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

The Cosmic Inflation Never Happened

The Big Bang theory holds the premise that the universe originated from a singularity which came into being out of nothing through a single massive explosion. The concept of the minuscule size of such primeval singularity born from the thought projection of the current universe's expansion backward far in time.

The theory has at least two dubious primary grounds. The first one is the speculative concept of nothingness. The Big Bang theory presumes, violating the first law of thermodynamics, that energy (and matter) was created out of nothing. This idea came from the mindset that the creation of the universe (4-spacetime) was the beginning of everything. Notwithstanding, the theory takes for granted that the quantum fluctuation which stimulated the primeval explosion held in the nothingness before such creation.

The second speculative ground is about the size of the universe which can be shrunk indefinitely backward in time from the current size into a singularity. Close to the moment of creation, the size exponentially shrunk about 10⁶⁰ smaller just within 10⁴ seconds, from 10^-33 to 10^-37 second posterior to the explosion, the rate of which was exceedingly faster than the speed of light¹.

As we have elucidated so far, there can be no such thing as nothingness. The energy, as the only reality in nature, can neither be created out of nothing nor destroyed into nothing. The universe was born as the result of the interplay between the opposite (positive and negative) energies that created the universe and everything within, not out of nothing.

We can mathematically describe energy in its pure condition as waves' spectrum of different frequencies and amplitudes expressed in terms of Fourier series or its complex form, the Laurent series:

f(z) = F⁺(z) + c₀ + F^–(z)

It is a wave function expressed as the sum of its positive frequency (F⁺(z)) and negative frequency (F^–(z)).

Globally, we can depict this wave function in terms of Riemann sphere, the positive frequency F⁺(z) extends holomorphically into the southern hemisphere, and the negative frequency F^–(z) extends holomorphically into the northern hemisphere, where the equator represents the real coordinate and the longitudinal circles its imaginary time coordinate.

The domain of the positive and negative frequencies, however, does not fully extend to the poles, as the Riemann sphere has an annulus of convergence which excludes the domain around the zero points (singularity) as well as the infinity (Figure-1).

This pure mathematical analysis indicates that the split of the energy cannot create a stable interface (hypersurface) from the beginning when the energy started to split up to a certain period where it reaches the minimum size (represented by the Riemann sphere's inner ring of convergence).  The interface created in this period would instantly dissolve into energy.

It is only after reaching this limit that the hypersurface comes into being where it stabilized until it reaches its maximum size (represented by the Riemann sphere's outer ring of convergence).

The doomsday comes when the hypersurface reaches its maximum size.  At this particular time, the hypersurface becomes extremely unstable that makes it break down into pieces dissolving back into pure energy.  We illustrate these phenomena in Figures-2 and 3A.

This cosmology scenario avoids the need of either the concept of singularity to represent the beginning of the creation or the big crunch at the end of the universe's life as well as the everlasting expansion where the universe has no dead end.

This cosmology theory also excludes the need of the concept of cosmic hyper-inflation in the early period of the creation (Figure-3B), as the baby universe was born in an exceedingly larger size than that of the singularity which the Big Bang theory presumed.

The interplay between the positive and negative energies generates quantum fields across through the interface (hypersurface) ^a), located in between the two, perpetually creates quantum sparks (fundamental particles), the building block of the universe. As the split (hypersurface) area is enlarging with time, new matters are created in the expanding horizon keeping the average matter density per area almost constant.

This cosmology concept resembles the one of the continuous creation, steady-state expanding universe put forward by Fred Hoyle².

Notes:

a) We use the split area, interface, hypersurface, and space interchangeably.

References:

1.     Guth, A.: "The Inflationary Universe," Basic Books, New York, 1997

2.   Gregory, Jane: "Fred Hoyle's universe," Oxford University Press, New York, 2005

The Cosmic Inflation Never Happened