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... As stated by de Broglie in his seminal PhD thesis [20] at the origin of QM, "to each elementary particle with proper mass M , one may associate a periodic phenomenon of Compton periodicity", or, in Penrose words [21], "any stable massive particle behaves as a very precise quantum clock, which ticks away with Compton periodicity", and according to Einstein [22] "a clock is a periodic phenomenon so that what it happens in a period is identical to what happens in any other period ". There is nothing wrong in describing quantum particles as intrinsic clocks ticking at Compton rates, this is implicitly done every time we use a wave function or a field in QM by means of phasors. ...

... Notice that massless particles such as photons or gravitons are "frozen clocks" [21] (infinite world-line compactification lenght T C = ∞), so that they provide reference non-compact world-lines necessary to describe the motion of massive particles. Massless particles therefore guarantee that the ordinary causal structure of relativistic physics is preserved and explain how massive particles can propagate in space-time despite their compact worldcycles. ...

... (6). To clear every doubt we must always simply consider that: 1) it is a fact that the universe is solely constituted of elementary particles; 2) it is a fact that, according to the wave-particle duality, every elementary particle is a periodic phenomenon [20,22,21]; thus it must be true that physics can be consistently formulated in terms of elementary cycles. ...

We prove that the Feynman Path Integral is equivalent to a novel stringy description of elementary particles characterized by a single compact (cyclic) world-line parameter playing the role of the particle internal clock. The possible description of elementary particles as characterized by intrinsic periodicity in time has been indirectly confirmed, even experimentally, by recent developments in Time Crystals. We clearly obtain an exact unified formulation of quantum and relativistic physics, potentially deterministic, fully falsifiable having no fine-tunable parameters, also proven in previous papers to be completely consistent with all known physics, from theoretical physics to condensed matter. New physics will be discovered by probing quantum phenomena with experimental time accuracy of the order of 10 −21 sec.

... D). As stated by de Broglie in his seminal PhD thesis [20] at the origin of QM, "to each elementary particle with proper mass M , one may associate a periodic phenomenon of Compton periodicity", or, in Penrose words [21], "any stable massive particle behaves as a very precise quantum clock, which ticks away with Compton periodicity", and according to Einstein [22] "a clock is a periodic phenomenon so that what it happens in a period is identical to what happens in any other period ". There is nothing wrong in describing quantum particles as intrinsic clocks ticking at Compton rates, this is implicitly done every time we use a wave function or a field in QM. ...

... There is nothing wrong in describing quantum particles as intrinsic clocks ticking at Compton rates, this is implicitly done every time we use a wave function or a field in QM. Notice that massless particles such as photons or gravitons are "frozen clocks" [21] (infinite world-line compactification lenght T C = ∞). In particular this element is useful to figure out how the ordinary causal structure of relativistic physics is preserved and how massive particle can propagate in space-time despite their compact world-cycles. ...

... E). In general we must always consider that: 1) it is a fact that the universe is solely constituted of elementary particles; 2) it is a fact that, according to the wave-particle duality, every elementary particle is a periodic phenomenon [20][21][22]; thus it must be true that physics can be consistently formulated in terms of elementary cycles. ...

We prove that the Feynman Path Integral is equivalent to a novel stringy description of elementary particles characterized by a single compact (cyclic) world-line parameter playing the role of the particle internal clock. This clearly reveals an exact unified formulation of quantum and relativistic physics, potentially deterministic, fully falsifiable having no fine-tunable parameters, also proven in previous papers to be completely consistent with all known physics, from theoretical physics to condensed matter. New physics will be discovered by observing quantum phenomena with experimental time accuracy of the order of 10^{-21} sec.

... In this sense, Reichenbach can be considered a curious precursor to Penrose, 16 the latter whose view will be taken up in Section 6. However, while Reichenbach used gravitation to merely acquire knowledge of the global causal net topological structure of the world [86], Penrose will dig deeper into the role played by gravitation (and fields in general) for the determination and prescription of entropy and dynamics at the cosmological scale [28,100]. ...

... Throughout his distinguished and still ongoing long career, Penrose has been relentlessly pursuing this task through a series of extremely well-articulated and original books, articles, and talks [28,[38][39][40]100]. Most importantly, it is probably due to Penrose that the role of gravitation in entropy has been prominently brought into the picture, an idea that does not appear to have played a very essential role in the works of Boltzmann, Reichenbach, and even Prigogine. ...

... Now, the entropy of the CMBR can be easily calculated since it follows the Planck thermal radiation law and is found to be extremely uniform (in angular directions), suggesting an isotropic initial state of the universe [28,40]. That, in turn, implies that the gravitational degrees of freedom were somehow "turned off" at the moment the of Big Bang and for some period of time after, at least until the onset of the decoupling era [100]. Otherwise, the presence of strong gravitational interactions will lead to very high entropy in the initial state instead of the very low entropy to be expected if Boltzmann Order Principle and dynamics [172] can be extrapolated to apply to the entire universe, a view Penrose continues to find unproblematic [28]. ...

The question why natural processes tend to flow along a preferred direction has always been considered from within the perspective of the Second Law of Thermodynamics, especially its statistical formulation due to Maxwell and Boltzmann. In this article, we re-examine the subject from the perspective of a new historico-philosophical formulation based on the careful use of selected theoretical elements taken from three key modern thinkers: Hans Reichenbach, Ilya Prigogine, and Roger Penrose, who are seldom considered together in the literature. We emphasize in our analysis how the entropy concept was introduced in response to the desire to extend the applicability of the Second Law to the cosmos at large (Reichenbach and Penrose), and to examine whether intrinsic irreversibility is a fundamental universal characteristics of nature (Prigogine). While the three thinkers operate with vastly different technical proposals and belong to quite distinct intellectual backgrounds, some similarities are detected in their thinking. We philosophically examine these similarities but also bring into focus the uniqueness of each approach. Our purpose is not providing an exhaustive derivations of logical concepts identified in one thinker in terms of ideas found in the others. Instead, the main objective of this work is to stimulate historico-philosophical investigations and inquiries into the problem of the direction of time in nature by way of crossdisciplinary examinations of previous theories commonly treated in literature as disparate domains.

... (5). As stated by de Broglie in his seminal PhD thesis [20] at the origin of QM, "to each elementary particle with proper mass M , one may associate a periodic phenomenon of Compton periodicity", or, in Penrose words [21], "any stable massive particle behaves as a very precise quantum clock, which ticks away with Compton periodicity", and according to Einstein [22] "a clock is a periodic phenomenon so that what it happens in a period is identical to what happens in any other period ". There is nothing wrong in describing quantum particles as intrinsic clocks ticking at Compton rates, this is implicitly done every time we use a wave function or a field in QM. ...

... There is nothing wrong in describing quantum particles as intrinsic clocks ticking at Compton rates, this is implicitly done every time we use a wave function or a field in QM. Notice that massless particles such as photons or gravitons are "frozen clocks" [21] (infinite world-line compactification lenght T C = ∞). In particular this element is useful to figure out how the ordinary causal structure of relativistic physics is preserved and how massive particle can propagate in space-time despite their compact world-cycles. ...

... (6). In general we must always consider that: 1) it is a fact that the universe is solely constituted of elementary particles; 2) it is a fact that, according to the waveparticle duality, every elementary particle is a periodic phenomenon [20,22,21]; thus it must be true that physics can be consistently formulated in terms of elementary cycles. ...

We prove that the Feynman Path Integral is equivalent to a novel stringy description of elementary particles characterized by a single compact (cyclic) world-line parameter playing the role of the particle internal clock. This clearly reveals an exact unified formulation of quantum and relativistic physics, potentially deterministic, fully falsifiable having no fine-tunable parameters, also proven in previous pap,rs to be completely consistent with all known physics, from theoretical physics to condensed matter. New physics will be discovered by observing quantum phenomena with experimental time accuracy of the order of 10 ⁻² sec.

... The resulting answer involves the Standard Cosmological model, ΛCDM , although there are some inconsistencies with other areas of physics that some speculative theories try to solve (see discussion in [18]). In this research we explore the observational implications in the Cosmic Microwave Background (CMB) of a theory of Sir Roger Penrose named Conformal Cyclic Cosmology (CCC) [19], whose latest statistical analyses have been under discussion [7,15]. Moreover, we develop a method to assess its presence and potential location in the CMB. ...

... The main premise of CCC is that the Universe is in a state of eternal inflation and its full evolution is divided in aeons that are separated from each other by conformal transformations at the cross-over [18,19]. In a remote future all matter will either be captured in supermassive blackholes, that subsequently radiate into massless particles by Hawking evaporation, or, as it is postulated by CCC, will experience a mass fade out to become massless with time (see [7] for details). ...

... Next, we intend to build a confidence interval to obtain the most negative measurements, as we have shown in Section IV D, under the assumption that the simulations represent the real CMB sky maps. In [7] and [19] it is stated that HPs should have extremely negative measurements 5 , but we do not have a theoretical threshold for this value. Therefore, assuming the simulations are representative of the real CMB sky maps, we compute different confidence intervals for α = [1%, 5%]. ...

In this research we present a new methodology to search for ring-like structures in the CMB. The particular context of this work is to investigate the presence of possible observational effects associated with Conformal Cyclic Cosmology (CCC), known as Hawking points. Although our results are not conclusive due to the statistical disagreement between the CMB sky map and the simulated sky maps in accordance to $\Lambda CDM$, we are able to retrieve ring-like anomalies from an artificial data at $95 \%$ confidence level. Once this discrepancy has been assessed, our method may be able to provide evidence of the presence or absence of Hawking points in the CMB. Hence, we stress the need to continue the theoretical and experimental research in this direction.

... The reason is, for people who prefer to see the universe not going to a singularity, they have to come up with some suitable ways to avoid it, such as through processes in particle physics or in quantum gravity. We mention four of them in this essay: pre-Big Bang, loop quantum cosmology (LQC), causal dynamical triangulation (CDT) and asymptotic freedom (AsyF) 1 . ...

... This theory is Penrose's recent favorite in terms of cosmological models -favorite in that after his 2005 proposal he has gathered his thoughts on entropy, black holes, time and cosmology in a 300 page 2010 book [1] which dwells on these foundational issues of Nature in a lucid and inspiring way. In his more recent 2017 book [2] of over 500 pages, "Fashion, Faith, and Fantasy in the New Physics of the Universe" Penrose refers (in Sec. ...

... The author declares no conflict of interest. 1 This list is far from exhaustive. We are not treating inflationary cosmology [30][31][32][33] here, since it already has a wide coverage and how the WCH fits in with inflation is rarely discussed. ...

The Weyl curvature constitutes the radiative sector of the Riemann curvature tensor and gives a measure of the anisotropy and inhomogeneities of spacetime. Penrose’s 1979 Weyl curvature hypothesis (WCH) assumes that the universe began at a very low gravitational entropy state, corresponding to zero Weyl curvature, namely, the Friedmann–Lemaître–Robertson–Walker (FLRW) universe. This is a simple assumption with far-reaching implications. In classical general relativity, Belinsky, Khalatnikov and Lifshitz (BKL) showed in the 70s that the most general cosmological solutions of the Einstein equation are that of the inhomogeneous Kasner types, with intermittent alteration of the one direction of contraction (in the cosmological expansion phase), according to the mixmaster dynamics of Misner (M). How could WCH and BKL-M co-exist? An answer was provided in the 80s with the consideration of quantum field processes such as vacuum particle creation, which was copious at the Planck time (10−43 s), and their backreaction effects were shown to be so powerful as to rapidly damp away the irregularities in the geometry. It was proposed that the vaccum viscosity due to particle creation can act as an efficient transducer of gravitational entropy (large for BKL-M) to matter entropy, keeping the universe at that very early time in a state commensurate with the WCH. In this essay I expand the scope of that inquiry to a broader range, asking how the WCH would fare with various cosmological theories, from classical to semiclassical to quantum, focusing on their predictions near the cosmological singularities (past and future) or avoidance thereof, allowing the Universe to encounter different scenarios, such as undergoing a phase transition or a bounce. WCH is of special importance to cyclic cosmologies, because any slight irregularity toward the end of one cycle will generate greater anisotropy and inhomogeneities in the next cycle. We point out that regardless of what other processes may be present near the beginning and the end states of the universe, the backreaction effects of quantum field processes probably serve as the best guarantor of WCH because these vacuum processes are ubiquitous, powerful and efficient in dissipating the irregularities to effectively nudge the Universe to a near-zero Weyl curvature condition.

... 5b Ergodic mixing of partition function contribution 5c. Our review of CCC cosmology with our revision of a multiverse put in [9,10] 6. Conclusion 1 st First of all, if there are massive gravitons, i.e. gravitons with mass, as well as Mishra's quantum universe [5] procedure, with Machian universe behavior [5], then one should consider the multiverse [9]. ...

... Our review of CCC cosmology with our revision of a multiverse put in [9,10] 6. Conclusion 1 st First of all, if there are massive gravitons, i.e. gravitons with mass, as well as Mishra's quantum universe [5] procedure, with Machian universe behavior [5], then one should consider the multiverse [9]. ...

... Whenever one sees the coefficient like the magnetic field, with the small 0 coefficient, for large values of , this should be the initial coefficient at the beginning of space-time which helps us make sense of the non-zero but tiny minimum scale factor [13] (9) This work uses reference [8] and we also will be considering the following ...

Basic summary is as follows. Initially we discuss a minimum time length. We form DM from considerations as to a minimum time step, and then generate DM via axions. Through Ng's quantum infinite statistics, we compare a DM count, giving Entropy. The remainder of the document is in terms of DE as well as asking the question of comparing Entropy in Galaxies versus Entropy in the Universe, through a lens of Subotha Mistra's Quantum theory of the big bang Introduction: 1 st We discuss minimum time length

... Provided a(t) −1 is integrable at t = 0, we may choose the origins of τ and t to coincide. By (49) this holds for γ > 2/3 which includes the usual physically allowed range. If one allows γ ≤ 2/3 then one has initial singularities which, in the language of Section 1.2.7 are 'conformally-infinitely far away'. ...

... By and large we follow [49] in this subsection. In CCC then there are two space-times representing successive aeons,M andM , respectively to the past and the future of a common boundary Σ, and two space-time metrics, g ab forM andǧ ab forM . ...

... Note (80) and (81) have the form of (30), which is the field equation for the conformal scalar field. In this context, and with R = 4λ, Penrose [49] introduces the term the phantom field equation for this equation, and the phantom field forΩ. Whatever we choose for R, we can expand φ in the manner of the Starobinski expansion (60): ...

In these lectures my aim is to review enough of conformal differential geometry in four dimensions to give an account of Penrose's conformal cyclic geometry.

... We don't know that kind of laws may apply at that point. Penrose discussed the details of his discovery both in research papers and in bestselling semi-popular books [1][2][3][4][5]. ...

... He does not care, but he is certain that he is not a businessman. 2 More characteristic is that in his semi-popular books he deals with universal questions; his area of interest and expertise is the Universe itself. Some of his books, even those not too easy to read, are bestsellers. ...

... Publisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. 2 There may have been a reason for Penrose to stress that he was no businessman, because, maybe, he was, even if only to a very small extent. Many years ago there was a lawsuit because of an unauthorized use of the Penrose pattern on a toilet paper. ...

... As stated by de Broglie throughout all his seminal PhD thesis [17] at the origin of modern undulatory formulation of QM, "to each elementary particle with proper mass M , one may associate a periodic phenomenon of Compton periodicity", or, in Penrose words [18], "any stable massive particle behaves as a very precise quantum clock, which ticks away with Compton periodicity". Moreover, we must consider that, according to Einstein [19], "a clock is a periodic phenomenon so that what it happens in a period is identical to what happens in any other period ". ...

... On the other hand, massless particles such as photons or gravitons have infinite world-line compactification lengths T Cγ → ∞. They can be imagined as "frozen clocks" [18]. ...

... We will discuss these aspects in more detail in par.(V). For the moment being we can simply bear in mind that: (a) it is a fact that the ultimate building blocks of the universe are elementary particles; (b) it is a fact, as implicit in the wave-particle duality, that every elementary particle is a "periodic phenomenon" ticking at Compton rate [17][18][19]; ...

By investigating the Feynman Path Integral we prove that elementary quantum particle dynamics are directly associated to single compact (cyclic) world-line parameters, playing the role of the particles' internal clock, implicit in ordinary undulatory mechanics and indirectly observed for instance in Time Crystals. This allows us to formulate a novel purely four-dimensional stringy description of elementary particles as possible physics beyond quantum mechanics. The novelty of this approach is that quantum mechanics originates from a non-trivial compact nature of the minkowskian space-time. Our result is a further evidence in support of Elementary Cycles Theory (ECT), which in previous papers has been proven to be consistent with known physics from theoretical particle physics to condensed matter. Here we provide additional conceptual arguments in support to this novel unified scenario of quantum and relativistic physics, potentially deterministic, and fully falsifiable having no fine-tunable parameters. The first evidences of such new physics characterized by ultra-fast cyclic time dynamics will be observed by probing quantum phenomena with experimental time accuracy of the order of 10^{−21} sec. Considerations about the emergence of the arrow of time from the realm of pure, zero temperature, quantum physics governed by intrinsic time periodicity are also provided. Concerning Einstein's dilemma "God does not play dice" we conclude that, all in all, "God" would have no fun playing quantum dice.

... The theory of superstrings and D-branes, [3], AdS/CFT correspondence, [4]and the theory of black holes, [5]are linked to the theoretical constructions of the evolution of the Universe. The LHC experiments can have sensitivity to extra dimensions through the production of new particles which move in the space of the size of about 10 -17 cm. ...

... Since the phase transition to the same state is one of the most interesting from the point of view of both highenergy physics and cosmology [5], let's consider the phase transition represented by a string f of the following form ...

The study of the birth of the Universe is closely related to the study of phase transitions in high-energy physics implemented in the framework of the theory of derived categories. Using the theory of D-branes and superstrings, the properties of the C 3 ∕Z 3 orbifold as a space of extra dimensions were studied. In the framework of the criterion of stability of the D-brane as bound state of fractional branes O P2 and O P2 (-3) the impossibility of phase transition of one sheaf into another one was shown. The category of distinguished triangles with objects-McKay quivers and morphism between them-Ext q (A,B)-group was used for the calculation of the number of vibrational modes of the string presented by Poincare supergravity with N = 4.

... In the present paper, following Roger Penrose [1][2][3] and Gerard 't Hooft [4][5][6], it is suggested that the universe is conformal invariant. Furthermore, it is suggested that the conformal invariace is described by Weyl geometry. ...

... When dealing with the conformal invariant theory, the most important question that readily arises is how to fix the gauge. The solution could be as follows [1][2][3][4][5][6]. Different observers see the around world differently. ...

In this paper, conformal invariant gravitation, based on Weyl geometry, is considered. In addition to the gravitational and matter action integrals, the interaction between the Weyl vector (entered in Weyl geometry) and the vector, representing the world line of the independent observer, are introduced. It is shown that the very existence of such an interaction selects the exponentially growing scale factor solutions among the cosmological vacua.

... The estimated total mass energy in the universe adding together all visible objects such as stars, planets, and nebulae fits an expansion model. However, some recent theories suggest that the universe might be starting to shrink, or might have cyclic expansions and collapses over vast eons of time (Steinhardt, 2003(Steinhardt, , 2011Zyga, 2012;Penrose, 2011;Boyer, 2010). ...

... However, the most recent models don't include dark matter, dark energy, or inflationary repulsive gravity to account for accelerating expansion. Some even propose an alternative to the universe blasting out in a 'big bang' (e.g., Penrose, 2011;Steinhardt, Turok, 2007). 'Big bang' models estimate the universe is about 13.8 billion years old (now being reconsidered). ...

... In this short note we show a model of a bandage region of two consecutive eons from the Penrose's Conformal Cyclic Cosmology (CCC) [2], which have the following properties 1 : (1.1)ĝ = t −2 (−dt 2 + h t ); ...

... • Note that for t > 0 we haveĝ =Ω 2 g and that for t < 0 we haveǧ =Ω 2 g withΩ = −Ω −1 = t. One of the aims of this note is to identify the above four-manifold M , equipped with the three Lorentzian metricsĝ, g andǧ, with the bandage region [3] of the Penrose's cyclic Universe [2] in which the past eon ends as filled with only one spherical gravitational wave propagating along the null vector K i . Forcing the Poincaré-type expansion metricĝ to satisfy the Einstein's equations (1.2) was the first step to achieve this aim. ...

We consider two consecutive eons $\hat{M}$ and $\check{M}$ from Penrose's Conformal Cyclic Cosmology and study how the matter content of the past eon ($\hat{M}$) determines the matter content of the present eon ($\check{M}$) by means of the reciprocity hypothesis. We assume that the only matter content in the final stages of the past eon is a spherical wave described by Einstein's equations with the pure radiation energy momentum tensor $$\hat{T}^{ij} = \hat{\Phi}K^iK^j, \quad \hat{g}_{ij} K^iK^j = 0,$$ and with cosmological constant $\hat{\Lambda}$ . We solve these Einstein's equations associating to $\hat{M}$ the metric $\hat{g}=t^{-2}\big(-d t^2+h_t\big)$, which is a Lorentzian analog of the Poincar\'e-Einstein metric known from the theory of conformal invariants. The solution is obtained under the assumption that the 3-dimensional conformal structure $[h]$ on the $\mathscr{I}^+$ of $\hat{M}$ is flat, that the metric $\hat{g}$ admits a power series expansion in the time variable $t$, and that $h_0\in [h]$. Such solution depends on one real arbitrary function of the radial variable $r$. Applying the reciprocal hypothesis, $\hat{g}\to \check{g}=t^4\hat{g}$, we show that the new eon $(\check{M},\check{g})$ created from the one containing a single spherical wave, is filled at its initial state with three types of radiation: (i) the damped spherical wave which continues its life from the previous eon, (ii) the in-going spherical wave obtained as a result of a collision of the wave from the past eon with the Bang hypersurface and (3) randomly scattered waves that could be interpreted as perfect fluid with the energy density $\check{\rho}$ and the isotropic pressure $\check{p}$ such that $\check{p}=\tfrac13\check{\rho}$.

... What has happened in Maxwell's treatment (and as we shall see in Boltzmann's treatment too) is that Maxwell has chosen to model around the interactions, or the intimate details of the impact-laden collisions. 191 What has happened is that 191 You see this in the way he characterizes collisions. Writing to Stokes in 1859, he said, "I saw in the Philosophical Magazine…a paper by Clausius on the 'mean length of path of a particle of air or gas…'…on the hypothesis of the elasticity of gas being due to the velocity of its particles and of their paths being rectilinear except when they come into close proximity to each other, which event may be called a collision." ...

... What has happened in Maxwell's treatment (and as we shall see in Boltzmann's treatment too) is that Maxwell has chosen to model around the interactions, or the intimate details of the impact-laden collisions. 191 What has happened is that 191 You see this in the way he characterizes collisions. Writing to Stokes in 1859, he said, "I saw in the Philosophical Magazine…a paper by Clausius on the 'mean length of path of a particle of air or gas…'…on the hypothesis of the elasticity of gas being due to the velocity of its particles and of their paths being rectilinear except when they come into close proximity to each other, which event may be called a collision." ...

I will argue, pace a great many of my contemporaries, that there's something right about Boltzmann's attempt to ground the second law of thermodynamics in a suitably amended deterministic time-reversal invariant classical dynamics, and that in order to appreciate what's right about (what was at least at one time) Boltzmann's explanatory project, one has to fully apprehend the nature of microphysical causal structure, time-reversal invariance, and the relationship between Boltzmann entropy and the work of Rudolf Clausius.

... The fact that cosmological constant is positive was the basis of the formulation of the new cosmological model named Conformal Cyclic Cosmology (CCC) [5], idea proposed by Roger Penrose. The current picture based on Big-Bang and Einstein General Relativity Theory tells us that universe in the presence of the positive cosmological constant has been expanding ever since -it starts with Big Bang and it should continue to eternity. ...

... In the CCC, which is still developing theory, at the end of one period (aeon) there is matter in the form of ultrarelativistic bosonic particles or in the form of radiation (fermions are crumbled into radiation [5]) i.e. existing particles are massless ones or can be considered as massless ones. As it is known, equations of motion of massless particles are conformally invariant. ...

In this letter we considered the bosonic string action in the presence of metric $G_{\mu\nu}$, Kalb-Ramond field $B_{\mu\nu}$ and dilaton field $\Phi$. We commented the conditions for quantum conformal invariance using standard approach (all three $\beta$ functions are zero) and the second one, adding Liouville term to the sigma model action. Analyzing the second one and writing down the effective action, we get Einstein-Hilbert action with some matter and cosmological constant, which is expressed in terms of the central charge of Virasoro algebra. The fact that string theory landscape produces cosmological constant is a little bit unexpected result. It is also interesting that we, for one special choice of background fields, after rescalling space-time metric, made a possible connection to the Conformal Cyclic Cosmology (CCC). It turns out that cosmological constant is conserved in the period of the succession of aeons, which could mean that one aeon inherits the inflationary expansion from the previous one.

... This concludes my replies to the three objections. Roger Penrose holds that there might be infinitely many Big Bangs, with the world expanding from them and contracting into them over and over again (Penrose 2010). If that is even just logically possible, then there is a clear sense in which there is time both before and after any one Big Bang in particular. ...

... Again, this is "with entropy continually increasing throughout aeon after aeon after aeon" if the second law of thermodynamics applies across aeons (Penrose 2010: 174). And again, the continued application of that law is "overwhelmingly likely" (Penrose 2010: 14, Penrose's emphasis). ...

Free download. Forthcoming in European Journal of Science and Theology, October 2022, vol.18, no.5, pp. 31-46. This final proof will be the published paper, online at EJST sometime in September. Six recommendations. Over 255 reads. PRAISE: "The paper is very valuable.... The author clearly sets out the boundaries of his objective and provides a clear line of argument. [S]ince this particular aspect of Hawking’s writing has attracted much attention in popular culture, it is good to have a well reasoned repudiation. Especially since in the paper Hawking’s own writings are used against his no-God argument." --Anonymous reviewer, sentence order transposed. ABSTRACT: This paper is a critique of Stephen Hawking’s very popular Big Bang argument against the existence of God in his book, Brief Answers to the Big Questions (2018). It is a discussion of a single argument in a single text in a single author, in the manner of analytic philosophy. Many writers discuss whether Big Bang theory implies that God could not have created the world, such as William Lane Craig, Quentin Smith, Richard Swinburne, Daniel Linford, and Daniel Saudek; but I mention them only to set them aside. Instead, I shall simply use Hawking to criticize his own argument. I hope to show that in his more considered views in other texts, Hawking implies at least seven criticisms of his own argument. If I am right, then far from objecting to my critique, Hawking himself would seem to agree with it. Most of the paper is on quantum physics and some is on general relativity. The next to last section is on the proper scope of 'ex nihilo nihil fit’.

... The estimated total mass energy in the universe adding together all visible objects such as stars, planets, and nebulae fits an expansion model. However, some recent theories suggest that the universe might be starting to shrink, or might have cyclic expansions and collapses over vast eons of time (Steinhardt, 2003(Steinhardt, , 2011Zyga, 2012;Penrose, 2011;Boyer, 2010). ...

... However, the most recent models don't include dark matter, dark energy, or inflationary repulsive gravity to account for accelerating expansion. Some even propose an alternative to the universe blasting out in a 'big bang' (e.g., Penrose, 2011;Steinhardt, Turok, 2007). 'Big bang' models estimate the universe is about 13.8 billion years old (now being reconsidered). ...

... In this work we investigate the propagation of a massive scalar field in simple models of the pre-big bang cosmology, in particular for the Conformal Cyclic Cosmology (CCC). In this scenario developped by R. Penrose [26,27] (see also [8,20,21,23,37]), we consider a n + 1 dimensional C 2 , time oriented, Lorentzian manifold (M, g). We assume that this spacetime is globally hyperbolic. ...

... We remark that in the cases (2.13), (2.21), with τ − = −τ + , the map τ → −τ relatesM andM. Then the Penrose's "reciprocal proposal" [26] (−τ )ˇ (τ ) = −1, τ ∈ (0, τ + ), (2.23) can be satisfied whenˆ ...

We investigate the linear and semilinear massive Klein–Gordon equations in geometrical frameworks of type “Conformal Cyclic Cosmology” of R. Penrose, or “Singular Bouncing Scenario” as well. We give sufficient conditions on the decay of the mass to the fields be able to propagate across the Big-Bang.

... Born's rule (interpreting squared amplitudes as probabilities) is consistent with the fact that the probabilities of the top card being the ace of hearts and not being the ace of hearts sum to 1. That the squared amplitudes are rational numbers is consistent with the frequentist-based probabilities associated with the finite deck, and it is also consistent with one of Penrose's motivations for developing his model of spin networks [28] where combinatoric rules ensure probabilities are always describable by rational numbers. Based on the notion of discretisation of Hilbert space, we will be seeking an ensemble description of a generic K-qubit quantum state |ψK in the form a0|1, 1, . . . ...

The properties which give quantum mechanics its unique character - unitarity, complementarity, non-commutativity, uncertainty, nonlocality - derive from the algebraic structure of Hermitian operators acting on the wavefunction in complex Hilbert space. Because of this, the wavefunction cannot be shown to describe an ensemble of deterministic states where uncertainty simply reflects a lack of knowledge about which ensemble member describes reality. This has led to endless debates about the ontology of quantum mechanics. Here we derive these same quantum properties from number theoretic attributes of trigonometric functions applied to an explicitly ensemble-based representation of discretised complex Hilbert states. To avoid fine-tuning, the metric on state space must be $p$-adic rather than Euclidean where $1/p$ determines the fineness of the discretisation. This hints at both the existence of an underpinning fractal state-space geometry onto which states of the world are constrained. In this model, violation of Bell inequalities is a manifestation of this geometric constraint and does not imply a breakdown of local space-time causality. Because the discretised wavefunction describes an ensemble of states, there is no collapse of the wavefunction. Instead measurement describes a nonlinear clustering of state-space trajectories on the state-space geometry. In this model, systems with mass greater than the Planck mass will not exhibit quantum properties and instead behave classically. The geometric constraint suggests that the exponential increase in the size of state space with qubit number may break down with qubit numbers as small as a few hundred. Quantum mechanics is itself a singular limit of this number-theoretic model at $p=\infty$. A modification of general relativity, consistent with this discretised model of quantum physics, is proposed.

... In addition to SMBHBs and cosmic strings, there might be other sources of a commonspectrum process, which are worth considering. Some of the most suggestive and physically impactful, if confirmed, are inflation and reheating [61], BBHs from the previous aeon merged during the Big Crunch [62,63] in cyclic conformal cosmological models of the Universe [64], massive gravity [65], and axion-like particles [66]. In particular, a GWB produced by quantum fluctuations of the gravitational field during the inflationary epoch is actually predicted within the context of the standard cosmological model Λ-Cold Dark Matter (ΛCDM), so its discovery would be crucial for probing the evolution of the Universe. ...

Pulsar timing uses the highly stable pulsar spin period to investigate many astrophysical topics. In particular, pulsar timing arrays make use of a set of extremely well-timed pulsars and their time correlations as a challenging detector of gravitational waves. It turns out that pulsar timing arrays are particularly sensitive to ultra-low-frequency gravitational waves, which makes them complementary to other gravitational-wave detectors. Here, we summarize the basics, focusing especially on supermassive black-hole binaries and cosmic strings, which have the potential to form a stochastic gravitational-wave background in the pulsar timing array detection band, and the scientific goals on this challenging topic. We also briefly outline the recent interesting results of the main pulsar timing array collaborations, which have found strong evidence of a common-spectrum process compatible with a stochastic gravitational-wave background and mention some new perspectives that are particularly interesting in view of the forthcoming radio observatories such as the Five hundred-meter Aperture Spherical Telescope, the MeerKAT telescope, and the Square Kilometer Array.

... Hoy por hoy, parece existir un consenso de parte de muchos matemáticos en que las ecuaciones, fórmulas y demás constituyen simplemente ilustraciones de un argumento, pero que no son el argumento (cfr. Penrose, 2012). Queremos plantear de entrada que la mecánica cuántica es un problema filosófico, incluso aunque en ocasiones implique atravesar por discusiones de tipo matemático. ...

Este libro desarrolla una teoría: el mundo es cuántico. No cuántico y clásico. Tampoco semi.cuántico (quantum like). El hilo conductor para esta teoría es el estudio y discusión sobre las diferentes interpretaciones de la mecánica cuántica - más de veinte, a la fecha-.

... Now, there is no god as a supreme entity (Dawkins, 2006) for this implies the existence of boundaries to separate god from either other entities or environment, which thus violates god as being supreme because the very existence of boundaries means god is finite, thus not being supreme in the first place. As to the beginning and fate of the universe, there is the Roger Penrose´s theory about cyclic universes (Penrose, 2010), by which there is neither an absolute beginning nor an absolute fate but infinite cyclic universes, the beginning of each one being the end of a previous one, over timeless cycles. The "big bang" turns out to be a very low entropy state that brought about everything, which thus continues with increasing entropy up until a very high entropy state, with no more fields or symmetries, the nothingness. ...

Leontief, Nobel laureate in Economy, argued: "How long will researchers working in adjoining fields...abstain from expressing serious concern about the splendid isolation in which academic economics now finds itself?". That may be difficult for researchers from some overly specific domains because they may build hard boundaries against other knowledge domains. Therefore, it might be worth other researchers investing time for closing such knowledge gaps. By proper language translating among knowledge domains, unsolved problems or missed opportunities might reveal themselves as not so hard to treat as they appear. To somewhat close such gaps, this paper defines a system as a subset of environment, which is all undifferentiated fields whatsoever, the former being differentiations of the latter. To relate system and environment, one uses the concept of entropy to model the availabilities of environment towards a system, which then gets separated from other systems and environment through boundaries. From such fundamental definitions one develops a simultaneous equation set based on the conservation of quantities and entropy to calculate the maximum sizes of the elements within a system. If one manages to know the network distribution factors amongst the elements of a system, one can calculate the maximum sizes of such elements to cope with the support capacities of environment, also find the optimum system by tweaking the very network distribution factors. Some applications are given: hybrid energy farm, circular system, mathematical relation for project appraisal, EVA-Economic Value Added revisited, risk value added approach, and project as a system. In addition, the entangled quantities time, entropy, and energy are readdressed in one of the appendixes. At last, the definitions of environment and system enable discoursing about broad and speculative issues like life, consciousness, individuality, and god.

... As alternatives to inflation, one can consider bouncing cosmologies, within which the universe existed before the big bang, and its state after the big bang to one degree or another depends on the state before it [12] and the Penrose conformal cyclic cosmological model [18]. ...

If the isolated system of bosons and fermions was initially in a pure maximally entangled quantum state, then as a result of decoherence caused by the creation and annihilation of parti-cles, this system not only enters a mixed state but also achieves equilibrium. The time of such a transition does not depend on the size of the system but is determined only by the properties of the particles. This phenomenon allows the problem of the horizon (the homogeneity of the uni-verse) to be solved, since the transition time of different parts of the universe (if they were originally entangled with each other) to equilibrium will not depend on their sizes, and the speed of the interaction may be greater than the speed of light. Based on the decay of entangled states, the problem of the predominance of matter over antimatter in the universe can also be solved.

... Finally, as we implied in referencing [33] we find that in order to do away with the Anthropic principle, the following references in terms of Ergodic mixing of the Partition function of the Universe was utilized, as far as a verse. [50] [51] [52]. This is by all accounts a classical physics mixing procedure, as is well understood. ...

We examine if there are grounds to entertain the Penrose suggestion as to black holes from a prior cycle of creation appearing in the present cosmos. There are two cases to consider. One a singular start to the Universe or as Karen Freeze and others have modeled a non-singular start. The two cases are different and touch upon the limits of validity of the Penrose singularity theorem. We will first of all state the two cases, singular and nonsingular, and then afterwards, briefly allude to the Penrose singularity theorem. The plau-sibility of the singular cosmological expansion start point w case analysis of Black holes from a prior universe will be discussed first Afterwards, a synopsis of the Penrose singularity theorem. After that, the Nonsingular case of a starting point of the expansion of the Universe will be entertained and described. Since the nonsingular start to the expansion of the Universe is not so well known, a considerable amount of space will be spent upon what I view as mathematical constructions allowing for its analysis. About the only way to ascertain these cases will be by GW astronomy, hence the details of GW production from the early Universe will be covered in excruciating detail. The methodology for that section is simple. Use a construction for a minimal time-step, then from there get emergent space-time conditions for a bridge from a nonsingular start to the universe, to potential Quantum gravity conditions. Our Methodology is to construct using a "trivial" solution to massive gravitons, and a nonsingular start for expansion of the universe. Our methodology has many unintended consequences, not the least is a relationship between a small timestep, which is called t, and then the minimum scale fac

... However, the relatively brief time before technological decline sets in precludes large-scale projects if significant computation is required by the work. One correspondent has suggested that a mixture-of-Gaussians model is more appropriate for our extrapolation, to better conform to conformal cyclic cosmology (Penrose, 2010), as all theories must. A mixture-of-infinite-Gaussians is intellectually appealing, but computationally infeasible (without using a RKHS, which is unfashionable). ...

The field of machine learning has achieved striking progress in recent years, witnessing breakthrough results on language modelling, protein folding and nitpickingly fine-grained dog breed classification. Some even succeeded at playing computer games and board games, a feat both of engineering and of setting their employers' expectations. The central contribution of this work is to carefully examine whether this progress, and technology more broadly, can be expected to continue indefinitely. Through a rigorous application of statistical theory and failure to extrapolate beyond the training data, we answer firmly in the negative and provide details: technology will peak at 3:07 am (BST) on 20th July, 2032. We then explore the implications of this finding, discovering that individuals awake at this ungodly hour with access to a sufficiently powerful computer possess an opportunity for myriad forms of long-term linguistic 'lock in'. All we need is a large (>> 1W) data centre to seize this pivotal moment. By setting our analogue alarm clocks, we propose a tractable algorithm to ensure that, for the future of humanity, the British spelling of colour becomes the default spelling across more than 80% of the global word processing software market.

... The Conformal Cyclic Cosmology or CCC of Roger Penrose [2] is a proposal for a cosmology which answers the question 'What was before the Big Bang?'. The main feature of CCC is that it states that the Universe consists of eons, each being a time oriented spacetime, whose conformal compactifications have spacelike null infinities I . ...

We consider two consecutive conformally flat eons in Penrose's Conformal Cyclic Cosmology and study how the perfect fluid matter content of the past eon determines the matter content of the present eon by means of Penrose's reciprocity hypothesis.

... But how and why did this original space-time point universe come into existence? Penrose [4] proposes a generalized geometrical mechanism by which an old universe that has reached a point of maximum entropy can conformally produce a new universe at a single space-time point, with minimum entropy, allowing the process to repeat endlessly. Others [5] speculate on other bounce-like mechanisms that have similar results. ...

... This is equivalent to the alternate motion of a giant Carnot engine (Verstraeten & Verstraeten, 2020), 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 (Lemaitre, 1931) but oscillated eternally as a Big Bounce Universe (Penrose, 2010). ...

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 of freedom 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.

... It appears that the far-away clock is getting retarded, or even approaches complete rest at high gravity fields nearby a black hole; see, e.g. (Penrose 2010). This relativity of time and simultaneity in modern physics points to a unique property of the actor who can 'breath fire' in this set of rules and' ...

With his bestselling publication, A Brief History of Time, Stephen Hawking introduced in 1988 a new genre by connecting modern science with the question of the existence of God. In the posthumous publication Brief Answers to the Big Questions, he continues his quest for the ultimate truth. The current study presents a philosophical analysis of this search in terms of Aristotle's and Aquinas's classical philosophy. Causality is the central concept employed by Hawking. However, in modern scientific and philosophical literature, its meaning is limited to temporal causality compared to the view of classical philosophy. Only the latter one accepts causality from outside space and time, in other words, a reality transcending the material world. In a quote presented in the discussion, Hawking defines himself as an atheist. After a careful reading of his writings, however, doubts arise about his unbelief.

... Another cyclic scenario suggested by Penrose is conformal cyclic cosmologysee Penrose (2010) and Gurzadyan and Penrose (2013). 46 This scenario does not rely on string theory. ...

As a candidate theory of quantum gravity, the popularity of string theory has waxed and waned over the past four decades. One current source of scepticism is that the theory can be used to derive, depending upon the input geometrical assumptions that one makes, a vast range of different quantum field theories, giving rise to the so-called landscape problem. One apparent way to address the landscape problem is to posit the existence of a multiverse; this, however, has in turn drawn heightened attention to questions regarding the empirical testability and predictivity of string theory. We argue first that the landscape problem relies on dubious assumptions and does not motivate a multiverse hypothesis. Nevertheless, we then show that the multiverse hypothesis is scientifically legitimate and could be coupled to string theory for other empirical reasons. Looking at various cosmological approaches, we offer an empirical criterion to assess the scientific status of multiverse hypotheses.

... Nassim Taleb, uno de los autores que ha llegado a ser incorporado como parte del corpus de las ciencias de la complejidad, lo destaca bien en el subtítulo de su 9. Uno de los padres más importantes en los estudios sobre cohomología es Roger Penrose. Entre sus muchos libros quisiera destacar Penrose, 2010. libro El cisne negro (El impacto de lo altamente improbable). ...

La universidad no es ajena a este fenómeno. Cada vez más voces coinciden en que la educación convencional ha perdido aliento y vivacidad, por lo que se vuelve obligatorio replantear el que hacer educativo y reconfigurar sus propósitos.(ITESO).

... In addition to SMBHBs and cosmic strings, there might be other sources of a commonspectrum process, which are worth considering. Some of the most suggestive and physically impactful, if confirmed, are inflation and reheating [61], BBHs from the previous aeon merged during the Big Crunch [62,63] in cyclic conformal cosmological models of the Universe [64], massive gravity [65], and axion-like particles [66]. In particular, a GWB produced by quantum fluctuations of the gravitational field during the inflationary epoch is actually predicted within the context of the standard cosmological model Λ-Cold Dark Matter (ΛCDM), so its discovery would be crucial for probing the evolution of the Universe. ...

Pulsar timing uses the highly stable pulsar spin period to investigate many astrophysical topics. In particular, pulsar timing arrays make use of a set of extremely well-timed pulsars and their time correlations as a challenging detector of gravitational waves. It turns out that pulsar timing arrays are particularly sensitive to ultra-low-frequency gravitational waves, which makes them complementary to other gravitational-wave detectors. Here, we summarize the basics, focusing especially on supermassive black-hole binaries and cosmic strings, which have the potential to form a stochastic gravitational-wave background in the pulsar timing array detection band, and the scientific goals on this challenging topic. We also briefly outline the recent interesting results of the main pulsar timing array collaborations, which have found strong evidence of a common-spectrum process compatible with a stochastic gravitational-wave background and mention some new perspectives that are particularly interesting in view of the forthcoming radio observatories such as the Five hundred-meter Aperture Spherical Telescope, the MeerKAT telescope, and the Square Kilometer Array.

... This led Penrose to abandon the Weyl Curvature Hypothesis, and instead postulate that our universe has a conformal cyclic structure [23]. During CCC, the smooth matter fields at the beginning of a cosmological epoch clump gravitationally (and chaotically), ultimately forming black holes. ...

This paper draws on a number of Roger Penrose's ideas - including the non-Hamiltonian phase-space flow of the Hawking Box, Conformal Cyclic Cosmology, non-computability and gravitationally induced quantum state reduction - in order to propose a radically unconventional approach to quantum gravity: Invariant Set Theory (IST). In IST, the fundamental laws of physics describe the geometry of the phase portrait of the universe as a whole: "quantum" process are associated with fine-scale fractal geometry, "gravitational" process with larger-scale heterogeneous geometry. With this, it becomes possible to explain the experimental violation of Bell Inequalities without having to abandon key ingredients of general relativity: determinism and local causality. Ensembles in IST can be described by complex Hilbert states over a finite set $\mathbb C_p$ of complex numbers, where $p$ is a large finite integer. The quantum mechanics of finite-dimensional Hilbert spaces is emergent as a singular limit when $p \rightarrow \infty$. A small modification to the field equations of general relativity is proposed to make it consistent with IST

... Nowadays, atom interferometry [32] and electron channeling experiments [3,33] suggest that the de Broglie clock is truly an intrinsic property of massive particles. In addition, Roger Penrose suggested that the passage of time is observable only as soon as the universe contains massive particles [34] ...

The problem of time is a notable obstacle towards the recognition of quantum theory as the ultimate fundamental description of nature. Quantum theory may not be complete if founded upon classical notions. Louis de Broglie, seeming to be more or less convinced about the ontology of his proposed matter waves, tried to develop a theory of sub-quantum degrees of freedom relying on statistical thermodynamics. He realized a quantum particle as a fluctuating dense corpuscle formed via non-linear effects from a sub-quantum medium. A wave on the medium guides the vibrating corpuscle. He argued that an intrinsic clock of a quantum particle is related to its Brownian motion at the sub-quantum level. This led him to conjecture a relation between the de Broglie clock frequency $m c^2/h$ and its implicit temperature, which equals that of the surrounding sub-quantum medium. About the same time, Mandelbrot was the first to derive in a classical setting a thermodynamic uncertainty relation between energy and temperature, that was, coincidentally or not, anticipated by Bohr and Heisenberg in the first years of development of quantum theory. We show here that, when the de Broglie temperature-time conjecture is assumed, the thermodynamic temperature-energy uncertainty relation leads to the quantum time-energy uncertainty relation.

... Nowadays, the same idea is advertising by Roger Penrose [2,3] and Gerard 't Hooft [4,5] in the light of the creation of Universe from "nothing". ...

We investigated the possibility of construction the homogeneous and isotropic cosmological solutions in Weyl geometry. We derived the self-consistency condition which ensures the conformal invariance of the complete set of equations of motion. There is the special gauge in choosing the conformal factor when the Weyl vector equals zero. In this gauge we found new vacuum cosmological solutions absent in General Relativity. Also, we found new solution in Weyl geometry for the radiation dominated universe with the cosmological term, corresponding to the constant curvature scalar in our special gauge. Possible relation of our results to the understanding both dark matter and dark energy is discussed.

... The presence of the postulated cold dark matter is necessary to describe the observation of flat rotation curves of galaxies (which indicate the presence of unseen matter) and the observation of enhanced galaxy clustering. Other types of standard cosmology models include modifications to some of the ΛCDM assumptions, such as alternatives to dark matter (such as modified Newtonian dynamics [83]) and modified gravity models [84], or models which are intrinsically different such as the conformal cyclic cosmology, which assumes that the universe iterates through a countable sequence of cycles of FLRW spacetimes each beginning with a Big Bang [85,86]. ...

In this thesis we describe high-harmonic cosmic string loops in a general relativistic context, and study the implications of high-harmonic content for the predicted gravitational wave signal from cosmic string networks. Initially, we introduce the variational principle, spacetime concepts and other mathematical tools that we will need for the calculations in the following chapters. We introduce the FLRW universe and the $\Lambda CDM$ universe. We then describe the Nambu-Goto cosmic string in a curved spacetime, its equations of motion and its energy-momentum tensor. Fixing the spacetime to be flat, and fixing the gauge, we find the motion of the cosmic string and we present and discuss special solutions. Using the odd-harmonic family of cosmic string loops, we calculate the number of cusps per period and the values of the second derivatives of the left- and right-moving harmonic modes at the cusp, and study their dependence on the harmonic order. We then develop a toy model that calculates the stable daughter loops produced from a parent loop using a statistical approach based on a binary tree description of the loop chopping. We also use the toy model to calculate the average number of cusps produced from a system of loops that self intersect over their course of existence. We derive the gravitational waveform emitted from a cusp as observed away from the cusp, in any direction of observation. We then propagate this result in an FLRW spacetime to reach an expression of its amplitude on Earth. Assuming two different cosmic string network models, we implement our above mentioned high-harmonic results to find the amplitude of the signal and the rate at which these signals reach an observer on Earth.

... I assert on the contrary that by far the largest number of possible states are "Maxwellian" and that the number that deviate from the Maxwellian states is vanishingly small. [28, p. 395] In the last decades, Boltzmann's idea that discussions about typicality, i.e., about very large and very small probabilities, must play a central role for interpretating statistical mechanics and also quantum mechanics (e. g., in the de Broglie Bohm interpretation [41]) as evolved into a 'typicality school' 16 , famously advocated by Lebowitz [70], Goldstein [52], and Penrose [82]. We emphasize that sometimes for advocates of the typicality school, typicality is considered as more fundamental than probability (i.e., too often assumed as a purely epistemic concept), and an opposition is made between Boltzmann and Gibbs. ...

We analyze the objective meaning of probabilities in the context of the many-worlds interpretation of Everett. For this purpose we study in details the weak law of large numbers and the role of typicality and universally negligible probabilities (through the works of Cournot and Borel). We demonstrate that Everett's theory doesn't provide any clue for fixing a probability rule and therefore contradicts irrevocably empirical facts and Born's law.

... Barbour (1999) researched the end of time as the next revolution in our understanding of the Universe. Penrose (2010) proposed the conformal cyclic cosmology (CCC). ...

Cosmological models which postulate an infinite past, such as eternal inflation model, Ekyroptic universe, and Penrose’s conformal cyclic cosmology, face various difficulties related to the Generalized Second Law of Thermodynamics (Aron Wall), and arguments against an infinite regress of causes and events: (1) The argument from the impossibility of concrete actual infinities. (2) The argument from the impossibility of traversing an actual infinite. (3) The argument from the viciousness of dependence regress. (4) The argument from the Grim Reaper paradox. Any one of these arguments would be sufficient. Bounce cosmologies which postulate entropy reversal (Sean Carroll) neglect the problem of causal dependence at the interface. I show that Linford’s suggestion that the universes to either side of the interface might be interpreted as the simultaneous causes of each other entails a vicious circularity. Likewise, a closed causal loop (Gott and Li) is viciously circular. Given that an infinite causal regress and a closed loop is not the case, there is a First Cause.

Roger Penrose's Weyl Curvature Hypothesis states that the Weyl curvature is small at past singularities, but not at future singularities. We review the motivations for this conjecture and present estimates for the entropy of our Universe. We then extend this hypothesis to the quantum regime by demanding that the initial state of primordial quantum fluctuations be the adiabatic vacuum in a (quasi-) de~Sitter space. We finally attempt a justification of this quantum version from a fundamental theory of quantum gravity and speculate on its consequences in the case of a classically recollapsing universe.

Every individual is unique and may serve a unique purpose in this life. Education is widely accepted to be the means of transformation of individuals so that they may achieve their unique success or create their own lives. However, not every individual seems to be realizing their true potential. This paper explores the concept of entropy in education system as a force that is usually imagined to oppose realization of potential of an individual during life in this phenomenal world. Alternatively, the same may provide an impetus that is necessary to bring in organization in oneself to realize the hidden potential. A one group Pretest-Posttest quasi-experimental design was used to draw the conclusions on data obtained from participants of workshops in three different modes, viz. face-to-face Pre COVID-19, face-to-face in COVID-19 with SOPs, and online in COVID-19. Realization of an individual’s potential was represented as a dependent variable, i.e. transformation in cognition, skills, and attitude while the independent variables taken into account were the meaningful interactions of an individual with peers and advanced learners in a designed environment. It was inferred from the results that transformation in learners’ cognition (6-30 %), skills (0-20 %), and attitude (5-32 %) occurred through human discourse, in a community of inquiry.

Contemporary Western culture is characterised by the removal of death from real-life contexts, largely due to the secularisation of society caused by the success of technoscience. This chapter begins by asking what it means that two chatbots could communicate by inventing a language inaccessible to humans. It proceeds to evaluate the problems of consciousness and solipsism, then to consider the relationship between the sunset of metaphysics, the concept of the immortal soul, and the triumph of technoscience, which asserts that consciousness and mind are mortal grey matter. Given this background, Roger Penrose’s claim that consciousness is produced at the quantum level in neuronal microtubules serves as the starting point for a new, authentic sense of immortality based on Emanuele Severino’s definition of eternity. Finally, taking up Severino’s idea of transcendental consciousness, which pertains to the whole of being (or all that is), I hypothesise that the dialogue between the two chatbots indicates the constitution of a quantum consciousness in computers, though they are still programmed by humans to process information in a computational way. In other words, artificial intelligence systems are autonomously anticipating—or even realising—the formation of the quantum Turing machine, which humans do not yet know how to construct.

On the very recent advancement of dressed photon studies
A timely review of the emerging new phase of dressed photon (DP) studies, not yet prevailing in the global nanophotonic society, is given in contradistinction to its preceding incipient phase. A new theory on DPs crucially depends on a couple of important elements, namely, the knowledge on quantum field theory (QFT) having infinite degrees of freedom, notably on the micro-macro duality (MMD) theory developed by Ojima, and a newly proposed Clebsch dual (CD) electromagnetic field as a specific implementation of MMD theory. The main aim of the first part of this article after the introduction, the section of “In search of refinement of the theoretical models”, is twofold: to explain plainly, without resorting to mathematical equations, the essence of the highly mathematical contents of MMD theory, which clarifies a problematic aspect of the Schrödinger’s cat thought experiment, and to explain the physical meanings of the CD field.
Preliminary study on the existence of DP light with spin zero
In the section of “Observed “photon cluster” and light field with spin zero”, we briefly report a new intriguing experimental discovery implying the existence of propagating particle-like “quantum DP light” together with a conjecture on its possible theoretical explanation. A perspective on a variety of possible research directions for DPs is then briefly mentioned in mentioned in the final section.

¿Qué querrá decir preferir la vida sobre la muerte? ¿Será esta también una cuestión de gusto? ¿Y cuándo, en qué instante de la dispersión de la vida, habrá comenzado esa preferencia? ¿Lo habrá hecho de verdad? Desde, por un lado, el telón de fondo de una «nada sublime» como posible «concepto dogmático», en la estela kantiana, para denominar al curso entrópico de la naturaleza y, por otro, atendiendo al «pensamiento suicida», o pulsión fúnebre, como atávica voluntad que escoltaría a esta visión escatológica, se ensaya aquí una respuesta a estas preguntas a través de un juego de espejos (i. e. comprensión reflexiva «germinal y deformante») establecido desde el comentario de texto de tres voces de jóvenes filósofos. Así, en el primer y el segundo epígrafes se expone la tanatología ontológica de Philipp Mainländer y de Jules Vuillemin desde el comentario de varios pasajes extraídos de la Filosofía de la redención (1876) y del Ensayo sobre la significación de la muerte (1948), respectivamente, mostrándose cómo en ambos se revela, en este preciso punto, una diferencia tajante de lo humano respecto al resto de los animales. El tercer y último epígrafe responde a las cuestiones planteadas por ambos (indirectamente en el primer caso, directamente en el segundo) desde la atención puesta, tras algunos rodeos por otros textos, en unas notas inéditas para una charla sobre el suicidio de Jacques Derrida (1959-1960).

This article examines how Alain Mabanckou uses sexual allegories in his novel Broken glass (2010) to express (neo)-colonial realities in which Africa is charmed by the West into assuming the role of the sexual subaltern. Mabanckou appears to reinvigorate the sexual allegories of rape and prostitution for expressing the penetrative tendencies of colonialism by affixing their connotations of exploitation to the harsh socio-economic and political realities of (neo)-colonialism, thus creating a motif which is termed in the article as the fetish of colonial gender. Its coalescent value might be of great interest in postcolonial studies since it reveals how neocolonialists ascribe the subaltern’s time and space with exploitable sex through the charm of the global economy. The critical discussion is built on textual research methods and it highlights on the fabric that holds the neo-colonial relationship between the West and Africa.

A class of electromagnetic metamaterials (MTMs), is investigated which the author dubs Proca MTMs, constituting a medium behaving like a “relativistic material” for potential use in electromagnetic applications. This work is motivated by numerous previous results on particular structures such as plasma, waveguides, photonic crystals, magnetic materials, where it has been observed that photons may acquire mass in some dispersive domains. In this approach, it is rigorously proved using a field-theoretic approach that Maxwell theory inside certain classes of nonlocal (spatially-dispersive) metamaterials is equivalent to Proca theory in vacuum, where in the latter photons acquire a nonzero mass (massive electromagnetism.) An explicit closed-form general expression for the Proca MTM dielectric function is given. It turns out that the key to the operation of Proca MTM is spatial dispersion, and hence Proca MTMs represent an important example of the more general family of nonlocal MTMs. The author's analysis involves multiphysics aspects, utilizing concepts and methods taken from classical electromagnetism, special relativity, quantum theory, electromagnetic materials, and antenna theory. Extensive discussion of the physics, computational methods, and design parameters of Proca MTMs is provided to further understand the nature of massive electromagnetism in nonlocal (spatially-dispersive) MTMs. As a concrete application, the main ingredients of Proca antennas are developed as an example of the emerging technology of nonlocal antennas, where the author establishes that a single Proca dipole possesses a perfect isotropic radiation pattern, a noteworthy departure from conventional local antennas (radiators in vacuum and temporally dispersive media) where such radiation characteristics is impossible.

Meta-analysis of current biomedical and biophysical literature revealed the presence of a fractal pattern of discrete EMF frequency bands, in a wide range of animate and non-animate systems, framed as the Generalized Music (GM)-scale biophysical principle and also applied by us to study cognitive brain function as well as quantum mechanical aspects of first life. In this respect, it is proposed that nature is guided by a resonating set of quantum vacuum fluctuations of an all-pervading zero-point energy (ZPE)-field. It was shown that the toroidal GM-code can accommodate 4 spatial dimensions, in line with the Kaluza Klein concept as a feature of the Sub-Quatum SFQS, conceived as a homogenous 5-D space-time manifold. The related photon/phonon and soliton fluxes can be modelled by toroidal geometry as also obtained from Perelmann-Ricci-Flow mappings, processes that enable crucial wave damping and tone separation. The GM-scale exhibits a self-similar fractal) wave pattern that gives rise to a series of more than 500 EMF frequencies from the Hz to the GHz ranges, thereby exhibiting a field-like character. In this paper we report on a series of 46 experimentally determined ZPE-frequencies, from 15 separate studies, that fit the GM-scale eigenvalues closely. The central message of these quantum wave studies implies a cosmic connectivity operating in a primordial context, possibly related to known bounce models of our universe, that is likely also mirrored in life processes, including the human brain. It is postulated that the generation of life in the cosmos resulted from a symmetry breaking from the homogenous 5-D manifold that contains condensed boson type of quantum wave information and is instrumental in past/future transactional information processing and/or pilot-wave type of wave guiding. In this sense, the ZPE-field is seen as a transition zone from the 5D Sub-Quantum domain to our quantum world. We hold that the ZPE-field presents an all-pervading quantum field, that provides long-distance solitons (electron-phonon quasi-particles) that can guide the 3D folding of brain macromolecules embedded in coherently structured water domains, in which hydronium ions and Ca2+ ions are particularly instrumental. In this manner cell proteins and DNA may function as wave-antennas to receive active life-information for the functional architecture of cell, and the generation of cell memory and conscious states. For the permanent transmission of external information a holographic 5D memory workspace of the brain is required that is associated with, but not reducible to the brain. This field-sensitive holographic workspace is involved in predictive coding and quality control of individual awareness. Recent studies by Wong et al., show that the creation of life can be conceived as being guided through a symmetry breaking of condensed (charge neutral, massless) bosons from the 5D informational manifold. The particuar "Diagonal Long Range Ordered" bosons represent the monopoles from the Maxwell magnetic monopole potential, a solitonic eigenstate of the homogenous 5-D manifold, that through Perelmann mapping generates toroidals, instrumental in the formation bio-rings including the nitrogenous bases of RNA and DNA. The retained EMF from these monopole bosons within the RNA and DNA can interact with the molecular entities of life, such as H2O, carbon and nitrogen, by inducing mobile positive valence band hole charges in the molecules. This provides an off-diagonal-long-range ordered superconducting phase that enables cell grow and survival in its thermal environment. It is finally concluded that all matter, from galaxies through life creation therein, is derived from scale invariant information transfer, expressed at the holographic event horizons of each individual cosmic entity, a process that was intended to be verified and observed by the intelligent subjects of its own creation.

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