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 Quantum Reality Interpretation as It Should Be

Never physicists will be able to grip the reality as long as they rely on the current contradictory concepts of the macro and micro realm. The advent of quantum theory makes the picture of the micro world seem so outlandish that physicists give up describing its actual reality. They stick, instead, solely to mathematical formalism in place of the physical pictures of the reality. Physicists, on the other hand, are more confident with their picture of macroscopic reality as described in the relativity theory; at least that is what they think. However, they are wrong. The relativity theory wrongly takes the spacetime model of the primeval universe for the actual world. In the current [Minkowski] 4-dimensional spacetime model, physicists assume that the inextricable space and time dimensions are inherently dissimilar a). is where physicists fall into the pit. In an entirely unified state, space and time dimensions are equivalent. In such a state, the world is fully symmetric, continuous, isotropic and static. This static and eternal world is not the actual world which we are familiar with. In such a world, there was yet neither locality b) nor movement as there was no space for matter to exist, and no time for the matter to move. There was absolutely nothing; not even single matter existed but energy c). It was the primeval universe d), the embryo of the actual universe. So how and why space and time become so different as what they are now? In a cosmic scale, energy as a whole is geometrically manifested by its corresponding spacetime which dimensions reflex the degree of freedom of the energy as a whole. By itself, energy consists of two opposite parts, the positive and negative energy, which tend to segregate from each other turning the highly symmetric spacetime to become extremely unstable. As the positive and negative energy split gradually, a 3-dimensional [expanding] hypersurface (space) e) naturally takes place in between. We call such grand cosmic split phenomenon spontaneous symmetry breaking. Now here we come to a significant milestone that marks the beginning of time, the birth of the actual world. As the hypersurface came into being, the dimensions of the spacetime started to differentiate; those along its surface became spatial while normal to it became temporal. It is along this hypersurface that locality is taking place while the vast spacetime outside it non-locality reigns. It is precisely the elucidation related to Niel Bohr saying that the world around us is real, but it floats on a world that is not as real. The 3-dimensional localized hypersurface is the Bohr's real-world floating on the unreal vast non-localized 4-dimensional spacetime embedding the hypersurface. "There is no deep reality," was his confusing doctrine known as Copenhagen interpretation. The continuous interaction between the two opposing energies perpetually creates and annihilates the hypersurface (space) f) together with the quantum sparks (“quarks”) on its surface g). The reality in the deepest sense, therefore, consists of the alternating of brief existence and non-existence of the hypersurface. It is the Werner Heisenberg's duplex world which he defined as consisting of potentials and actualities, which we may correlate to the alternating real localized hypersurface and unreal non-localized "nothingness" h). What Walter Heitler meant by undivided wholeness was this non-localized world which alternately appears and disappears with the real localized hypersurface.  When the localized real hypersurface dissolves into the non-localized world, in a small fraction of second everything becomes entangled as undivided wholeness before the real world (hypersurface) reappears.  Hugh Everett interpreted this perpetual alternation of brief existence and non-existence of the hypersurface as there are out there "many worlds."   The gross sum of the alternating contribution of the world of potentials and actualities is described mathematically by the wavefunction. As the quantum observation can only gauge and record the world of actualities and not the complete series of potentials and actualities, it gives a perception as though the act of observation makes the wavefunction collapse and the real world emerge. It is another misleading Copenhagen interpretation which states that the reality is created by observation. However, it is not all. The 4-dimensional spacetime which embeds the 3-dimensional hypersurface we live in is not unique. The spontaneous symmetry breaking did not happen only once but in series from the highest dimensional spacetime down to the lowest 3-dimensional hypersurface.  As such, there exist out there a grand cosmos consisting of our world in the "center" embedded consecutively within higher and higher dimensional ambient spacetimes up to "infinite" i). The 10-dimensional world has a special place in the grand cosmos as its dimensions allow the 4-dimensional world to have a full degree of freedoms. This theory which we call the grand relativity theory will positively impact profoundly on human thinking about reality. For centuries people wrongly believing that the tiniest particles in nature are permanent, which is not the case. A grand paradigm shift is required.  A bunch of matter which we think will turn into  persistent and permanent fundamental particles in case we continually divided it into smaller and smaller parts, are in fact ephemeral, hardly existing, appearing and disappearing perpetually to and fro energy at the pace equal to the speed of light, a weird picture which is far from what most people imagine.   Notes: a.    Einstein gave vicious circle reasoning: "... the non-divisibility of the 4-dimensional continuum of events doesn't at all, however, involve the equivalence of the space coordinates with the time coordinate. On the contrary, we must remember that the time coordinate is defined physically wholly differently from the space coordinates." b.  At that time, space and time were not yet differentiated, and the locality did not have any meaning. The world was still in the state of entangled as an undivided wholeness where non-locality prevailed. c.      It is more appropriate to refer to it as action, the union of energy and time, Et. d.     The ancients seemed to be aware of the existence of such a primordial world which they called cosmic egg where chaos prevailed. e.     Physicists consider this phenomenon is wrongly interpreted as Big Bang, a primeval explosion that marked the beginning of the expanding universe. f.      We use the 3-dimensional space, hypersurface or hyperinterface interchangeably. g.   The interplay of the positive and negative energy at the opposite sides of the hypersurface creates quantum fields across through its surface igniting quantum sparks ("quarks") which we perceive as fundamental particles. h.  Just like a roll film of the movie consisting of a series of pictures separated by gaps of "nothingness," the reality consists of the real localized world (hypersurface) and the potential non-localized world of nothingness. i.    The gross sum of a composite spectrum of higher dimensional energies (eons) which can be expressed mathematically as the Laurent series and holomorphically mapped as Riemann sphere indicates that the dimensions of the outer ambient spacetime is limited and cannot be infinite. References: 1.     Einstein, A.:" The Meaning of Relativity," Princeton University Press, Princeton, New Jersey, 1988, p. 31. 2.     Penrose, R.:" The Road to Reality," Vintage Books, London, 2004, p. 387. 3.     Herbert, N.:" Quantum Reality," Anchor Book, Doubleday, New York, 1985.

The Quantum Reality Interpretation as It Should Be

Space Thickness

The relativity theory covers the macroscopic aspect of the world conceptualized as a flat or curved hypersurface.  However, hardly anybody is aware that we may incorporate the quantum phenomena into the theory by merely taking into account the hypersurface's thickness, its microscopic scale. We call such a unified theory the Grand Relativity Theory (GrRT).

Any physical object should have a thickness ^a) regardless of its dimensions; otherwise, it would disappear into thin air. Our physical space is no exception. The effect of space thickness, yielding a higher degree of freedom for particles to maneuver, intensifies as we probe to smaller distances approaching the thickness' magnitude (Figure-1).  

This scenery is spectacularly demonstrated by the string theory which, albeit of its imperfectness, can [mathematically] discover the ten-dimensionality of the ambient space. Whether the string theorists can properly portray such higher-dimensional space or not is a different story.

GrRT posits, on the contrary to the classical theory's premise, that the 4-dimensional spacetime doesn't at all represent the real but the primitive world. Inherently, the spacetime is symmetric, static and eternal. As such, all of its dimensions are entirely equivalent.

It is only when the spacetime splits in two ^b) that the dimensions are differentiating themselves into spatial and temporal. Following this spontaneously symmetry breaking, a thin 3-dimensional interface (hypersurface) ^c) is taking place in between the two halves of the split spacetime.

Now, the interfacial tension that holds the interface intact makes the dimensions extending along the hypersurface tenser and more "tangible" than that normal to it. We call the above dimensions spatial while the latter we call temporal. The hyper-interfacial tension which is responsible for this differentiation we recognize as the Gravity Constant.

The fourth [temporal] dimension extending normal to the hypersurface manifests the dynamical aspect of the world. The space thickness measured along this dimension is extremely thin, around 10 ^-33 cm or equivalent to 10 ^-44 second, the minimum thickness that nature allows, below which space and time have no meaning.

Because of its small thickness, the hypersurface is inherently unstable. Such a space barely exists, perpetually appears and disappears which makes the world extremely dynamic.

The size of the space thickness which determines the duration of space's presence we call now. Space and the now are the different aspects of the same thing. We perceive the sequence of space's appearance, presence, and disappearance as the successive transformations of the future into now and the past.

Matters exclusively present at now. They exist only along the thin hypersurface (space), not outside of it, which is nothing but pure energy ^d). The parts of the spacetime on either side of this thin space, we call the future and the past (Figure-2).

The extension of this concept for higher dimensional spacetime is straightforward, except that there come about successive spontaneous symmetry breakings. A hypersurface of one dimension lower than its embedding space, together with its corresponding temporal dimension, is created every time the split occurs.

Within the ten-dimensional ambient spacetime which the string theory reveals, a total of seven successive splits have taken place before our dynamical world comes to the existence. We thus have seven worlds embedded one within another, each with its corresponding temporal dimension.

Multidimensional time is still an alien concept for physicists. Physicists thought that the only vast and extended world existing in nature is that of four-dimensional. They believe that time is unique, the only dimension of its kind. The extra-dimensions, if they exist, should be spatial and curled up into extremely tiny loops.

This premise makes the task of string theorists extremely untenable as there are around 10⁵⁰⁰ possible ways on how the extra-dimensions may curl up. Nobody is crazy enough for not using the Occam’s razor to get rid of such problem and for good.

Notes:

a.   A physical object may have some thicknesses depending on the ambient space dimensions we take into account. Within our 3-dimensional ambient space, a 2-dimensional plane has one thickness, while the 1-dimensional thread has two thicknesses.

b.     The energy which is inherently composed of the opposing components tends to break up into its component, i.e. the positive and negative energies.  When this happens, the spacetime which is nothing but the geometrical manifestation of the [vacuum] energy, splits into two halves creating a hypersurface in between the two.

c.    We use the notation of space, hypersurface, and interface interchangeably. The hypersurface is a straightforward generalization of the concept from the geometry of surfaces embedded in the three-dimensional Euclidean manifolds.

d.    The mainstream physicists portray the 4-dimensional spacetime, dubbed the world, as being filled with matters throughout the full extensions. There are no [microscopic] universal now, matters existing in the past, now and future "have" an equal reality, as such that time travel becomes possible leading to paradoxes and chaos.

Space Thickness

The Crumple of the Spacetime

The General Relativity theory was developed based on the premise that the gravity force is the manifestation of the 4D-spacetime curvature ^a). This physical concept was derived from Riemann’s idea¹ that the force was nothing but a consequence of geometry, thus, banished Newton’s unnatural concept of “action-at-a-distance”.

However, Einstein mindset was to stick with intrinsic geometry in the sense that the spacetime as a system was regarded as having no surroundings or being embedded in nothingness ^b). In fact, when physicists talk about the wrinkle of the [4D-] spacetime they never care about which directions (dimensions) it wrinkles goes.

The strict concept of the geometry dictates otherwise ². The geometry concept of m-metric manifolds (hyperspaces) ^c) is a straightforward generalization of ideas of the study of surfaces embedded in 3D-space. However, it has been proven that in the circumstances in which an m-dimensional curved hypersurface can be embedded in the n-dimensional [Euclidean] ^d) manifold if at least n = ½ m(m + 1).

The crumple of the ordinary 2D-surface, a piece of paper, for example, requires a third dimension (3D-ambient space) for it to occur. But hardly anybody is aware that the crumple of 3D-space requires not only a fourth dimension but at least 3 additional dimensions (6D-ambient spacetime) ^e). Similarly, the crumple of 4D-spacetime would require at least 10D-ambient spacetime for it to occur without constraint in any direction (Figure-1). Does the nothingness have such properties for being able to embed something? What is nothingness anyway?

Nobody should blame Einstein on this negligence. People were just horrified about the idea of 4D-spacetime which had been introduced by Minkowski beforehand, not mention the 10D-spacetime. Had Einstein been aware of this higher dimensional surrounding requirement he would probably still prefer to take the surrounding as nothingness rather than 10D-ambient spacetime.

A more recent theory such as that of superstring requires 10D-ambient spacetime ^f) for its equations to be solvable.  Alas, being uncomfortable with such bizarre vast extension ^g) of the ambient spacetime, physicists blow down ^h) the majestic surroundings assuming the extra dimensions being curled leaving the ordinary 4 dimensions to remain intact.

Even after the superstring theory was established, Big Bang theory as the cosmological application of the General Relativity theory maintains its premise on the nothingness instead of 10D-ambient spacetime taken as the surrounding of the expanding 4D-spacetime. As such, Big Bang theory misses a bigger part of the “stage” that in no way it can explain the substantial missing dark matter and dark energy.

Having many defects in its premise Big Bang theory would eventually fall short except it takes among other the 10D-ambient spacetime as the surrounding of the universe (4D-spacetime) instead of nothingness.

Notes:

a)    Arthur Eddington expedition carried out to South Africa during the solar eclipse in 1919 verified the shifting of the position of a star within the field near the sun, thus, proving Einstein's general relativity prediction of the bending of light around a massive object.

b)   There is a vague definition of absolute nothingness or emptiness but we may guess that what most physicists mean by it is a sort of extension (spacetime) with an indefinite number of dimensions [zero or infinite dimensions?] having neither matter nor energy.

c)     The notation of n-spacetime is equivalent to n-hyperspace or n-hypersurface.

d)     This is the reason why the laws of nature look simpler in higher dimensions. If the dimensions of the surrounding spacetime are high enough then we might have a flat (Euclidean) surrounding where the physical laws become simpler.

e)    We may speculate that the existence of three generations of particles is the manifestation of 4D, 5D and 6D-particles abiding in the respective 4D, 5D and 6D-spacetime. The manifestation of the last two generations into our world could be only the cross-section of their whole body.

f)   The string theory accidentally derived the 10 dimensions mathematical requirement from Beta function originally dedicated to solving the strong force quest. The coincidence with the 10 dimensions geometrical requirement of the ambient spacetime embedding the 4D-spacetime is stupendous.

g)     Since they are not visible, the string theorists regard the extra-dimensions as spatial and being curled into tiny loops.

h)   Physicists assume that the 10D-ambient spacetime splits into a 4D-spacetime and a tiny curly 6D-metric manifold. This premise doesn't absolutely make sense just like the impossibility of splitting a 3D-cube into one 2D-plane and one 1D-line. The proper way to do it is successively splitting the 10D in two creating 9D as their interface and so forth down to 4D which we get as the interface of the two halves of the 5D split. We would, then, have a total of 7 spacetimes embedding each other in descending order of their dimensions.

The Crumple of the Spacetime

Why the Grand Relativity Theory? (Part III)

One of the significant physicists' misconceptions about nature is the uniqueness of time. When physicists encounter higher-multidimensional surroundings in their theory, they instinctively assign the extra-dimensions (beyond the ordinary four) as spatial. This premise, regarding the inequality of space and time footing, is evidence against the relativity principle.

The string theory, which had its origins in experimentally observed features of the strong force, requires the existence of six compactified extra spatial dimensions (a) and the four known spacetime dimensions. This presumption leads the theory to grave difficulties as it should deal with myriad different kinds of Callabi-Yau tiny manifolds or other similar bizarre things.

On the other hand, the grand relativity theory holds that the extra dimensions are temporal; thus, circumventing such complexities. Therefore, we may regard a system such as our world consisting of a 3D-space (hypersurface) embedded in 10D-manifold in which all extra dimensions are temporal ^b). Under the grand relativity theory, we have every right to transform it into, for instance, 9D-hypersurface embedding in the same 10D-manifold, by turning some of the temporal dimensions into spatial (Figure-1). The latter is exceedingly simpler than the former in terms of mathematical formulations, and yet it gives us the same solutions.

The grand relativity theory requires any physical objects or hypersurfaces having thicknesses, the number of which depends on the number of dimensions of the embedding manifold ^d) (Figure-2). However, physicists obliged to do a similar way by incorporating such forgotten thickness into their model called supersymmetry generators ^e).

In Brane theory, physicists assign some space and time's dimensions on and along its surface while off of it spatial. They certainly make a significant confusion as to the brane, like hypersurface embedding in a higher dimensional spacetime, should have solely spatial dimensions on and along its surface and temporal dimension[s] off of it.

The hypersurface or brane is the loci of things that co-occur if not at lower temporal dimensions it would certainly so at higher temporal dimension (Figure-3). 

The hypersurface or brane is the loci of things that co-occur if not at lower temporal dimensions it would certainly so at higher temporal dimension (Figure-3). 

The hypersurface tends to flatten out as it has higher dimensions. But how high should they be? Mathematically, a spacetime may embed an n-dimensional hypersurface properly only if the former has at least ½ n(n+1) dimensions. Our 4D-world, for example, requires a sufficient ample ambient space i.e., 10D-manifold, for having a complete degree of freedoms without being constrained at whatever directions.

It turns out that some theories, such as Supergravity, require an embedding spacetime of even higher dimensions. The Supergravity demands an eleven-dimensional ^f) embedding spacetime, but still, nobody can fully renormalize the Supergravity.

Notes:

a.  Physicists are assumed to be curled up into tiny loops as nobody ever directly experiences them.

b.   It can be expressed mathematically as Octonion, a Hypercomplex consisting of one real and seven imaginary variables. The real part is the spatial variables' function, while the seven imaginary parts represent seven different temporal dimensions.

c.  No real particle smaller than the hypersurface's thickness, except virtual particles perpetually emerge and submerge across the depth. This thickness size, which becomes the minimum size of the real particle is what physicists call hierarchy problem.

d.  Analogically under 3D-ambient space, a point has three thicknesses, string two thicknesses (cross-section), and plane one thickness. Otherwise, they would be evaporating into thin air.

e. Mathematically physicists may express such a framework in terms of Superalgebra equation whose ordinary and super parts are sometimes called body and soul, respectively ¹. It is equivalent to Octonion Hypercomplex with its real and imaginary parts. Amazingly, this is a proper way to describe a subtle structure such as [higher dimensional] soul embedding a body, contrary to what most people think the soul is inside the body.

f.  It is a sort of pseudo dimension representing the tip of the 11+ "iceberg" dimensions. The ancients (among other Empedocles: 490-430 BC) described the realms consisting of earth, water, air, and fire analogous to a changing phase from ice, water, vapor, and steam.  We may interpret that earth representing energy/material stable things in 3D-space, water representing energy in 4D - 10D-spacetimes, the air in 11D - 55D-spacetimes and fire in 56D - 1540D-spacetimes, the dimension ranges of which are speculated under the ½ n(n+1) rule, if we may do so. This metaphor shows us that the energy associated with particular spacetime is hotter as the spacetime dimensions become higher. The reality beyond those dimensions is far from our wildest imagination and concern.

Why the Grand Relativity Theory? (Part III)

Why the Grand Relativity Theory? (Part II)

As the dimensions of a drop of water to its water substance, the dimensions of spacetime are the geometrical manifestation of a particular cosmic energy.  Our world, together with its multidimensional surroundings (grand cosmos), comes into existence as the natural manifestation of a broad spectrum of different cosmic energies ^a). 

How these multidimensional worlds come into being? It begins with the separation of positive and negative energy in the highest-dimensional world. This separation creates a hypersurface (space) of one lower dimension between the two opposite energies. The newly created hypersurface, in turn, splits in two, and so forth. Thus, the separation happens successively, creating many hypersurfaces (spaces) embedding one after another in descending order of their dimensions. 

The energy segregation in each world, however, doesn't happen instantaneously. The area of the hypersurface formed in between the two opposite energies broadens up gradually from a specific minimum size to what the current magnitude is (Figure-1). It is the underlying reality that makes our universe expanding ^b). 

This kind of phenomenon also explains why our world is flat ^c).  As such, we don’t require buying the concept of inflationary phase happened in the early life of the universe (at around 10^-35 to 10^-30 second after Big Bang) whose inflation rate is far exceeding the speed of light. Besides, the existence of energies at the surroundings of our universe (hypersurface) may explain the possible source of dark energy we miss so dearly.

The advantage of using hypersurface over the hyperspace is clear. With the former, we can easily describe objects such as fields propagating on its surface (classical fields) as well as those off its surface traversing through its thickness ^d) (quantum fields)^, as depicted in Figure-2. 

The interaction of the opposite energies generates those quantum fields which propagate across through the hypersurface. As the quantum fields hit the hypersurface's surface, they ignite quantum sparks ("quarks"), which we recognize as fundamental particles. These sparks (particles) together with the hypersurface (space) which they abode ^e) perpetually appear and disappear at the rate equal to the speed of light ^f). 

The two interacting opposite energies move at the different directions forcing the normal axis of the hypersurface to rotate around the grand perimeter of the spacetime at the speed of light ^g). This dynamic grand rotation creates what we perceive as time (Figure-3). 

The combination of these two phenomena makes our physical space, together with all matters it contains, disappears completely as one moment passes, and reappear as a completely different space as the next moment arrives ^h). Most physicists overlook this underlying reality, which reflects both the relativity and quantum realms.

The interactions of the opposite energies also make the hypersurface rotate around its normal axis. It rotates, in turn, all objects it contains from super-galaxies, galaxies, solar systems, planets down to atomic and subatomic realms.

Notes:

a. The ensemble of such grand cosmos can be mathematically expressed in the form of the Laurent series or depicted as the Riemann sphere.

b. As shown by Riemann's annulus of convergence, the world can evolve only from a specific minimum size. It starts to get its stable form and expands to its maximum magnitude, beyond which it becomes precarious and tears apart into pieces doomsday. As nature abhors the singularity, do we need the Big Bang cosmology and black hole postulate?

c.  It is flat but locally curved and undulates due to the gravitation effect exerted by local concentrations of energy and mass.

d.  In the order of Planck distance i.e., 10^-33 cm or equivalent 10^-44 second, below which the hypersurface would disappear into thin air. Assuming a zero thickness of such hypersurface would lead us to many annoyance problems of infinity.

e. The separation of energy never creates a stable hypersurface between the two halves. Mathematically, in quantum mechanics, the square roots of the relativistic energy formula, E² = m²c⁴ + p²c², do not give a neat separation of its positive and negative roots. It means that physically, the split of the positive and negative energy never creates a stable interface (hypersurface) between them. It is ephemeral in the sense that it appears and disappears perpetually.

f.  It is just like sparks appear and disappear on the surface of large TV or computer screen. Amazingly, the display also appears and goes together with the flashes.

g. The energies’ movement as the result of their mutual interaction also makes the hypersurface rotate around its lateral axis resulting in a hyper-helical type of rotation. In a higher-dimensional ambient space, we can depict this hypersurface movement as a 3D-front wave propagating across the 4D-surface of a grand 5D-ocean.

h.  Heraclitus (500 BC) said that the world is in flux. We can never step into the same river twice. He also stated that the world was like a gigantic flame. At any instant, the fire we see is entirely different from the flame we saw just a moment ago. Everything in the world is always changing and yet is still exclusively itself.

Why the Grand Relativity Theory? (Part II)