Scientific Enlightenment, Div. Two B. Scientific Enlightenment Chapter 5: Parallel between Philosophy and Cosmology ACADEMY | previous section | Table of Content | next section | GALLERY

copyright © 2004, 2007 by L. C. Chin. All rights reserved.

1. General comment

As mentioned, the true, and ultimate, parallel between philosophy (enlightenment of the first axial) and modern physics -- so as to make the enlightenment of the second axial -- is to be sought in the principle of conservation, or more precisely in the conservation of existence -- as, really, nothingness. Anamnesis of conservation leads to Liebesakosmismus. We have distinguished two levels of the anamnesis of the conservational truth of existence. The "regular" level is that of the Daoist and the Neo-Confucianist. Hence Zhuangzi's: once one looks through the perspective of conservation, and recognizes that there is really no such thing as genesis and destruction or birth and death, but that all there is in Nature is endless cycle of transformation -- the Dao, the "Total (amount)" (with the rules governing transformations inclusive within), staying the same -- one comes to the non-judgmental attitude that everything is just what it is and that there is nothing to blame, nothing to praise, nothing to hate -- because there are no rights and wrongs -- and nothing to desire: the cosmos dissolves into an impersonal harmonious self-working machine. (Liebesakosmismus.) As we have put it in modern terms: "Confusedly within the nebulousness and blurriness [the complete vacuum...], a transformation occurred [say, vacuum (quantum) fluctuation] and there was "energy" [created out of inflation, the "hot soup" of the Big Bang cosmology]; the energy was transformed and there was form [from atoms to galaxies]; the form was transformed and there was birth [atoms assembling into organisms]; now there has been another transformation and the person is dead. This is like the progression of the four seasons -- from spring to autumn, from winter to summer." Or Zhang-Zai's same insight: "when energy condenses it becomes my body; when it disperses it is still my body." (Of course it is more correct to say "when energy condenses it becomes the 'matter' (the chemical elements) that then coalesces into my body...") There is only -- and one follows only -- the "thusness" (然) of Nature ("self-thusness": 自然).

The higher, transcendental level of the anamnesis of the conservational truth of existence is the Nibbana of Buddhism: "This is deliverance! Birth is finished, the holy life has been led, done is what had to be done, there is nothing further here [naparam itthataya, 'no more thusness']." Because the anamnesis of conservation is more differentiated here, leading to some sort of experience of nothingness (sunyata), here the "extinction" is not the acceptance and following of the "thusness" but the negation of it.

We are here to delineate the content of this higher level of the anamnesis of conservational truth. We see the highest and deepest understanding of the nature of existence following the anamnesis of conservation (the most primordial truth of existence) in the frequent pronouncement of the Buddhists concerning the meaning of existence as emptiness, such as Chi-Tsang's "middle-path": "things neither exist nor do not exist, but neither do they not exist nor do they not not-exist", (萬物非有非無,  而又非非有非非無) ; or Buddha's cited earlier: "And if anyone were to say to a monk whose mind was thus freed: 'The Tathagata [i.e. enlightened one] exists after death', that would be a wrong opinion and unfitting, likewise: 'The Tathagata does not exist..., both exists and does not exist..., neither exists nor does not exist after death.'" As we shall see, the Sunyavada Buddhists have made similar statement. Eventually the question of existence figures into "the ten avyākatāni or so-called indeterminates (better: 'undeclared points') or questions which the Buddha refused to answer" (Maurice Walshe, The Long Discourses of the Buddha, p. 554, ftnt. 219): it becomes meaningless to speak of things as existing or not-existing or whatever. As said (c.f. Plato's "theory of forms") "this is the sense in which the empirical, visible reality around us (beings) is virtual, existing but not really existing, and this virtual existence is in fact the only logically possible existence given the law of Conservation." Thus the Buddhist "all is emptiness." Although Plato's final statement concerning beings (the empirical world) "out'einai oute mh einai ouden autwn dunaton pagwV nohsai, oute amfotera oute oudeteron" (479 c, "it's not possible to think of them fixedly as either being or not-being, or as both or neither.") refers, in that context, more to the way they (the empirical world) appear (the "third sense") and not (or at least not explicitly) to the sense in which they can be said to exist (the "second sense"), the insight is there that this "world" (cosmos) of ours cannot be "real" in the way our common sense assumes it to be: it is an illusion (doxa), which is also Parmenides' conclusion. The salvational effect of such insight ("... there is no more 'thusness'": "nothing further for me here...") -- Nibbana -- is the heart of Buddhism.

The "parallel between philosophy and physics" then is that the virtuality of reality or existence is precisely what modern cosmology has shown the Universe to be.

To explain the genesis of the Universe there currently seem to be two models, the inflationary model first proposed by Alan Guth (now a whole class of "inflationary theories") and Stephen Hawking's no-boundary model of the Universe.¹ The inflationary model can be characterized as a "linear" model, in that it explains how the Universe can be created out of nothing, whereas the no-boundary proposal does not contain an actual "beginning" of the Universe: the "beginning" itself is to be shown to be an illusion. We have mostly adopted the inflationary model because it is now widely accepted as the most plausible scenario.

Alan Guth continues on the proposal of Edward Tryon, "Is the Universe a Vacuum Fluctuation?" (1973), "the first serious suggestion that the creation of the universe from nothing could be described in scientific terms". (The Inflationary Universe, p. 271) "In discussing the creation of the universe, a key issue is the choice of a starting point. In Tryon's proposal, the universe was created from the vacuum, or empty space. According to quantum theory, the apparently quiescent vacuum is not really empty at all, but on a subatomic level is a perpetual tempest, seething with activity. For example, it is possible for an electron and its antiparticle, the positron, to materialize from the vacuum, exist for a brief flash of time, and then disappear into nothingness. Such vacuum fluctuations cannot be observed directly, as they typically last for only about 10^-21 seconds, and the separation between the electron and positron is typically no larger than 10^-10 centimeters. Nonetheless, physicists are convinced that these fluctuations are real, as they can be 'seen' by indirect methods. For example, every electron acts like a tiny magnet, and atomic physicists can measure the magnetic strength of an electron to the extraordinary precision of 10 decimal places. Theorists can calculate this number using quantum theory, and they find that it is influenced by the materialization of electron-positron pairs. If the effect of this materialization is left out of the calculation, then the answer agrees with experiment for the first five decimal places, but the sixth, seventh, eighth, ninth, and tenth decimal places turn out wrong. But if the effect of electron-positron pairs is included, all ten decimal places agree!" (Ibid., p. 272) This seems to refer to the "Lamb shift". "[Virtual particle pairs] are predicted to have a calculable effect upon the energy levels of atoms. The effect expected is minute - only a change of one part in a billion, but it has been confirmed by experimenters... In 1953 Willis Lamb measured this excited energy state for a hydrogen atom. This is now called the Lamb shift. The energy difference predicted by the effects of the vacuum on atoms is so small that it is only detectable as a transition at microwave frequencies. The precision of microwave measurements is so great that Lamb was able to measure the shift to five significant figures. He subsequently received the Nobel Prize for his work. No doubt remains that virtual particles are really there." (John Barrow & Joseph Silk, The Left Hand of Creation, 1993, 65-66; cited at Creation ex nihilo)

"Any object, in principle, might materialize briefly in the vacuum -- even a refrigerator or a pocket calculator" (Ibid.) (But this, only provided that it comes with a anti-refrigerator or anti-calculator with the opposite electrical charge [refrigerator or calculator running backward in time] in order to maintain the conservation of charge: "The conservation laws, however, cannot be violated. If the object has positive electrical charge, for example, then it can materialize only if it is accompanied by the production of an equal magnitude of negative charge. Energy never poses an absolute barrier, however, because it can be supplied temporarily by the stormy climate of the quantum vacuum" and then returned after time Dt whose product with the energy supplied DE is conserved around h/2p: the energy-time conjugate of the uncertainty principle. (Ibid.) Thus "[t]he probability for an object to materialize, however, decreases dramatically with the object's mass and complexity. Normally, only particle-antiparticle pairs need to be considered. In his controversial two-page paper, Tryon advanced the startling proposal that on rare occasions, whole universes might materialize from the vacuum, and that our universe may have begun in this way."

"Since quantum fluctuations are normally very short-lived, it would seem preposterous for Tryon to claim that a 10 billion-year-old universe could arise by this mechanism. In general the lifetime of a fluctuation depends on its mass, becoming shorter as the mass becomes larger. For a quantum fluctuation to survive for 10 billion years, the mass should be less than 10^-65 grams, which is 10^-38 times smaller than the mass of one electron! Here Tryon invoked the fact... that the energy of a gravitation field is negative. Furthermore, as Tryon learned from the well-known general relativist Peter Bergmann, in any closed universe the negative gravitational energy cancels the energy of matter exactly. The total energy, or equivalently the total mass, is precisely equal to zero. With zero mass, the lifetime of a quantum fluctuation can be infinite." (p. 272 - 3) Thus the first obstacle to the creation of the Universe ex nihilo -- how to circumvent the law of conservation, the inviolable fact that nothing can come out of nothing -- has been removed: the Universe is nothing fundamentally: nothing did come out of nothing. What remains is just the description of how nothing did come out of nothing, in other words, in what manner the Universe -- existence in short -- is nothing.²

"While the basic thrust of the idea looks attractive, today many theorists would question Tryon's starting point. If our universe was born from empty space, then where did the empty space come from?" (p. 273) The overcoming of this second obstacle will involve explaining how nothing (i.e. everything) came out of nothing (really nothing). "In our everyday experience, we tend to equate empty space with 'nothingness.' Empty space has no mass, no color, no opacity, no texture, no hardness, no temperature -- if that is not 'nothing', what is? However, from the point of view of general relativity, empty space is unambiguously something. According to general relativity, space is not a passive background, but instead a flexible medium that can bend, twist, and flex. This bending of space is the way that a gravitational field is described. In this context, a proposal that the universe was created from empty space seems no more fundamental than a proposal that the universe was spawned by a piece of rubber. It might be true, but one would still want to ask where the piece of rubber came from."

"In 1982, Alexander Vilenkin of Tufts University proposed an extension of Tryon's idea. He suggested that the universe was created by quantum processes starting from 'literally nothing', meaning not only the absence of matter, but the absence of space and time as well. This concept of absolute nothingness is hard to understand, because we are accustomed to thinking of space as an immutable background which could not possibly be removed. Just as a fish could not imagine the absence of water, we cannot imagine a situation devoid of space and time. At the risk of trying to illuminate the abstruse with the obscure, I mention that one way to understand absolute nothingness is to imagine a closed universe, which has a finite volume, and then imagine decreasing the volume to zero. In any case, whether one can visualize it or not, Vilenkin showed that the concept of absolute nothingness is at least mathematically well-defined, and can be used as a starting point for theories of creation."

"As with Tryon's suggestion, Vilenkin's proposal was based on a quantum description of general relativity. While a completely successful merging of these two theories does not yet exist, we know enough about each theory to develop a plausible scenario. From general relativity, Vilenkin took the idea that the geometry of space is not fixed, but that instead space is plastic and capable of distortion. There are many different possible geometries, including the closed universe, the open universe [on these two the early indecision of the Big Bang cosmology -- whether the Universe will continue to expand in the future until the existence of the galaxies be diluted to almost nothing, or will stop expanding and re-contract to end in a "Big Crunch" -- depended], and many less symmetric contortions of space and time. Among all possible geometries is the totally empty geometry, a space that contains no points whatever. From quantum theory, Vilenkin took the notion of quantum tunneling: A quantum system can suddenly and discontinuously make a transition from one configuration to another, as long as no conservation law makes the transformation impossible. Putting these ideas together, one can imagine that the universe started in the totally empty geometry -- absolute nothingness -- and then made a quantum tunneling transition to nonempty space. Calculations show that a universe created this way would typically be subatomic in size, but that is no problem. While Tryon had fretted over the implausibility of a quantum fluctuation of cosmic proportions, Vilenkin was able to invoke inflation to enlarge the universe to its current size." (p. 273 - 5)

This "primordial tunneling", which is the most primordial symmetry-breaking, is -- in order not to violate the law of conservation -- one from symmetric nothingness (the empty space-time geometry) to asymmetric nothingness, i.e. nonempty space-time geometry, which, with its curvature³, contains a gravitation field (negative energy) which generates, as a matter of conservation, positive energy, from which "existence" is to come. This is the first "quantum leap", the moment of the first Planck (smallest possible) time 10^-43 second at which gravity ("negative existence") separates from "positive existence" (fermionic and bosonic fields). This new state which has decayed from the primordial symmetry is to be the Macrocosmic background, at this point extremely small, which goes into the state of false vacuum, "inflates", then (regionally) decays, but only in "bubbles", within one of which a second spontaneous symmetry-breaking occurs which causes the break-up of the 3 other forces (strong, weak, and electromagnetic) and the distinguishability between the different elementary particles of the Standard Model, and, also, the breaking of the CPT (symmetric) conservation which results in the creation of all the fermions as we know them through the slight over-production of matter over anti-matter.

(The term Macrocosmos is borrowed from Hotu.org. Our observable universe is a tiny speck of the "Cosmos", which itself is a tiny bubble of the whole Macrocosmos which, as false vacuum, continues expanding forever after its creation from nothing: figure left.)

Guth explains (in "A Universe in your backyard", Third Culture, Edge.org): "There are two key features that are different in inflationary cosmology from the standard big bang. One is that the inflationary model contains a mechanism by which essentially all the matter in the universe can be created during the brief period of inflation. [The other one later.] In the standard big-bang model, by contrast, it was always necessary to assume that all the matter was there from the beginning, and there was no way to describe how it might be created. By the way, the inflationary production of matter [in the Macrocosmos] is consistent with the principle of energy conservation, even though it can literally produce a universe from almost nothing. Energy is still conserved — this is all calculated in the context of standard classical general relativity. The unusual feature is that gravity plays a major role in the energy balance. It turns out that the energy of a gravitational field — any gravitational field — is negative. During inflation, as the universe [actually, the Macrocosmos] gets bigger and bigger and more and more matter is created, the total energy of matter goes upward by an enormous amount. Meanwhile, however, the energy in gravity becomes more and more negative. The negative gravitational energy cancels the energy in matter, so the total energy of the system remains whatever it was when inflation started — presumably something very small. The universe [Macrocosmos] could, in fact, even have zero total energy, with the negative energy of gravity precisely canceling the positive energy of matter. This capability for producing matter in the universe [Macrocosmos] is one crucial difference between the inflationary model and the previous model." Matter-energy is all "created" during the inflation of the false vacuum in which the Macrocosmos is trapped, but it is really just nothing, since the total energy density of the false vacuum remains unchanged as it inflates: zero. Again, nothing did come out of nothing.

This original model of inflation, proposed by Alan Guth in the early 1980s, "a scenario wherein the universe got trapped in a 'false-vacuum state' [after the divergence of gravity from 'everything else' and] during a cosmological phase transition associated with the breaking of symmetry between the strong, weak and electromagnetic forces" (Wendy Freedman), did not work out in the end and had to be contrivedly modified so as to work as of today. The result is that, to get to the existence of our universe, two events of symmetry-breaking have to be posited: the first associated with the inflaton and the second with the Higgs fields that results in the Standard Model. For now let us first concentrate on the general lesson of the inflationary model for the genesis of everything and the nature of existence. Existence as we know it -- all the matter and energy on earth and in the Universe -- was originally "inflated" from a minuscule amount of matter (like 1 gram? C.f. "The inflationary universe", Guth on Edge) which itself was born out of quantum tunneling or fluctuation. Existence is illusion because it is one aspect of the asymmetric nothingness which is the whole aspect of existence. It is something -- there are galaxies and lifeforms -- but really nothing -- the total energy level of the Universe (the "total amount") is zero: and this is the only possible way for anything to exist -- as virtual -- given that "nothing can come out nothing". "Existence is a debt", and so virtual in this sense: when the Universe first came into being from nothing through quantum tunneling, it was a mere quantum fluctuation whose amount was still nothing. "Yet there are now at least 10⁸⁰ [like 10⁸⁹] particles in the part of the universe that we can observe. Where did all these particles come from [of which we, and everything around us, are made]? The answer is that relativity and quantum mechanics allow matter to be created out of energy in the form of particle/antiparticle pairs. And where did the energy come from to create this matter? The answer is that it was borrowed from the gravitational energy of the universe [which 'inflated' exponentially during the inflationary era]. The universe has an enormous debt of negative gravitational energy, which exactly balances the positive energy of the matter. During the inflationary period the universe borrowed heavily from its gravitational energy to finance the creation of more matter... The debt of gravitational energy will not have to be paid until the end of the universe." (Stephen Hawking, Black Holes and Baby Universes, p. 97) This ability to get everything from nothing because this everything is really just nothing by virtue of being virtual or a temporary loan is the reason behind the saying "The Universe is the Ultimate Free Lunch". This is how, when their reflection on the nature of existence within the anamnesis of its conservational truth is carried to the logical conclusion, the deepest-thinking philosophers finally have to admit something like: things neither exist (since the "total" is necessarily zero) nor do not exist (since there are things), nor both exist and do not exist (since, obviously, one can't have both ways) nor neither (or: and neither not-exist nor not not-exist). In myths and their hypostatized "gnostic" form the original symmetry-breaking which resulted in the "creation" (of the bud of the Macrocosmos) is symbolized as the "Fall". Thus in Valentinian cosmognoic myth the "original nothingness" (empty space-time geometry) corresponds to the original infinite and indescribable Godhead; the emanation of the Godhead through its male and female aspects and the Son resulting in the 26 Aeons arranged in paired concentric circles (the stage of the fullness, Pleroma, of the Godhead) and their subsequent "imbalance" (the separation of Sophia and her entrapment) which requires the creation of the material cosmos in order to be restored to balance (symmetry) -- these correspond to the original symmetry-breaking between the negative (space-time curvature: gravity) and the positive (fermionic and bosonic fields) after the empty space-time geometry tunnels into a non-empty one. The original divinity-infinity (nothingness) is good and the material world is evil because of the finitude (thermodynamic delimitation: our spatial delimitation and temporal mortality plus the irreversibility of time) this "creation" of the "material world" (the non-empty space-time geometry) imposes on existence (such as us). (The thermodynamic delimitation actually would not be complete until after the second-symmetry breaking; below.) In general, the ideal type of mythic imagery of the Fall -- humans originally immortal and living in paradise, with no disease, hunger, or need of toil, then falling or deteriorating into mortal existence of finitude where they have to labor, eat, suffer diseases, and die -- approximates to this scenario of creation ex nihilo in modern cosmology (and the second symmetry-breaking), and the ancients come to this through the intuition of the inexorable bound of conservation (nothing can come from nothing): paradise and immortality (symbols of original infinitude) symbolize the original symmetry of nothingness which is infinitude but which, something happening (an accident or a faulty act on the part of mankind, e.g. against gods), "falls" (symmetry broken) into the finite, material world (Universe). These imageries are only preliminarily compared here. What we need to understand is how inflation happened and how -- as we have already seen the way in which the second symmetry-breaking was able to get the slight predominance of particles over anti-particles so that "(positive) existence" might be actually in the form of matter rather than just energy (such that we, and things around, may exist) -- the whole modern scenario of creation (inflation plus the spontaneous symmetry breaking associated with the GUT) may through its parallel with past imageries and wisdoms point toward a "spirituality" and "salvation" proper to our stage of consciousness.

But before proceeding further, we need to be clear about (1) what negative energy is and (2) how gravity is negative energy. The first can best be understood by drawing "attention to what negative energy is not. It should not be confused with antimatter, which has positive energy. When an electron and its antiparticle, a positron, collide, they annihilate. The end products are gamma rays, which carry positive energy. If antiparticles were composed of negative energy, such an interaction would result in a final energy of zero. One should also not confuse negative energy with the energy associated with the cosmological constant, postulated in inflationary models of the universe ["cosmological antigravity"]. Such a constant represents negative pressure but positive energy. (Some authors call this exotic matter; we reserve the term for negative energy densities.)" (Lawrence H. Ford and Thomas A. Roman, Negative Energy, Wormholes and Warp Drive, Scientific American, Jan., 2000)

The nature of creation and of "existence" (of such "things" as around us in our everyday life) can therefore be diagrammtically represented:

                  "positive energy": matter (+/- chrg.) & antimatter (-/+ chrg.)
                                      |           
0 -> symmetry-breaking ----> -------- |  
                                      |
                  "negative energy": gravitational energy/ inverted world 

Elsewhere (footnote 1 in Yijing metaphysics, sect. 1) is cited Dirac's explanation that an "antiparticle", such as the positron for the electron, is really just the impression exerted upon this world of ours (of positive energy) by the absence of an electron of negative energy in the world of negative energy. In the same way, the presence of electron may just be the absence of a positron in the world of negative energy. This (inverted world) would then be another way to characterize the negative energy of the gravitational field.

"Since the negative energy of a gravitational field is crucial to the notion of a zero-energy universe, it is a subject worth examining carefully." (Guth, ibid., p. 289) It is also crucial to the ultimate parallel between philosophy and modern cosmology, that our existence or existence of everything around is fundamentally ambiguous, not real in the sense of "not positive", but illusory. Guth's explanation of "how the properties of gravity can be used to show that the energy of a gravitational field is unambiguously negative" will be cited in full (ibid., p. 289 - 293). "The argument will be described in the context of Newton's theory of gravity, although the same conclusion can be reached using Einstein's theory of general relativity."

"A simple way to demonstrate the sign of gravitational energy is to imagine a thin spherical shell of mass, as shown in Figure A.1 (a). The shell will create a gravitational field, which at each point in space provides a measure of the force that would be experienced by a mass if it were located at that point. The gravitational field can be calculated by using Newton's methods. Newton first considers an ideal point mass -- a mass concentration that is so small that it can be treated as if all the mass were located at a single point in space. For this case the gravitational field points directly toward the mass, with a strength that is described by the inverse square law -- that is, the strength decreases as the square of the distance from the point mass. For a more complicated object such as the shell of Figure A.1 (a), the gravitational field is in principle determined by mentally dividing the object into an infinite number of point masses, each with a mass that is infinitely small. A schematic illustration of this division into point masses is shown in part (b) of the figure. For each point mass one uses the simple inverse square law [F = GmM/r²], and then one has to add the infinite number of contributions [with integral calculus] to obtain the final answer..." So the total gravitational force felt between the shell and mass A outside is Gm₁A/r² + Gm₂A/r² + Gm₃A/r²... =

"The result for the gravitational field of a spherical shell of mass was first calculated by Newton... [He] found that, outside the shell, the gravitational field at any point is directed radially inward toward the center of the shell. This answer could have been anticipated from the symmetry of the problem: there is no other reasonable answer to the question 'What direction could it possibly point?' The strength of the gravitational field outside the shell can be described with surprising simplicity: the gravitational field has exactly the same strength as it would if all of the mass were concentrated at the center point of the shell."

"What is the gravitational field inside the spherical shell? Consider, for example, the force on a particle at position B, as shown in part (c). By symmetry the force will be along the horizontal broken line, because the upward force caused by attraction toward the mass in the upper half of the diagram will be canceled by an opposing downward attraction toward the mass in the lower half of the diagram. We still must decide, however, if the force will point to the right or to the left. There is a persuasive argument which says that the force should be to the right: since the matter to the right is much closer than the matter to the left, the inverse square law should mean that the attraction to the matter on the right should dominate. There is also, however, a persuasive argument which says that the force should be to the left: There is more matter on the left, so the attraction toward it should dominate."

"Which of the argument... is correct? Newton showed that these two arguments are equally valid, and in fact the forces cancel out exactly for a particle placed at any point inside the spherical cavity."

"To proceed with the discussion of gravitational energy, we need to answer one more question: How will gravity affect the spherical shell itself? Each point on the spherical shell will be attracted gravitationally toward each of the other points on the shell, and the net effect is a force pulling each point toward the center of the sphere. If the matter from which the shell is constructed is soft and compressible, then gravity will cause the shell to contract."

"The situation is illustrated in Figure A. 2., where part (a) shows the thin shell and the gravitational field that it generates. Outside the shell the gravitational field points inward, and inside the gravitational field is zero. Now imagine what would happen if the shell were allowed to uniformly contract, keeping its spherical shape. One can imagine, for example, extracting energy by tying ropes to each piece of the shell, as is illustrated in part (b). These ropes can be used to drive electric generators as each piece is lowered to its new position. Part (c) shows the sphere after the new radius is attained. The dashed circle indicates the original radius of the shell, and outside of the dashed circle the gravitational field is identical to that in part (a). (Recall that the field outside is the same as if all the mass were concentrated at the center, so it does not depend on the radius of the shell.) Inside the shell in its new position, the gravitational field remains zero. However, in the shaded region between the original and new positions of the shell, a gravitational field now exists where no field had existed before."

"Part (b) shows how energy can be extracted as the shell is allowed to uniformly contract. Each piece of the shell is tied by a rope to an electrical generator, producing power as the piece is 'lowered' toward its final position. Part (c) shows the final configuration, which includes a gravitational field in the shaded region where no field existed before. Thus, the creation of the gravitational field is associated with the release of energy." (Guth, p. 292)

"The net effect of this operation is to extract energy, and to create a new region of gravitational field. Thus, energy is released when a gravitational field is created. The energy contained in the shaded region must therefore decrease, just as the water level in a tank decreases if water is released. Since the region began with no gravitational field and hence no energy, the final energy must be negative. In most physical processes the exchange of gravitational energy is much smaller than the rest energy (mc²) of the particles involved, but cosmologically the total gravitational energy can be very significant."

As we have seen, the second symmetry-breaking was responsible, on the side of forces, for the breaking-up of the Grand Unification, and, on the side of matter, for distinctions among the various subatomic particles of the Standard Model and then for the CPT symmetry-breaking that resulted in the predominance of particles over anti-particles. The breaking-up of Grand Unification involves the settling of the Higgs fields from zero to non-zero values and, as mentioned, Guth's original inflation was tailored to fit this "Higgs fields scenario". Later on when the need to get the right magnitude of the density perturbations (across the uniform Universe created by inflation) which was required for the formation of galaxies conflicted with the shape of the settlement of the Higgs fields, a separate field, the inflaton, had to posited; the contrived nature of such inflationary model revealed that it was not yet correct, and different versions of inflation now abound.

Footnotes:

1. In 1988 Hawking and Neil Turok also "suggested the spontaneous creation of an open inflationary bubble from nothingness. This new version of open inflation bypasses the need for false-vacuum decay, but Vilenkin and Andrei D. Linde... have challenged the assumptions in the calculation... [Then] J. Richard Gott III and Li-Xin-Li... recently proposed that the universe is trapped in a cyclic state, rather like a time traveler who goes back in time and becomes her own mother. Such a person has no family tree; no explanation of her provenance is possible. In Gott and Li's hypothesis, our bubble broke off from the cyclic proto-universe; it is no longer cyclic but instead is always expanding and cooling." Martin A. Bucher and David N. Spergel, "Inflation in a low-density university", Scientific American, Jan., 1999, p. 68) Some other, latest ones, proposed under the influence of "string" or "brane" theories, are also problematic.

2. John Gribbin was actually the one who first proposed the idea of the creation of the Universe ex nihilo. As he recounted the story in In Search of Schroedinger's Cat (1984), p. 270 - 2: "For, according to one idea that has progressed over the past 10 years or so... the universe and everything in it may be no more, and no less, than one of those vacuum fluctuations that allow collections of particles to burst forth out of nothing, live for a while, and then be reabsorbed into the vacuum. The idea ties in very closely with the possibility that the universe may be gravitationally closed. A universe that is born in the fireball of a Big Bang, expands for a time and then contracts back into a fireball and disappears, is a vacuum fluctuation, but on a very grand scale. If the universe is exactly balanced on the gravitational edge between infinite expansion and ultimate recollapse, then the negative gravitational energy of the universe must precisely cancel out the positive mass energy of all the matter in it. A closed universe has zero energy overall, and it is not so difficult to make something with zero energy overall out of a vacuum fluctuation, even if it is a rather neat trick to make all the bits expand away from one another and allow, temporarily, for all the interesting variety we see about us."

"I am particularly fond of this idea because I played a part in its appearance in its modern form in the 1970s... In 1971 the variation that caught my fancy, and which I wrote about in Nature, was the possibility of the universe being born in fire, expanding, and then recollapsing into nothing [Nature, vol. 232, p. 440, 1971]. 2 years later, Edward Tryon... submitted a paper to Nature developing the idea of the Big Bang as a vacuum fluctuation but referring in his covering letter to my anonymous article as the jumping-off point for his speculations [Nature, vol. 246, p. 396, 1973]. So I have a special interest in his particular cosmological model... Nobody though of it first, but as he pointed out at the time if the universe has zero net energy then the amount of time it is allowed to exist, in line with DEDt = h-cross, can be very long indeed. 'I do not claim that universes like ours occur frequently, merely that the expected frequency is non-zero,' he said. 'The logic of the situation dictates, however, that observers always find themselves in universes capable of generating life, and such universes are impressively large.'" This is, in Stephen Hawking's words, the "weak anthropic principle".

3. It is certainly necessary for nonempty space-time to have curvature, at the very least because of quantum fluctuations.