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?

Superstring Theory and the Seven Heavens

The superstring theory indicates for the first time the existence of multidimensional universes. It is supposed to be able to provide a comprehensive explanation of all known physical phenomena and answers the questions that the Big Bang theory cannot do: What happened before the creation (Big Bang)? Why did the universe explode?

 According to the superstring theory the universe initially existed in ten dimensions. However, because the ten-dimensional universe was unstable ^a), it creaked into two pieces, i.e. a four- and a six-dimensional universe ¹. The ordinary four dimensions well extended while the other six extra dimensions shrunk and curled to an incredibly small size (10^-33 cm), the reason why humans can not reach it.

Most physicists have deeply penetrated the mathematical aspect of the theory, but when come to translate it into physical reality it happened that they did it very lightly and carelessly. How come that a ten-dimensional body can be split in two to get a four- and a six-dimensional body? Surprisingly, nobody challenges and fixes such a bizarre idea. The perturbation theory, or whatever theory it is, would certainly fail to break a ten-dimensional body down to a four- and a six-dimensional body.

Let take an example of a three-dimensional body, say a cube of cheese. If we split it in two, indeed we did not get a thin piece of cheese and a fiber-like cheese (Figure-1A). In order to get a fiber-like form, we should make a series of slices; the first slices produce thin pieces of cheese, and the subsequent slices produce fibers of cheese (Figure-1B).

Now, how do we get a four-dimensional universe from the original ten-dimensional one? As the string theory postulated, the original ten-dimensional universe was so unstable that it broke in two parts. However, instead of creating one four- and one six-dimensional universe, a nine-dimensional universe was created in between the two separated parts of the original universe ^b). A series of subsequent splits took place successively in a similar way from higher down to the lower-dimensional universe.

In the end, we have a total of seven universes ^c), the one embedding the other in a successive lowering order of their dimensions.  As such, there is a ten-dimensional universe at the outermost embedding nine-dimensional one, the later embedding eight-dimensional one and so forth. At the end of the series we get the four-dimensional universe embedding a rotating ephemeral three-dimensional space, where we live in, perpetually appearing and disappearing across it (Figure-2) ^d).

Each universe contains the qualities and interactions of the one above, so that each descending level of the universe is in turn under more laws, more complex, and having much more varieties of kinds of stuff. It is the underlying purpose of the grand unification which hardly any physicist is aware. Regressing such cosmic creation process to the original condition of the ten-dimensional universe would give us a much simple physical law with fewer quantum kinds of stuff in it ^e).

Why, then, we cannot directly experience these extra higher-dimensional worlds? Just because the extra dimensions are temporal, not curly spatial dimensions as what the superstring theory hypothesizes. Each universe has its owned light ^f) with its corresponding speed (c_i), Planck constant (h_i) and gravity constant (G_i), depending on the degree of its dimensions.

The brane theory, as the extension of the superstring theory, should be adjusted accordingly. We better regard a brane as an interface lies between two [liquid-like] bodies, instead of a piece of paper floating in thin air. The brane’s dimensions which extend along its surface are spatial and off of it temporal.

The gravity fields propagate along the surface of the brane and not in the direction off of it as the brane theorists hypothesize ². We should, therefore, regard parallel branes as two sides of the same brane; otherwise, they coexist in different time which is absurd.

Notes:

a)    The superstring theory cannot elaborate on the reason why such a universe is inherently unstable. The bold answer to that is that the energy intrinsically consists of the opposites, the positive and negative energy. These two parts tend to segregate arousing [rotational] opposite motions within and eventually the universe creaks into two pieces.

b)  We may easily imagine this phenomenon as a separation of oil and water creating an interface in between. However, instead of three-dimensional, we have here ten-dimensional oil-water system.

c)    The ancient term of such worlds was the seven heavens

d)    The knowledge of such cosmic structure has been known since the antiquity but degraded as time evolves to become just that of the planetary orbits of our solar system. The conflicting misinterpretation of such gigantic macro-cosmic concept, which was beyond both the church and Galileo's imagination, had tragically taken Galileo's life.

e)   Peter Freund, one of the pioneers, worked in multidimensional space, even though he did not know about the geometrical structure of such worlds, accurately stated that the laws of nature become simpler and elegant when formulated in higher dimensions.

f)    In the ancient relative term: light upon lights.

References:

1. Kaku, M.:" Hyperspace," Anchor Books, Doubleday, New York, 1994, p. 195, 207.

2. Randall, L.:" Warped Passage," Harp

Superstring Theory and the Seven Heavens

The Nature of Reality Revealed

One of the historical misfortunes that put the physics down in trouble was Minkowski's "sudden" death, one year after his important spacetime discovery. He did not have a chance to go after and fixed whichever idea diverged from his own or elaborate his idea that he might not yet express adequately ^a).

The crucial issue that Minkowski did not have a chance to touch was the nature difference of the space and time albeit their complete union. Einstein took charge on it but with an indecisive elucidation¹: "The non-divisibility of the four-dimensional continuum of events does not 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".

Einstein certainly knew that any indivisible continuum [no matter how many numbers of its dimensions] should be completely symmetric, homogeneous and isotropic, in the sense that all of its dimensions are equivalent. However, he did not know why in the real world we experience with such different kinds of dimensions such as spatial and temporal. He had no better answer than taking for granted their difference as intrinsic. However, the cost we have to pay for it is too high.

At those days physicists knew nothing about the concept of symmetry breaking that would be developed later on in the quantum theory. The relativity theory has missed this kind of phenomenon which marked the beginning of the world we know today, a mechanism that broke the spacetime dimensions into spatial and temporal.

Ocean of Action, the Aeon

The discovery of quantum, if it were interpreted correctly would make the progress of physics much faster than it is now. Planck was unaware that he had revealed the fundamental nature of reality i.e., the union of energy and time (Et), the 4-dimensional quantum of action.

The spacetime, the union of space and time, that Minkowski had discovered, on the other hand, was merely a geometrical structure of 4-dimensional ocean of quanta. This ocean of temporal energy resembles eon_, a timeless undifferentiated epoch, the name which we propose to adopt ^b). As the current "broken" unit used for quantum does not reflect the inextricability of energy and time, we may use a more natural unit "eon," so that one eon = 6.63 10^-34 joule-second.

Nobody points to Planck discovery as the unification of time and energy as what Minkowski did on space and time. Energy and time are inherently inextricable just as space and time to be. Similarly, the dimensions of the spacetime in its undivided state are in a complete union; all are inherently equivalent, i.e. temporal.

A Series of Symmetry Breakings, the Aeon Split

One of the oft-abused expressions that physicists use is word creation. In the relativistic world there is no creation but separation ^c). Nature tends to break down unity into duality, and duality into plurality ^d). It is the underlying principle of what physicists call spontaneous symmetry breaking.

The beginning that marks any symmetry breaking is relative as such event happens successively in series. The beginning in physics always points to a relative one, even if it is about the beginning of the universe.  The absolute beginning is far away remote in time veiled by layers of worlds of various dimensions came into being in a series through symmetry breakings happened successively.

The symmetry breaking works on the premise that everything exists in pair, either in actuality or potentiality. The case also applies to the eon. Without its opposite partner, the eon will remain sterile. As such, there will be no reaction or interaction and no world "creation."

The eon is primordial, can neither be created nor destroyed.  All changes are just the manifestation of its transformations.  In its primordial state, the eon was extremely unstable as its opposite parts tended to segregate.  As it split apart a boundary (3-dimensional interface) appeared in between the embedding parts, which was much more tenser than the surrounding due to its [interfacial] tension ^e).

Due to its “rigidity” the dimensions along the interface ^f) are no longer equivalent with those of the surrounding. We perceive the former dimensions as spatial and the latter temporal, its original nature, and the interface as the space in which we live.

The Geometry and Reality of Space

The geometrical elements such as point, line, and plane are defined conceptually as having zero, one and two dimensions, respectively. These configurations are only in imagination and utterly different from those in the real world. However, physicists take those geometrical elements for granted for their world model both microscopically and macroscopically.

In real [3-dimensional] world what we call point is, in reality, a 3-dimensional small grainy object, a line is 3-dimensional small cross-section thread-like and plane is 3-dimensional thin surface-like. No wonder, as those elements in the model miss some "thicknesses," physicists are confronted with problems such as singularity or infinity in searching for solutions.

In dealing with the quantum realm where any things are small, one cannot neglect any thickness whatever small it is. The minimum thickness that nature allows is 10^-33cm or equivalent to 10^-44 second, below which everything would just disappear into thin air.  Such case also valid for the interface discussed so far in the sense that its thickness cannot be zero. Its small thickness reflects its brief lifetime, the universal now. The space as a whole and the universal now are two different aspects of the same thing.

At such interface exists only in a short time, the action (Et) is reduced to become [3-dimensional] energy E (Figure-1). It is the underlying quantization procedure in which a crazy looking differentiation to time replaces energy: E = iℏ  ∂/(∂ t).

On top of the interface's thickness other feature that most people overlook is its two-sided surface. As the interface is embedded in the opposite eons, one side that faces the positive eon has positive energy; the other side has negative energy. These opposing energies are the implicit solution of the relativistic energy equation E² = m²c⁴ + p²c². The Cashimir effect experiment demonstrates the existence of negative energy.

As Einstein equation E = mc² indicates, the side having positive energy will become the locus of matter while the opposite side the locus of antimatter. The transformation of energy into matter and vice versa takes place at the pace equal to the speed of light as implicitly indicated by Einstein equation. It is the reason why no matter can move faster than the pace of its perpetual creation.

Grand Cosmos, the Ensemble of Multidimensional Aeons

As mentioned previously there are many worlds of various dimensions as a result of symmetry breaking happened successively. Some recent theories, among other the string theory, support the existence of such multiple worlds indirectly, hence, the existence of eons of various dimensions.

The ensemble of those worlds, the grand cosmos, can be described in term of their respective positive and negative (frequency) eons. At the lowest level, we have 3-dimensional energy (E), at higher levels we have consecutively 4- aeon, Et₁, where t₁ is its corresponding time, 5- aeon (Et₁)t₂, 6- aeon (Et₁t₂)t₃ and so on and ultimately n- aeon (Et₁t₂t₃ …. t_n-1)t_n,  where t₂, t₃…t_n are their corresponding time, respectively.

The ensemble of positive (frequency) aeons:

       F⁺ = Et₁ + Et₁t₂ + Et₁t₂t₃ + ….. Et₁t₂t₃ ... t_n

As those multiverses have their own speed of [multidimensional] light c₁, c₂, c₃ …. c_n, then we may express t_1 = i µ₁ c₁t₁, t₂ = j µ₂ c₁t₁, t₃ = k, … µ₃ c₁t₁… t_n = w µ_nc₁t_1,

where µ_p = c_p / c₁ , the relative speed of the higher-dimensional light, in which

p = 1,2…….n, and  i,j,k…..w are imaginary numbers.

For the sake of simplicity we just write c₁ as c and t₁ as t:

F⁺ = iµ₁cEt + ij (µ₁µ₂) cEt² + ijk (µ₁µ₂µ₃) cEt³ + ….. ijk..w (µ₁µ₂µ ₃ … µ_n) cEtⁿ

F⁺ = a₁ Et + a₂ Et² + a₃ Et³ + ….. a_n Etⁿ

       where

a_{1 =} iµ₁c_, a₂ = ij (µ₁µ₂) c_, a₃ = ijk (µ₁µ₂µ₃) c_, a_n = ijk..w (µ₁µ₂µ ₃ … µ_n) c

Similarly the ensemble of negative (frequency) aeons:

F^- = a _-1 Et^-1 + a _-2Et^-2 + a _-3Et^-3 + ….. a_-n Et^-n

The totality of aeons within the grand cosmos ^g):

       F = F⁺ + E+ F⁺

which is nothing but the formulation of Laurent series.

This representation provides us with a deeper insight into nature.  We may recall that these Laurent series can be holomorphically mapped as Riemann sphere with its respective annulus of convergence (Figure-2). F is expressed as a sum of the positive frequency part (F⁺) which extends holomorphically into the southern hemisphere together with the negative frequency part (F^-) extending holomorphically into the northern hemisphere. The energy (E) as the constant term of F is located at the equator of the Riemann sphere.

This Riemann sphere represents reality faithfully. Its annulus of convergence indicates that nature abhors the singularity and infinity. The Big Bang and the black hole theories which heavily rely on the possible existence of such singularity may be unphysical. Likewise, the universe is forbidden to expand forever to infinity.  In the future, as the world becomes extremely unstable, it would be broken apart … the doomsday.

Notes:

a.    Minkowski concluded²:” We should then have in the world no longer space, but an infinite number of spaces, analogously as there are in three-dimensional space an infinite number of planes. Three-dimensional geometry becomes a chapter in four-dimensional physics…” Physicists seemed at lost as he did not elaborate explicitly whether those spaces may exist simultaneously or potentially. They refute the existence of even a single [universal] space.

To avoid further confusion, I wish to make it clear that all those spaces exist in successive order, in the sense that the individual space appears and disappears one after another successively [at the pace equal to the speed of light]. It is the underlying mechanism of what we perceive as the succession of time.

Now, from a time perspective, we see all things upside down. We say that we have a different space for each moment in time. Penrose defined this "alarming" situation as Galilean spacetime³: “space seems to be of something that evaporates completely as one moment passes, and reappears as a completely different space as the next moment arrives." Nobody knows that this is precisely the reason why the [quantum] world looks so bizarre. It underlies quantum jump and quantum entanglement phenomenon. The former is a kind of inherent micro-teleportation across time while the latter is the mechanism required to avoid chaotic teleportation from one fading space to the next arising space as a whole.

b.    We better use the term 'eon' instead of action to underline the tangibility of this ocean of temporal-energy continuum. What we perceive as fields are nothing but the "surface" manifestations of the 4-dimensional ocean of this immaterial substance. Nature only allows the use of this action modestly and economically.

c.    In a simple ordinary case, when one rubs the glass rod with a piece of silk, the glass rod becomes charged with positive electricity and the silk with a precisely equal negative charge. The friction does not generate but only separate the two kinds of electrification.

d.  The dynamics undergo from simplicity to complexity and from the state of higher order into disorder. The measure of such changes is the entropy of the system.

e.   From an earthly perspective, this tension is equivalent to what we know as the gravitational constant.

f.    It is more convenient to use the concept of a hypersurface, which is an extrinsic concept of the world as a system together with the surrounding rather than hyperspace which is an intrinsic view covering only the system.

The brane theory also adopts the concept of the hypersurface but in the wrong design. The dimensions along the brane should be a strictly spatial while off the brane temporal. Another hint to fix the theory is that the graviton should not allow floating off the brane; otherwise, the brane will be broken apart.

g.  This expression clearly shows that time is intrinsically multidimensional. The extra dimensions are invisible because they are temporal. We used to see the world upside down. Time dimensions are more fundamental than space dimensions. Space, no matter their dimensions, is incidental and ephemeral.

Physicists, like anybody else, used to consider that time is unique. They believe that there can be only the same time dimension prevails in the universe and anywhere beyond. Moreover, physicists hold that all spatial dimensions other than the ordinary three should be curled-up into tiny loops; hence, their invisibility. It leads us to exceedingly complex formulations with its many possible solutions.

References:

1.  Einstein, A.:" The Meaning of Relativity," Princeton University Press, New Jersey, 1954, p. 31.

2.  Einstein, A. et al.:” The Principle of Relativity,” Dover Publication, Inc., New York, 1952, p. 79-80.

3.    Penrose, R.:" The Road to Reality,"  Vintage Books, London, 2005, p. 387.Bottom of Form

The Nature of Reality Revealed