interacting with the ℂ 4 -SQS and additionally integrating ℂ 4 -SQS energy into its structure. Relativistic energy E of a given accelerated particle is the sum of the rest energy E 0 and kinetic energy E K which is incorporated energy of ℂ 4 -SQS due to the motion of the particle: where γ is Lorentz factor, 0 is proton rest energy, is Planck energy density, is additionally diminished energy density of ℂ 4 -SQS in the centre of the proton because the proton is additionally absorbing ℂ 4 -SQS energy and so increasing its mass and energy, is the volume of the proton at rest.

Complex time-invariant ℂ 4 -SQS is the medium of quantum entanglement
In the complex ℂ 4 -SQS time is not the fourth dimension. In the complex ℂ 4 -SQS imaginary dimensions 1 , 2 , 3 , 4 act as the "hidden variables" proposed by Albert Einstein. These hidden variables enabling ℂ 4 -SQS as the medium of the immediate information transfer by EPR-type experiments [13].
As the entire material world is made out of elementary particles which are structures of four-dimensional continuum, a result following by the consideration of the preceding section" [15]. In the above citation, Einstein suggestion that we can choose the time variable t as the imaginary variable can be written as follows: Einstein did a mistake keeping and interpreting time as the dimension of a four-dimensional continuum. Physics is still today suffering this misinterpretation of time that is solved in this article: time is the duration of a given physical object motion in time-invariant space.
Several authors are proposing that entanglement is induced by gravity [16,17,18]. On the other hand, there is a proposal that entanglement influences gravity: "To summarize, we have shown that entanglement can affect the gravitational field. This suggests that entanglement "has a weight". The perturbations in the gravitational field depend on the amount of entanglement and vanish for vanishing quantum correlations" [19]. I have shown in this article that gravity and entanglement are carried by the same medium which is SQS. In the model presented in this article gravity force between two physical objects does not induce entanglement and entanglement has no impact on gravity. Two entangled physical objects are entangled via SQS which variable energy density is also carrying gravity. Gravity does not influence entanglement and vice versa is also valid. In the article here presented gravity and entanglement are both induced by the superfluid quantum space that is time-invariant.

Conclusions
The unified field theory of Albert Einstein is one of the main goals of modern physics.
This goal can be achieved by the development of complex ℂ 4 -SQS as the fundamental arena of the universe. Elementary particles and consequently strong nuclear force and electroweak force forces are different structures of ℂ 4 -SQS. Gravity does not require the existence of some hypothetical particle graviton. It is carried directly by the variable energy density of timeinvariant complex ℂ 4 -SQS that is the medium of quantum entanglement EPR-type phenomena.