What’s Wrong with Dirac Sea’s Existence?

The attempts to incorporate the special relativity principle into quantum mechanics always leads to the solution of negative energy states pairing with positive energy states. Klein-Gordon's and Dirac equations are among those having such property.  However, physicists cannot afford to take on such energy's negativity as physical reality since they believe that it may lead to a catastrophic instability of the entire universe.

The root of the problem comes from the solution ambiguity of the relativistic expression for energy, E = ± (m²c⁴ + p²c²) ^½. In classical physics, one can straightforwardly keep the solution bearing positive values separated from that taking the negative ones.  In quantum mechanics, however, things become complicated. One should then deal with operators acting on complex functions, giving way two square roots of complex-number terms that do not tend to separate neatly into positive and negative in a globally consistent way ¹.

But this is what happens in reality. In the real world, those two opposite energies split only momentarily before they once again mingle together. This phenomenon repeats itself, making the 3-interface between those two energy oceans appear and disappear perpetually.

This interface, the 3-dimensional space we live in, seems to be something that evaporates completely as one moment passes and reappears as a completely different space as the next moment arrives ^two, which makes our universe incredibly dynamic.

Such as the beautiful translation of the mathematics formulation to the deeper workings of the physical universe may go beyond most people's wildest imaginations. Alas, even a prominent mathematical physicist such as Roger Penrose, has missed such insight. This continuous "catastrophic" instability that he was worrying so much is, in fact, the underlying reality of dynamic time. The energy's duality and polarity are the most fundamental of the relativity principles, the cosmos' prime mover, without which the world would remain sterile, timeless, and standstill.

When Dirac formulated his equation, being unable to get rid of the unwanted negative energy. He posited the presence of the sea of negative energy states, later known as the Dirac Sea. However, physicists are not comfortable with such a bold idea and reinterpret it as corresponding to antiparticles with positive energy.

Dirac, alas, didn't elaborate further about his energy sea, such as its location, how it came to be, etc. The answer is, in fact, relatively simple. The Dirac Sea must be present side by side with the sea of positive energy we refer to as anti-Dirac Sea (Figure-1). Both of them should be 4-dimensional conforming to the dimensionality of the spacetime they "occupy." The 3-dimensional interface naturally occurs between the two energy seas is nothing but the physical space we inhabit.

This kind of depiction greatly facilitates us in describing quantum fields, which so far seem to appear from nowhere, omnipresent, capable of creating and annihilating quantum particles. The interaction between the opposing energy potencies in Dirac and anti-Dirac seas giving rise to quantum fields, piercing through the 3-interface igniting quantum sparks ("quarks"), which appear and disappear perpetually on its surface (Figure-2).

Having elaborated that, we can now explain Fred Hoyle's C-field in a similar way. Hoyle hypothesized the existence of something similar to the Dirac Sea that continuously generates the fields. He further posited that the C-field had negative pressure and drove the expansion of the universe.  

Subsequently, within the context of the standard model, Peter Higgs introduced fields, which later bore his name, capable of stimulating particles to acquire mass. Alas, he was silent about the nature and origin of Higgs fields or the existence sort of negative energy sea.

Another fundamental relativity principle underlying any process of creation is the spontaneous symmetry breaking. A preexisting energy sea, later on, splits into positive and negative energy (Dirac anti-Dirac seas) as what they are now. However, that symmetry breaking doesn't take place all at once but gradually (Figure-3), giving us a perception that the universe is expanding. This hypothesis is evidence against that of the "quantum" primordial explosion of Big Bang theory.

References:

1.     Penrose, R.: ”The Road to Reality," Vintage Books, London, 2005, p. 615

2.     ibid, p. 387

What’s Wrong with Dirac Sea’s Existence?

The Nature of Quantum Fields, Hoyle’s C-Field and Higgs Fields

Nobody can explain so far the nature of quantum fields as where do they originate and why are they omnipresent? The list of those fields may include the Creation field (C-field) introduced by Fred Hoyle, now losing its popularity and Higgs fields, the source of Higgs particles that CERN scientists claimed to have discovered.

The Grand Relativity Theory that we have been developing so far may answer such hard questions. Let us review a little bit about it.

The central premise that the theory hinges on is the union and nature of energy and spacetime. As we have elaborated previously, the spacetime is not an independent entity but a mere geometrical aspect of the energy. The number of spacetime's dimensions reflects the energy's potency (degree of freedom). This energy-spacetime feature is not uniquely limited to the conventional 4-dimensional but any higher dimensional world.

The second premise that the theory holds is the polarity of energy. At the cosmic scale, as this polarity starts to manifest, the opposing energies viz. the positive and negative energies split naturally creating a hyperinterface in between. The segregation of those opposing energies does not take place at once but gradually.  It makes the hypersurface expand as the effect of the widening of the split area. In the human perspective, one recognizes the broadening of the 3-hypersurface (3-space) recognised as the expanding universe (Figure-1).

The interplay between the positive and negative energies at the opposite sides of the interface gives rise to quantum fields piercing through the 3-hypersurface igniting quantum-sparks ("quarks") on it like the sparked dots appearing and disappearing at a TV screen. We perceive this individual quantum spark as a fundamental particle, merely exists, perpetually appears and disappears behaving as though it is both wave and particle (Figure-2).

In human perspective, these generated quantum fields seemed as though they are coming from nowhere, omnipresent, filling all of space throughout the entire universe (Figure-3). It is the reason why physicists eventually come to the concept of fields which capable of creating and annihilating particles through the introduction of what so-called creation and annihilation operators in their relativist mathematical quantum model.

 

Fred Hoyle in 1950s introduced the Creation field popularly abbreviated as C-field to justify his theory on the expanding quasi-steady state cosmology. This C-field is capable to perpetually create matter between galaxies over time, as such that despite galaxies get further apart, new ones that develop between them fill the space they leave.

He could not elaborate, however, as to why and how the C-field came to be. Within the context of Grand Relativity Theory, Hoyle's theory is right in some respects such that the number of creative fields will increase with the expansion of the 3-hypersurface. As such, the density of matters filling the expanding universe will remain constant (steady-state).

However, to be more precise, Hoyle should have introduced a more general creation and annihilation field instead of C-field. Nature, through the polarity of energy, does not, at this very moment, only create new matters in the expanding space between galaxies but perpetually does create and annihilate all existing matter, every material thing in the universe.

We can also explain Higgs fields which can produce particles anywhere in space in a similar way. We can now at least explain in a language of physics on how and why the Higgs fields, which seemed like coming from nowhere, omnipresent,  filling all of empty space throughout the entire universe, do generate massive particles.

The Higgs boson which is theoretically so heavy might be not an ordinary 3-dimensional particle. As it penetrates the universe only at a tiny section of it (across the thickness of the 3-hypersurface which is around 10^-33 cm distance as depicted in Figure-3), they might never be observed even in experiments performed at ultra-high energy accelerators. CERN scientists claimed that they have successfully discovered such particles in their Large Hadron Collider (LHC). Or haven’t they?

 

The Nature of Quantum Fields, Hoyle’s C-Field and Higgs Fields