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

The Nothingness, Implicate Order and Non-locality

Most people wrongly perceive matter as an object existing in an empty space. Space is far from the vacuum, it is a plenum full of energy, the ground for all existence, inanimate and animate beings.

The matter is merely an ephemeral derivative of energy perpetually created and annihilated at the interface of the positive and negative energy as the result of the interaction of those opposite energies ^a). Despite its apparent materiality and enormous size, this interface - the 3D-space and its content (universe) - does not exist in and of itself. Together with the matter, it contains, space perpetually appears and disappears at the rate equal to the speed of light creating a dynamic dimension which we call time.

In a deeper reality, this dynamic ephemeral space might be described as a front wave propagating at the speed of light across an unimaginably vast ocean of high energy (Figure-1A). This front wave perpetually rises and dissipates above and to the surface of the ocean, manifesting respectively, using Bohm’s terms, the unfoldment of the implicate order and the enfoldment of the explicate order ^b).

It is only at this wave structure (unfolded order) that every materialized thing is localized. In this front wave, the universe where we live, the local order implies. Its surrounding (enfolded order), in front and behind the wave as well as in the vast ocean beneath it, is non-local ^c). The surrounding of our universe, the undisturbed vast ocean of energy, which we used to think as nothingness, is, in fact, a real plenum. Nothingness, emptiness, vacuum, nonexistence ^d) or whatever you call it is just pure human imagination.

Bohm was awfully correct when he stated that because the implicate order is the foundation that has given birth to everything in our universe, this infinite sea of energy must contain every configuration of matter that has been or will be created, energy, information (knowledge), consciousness, intelligence, and life ^e).

But again Bohm had no idea on how to describe physically these deep layering realities. He talked about super-implicate order by extending the notion of implicate order to quantum fields instead of particles ^f). The whole idea of implicate order could be extended in a natural way implying indefinitely higher levels of implicate order. In order to visualize the Bohm’s idea, we may enhance it by figuring out that each of those multi-layered implicate orders (energy, information, consciousness, intelligence, and life) is embedded one within another, in successively higher and higher dimensions (Figure-1B, C and D) ^g).

Notes:

a. The 4-dimensional spacetime is split into two parts as the positive and negative energies segregating from each other. The interface of these opposite energies is the 3-dimensional [hyper] surface on which particles are created as the result of those energies’ interaction. This interaction takes place as the quantum fields generated by the opposite energies piercing through the interface igniting quantum sparks we perceive as particles.   

b.  Bohm ¹ described the universe as a comparatively small pattern of excitation, a ripple on the infinite ocean of energy which is a deeper order enfolded in the warp of the reality. Bohm failed to elucidate his idea more explicitly by describing geometrically i.e. the relative dimensionality of the ripple vis-a-vis that of the ocean of energy. As such, his description of the universe in term of implicate and explicate order was blamed to be merely a metaphor.

c.   Our classical notions of localized order imply in spacetime arise as limiting cases of the deeper implicate order. The manifest level of ordinary experience and the quantum level underlying it emerge from a still deeper implicate level in which the classical Cartesian notions of form, order, and structure have more or less dissolved. Bohm believed that the implicate order would be more suitable for expressing the basic laws of nature than the explicate order which is only a particular case of the general order.

d.    Nothingness in the sense of an absolute term in which it is devoid of matter as well as energy or anything else. 

e.  We may call all of the later (information, consciousness, intelligence, and life) energy but in different degree of sophistication (dimensions).

f.     There is indeed no distinction between the fields and spacetime itself.

g.   The dimensions shown in the figure are relative. We should bear in our mind that each of those individuals (energy, information, consciousness, intelligence, and life) may have different levels of existence and, those, the variety of their dimensions.

References: 

1.    Bohm, D. et al.: “The Undivided Universe”, Routledge, London, 1993, p. 374-380.

2.    Talbot, M.: "The Holographic Universe", HarperPerennial, New York, 1992, p. 46-49

The Nothingness, Implicate Order and Non-locality

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