Mass Gap Problem Physical Solution

A given problem in physics can be solved if it is well formulated. Well formulated means that it has a bijective correspondence to physical reality. Mass Gap Problem has no bijective correspondence with the physical reality and is that’s why not solvable mathematically. It can be solved physically by the formulation of the photon’s mass accordingly to the Planck-Einstein relation.


Introduction
To solve the Yang-Mills Mass Gap Problem [1] we have to understand well what mass is. I propose a bijectivity solution for the mass-gap problem where every element in the model of physical reality has exactly one correspondent model in physical reality. The model of physical reality is set Y and physical reality is set X. Every element in set Y has exactly one element in the set X. For example, element mass in the physical universe has correspondent element mass in the model of the universe. They are related by the bijective function of set theory: : → (1).
Every object with mass is existing in space we call today a superfluid quantum vacuum.
Space is not "empty", space is energy in the same way as mass is energy [2]. The idea of "empty" space as something real is harming physics for more than 100 years. It is time we demolish the idea of empty space. Mass is in physics an element with the attribute of energy . It is false to think that this element mass can exist in space that has no attribute of energy .
The formula (3) below is false: Mass of a given physical object is related to the energy of space accordingly to the wellknown physical law of homogenous distribution of energy. Every physical system tends that the energy of the system is distributed in a homogeneous way. Every physical object with mass is diminishing the energy density of space exactly for the amount of its energy : where is the energy density of the space infinitely far away from the physical object surface, is the energy density of the space in the centre of a given physical object and is the volume of the object. In the Newtonian perspective, the area of space with a higher density is asserting a given pressure towards the area of space with a lower density. From a quantum physics perspective, universal space has the vector orientation towards lower energy density, or in space are quantum fluctuations towards lover energy density of space.
The variable energy density of space is giving the origin to the inertial mass and gravitational mass as follows in Eq. (5) below: where is the energy density of the space in interstellar space; is the energy density of the space in the centre of the proton, and is the volume of the proton. Formula (5) shows that inertia and gravity are the results of the dynamics between given mass and a variable energy density of space. It is false to think that inertial mass is the same phenomenon as the mass as the amount of energy . Formula (6) below is false:

Physical Origin of the Planck Constant
We can combine equation = 2 and equation = ℎ and we get: Photon is massless in the sense that it has no inertial mass . But photon has energy and so it has correspondent mass . Formula (8) is showing the mass of the photon related to its frequency.
The space pressure − we can express as = − and we get: Eq. (11) shows the relation between the space pressure , volume V of a given particle and frequency ν of a given particle is constant, we call it Planck constant ℎ.

Physical Aspects of Mas Gap Problem
For Yang-Mills Mass Gap Solution is required: "It must have a "mass gap;" namely there must be some constant ∆ > 0 such that every excitation of the space has energy at least ∆ " [1]. Eq. (11) shows this constant Δ > 0 is Planck constant ℎ. Namely, every particle can be seen as the excitation of the space and is defined by the difference of vacuum pressure , volume V and frequency ν of a given particle. These three elements are defining the Planck constant ℎ. A given excitation of space is a given elementary particle with energy . We know the origin of the Planck constant (Eq. 11) and we see that the minimal "mass gap" in the excitation of space is defined by the Planck constant ℎ. In physical terms "mass gap" would be better named as "mass-energy gap", because Einstein told us already that mass and energy are made out of the same "stuff". What's this "stuff" is being clearly explained by Erving Schrodinger who also regarded space as the fundamental energy of the universe: "What we observe as material bodies and forces are nothing but shapes and variations in the structure of space".
In the Bohr model of the Hydrogen atom, it is supposed that the photon is released when an electron jumps from higher on a lower orbit, see figure below:

Figure 2: Bohr Hydrogen atom
We will perform a simple experiment. We close the hydrogen gas in a glass chamber in and we heat the chamber. The gas will heat, the electrons will jump on higher orbits and gas will emanate photons. From where are coming these photons? Are they hidden somewhere on the atomic structure of the Hydrogen? They are not hidden in the atomic structure; they are hidden in the space [3]. By heating gas, we are also heating the vacuum, because hydrogen atoms exist in the vacuum. In the heated vacuum (space) virtual photons become visible, they emanate from the gas. When we stop heating the glass chamber the hydrogen gas too will start cooling.
Electrons will turn from higher to the lower orbits and gas when cooling down will stop emanating photons because the space (superfluid quantum vacuum) will also cool down. The fact is, the hydrogen atom and in generally every atom is the energy structure of the space. We should not see atom as an isolated structure apart from the space.
Max Planck formulated the quantum theory by saying that light that was emitted had discrete levels of energy, and that energy that was radiated was quantized: that is orthogonal to the "space directions" [4]. With Fiscaletti and Čelan we proved time is not the 4th dimension of the universal space and has no direction. There is no such thing in the universe as "time direction". Universal space is time-invariant. In the universal space, time is the duration of change, i.e., motion. Duration, in order to exist, has to be measured from the side of the observer [5,6].
Einstein has interpreted the time t as the 4 th coordinate X4 of a Minkowski manifold. He wrote: "If we replace x, y, z, 1 − ct by x1, x2, x3, x4, we also obtain the result that ds 2 = dx1 2 + dx2 2 + dx3 2 + dx4 2 is independent of the choice of the body of reference. We call the magnitude ds the "distance" apart of two events or four-dimensional points. Thus, if we choose as time variable the imaginary variable 1 − ct instead of the real quantity t, we can regard the continuum space-time, in accordance with the special theory of relativity, as an "Euclidean" four-dimensional continuum, a result following by the consideration of the preceding section" [7]. In the above citation, Einstein suggestion that we can choose the time variable t as the imaginary variable can be written as follows: to point out here that every model of physical reality which is based on bijectivity has no "internal inconsistencies" and so no "problems". The physical solution "mass gap" problem is that minimal change of "mass-energy" excitation of the space is defined by Planck constant ℎ.

Conclusions
My proposal for the physical solution of the "mass gap" problem is in accordance with the Planck-Einstein relation. The mathematical solution of the "Yang-Mills Mass Gap Problem" will not be found because Euclidean green functions do not have bijective correspondence with physical reality. "Yang-Mills Mass Gap Problem" is of a mathematical character and is the result of missing bijectivity research methodology in physics. Once we apply bijectivity in physics, where every element of a given equation will have a bijective element in the physical world such problems will not appear anymore.