Dark Energy versus Dirac and anti-Dirac Seas

A big mystery arose from the Hubble Space Telescope (HST) observations of very distant supernovae carried out in 1998 that the Universe was expanding more slowly than it is today. The expansion of the Universe has been accelerating instead of slowing down due to gravity. No one knew how to explain the mystery, and it remains so until today.

Physicists came up with several explanations. Some of them posited that energy is a property of space ^a) and some other brought in the existence of a strange kind of energy-fluid that fills space.  Both theories imply that such energy would not dilute as space expands. The remaining directly challenged Einstein's theory of gravity and proposed a new theory which includes some field that creates the cosmic acceleration.  

Physicists could not say for sure which explanation was correct except that they only offered a solution by giving it a name: dark energy ^b). They tried to explain how space acquires energy from the quantum theory of matter. The so-called 'empty' space is actually full of virtual particles that continually appear and disappear. When physicists tried to calculate how much energy this space would give, they believed that the answer came out exceedingly wrong, i.e. 10¹²⁰ times too big. There is no way that physicists could explain such mysterious phenomenon as far as they stick to the Big Bang cosmology. 

Now, the Grand Relativity Theory that we propose can reveal the mystery of dark energy in a different way. Dark energy is nothing but the unfathomable gigantic 4D-Dirac and anti-Dirac energy seas contained “beneath” our 3D-universe (hypersurface) whose effects are piercing through it (Figure-1). It was not surprising that physicists found that the vacuum energy was enormous, about 120 orders of magnitude too large than that of measured ^c).

The 3D-energy measured in our daily experience is merely the gauge against this enormous 4D-vacuum energy. However, why can't we see this "dark" energy? It is the beautiful mystery of the higher dimensional spaces' properties that most people overlook. The being that lives in 3D-world cannot see something that resides in 4D-world or higher. The 3D-electromagnetic waves ^d) can only propagate across the 3D-hypersurface, not off of it (Figure-2). 

The universe' expansion is the result of the gradual split of 4D-Dirac and 4D-anti-Dirac energy seas, and the tremendous strong opposite angular momentum exerted globally by those two opposing energy seas on either side of the 3D-hypersurface ^e) cause its acceleration. Meanwhile, the local effect of such momentum exerting the orbital speed of galaxies we perceive as though clumped dark matters ^f) exist in there.

The 4D-dark energy is omnipresent, not necessarily in the far away galaxies but even extremely close to us piercing through within the inside of our body. We can discern its effect only within on enormous astronomical scales. We may perceive it along the direction of y4^th dimension (time-like distance) which d) we cannot. It is from this same direction that the Hoyle C-fields or Higgs fields bombarding our 3D-universe (hypersurface) across to create and annihilate “normal” matter composing 5% of the total energy that affects our 3D-universe.

Notes:

a. It is related to a long-discarded mathematical cosmological constant contained in Einstein's theory of gravity.

b.  It turns out that this dark energy composes of roughly 68% of the Universe, the remaining is made up by 27% dark matter and 5% matter. 

c.  What physicists measured as [3D-] vacuum energy was superficial, i.e. the balance of those two polar 4D-energy seas which, if not zero (mirror symmetry), is a relatively small number (skew symmetry).

d.  There exist in grand cosmic higher dimensional electromagnetic waves which propagate in corresponding dimensional spaces. 

e.  We may refer to this 3D-hypersurface as 3D-Dirichlet brane as the superstring theory does. The theory, however, should structure the brane similar to that for a hypersurface in the Grand Relativity Theory. Alternatively, if we are religious enough, we may refer it to as Genesis' 3D-firmament (firmamentum, Lat, raqia, Heb.) which lies between [4D-Dirac] water which is above and [4D-anti-Dirac] water which is below.

f.   There is no such dark matter exists in nature. What one observes as the galaxies' fast orbital phenomenon is nothing but the effect of the tremendous strong opposite angular momentum exerted locally by those two polar energy seas on either side of the 3D-hypersurface (our universe). We can rule out, therefore, the use of gravitational lenses effect, as what some astrophysicists tried to do, as a tool to detect the existence of dark matter because the attractive gravitational effects attributed to dark matter are merely a side-effect of dark energy. Some physicists have already speculated that dark matter and dark energy is a single energy field that produces different effects at different scales, but they did not know how to model it physically. 

 

Dark Energy versus Dirac and anti-Dirac Seas

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)

Expanding Space, Convergence and Hyperfunction

So far we have shown that the process of the spacetime splitting can be described purely from mathematical analysis. We transformed the complex plane into a Riemann sphere to get a more pictorial representation of the entire spacetime, including the infinities. The real space axis (X) on the complex plane is now represented by the real equatorial circle while the imaginary time axis (it) of the complex plane by the imaginary longitude circle of the sphere (Figure-1).

Since the energy in its purest nature can be described as a wave, mathematically it can be best formulated in the form of Laurent series f(z) expressed as a sum of its positive frequency part and the negative frequency part:

f(z) = F⁺(z) + c₀ + F^–(z)

When it is mapped on the Riemann sphere ^a), the positive frequency F⁺(z) extends holomorphically into the southern hemisphere, and the negative frequency F^–(z) extends holomorphically into the northern hemisphere.

The constant c₀ is represented by the real equatorial circle which is the shared boundaries of those opposing frequencies.

This is how the energy split is described mathematically into its positive and negative energies. Physically, we can explain such energy split through the division of the spacetime into two halves. One half, the southern part of the spacetime, represents the positive energy zone and the other half, which is the northern part, the negative energy zone.  The interface between those two opposing zones is the space where all material things, the super-galaxies, a cluster of galaxies, galaxies, stars, solar system, and the earth are located.

So far we have assumed that the size of the real equatorial circle on the Riemann sphere or the space in the spacetime is not changing in time.  The whole spacetime is completely split instantly which makes the universe static. In term of the Riemann sphere the real circle, which physically represents the space, immediately gains the infinite equatorial size. 

In reality, there is no such a static universe as supported by the astronomical observations (among other the Hubble's redshift)^b). In line with that, space should be gradually expanding in time ^c), depicted by an expanding interface in the spacetime (Figure-2B). In term of the Riemann sphere, this is represented by an expanding real circle (Figure-2A).

Now we come to an essential question as to whether the expanding real circle is starting from the beginning as a point (singularity) or from certain definite size? As we remember, the Riemann sphere has a kind of annulus of convergence which excludes a particular area surrounding the zero point and that of the infinity (Figure-3).

The real circle starts to appear only after gaining a certain size. This means that space begins to materialize just after achieving a certain minimum size, below which nature abhors the existence of such space and all materials within. Also, the annulus of convergence also indicates that space will disappear entirely after gaining a certain maximum size for the space to exist.

Does nature allow a partial spacetime split? According to excision theory, the hyperfunction of the shared boundaries (the real circle of the Riemann sphere) is independent of the particular choice of the region of the f(z) as shown in Figure-4.  

This means that the real circle (space) ^d) can take any size as far as it is within the annulus of convergence. Space appears only after it gains a sufficiently large size and expands afterward up to a maximum allowable size for the space to exist. After that space dissolves completely into pure energy. Nature keeps the physical world to take place outside the vicinity of the singularity and infinity.

Notes:

a)     As the spacetime is the structural quality of energy, the Riemann sphere becomes the domain of the energy wave function.

b)     The interpretation of which gave rise to the Big Bang theory

c)     According to the Big Bang [and the general relativity] theory, it is the spacetime instead of space which is expanding.

d)     The real circle on the Riemann sphere or the physical space within the spacetime framework is not necessarily flat and may be curved more or less significant.

References: 

1. Penrose, R.: "The Road to Reality," Vintage Books, London, 2005, pp. 159, 172-175.

Expanding Space, Convergence and Hyperfunction