3.3.7 Mass Gap and Yang-Mills Conjecture

If the geometrical points of the object were all real at the same real instance of time, as we usually intuitively think, the object should become “lighter” as it moves faster because more points are moving at the speed of light, until when all its points are moving at that cosmological speed, then it becomes all-light and its mass becomes zero. That does not happen in reality, and that is why Relativity is counter-intuitive. In reality, however, because this motion is happening in the outward imaginary time, which is perpendicular on the real flow of time that is creating space, and both are related according to the hyperbolic split-complex geometry as we have shown in Chapter V of Volume II, which means that all objects are effectively at rest at the time of measurement, so their mass is always the rest mass, and their total complex momentum remains invariant, even when the velocity changes. That is exactly why the effective mass appears to be increasing with velocity, because we always need the same energy to accelerate it to the speed of light no matter how much its initial velocity is, since it is effectively zero. Without this hyperbolic relation between the real and imaginary momentum, it is not possible to derive this relativistic relation which is the only way that leads to the exact mathematical derivation of the equivalence principle as well as the mass-energy equivalence E=mc² that has been derived mathematically, in various different methods, in Chapter V of Volume II.

The energy of the whole existence is the energy of the 3D flat space described by (c, c), which contains all possible entities in the world. We shall denote this “maximum energy state” as “1” or “Monad” . Opposite to that is the state of non-existence, or void, that corresponds to (0, 0), and we shall denote this “ground energy state” as “0” . Contrary, to our common conception, the maximum energy state corresponds to zero mass, while the ground state corresponds to infinite mass. This is because the state of existence is absolutely one, while void contains infinite possibilities which require infinite time to become realized, while existence is realized every instance. Still, however, energy and mass are equivalent, but not equal! So potentially, the energy or mass of the world is infinite and continuous, but in reality it is finite and discrete. This discreteness of energy or mass, depends on the levels of time and the resulting dimensions of space. On the normal level this energy appears in the form of mass, while in lower dimensions it takes other forms such as electric charge and color charges.

Therefore, the property of mass is the coupling between the points of 2D space, that are kinetically moving in the imaginary time direction, while we are wrongly imagining them to be co-existing together in 3D space. So at any given real instance, only one point is real, and in order to maintain an object of N>1 points we need the imaginary time and the corresponding inertial mass. The case of N=1 corresponds to photons and other massless particles, depending on the number of dimensions.

Therefore, all excited states, above the ground state, correspond to particles with mass, when the number of monads is more than one: N>1, because only one of them exist at any real instance of time, so we need at least two instance, or a duration of time, to create any of such particles. This duration of time is translated inwardly into space composing of at least two points, although in reality, since mass a property of three-dimensional objects, we need at least eight points to create one such three-dimensional objects. In all cases, there is a minimum non-zero energy or mass that microscopic objects can have, because zero corresponds to absolute void.

This provide the conceptual ground that can prove the Yang-Mills existence and mass gap, one of the unsolved problem in physics and mathematics as we described in Chapter III of Volume II, and one of the seven Millennium Prize Problems defined by the Clay Mathematics Institute. It was accurately anticipated by Jaffe and Witten in the Official Problem Description that establishing the existence of Yang-Mills theory and mass gap requires the introduction of fundamental new ideas both in physics and in mathematics.