Accessing a Big Bounce Universe with Concealed Mass and Gravitation

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Accessing a Big Bounce Universe with Concealed Mass and Gravitation

Guido J.M. Verstraeten

Doctor of Philosophical Sciences and Doctor of Physics, University of Applied Sciences

(Bjorneborg-Pori, Finland)

Willem W. Verstraeten

Doctor of Bio-engineering, Royal Meteorological Institute of Belgium (Ukkel, Brussels, Belgium)

According to Whitehead, nature is disclosed to mind by an ensemble of events characterized by unobservable hidden intrinsic factors (e.g., mass, gravitation) and observable extrinsic factors (e.g., motion, density). Mass is not the substratum of dynamics. It implies spatial extension and temporal duration, which are both necessary conditions of observable natural phenomena. Therefore, an instant, deprived of duration, is immeasurable. Whitehead's claims on mass, space, and time corroborate Verlinde's alternative conception of quantum gravitation. Within the de Sitter space-time, this conception starts from the competition of the short distance degrees offreedom of the Ryn-Takanayagi tensor with long-distance thermalized excitations. This enables the creation of a baryonic mass and a decrease in de Sitter entropy. The memory effect of the original baryon creation leads to gravitation and the production of extensive thermodynamic entropy. However, the baryon production shrinks, and the dissipating space-time transforms into a space-timeless cold sink with an accompanying strong contracting memory effect. This is equivalent to the alternate motion of a giant Carnot engine, where the heat source and sink energy exchange produce the eternal periodic dynamics of the Universe. This suggests that the Universe did not start from Big Bang but oscillated eternally as a Big Bounce Universe.

Keywords: gravity, mass, observability, entanglement entropy, baryonic creation, hysteresis

1.Database of observable facts according to Whitehead

Celestial body luminosity appears as a discerness of place over a period of time (duration), related to a complex of events such as its velocity and the solar global neutral hydrogen line width, both by two relations of extension and congredience (Tully & Fisher, 1977). How can a database of observable facts be produced, and what are the consequences for scientific claims?

Within an ensemble of events 8 a series of congredient events E_I, E₂...E....E_n, E_n+I is given, all making part of the same duration with index i indicating countable extensions (Whitehead, 2007). The event-particle e is the result of converging extrinsic properties connected to surrounding events of the ensemble 8. Within the ensemble 8, particle-events require a “Moment” as the duration of minimum extension representing all nature at an instant “now” as well as a spatial “Station” at a location “here” (Whitehead, 2007). Given event- particle e as the intersection of a particular moment and station, three possibilities exist:

i. Other event-particles are all disjunctive to e.

ii. All events involved with the particular event-particle are inside the Moment containing e.

iii. All involved events overlap by a duration containing those event-particles which are covered by corresponding bounding moments. The boundary consisted of two 3D spaces. Such a subset ,M of events occupies the aggregate of the event particles within. Consequently, all subsets ^ of 8 (^ c 8) containing the series of a particular event e are closed. The set 8 of experimental countable outcomes forms a topological space.

This implies the definition of a Borel algebraic set on Whitehead's set of particle events. If a collection ^ of duration subsets of the set 8 of event-particles including 8 is containing (i) all countable unions of subsets of 8, and (ii) all countable subsets of intersections of subsets of 8, and (iii) all subsets of event-particles included in the countable union of subsets, then (^, 8) is a Borel Space.

In order to be distinguishable, the ensemble of event-particles must be endowed by a Hausdorff topology so that any extrinsic character (e.g., velocity, position, time, luminosity) can be mapped by a homeomorphism on hW. Furthermore, a measurement protocol produces a countable ensemble of experimental data 8 as separable final results of a cyclic process starting from and ending within the experimental setting. In addition, there is always a transfer of energy Q and, consequently, a Kelvin-Planck thermodynamic theory is involved. The limiting points of the converging series e. of 8 are mapped on a data base within hW. As it contains all limiting points, this database of observable events is a compact set. Within any time-like cone containing the ensemble of events 8, the experimental setting detects a physical phenomenon ^ (i.e. luminosity) and collects irreversibly the data in an ensemble 8. In consequence, a finite regular Borel measure B is defined on the set 8 of event-particles in order to connect the event- particles irreversibly to the compact data^presuppose the intervention of the existence of

a Kelvin-Planck thermodynamic theory which is a necessary and sufficient condition for the Clausius-Duhem inequality representing the second law of thermodynamics (Truesdell, 1983). The proof is based on the separation theorem of Hahn-Banach that admit a hyperplane within a Hausdorff ensemble, including one closed ensemble 8 and one compact ^"so that there exist canonical adjoint functionals T and S, called thermodynamic temperature and entropy so that dQ/T<dS is applicable on the closed set of event-particles 8. This implies that at the separation hyperplane, the entropy is zero, and in consequence the system has a condition characterized with a low entropy state dQ/T> dS on the compact set

2.Verlinde's conception of quantum gravitation within Whitehead's conception of observability

Experimental support for Verlinde's conception of quantum gravitation is provided by the Tully-Fisher relation (Tully & Fisher, 1977). This relationship connects the luminosity of the galaxies to their mass and diameter. Absolute magnitude, global profile, and diameter are functions of the velocity of the relative motion between the galaxy and observer. In Whitehead's concept, observable galaxies are natural events. The corresponding relative velocity and luminosity are extrinsic observable characters, but mass, profile, diameter, and gravitation are intrinsic (Whitehead, 2007). Instrumental observations in a laboratory setting are clearly the result of intelligible discursive processes, thereby not detecting events but entities represented by observable and experimental data, resulting from (mental) thought (Whitehead, 2007). Observable events make room for the set-up of a countable database of experimental facts (Whitehead, 2007). All observed data of events e under consideration form part of the ensemble 8 containing series E. of the observed events. The limit of the above mentioned series with the intrinsic property of e's is the abstract of the converging series E . (Whitehead, 2007) and is projected on abstract dimensionless instants of time of a four dimensional (4D) compact space-time manifold Instants of time are dimensionless. Instead of a countable ensemble, instants of time make part of space-timelike space; however, they are the ideal of the non-entity and, therefore, neither a database nor entities (Whitehead, 2007), as was explained in section 1.

3.Whitehead's conditions of observability and the Einstein-Friedmann cosmology

What is disclosed to mind by nature, and what is disclosed by nature by the mind (Whitehead, 2007), that is the question. According to Whitehead, the ensemble 8 discloses nature to mind, contrary to the Einstein-Friedmann cosmological theory where the formal compact space-time ^"discloses nature. Einstein started from the Newtonian conception of space and time as an a priori 4D Minkovski manifold containing matter as a substratum of elementary particles endowed by dynamical characteristics. According to Noether's first theorem (Noether, 1971), the homogeneity of space and time implies the conservation of linear momentum and energy, respectively, while the isotropy of space involves conservation of angular momentum. The symmetry properties are put a priori on the Minkovski container, and the three physical parameters (linear and angular momentum, and energy) are part of the dynamics. However, the dynamic equations are derived from the d'Alembert variation principle of minimum action so that any dynamic event is reduced to a static substratum (Misner et al., 1973).. In the scope of relativity, those patterns governed by dynamical gravitation laws are formally equivalent within any inertial reference system linked by a Lorentz transformation, the so-called equivalence principle (Udwadia & Kalaba, 2002). Constant gravitation is equivalent to a noninertial reference system. The matter is considered as the intrinsic factor of any substratum, while the extensive factor of any substratum is reflected in the curvature of its occupied space-time. Consequently, only geometric deviations of the 4D Minkovski space-time provide experimental support for the action of gravitation. Formally, the Einstein equation connects the substratum of the stress-momentum-energy- pseudo-tensor T and G, which represents the new universal gravitation constant, to the curvature R.j of the space-time container as follows:

Here, R is the determinant of the R . curvature tensor, and g is the metric tensor. The indices i and j vary between 1 and 4, corresponding to the time and space coordinates, respectively.

According to Whitehead's conceptions, action T and reaction R are completely turned back. Instead of the observability of the extrinsic dynamical factor of any event to provide evidence for its intrinsic gravitation and mass factor, experimental evidence - in the scope of relativity - evolves from the unobservable intrinsic factors within a priori static spacetime: the universal gravitation constant G and mass are causes of the varying geometry of its environment. According to Whitehead, however, elements of geometry, that is, space and time, are the a priori conditions of the observable effects of gravitation. Consequently, Whitehead's boundary conditions of observation become the final relativistic results of the experimental observations. Stated otherwise, the cart was placed before the horse. The cosmological consequences of the Einstein-Friedmann model follow directly from the aforementioned a priori symmetry boundary conditions of space-time and from the a priori dual conception of mass. On the one hand, mass is the substratum of any dynamic event as an intrinsic factor; on the other hand, it makes part of dynamic observable extrinsic factors of events such as the conservation of linear momentum and energy. Furthermore, two additional corollaries about the nature of the Universe evolve from the Friedman model. First, the calculated average density of matter of the Universe (10 x e^-29 g/cm³) is 100% of the estimated matter density (10 x e'³¹ g/cm3) in the environment of a galaxy. Second, the negative open radius curvature provides support for an expanding universe from time zero to infinity with just one singularity, while the positive closed radius curvature implies an oscillating universe with periodic singularities. The first corollary endowed the Universe with unobservable Black Matter, and the second makes room for the Big Bang, provided the Universe has the curvature of the Anti-de Sitter Space (Misner, Thorne & Wheeler, 1973). Both substantial elements of the Universe evolve from mathematical products of mind without disclosure of nature to mind.

4.Whitehead's conditions of observability for Pound-Rebka en Redshift experiments

What are the consequences for basic experiments of relativity, such as the experiment of Pound-Rebka (Pound & Rebka, 1959) and the redshift deviation of electromagnetic rays in the environment of Mercury (Treschman, 2014) given the mentioned controversy? Pound-Rebka's setup was based on the Mossbauer effect measurement of travelling y-rays produced by a 57Fe source along with a tower with a distance of 22.56 m in order to provide experimental evidence of the above-mentioned equivalence principle of gravitation and inertial reference systems. The gravitational energy shift of massless photons during their downward and upward motion with increasing wavelength demonstrates the gravitational action and, consequently, the length contraction and time dilatation as predicted by the Lorenz-transformation between two inertial reference systems, provided the Sun spectrum is supposed to be standard. At first glance, it concerned a measurement of the extrinsic factor of the gamma-decay shift, while the intrinsic gravitation factor and the equivalence principle were taken for granted. The same remark is valid on classical tests of the deflection of light by the sun and the gravitational redshift in the environment of Mercury. The shift to infrared, however, is the measurement of acceleration and motion. These are extrinsic characteristics of events; moreover, the equivalence principle is also taken for granted. At face value, these experiments corroborate the formal equivalence of gravitation and inertia; however, both experiments provide evidence for the varying curvature of the 4D Minkovski space-time.

However, this varying curvature of the 4D Minkovski space-time is precisely the a priori condition of the observability of any event. Moreover, the ensemble of particle events disclosing the extrinsic energy shift of gamma particles and redshift of light in the Mercury environment is the result of interactions of the involved series of events, but it is not the result of the hidden intrinsic characters of the events. Thus, the data of these experiments only corroborate the geometric a priori conditions of their observability. They cannot disclose the deep essence of their intrinsic characters, such as mass and gravitation. Hence, is the interpretation of these experiments from the principle “what is disclosed of nature by mind?” shed more light on the deep nature of gravitation, or are they just obscuring some cosmological phenomena, such as the accelerated expansion of our Universe by presupposing the non-observable dark matter? Evidence for dark matter claims to explain excess gravity is supported by recent references (Brouwer et al., 2021). However, in this study, measurements of hydrogen profiles beyond and within the optical discs of galaxies, dynamics of galaxies in clusters, and other new methods such as weak gravitational lensing, only demonstrate baryon acoustic oscillations and cosmic microwave oscillations. What is more, Brouwer et al. (2021) provided more evidence for Milgrom's non-general relativistic Modified Newtonian Dynamics (Milgrom, 1983, 2013), although the experimental support discloses the a priori conditions of observability rather than shedding light on the essential nature of mass and gravitation. These attempts, based on the equivalence principle of gravitation and inertia, discover the extrinsic characters of the entire Universal Event, but they do not disclose the deep essence of intrinsic characters such as mass and gravitation. As such, they corroborate the varying conditions of observability. We provide answers to the above questions by analysing Verlinde's claims about the nature of gravitation and apparent dark matter in the scope of Whitehead's concepts of matter, space, and time.

5.Verlinde's alternative conception of gravitation

Verlinde suggests the existence of apparent positive dark matter in order to explain the accelerated expansion of our Universe. Contrary to the widely accepted theoretical approach involving dark matter, Verlinde's conception of matter does not reduce this factor to the substrate of energy and linear momentum. The matter is deeply connected to pressure-less fluid, revealing the emergent nature of gravitation as the intrinsic elastic response of spacetime to excitations of the meta-stable micro-ground state of the de Sitter Space. Verlinde's propositions about the deep origin and the essential nature of gravitation start from the de Sitter space, in which a part of the microscopic degrees of freedom are thermalised. A nonlocally stored thermodynamic entropy S(V) emerges besides the Bekenstein-Hawking area law entropy, proportional to the cosmological horizon (Verlinde, 2017). According to the holographic principle, the stored Mogic qubits at the surface spread out over n physical qubits in bulk. The area law due to the short-distance entanglement of neighbouring degrees of freedom of the Ryu-Takanayagi tensor formulation of emergent space-time generates the entanglement entropy S(V) (Vidal, 2007), which is well-known as the area law for entanglement entropy (Casini, & Huerta, 2009). However, the entanglement entropy is the entropy of the non-observable (Casini & Huerta, 2009) according to the Ryu-Takanayagi conjecture about contributing short-range and long-range areas. Consequently, this entropy is out of the range of Whitehead's observable ensemble of events. The extensive thermal entropy S _t(V), on the contrary, implies extension and duration, and consequently, S (V) implies observability of the involved events. The corresponding entropy decline by mass M gives S_M=2nM/ha_g. A long-time scale creates eigenstate thermalisation accompanied by a thermal volume law contribution of entropy S(V) that competes with the Bekenstein- Hawking entanglement entropy S_BH. This means that the so-called Coulomb branch mass and gravitation branches off from Higg's branch stress-strain response of the pre-baryonic Universe. Furthermore, Verlinde also recovers the equivalent of the scaling Tully-Fisher relation between baryonic and apparent positive dark mass (Verlinde, 2017):

G is the Newtonian gravity constant measured by Cavendish in 1798. Furthermore, the thermal entropy decreases because thermal entropy contributes to the de Sitter entanglement entropy. Consequently, the thermal volume entropy transforms the space-time into a reactive elastic medium. Moreover, the gravitation, fed by the created positive dark energy, emerges from the elastic reaction of the de Sitter space within the cosmological horizon in the competition of both long-and short-range entanglements, while the horizon stabilises. Verlinden's claims about gravitation as the memory effect of entanglement entropy producing and competing short-and long-range dynamic tensor energy involve a universe that behaves as a condense elastic medium.

Here, gis the stress, e is the strain, 5 is the Kronecker delta, the indices i and j vary between 1 and 4, corresponding to the time and space coordinates, and k indicates the diagonal terms of the matrix. g and 1 are the Lamй parameters. Stress is followed by entropic elasticity due to adiabatic expansion, and by elastic reaction, adiabatic compression. The reactive action of gravitation to the baryon mass escape minimises the memory effects on external perturbations in condensed matter. Verlinde identifies the latter as the emergence of an apparent positive dark energy. The hysteresis curve describing the stress and strain is a measure of the entropy production in glassy materials identified as positive black matter in the scope of Verlinde's concept of gravitation. The relationship between strain and stress is well established in glassy materials (Radhakrishnan et al., 2017).

6. Whitehead's support for Verlinde's alternative conception of gravitation

Since Verlinde does not put a substratum status on mass, and since he does not make the curvature of space equivalent to gravitation, he reformulates cosmology in Whitehead's concept of nature. Whitehead tacitly implies the creation of an appropriate gravitational environment by mass excitation escape to settle down energy and momentum in the web of space- and time-like events. Consequently, space and time just emerge after the escape of the baryonic mass and the reactive force of gravitation. Verlinde's attempt requires experimental evidence of additional positive energy to explain the border flattering of galaxies. Therefore, he links his results about visible baryonic matter density with positive apparent matter using the Tully-Fisher scaling relation. Given the acceleration g_D due to the apparent positive dark mass with g_D = G.M_D(r)/r², the baryonic Tully-Fisher relation becomes (Verlinde, 2017):

Here, v_f is the asymptotic velocity of the flattened galaxy (see Papastergis, Adams, & van der Hulst, 2016 for recent experimental support).

However, we emphasise the deep difference between the classical Einstein-Friedmann conclusions from the Tully-Fisher scaling relation and Verlinde's experimental gauge claims for the elastic response of the nature of the essence of gravitation. Within the EinsteinFriedmann concept, luminosity is linked to the intrinsic factor of gravitation, and the conclusion of the Ј-shift is considered to provide evidence for mass as substratum, notwithstanding the fact that mass as substratum is already tacitly assumed, because the observability conditions of extension and duration are pre-supposed. According to Verlinde, gravitation and mass correspond to the expanding or shrinking space-time, and indirectly, this space-time variation is measured, not the motion of the hypothetical substratum mass. Gravitation, as the memory effect of the mass escape due to the competition of long-distance and short-distance quantum states, can be considered as an intrinsic characteristic of the escape event.

7. The Big Bang as the ideal of the non-entity

Observability and experimental databases start when space and time are created by the mass escape due to competition of short-range and long-range entanglement of degrees of freedom of stress tensors. By baryonic mass creation, the de Sitter entropy decreases, and the measurement of this event implies that the observable creation of baryonic mass makes part of a closed set of event-particles while the observed event is mapped on a compact set of experimental data, provided that on this compact set of data, the Kelvin-Planck thermodynamic theory is valid.

This observed baryonic mass creation matches the branch off within the fact-like thermodynamic reduction of the Arrow of Time by Reichenbach (1956) and Grunbaum (1973). The branch-offs were first mentioned by Reichenbach (1956) and subsequently by Grunbaum (1973). These branch states are nothing more than the emergence of baryonic matter of ensemble E. Consequently, the entropy of a separated galaxy or a solar system increases after gravity and separation starts. The cut-off by hyperplanes explains the apparent paradox of the asymmetric evolution of galaxies and our solar system, while the interactions on the microscale are completely symmetric.

While Reichenbach and Grunbaum define their branch off as a factlike reduction of the Arrow of Time, Verlinde's claims imply a lawlike reduction of the Arrow of Time based on the emergence of baryonic matter. However, there is an important restriction to be added. The arrow of time is not a universal unique time direction but is directly connected to the respective Higg's branch entity from which the baryonic escape creates the respective low- entropy branch off. Consequently, time asymmetry does not reduce to thermodynamic entropy unless it is a relative time within the separated sub-ensemble of the Universe, and there is no evidence for an absolute Arrow of Time. However, this branch cut-off or the creation of the Coulomb branch out of Higg's branch is presented as an instant of time. However, according to Whitehead, an instant is the ideal real of all nature without any temporal extension, so

the ideal of immeasurable non-entity. However, physical theories admit concepts such as dimensionless instants of “now” and “here,” notwithstanding that nature does not allow absolute instants of time “zero” and dimensionless particle events of spatial 'here' because they are non-events, and hence immeasurable (Whitehead, 2007).

Whitehead's conception of matter, space, and time does not imply a unique “first energy-momentum entity” or an absolute beginning of the Universe. However, it has a very remarkable logic collorary: it does not exclude speculations about partial short-range as well as long-range entanglements within the pre-space-time energy-momentum entity that evolves to the above-mentioned excitations of the meta-stable micro-groundstate of the de Sitter Space. Consequently, the origin of baryonic matter escape can be monistic by a unique entanglement or plural by multiple partial entanglements. Obviously, the probability of plural baryonic creation evolving from a unique cause is rather negligible unless a fundamental uncertainty which is a basic property of the space-timeless entity and governs the different baryonic creation.

8. The Giant Carnot Cycle as the Big Bounce Universe

The “space-timeless entity” is not an infinite source of baryonic mass creation. Thermodynamic entropy appears in the dissipating and expanding Universe. The baryon part of the Universe produces space-time from energy taken from the space-timeless entity, and its free energy dissipates into the energy sink of the produced space-time. This mechanism is sustained by the “Heat” source of the space-timeless entity. This space-time, however, shrinks when mass and gravity production is accelerated beyond the cosmological horizon. Indeed, the gravitation response on baryonic creation as a memory effect of the pre-baryonic Universe can exceed the stress factor. In that case, the hysteresis energy is negative, notwithstanding the positive dark matter that provokes the expansion of the Universe. Instead of expansion, contraction is the right response to stress created by baryonic production. The huge memory effects of the original baryon creation appear, and space-time shrinks into a space-timeless cold sink. In addition, entropy as an extensive physical parameter decreases, so that the temperature is raised in the sink. Short and long-distance entanglements arise with thermalised excitations, and the “cold” sink becomes the “heat” source and vice versa; the residue of the former space-timeless heat source becomes the cold sink. It looks like the periodic motion of a giant Carnot engine where the heat source and sink alternately share their functions in order to produce the eternal periodic dynamics of the Universe. The Universe did not start from the Big Bang, but oscillated eternally The concept that the Universe did not start from the Big Bang but oscillates eternally just like the Big Bounce is corroborated by Popper's claims about the nonexistence of a central source causing the singularity of the outgoing and contacting waves (Popper, 1956a,b; 1957). According to Popper's claims, even the singularity of the Big Bang evolving from a central source sounds rather odd.

Thus, the alternative conception of gravitation formulated by Verlinde is supported by Whitehead's view on the matter, space, and time, and this results in the decline of the Big Bang in favour of the Big Bounce Universe. Within this Giant Carnot Universe, different stages of the expansion of the Universe exist. This implies that the reported values of the Hubble constant, derived from different experiments (Di Valentino et al., 2021), could all be exact acceleration values, although an only representative for different stages of the oscillating Universe.

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