Perspectives on the Scriptures: Genesis Day Two – Expansion

Before dealing with Day Two, we should just remind ourselves of the methodology employed by Genesis to describe the events in Day One.

We started with “the heaven and the earth”, which were then subsequently described collectively as “the waters”. The “waters” were then ‘converted’ into “light” when matter and antimatter interacted to create photons of light. But because there was a slight excess of matter over antimatter, some matter was not converted into light, and that excess matter was described as “the darkness”, which was separated from the “light”. This excess matter would form the building blocks of the physical universe.

So when we get to Day Two, we find “light and darkness” themselves being described as “the waters”. And as we saw in Day One, water symbolizes life-giving properties; in this case, the life-giving properties of “light and darkness”.

So Day Two starts with this:

And God said, Let there be a firmament in the midst of the waters, and let it divide the waters from the waters.” [Genesis 1: 6]

Now the very first thing to clear up here is what is meant by the word “firmament”. It is a new concept which does not feature in Day One. This particular word puzzled me for quite some time, because in my King James Version of the Bible, the reference relating to the word “firmament” says “Heb. [Hebrew] expansion”. I never paid much attention to it until I started researching the science in more detail for my book A ‘Final Theory’ of God. The reference to “expansion” then began to make a lot of sense.

Verse 6 should thus read, “And God said, Let there be an EXPANSION in the midst of the waters …” Now suddenly these words take on an entirely different meaning.

But what did ‘expansion’ mean in the ancient Hebrew? The Hebrew word is raqiya`, which loosely means to hammer out something small into something large. But I still thought it highly improbable that it meant “expansion” in the scientific sense. There has actually been a lot of debate about whether the word could be used in relation to the scientific concept of expansion and, of course, the answer always depends on the objective of those making the argument.

But there is a more reliable way to determine what it actually means. And that is to see what Jewish scholars of the original Torah thought it meant before there was any inkling in the scientific community about the importance of expansion in the ‘creation’ of the universe and life. And for that we have to return to Nahmanides, whom we referred to in respect of Day One.

We should just remind ourselves what Nahmanides (1194 – 1270 AD) said in his commentary on Genesis 1: “… At the briefest instant following creation all the matter of the universe was concentrated in a very small place, no larger than a grain of mustard. … From the initial concentration of this intangible substance in its minute location, the substance expanded, expanding the universe as it did so. As the expansion progressed, a change in the substance occurred. This initially thin noncorporeal substance took on the tangible aspects of matter as we know it. From this initial act of creation, from this etherieally thin pseudosubstance, everything that has existed, or will ever exist, was, is, and will be formed.[1]

Now since Nahmanides died some 700 years before the scientific concept of expansion, or inflation, was proposed by Alan Guth and Henry Tye in the late 1970’s, he could hardly have been trying to fit his translation of Genesis with the science. So for all the debate back and forth about what the word means, this evidence is by far the most reliable.

With that in mind, we can now move on to consider what constituted “the waters”. As we have already seen, the word is used as a collective description of “light and darkness”, which necessarily includes visible matter and energy, as well as dark matter and energy. Of visible energy, it includes energy in the form of photons; and of visible matter, it comprises fundamental particles like electrons, protons and neutrons, the latter two of which are composed of 3 quarks each. Although scientists still know little about dark matter and energy, they do know that they have an effect on visible (light) matter and energy. And as we shall see, so did the author/s of Genesis.

Of the visible matter that was ‘created’ by the Big Bang, the electrons, protons and neutrons had joined together to form the first basic elements (atoms). “Our most refined theories of the origin of the universe – our most refined cosmological theories – tell us that by the time the universe was a couple of minutes old, it was filled with a nearly uniform hot gas composed of roughly 75 percent hydrogen, 23 percent helium, and small amounts of deuterium and lithium.[2]

Weinberg says that the Big Bang theory enables scientists to calculate that “the matter formed in the first few minutes of the universe was about three-quarters hydrogen and one-quarter helium, with only a trace of other elements, chiefly very light ones like lithium. This is the raw material out of which heavier elements were later formed in stars.[3]

So at this stage, the universe was “dense and opaque, like the glowing gas inside a star.[4]

Michio Kaku explains the reason for this. He says that “for years after the big bang, the temperature of the universe was so hot that anytime an atom formed, it would be ripped apart; hence there were many free electrons that could scatter light. Thus, the universe was opaque, not transparent. Any light beam moving in this super-hot universe would be absorbed after travelling a short distance, so the universe looked cloudy.”[5]

So this was the state of the universe at the conclusion of Day One, and the start of Day Two. There were “the waters” – “light and darkness,” which were called “Day” and “Night”. As we have already noted, this naming is important not just to emphasize the ‘locking in’ of probabilities, but to highlight the change in the nature of the matter and energy as it is ‘processed’ through the ‘six days’.

Day Two tells us that it is into this state of the early universe, re-described as “the waters”, that God is said to have inserted an ‘expansion’ to separate some parts of “the waters” from other parts of “the waters” – “to divide the waters from the waters.”

When God is said to put this plan into effect, this is what happens:

And God made the firmament (expansion,) and divided the waters which were under the firmament (expansion) from the waters which were above the firmament (expansion): and it was so.[Genesis 1: 7]

It should be noted that the underlined emphasis on the words ‘were’ are the original. Clearly they suggest a pre-existing state in which certain parts of “the waters” were in different places – “under” or “above”. If that were the case, then clearly it resulted from what happened in Day One. And Day One was about inflationary cosmology.

Greene identifies one specific consequence of inflationary cosmology which was crucial to the formation of the universe as we now see it.

According to Greene, “the initial nonuniformity that ultimately resulted in the formation of stars and galaxies came from quantum mechanics.”[6] Like particles, fields are also subject to quantum phenomena, so the “rate of change” of a field is not uniform but “will undulate up or down” at various speeds, or “assume a strange mixture of many different rates of change, and hence its value will undergo a frenzied, fuzzy, random jitter.”[7] This means that the “amount of energy in one location would have been a bit different to what it was in another.”[8]

These small differences in the quantum world of the pre-inflationary universe were then amplified by inflationary expansion, causing certain areas of the expanding universe to be more ‘dense’ in particles and energy than others. This has been confirmed by measurements of the temperature differences of microwave photons arriving from space. Greene says that “observations have shown that … tiny temperature differences fill out a particular pattern on the sky …[9] confirming slight differences in the density of matter and energy in different locations in the universe. And these variations were “set down nearly 14 billion years ago … [and arose] from quantum uncertainty.”[10]

Greene attributes this to the inflaton (Higgs) field, which we referred to in Day One. We should remember that it was this field that scientists now believe was the engine for inflationary expansion in the earliest moments of the universe. According to Greene, the inflaton field “reached the value of lowest energy at different places at slightly different moments. In turn, inflationary expansion shut off at slightly different times at different locations in space, so that the amount of spatial expansion at different locations varied slightly …”[11]

This resulted in different densities of matter and energy in different regions of space, or more accurately, the expanding universe. Rees says that this meant that “slightly overdense regions, expanding slower than average, were destined to become galaxies and clusters; others, slightly underdense, were destined to become voids.”[12]

So it seems that describing some of ‘the waters’ as being in different places – “under” or “above” – in relation to the “expansion” is quite accurate, according to inflationary cosmology. Without it, the universe as we know it, and life itself, would not exist.

We should also recall that there is a subtle but crucial difference between the explanation of what took place on Day Two, and what took place in all the other ‘days’. After God is said to have ‘instructed’ there to be an “expansion”, He then “made the expansion”; but there is no ‘observation’; that is, the words “And God saw …” do not appear in Day Two.

However, if Greene is right in his explanation of how ‘expansion’ works in scientific terms, then it seems Genesis may be pointing to that scientific explanation.

To understand Greene’s thesis, it is best to start with his conclusion, then work backwards. He says this: “as the universe expands, matter and radiation lose energy to gravity while an inflaton field gains energy from gravity.”[13]

Let me now attempt to explain that in non-scientific terms – bearing in mind that we are trying to understand why Day Two leaves out the ‘observation’ element of ‘creation’ according to Genesis.

First, we should recall how everything started. “Through a chance but every so often expectable fluctuation from an unremarkable primordial state with high entropy (chaotic), a tiny, twenty-pound nugget of space achieved conditions that led to a brief burst of inflationary expansion.[14]

This event resulted in the production of billions upon billions of particles and anti-particles which joined together to form photons. But remarkably, this ‘grand annihilation’ did not result in all the particles joining up with anti-particles, which would have left no matter in the universe, only radiation. Instead, there was a slight excess of particles over anti-particles, which meant that there was some matter left over. This matter comprised electrons, protons and neutrons which, after the Big Bang, joined together to form the first atoms (elements) – hydrogen, helium and traces of deuterium and lithium.

However, it is not only that there was some matter left over, but that it was in the precise quantity needed to ensure that it could produce a life-sustaining universe. This is what Rees says: “There must be  … enough ordinary atoms, initially in diffuse gas, to form all of the stars in all of the galaxies.”[15] Furthermore, there must also be enough material (dark matter and atoms) so that the cosmic number Ω (omega) was “very close … to unity” after the initial inflationary expansion and Big Bang.

If there had been too many atoms and too much dark matter, gravity would have pulled all the matter together very quickly, thus causing the universe to collapse in on itself. If there had been too few atoms and too little dark matter, then gravity would not have been strong enough to act as a balance against the expansion force, and the atoms would never have formed together into larger lumps of matter, and there would have been no stars or galaxies or life.

However, the expansion force itself (lambda λ) also had to be ‘finely tuned’. If it had been too high (strong), given the force of gravity and the quantity of material in the universe (atoms and dark matter), it would have “overwhelm[ed] gravity before galaxies [could have] formed.[16]

This shows that at the start of Day Two, four of the six numbers that Rees says are crucial to a life-sustaining universe had already been ‘finely tuned’. But as we shall see, the other two numbers were also in fact ‘finely tuned’ – they were just not yet apparent. They needed the effect of the slight density discrepancies to be realized as the universe expanded before they could be revealed as having been ‘finely tuned’.

Consequently, the first numbers are the cosmic numbers omega (Ω) and lambda (λ). These numbers ensured that the gravitational force pulling material together, and the expansion force pushing the material apart, were precisely balanced in relation to the amount of matter there was in the early universe for those forces to operate on. Yet, on the other hand, the amount of material in the universe was ‘finely tuned’ by a small excess of matter over anti-matter in the early universe. Given the forces of gravity and expansion, if there had been much more matter in the universe, gravity would have overpowered the expansion force; if there had been less, expansion would have overpowered gravity. Remarkably, all of these factors are inter-related and inter-dependant. They all appear to have been ‘finely tuned’ at the same moment in time so as to ensure that the desired result could be achieved.

Secondly, the ‘creation’ of “light and darkness” produced three dimensions, and the expansion (motion) of matter and energy created the concept of time. That satisfies another of Rees’ six numbers. “The sixth crucial number … is the number of special dimensions in our world, D, and equals three. Life couldn’t exist if D were two or four. Time is a fourth dimension … [and] … has a built in arrow: we move only towards the future.[17]                        

Thirdly, as we have seen above, the ‘creation’ of “light and darkness” was, in effect, the creation of fundamental particles with the ability to bind together to form atoms (elements). For that to happen, the number ε had to be tuned to the correct value. This number, “whose value is 0.007, defines how firmly atomic nuclei bind together and how all the atoms on earth were made. … If ε were 0.006 or 0.008, we could not exist.”[18]

This number is important to the issue of expansion, because it is the effect of expansion, in conjunction with the ‘balancing’ of the other numbers, that enables the first atoms (elements) to build up more complex and heavier atoms. But for expansion to bring that about, “the waters” needed different densities in different locations in the expanding universe – otherwise the ‘fine tuning’ of the other numbers would have been of no effect.

And since this density discrepancy had not yet had an opportunity to have any effect by the end of Day One, it concealed the fact that another of Rees’ numbers had also been ‘finely tuned’. That number is N, which “measures the strength of the electrical forces that hold atoms together, divided by the force of gravity between them.”[19] It is only when the density discrepancies in different parts of the expanding universe are subjected to the effects of expansion that the ‘fine tuning’ of N can be revealed.

And that brings us to the last of Rees’ six numbers, the number Q. This number relates to the density differences which are the “initial irregularities [that] ‘seed’ the growth of structure[s][20] like stars and galaxies. According to Rees, “the number Q measures the amplitude of these irregularities or ‘ripples’. Why Q is about 10­-5 is still a mystery.[21]

For our consideration of the lack of an ‘observation’ in Day Two, it is important to understand, as Rees says, that “[w]hen the universe was a million years old, everything was still expanding almost uniformly.[22]

However, “[i]f our universe had started off completely smooth and uniform, it would have remained so throughout its expansion It would [have been] cold and dull: no galaxies, therefore no stars, no periodic table, no complexity, certainly no people.”[23]

Furthermore, as mentioned above, the balance between “expansion energy and gravitational energy” (Ω) which “is now at least 0.3was very close to unity in the early eras” of the expanding universe.

Accordingly, at the start of Day Two, there would have appeared to be no reason to expect that the expanding universe, as observed at that time, should begin to concentrate matter and energy in different locations.

The expansion force needed something to bring together all the other forces (numbers) that had been ‘imprinted’ on Day One. And that something is the slight density differences in the matter and energy that was expanding throughout the universe. As we have seen, Genesis describes these density differences as some of “the waters” being “under the expansion”, and others being “above the expansion”.

Now, scientists calculate the length of the events recorded in Day One as about 300,000 years of Earth time. And that would have meant there was a near uniform density of matter, energy and forces throughout the universe at the start of Day Two.

However, at about this time, the expanding universe begins to cool from the extreme temperatures following the Big Bang. Kaku explains it this way: “After 380,000 years … the temperature dropped to 3,000 degrees. Below that temperature, atoms were no longer ripped apart … [and] … stable atoms could form, and light beams could now travel for light-years without being absorbed.”[24]

Rees says that “after half a million years of expansion, the temperature dropped to around 3,000 degrees … As the universe cooled further, it literally entered a dark age … [which] persisted until the first protogalaxies formed and lit it up again.”[25]

According to Greene, in the “early history of the universe, matter was spread uniformly throughout space.[26] Furthermore, “although attractive gravity causes clumps of matter and creases of space to grow, repulsive gravity (expansion) does the opposite: it causes them to diminish, leading to an ever smoother, ever more uniform outcome.[27]

Now, we should remind ourselves of what Kaku said regarding quantum theory: “The quantum theory is based on the idea that there is a probability that all possible events … might occur. This, in turn, lies at the heart of inflationary universe theory …”[28]

However, Kaku also acknowledges that “physicists realize that if we could somehow control these probabilities” then anything “is possible.”[29]

Gradually, therefore, the description of Day Two starts to make sense. The scientific consensus is that the matter and energy density in the early universe was almost perfectly uniform. Furthermore, gravity and expansion were evenly balanced thus tending to “an ever smoother, ever more uniform outcome.”

And since there is a probability that all “possible events … might occur”, at this early stage of the universe there must have been a probability that the almost perfect uniformity could have become perfectly uniform, in terms of both matter and energy density, as well as the balance of the gravitational and expansionary forces. That would have meant that no universe as we know it would have formed, and thus no life.

So the inclusion of the words “And God said, Let there be an expansion …” does seem to be deliberate. It suggests a manipulation of probabilities. But in Day Two, the manipulation doesn’t suggest a change to the existing state of affairs, but maintenance of the state of affairs following Day One. In other words, it suggests the exclusion of other probabilities – exclusion of the probability of perfect uniformity, or of the probability of over-dense areas of matter and energy forming. And this is important, because as Rees said, in the former case, the “universe would be inert and structureless”; and in the latter case, “it would have been a violent place in which no stars or solar systems could survive …[30]

But according to Genesis, that is not what God intended.

Instead, Day Two was to be a bridge to Day Three. And so no reference to “And God saw …” was necessary, because the slight density contrasts which existed at the start of Day Two, symbolized by “the waters” being in different locations – “under” or “above”, were crucial to bring about the next intended steps in constructing a universe capable of sustaining life, and especially human life endowed with a moral capacity. All that was necessary at this stage was to ensure that other probabilities did not intervene. In effect, particles, and the early elements, had to be ‘compelled’ to adopt the “path” suggested by Feynman’s “sum over paths” equations – the “path” that leads to the Classical laws of physics.

And the probability that had to be maintained was the number Q, which “measures the amplitude of these irregularities or ‘ripples’.”[31]

Which brings us back to the quote from Greene mentioned above: “as the universe expands, matter and radiation lose energy to gravity while an inflaton field gains energy from gravity.”[32]

According to Greene, the “total energy carried by ordinary particles of matter and radiation drops because it is continually transferred to gravity as the universe expands. … gravity depletes the energy in fast moving particles of matter and radiation as space swells.[33] On the other hand, “a uniform inflaton field exerts a negative pressure within an expanding universe. … [thus] the total energy embodied in the inflaton field increases as the universe expands because it extracts energy from gravity.”[34]

Now this ‘exchange’ of energy away from gravity and to expansion, is important in respect of the matter density in the expanding universe. If the density of energy and matter were absolutely uniform, this exchange would be uniform, and no stars and galaxies could form. But where there are greater densities of matter and energy in certain regions of space, expansion will cause a greater transfer of energy to gravity than in less dense regions, and that increased gravity will attract other nearby matter, thus forming lumps.

As Rees says, “the dominant gravitational stuff is … ‘dark matter’ … [which is] … influenced by gravity. … Swarms of dark matter on subgalactic scales condense out first; these merge into galactic-mass objects, which then form clusters.”[35]

But this clustering of dark matter needs atoms. According to Rees, the atoms “ride along passively [on the dark matter], constituting a dilute gas that ‘feels’ the dark matter’s gravity.[36] And this ‘gas’ of atoms “exerts a pressure as well … [which] … prevents the gas from being pulled by gravity into very small ‘clumps’ of dark matter.[37]

Genesis suggests that it was important to preserve the density differences in different locations in space, and the balance between the opposing forces of gravity and expansion, if the intended objective of ‘creation’ was to be achieved. But it is important to note again that Day Two does not have a reference to “And God saw …” It seems that the interaction between the density discrepancies and the balance of the gravitational and expansionary forces were required to run their course for a time before the results were ‘locked in’ with an observation. And according to science, there was a good reason for that.

The reason relates to the conditions necessary to produce the number of elements required to create and sustain life – the elements that constitute the Periodic Table.

As we have already seen, the Big Bang created the lightest elements like hydrogen, helium, deuterium and lithium. However, it did not produce sufficient heat to produce heavier elements – “… elements with 5 and 8 neutrons and protons are extremely unstable and hence cannot act as a ‘bridge’ to create elements that have a greater number of protons and neutrons.[38]

In the 1950’s, Fred Hoyle, an English physicist at Cambridge University, had a moment of ‘insight’ which went a way to resolving how the heavier elements could have been created. As Kaku says, “[i]n a stroke of genius, Hoyle realized that IF there were a previously unnoticed unstable form of carbon, created out of three helium nuclei, it might last just long enough to act as a ‘bridge,’ allowing for the creation of higher elements. … When this unstable form of carbon was actually found, it brilliantly demonstrated that nucleosynthesis could take place in the stars, rather than the big bang.[39]

However, not all stars are heavy enough to produce the heat necessary to create the heavier elements. This requires heavier stars with greater gravity. According to Rees, such stars can reach a “billion degrees” and thus “release further energy via the build-up of carbon (six protons), and by a chain of transmutations into progressively heavier nuclei.[40] But once we get to iron, which has the most “tightly bound” nucleus, “energy must be added” in order to create the even heavier elements beyond iron. And so, as Rees says, “a star therefore faces an energy crisis when its core is transmuted into iron … [and] …the consequences are dramatic.[41]

The intense gravity causes the core of the star to implode which “releases enough energy to blow off the overlying material in a colossal explosion – creating a supernova.[42]

The supernova then ‘fertilizes’, so to speak, the universe by blasting its mix of elements into space. “The debris thrown back into space contains this mix of elements. Oxygen is the most common, followed by carbon, nitrogen, silicon and iron. The calculated proportions … [depend on the] … types of stars and the various evolutionary paths they take …[43]

This mix of elements was a pre-requisite for life. As Kaku says, “our true ‘mother’ sun was actually an unnamed star or collection of stars that died billions of years ago in a supernova, which then seeded nearby nebulae with the higher elements beyond iron that make up our body.”[44]

But all this chemistry in the stars depends on the number ε (the strong nuclear force) being ‘finely tuned’ to 0,007. “Hoyle therefore argued that our existence would have been jeopardized by even a few percentage points’ change in ε.[45]

And so the account of Day Two in Genesis becomes even more intriguing, and in doing so it also takes us into the first part of the account of Day Three.

All the ‘fine tuning’ of the various cosmic numbers identified by Rees would have been of no effect if there were not the crucial differences in density of matter and energy in different regions of the expanding universe.

Genesis emphasizes the importance of these density differences by referring to some of “the waters” being “under the expansion” and others being “over the expansion”. Genesis devotes a whole ‘day’ to make the point.

And Day Two concludes its account of the division of “the waters” with this: “And God called the firmament Heaven.[46] As we have already noted, this naming (always with a capital letter) signifies a change from the state of the universe as at the start of the ‘day’. At the start of Day Two there were “the waters” into which was inserted an “expansion”. At the end of Day Two the “expansion” had divided “the waters”, resulting in what God is said to call “Heaven”. We should now recall what Rees said about the effect of the density differences in matter and energy in different parts of space: “slightly overdense regions, expanding slower than average, were destined to become galaxies and clusters; others, slightly underdense, were destined to become voids’.[47]

The “voids” are clearly what Genesis calls “Heaven” – those areas of space that were left ‘free’ of matter. When we look up at the night sky, it is those areas that are not lit up by stars. As Greene says, “according to inflation, the more than 100 billion galaxies, sparkling throughout space like heavenly diamonds, are nothing but quantum mechanics writ large across the sky.[48]

Day Two ends at just about the time Rees says the “first protogalaxies formed” which lit up the universe again following the “dark age”.[49] According to Rees’ depiction of the time-line of the universe, that would have been about 1 billion years after the Big Bang.[50] Thus “the evening and the morning” of Day Two were approximately one billion years less the 300,000 years for Day One. However, as already noted, it was important that the effect of the “expansion” up to this time should not yet be made “irreversible”, hence there is no reference to “And God saw …” at the end of Day Two. That only comes halfway through Day Three. In the language of the delayed-choice experiments, the effect of the density differences should not be “fully settled” by an observation (measurement) until all the elements had been created, and the universe ‘fertilized’ with their life-giving, and life-supporting, properties.

That leaves just one final point to make regarding Day Two. What makes the Genesis account of “expansion” so remarkable is that it does separate, so to speak, the initial “inflation” we discussed in Day One, from the “expansion” which is said to start in Day Two. And that perfectly corresponds to Rees’ description of the process up to this point: “The fierce repulsion that drove inflation must have switched off, allowing the universe, having by then enlarged enough to encompass everything that we now see, to embark on its more leisurely expansion.[51]

Day Two thus puts in place the next element of the deterministic, ordered world of Classical physics. And Genesis emphasizes the point with the symbolism of God ‘naming’ the new state of the physical universe – He “called the firmament Heaven.”

In the next article we will address the even more remarkable revelations in Day Three.

Joseph BH McMillan. This article is an abridged extract of Chapter 4 of A ‘Final Theory’ of God, which is available from Amazon.com

jbhmcmillan@yahoo.comImagebook

www.josephbhmcmillan.com

Copyright © Joseph BH McMillan 2014 All Rights Reserved

[1] Commentary on Torah, Genesis 1, Nahmanides, quoted in Gerald Schroeder Genesis and the Big Bang, Bantam Books, 1992 (paperback), page 65.

[2] Greene, Brian. The Fabric of the Cosmos, Penguin, London, 2005 (paperback), page 171 (emphasis in bold is Greene’s).

[3] Weinberg, Steven. Dreams of a Final Theory, Vintage, New York, 1994 (paperback), pages 33 – 34.

[4] Rees, Martin. Just Six Numbers, Phoenix, London, 1999 (paperback), page 119.

[5] Kaku, Michio. Parallel Worlds, Penguin, London, 2006 (paperback), pages 57 – 58.

[6] Greene, page 305.

[7] Greene, page 306.

[8] Greene, page 306.

[9] Greene, page 311.

[10] Greene, page 311 – 312.

[11] Greene, page 307 – my emphasis in bold.

[12] Rees, page 119.

[13] Greene, page 312.

[14] Greene, page 321.

[15] Rees, page 127.

[16] Rees, page 127.

[17] Rees, page 3.

[18] Rees, page 2.

[19] Rees, page 2.

[20] Rees, page 127.

[21] Rees, page 128.

[22] Rees, page 121.

[23] Rees, page 117.

[24] Kaku, page 58.

[25] Rees, page 119.

[26] Greene, page 314.

[27] Greene, page 315.

[28] Kaku, page 147.

[29] Kaku, pages 147 and 146 respectively.

[30] Rees, page 3.

[31] Rees, page 128.

[32] Greene, page 312.

[33] Greene, page 311 – bold emphasis is Greene’s.

[34] Greene, pages 311 to 322 – bold emphasis is Greene’s.

[35] Rees, page 119 – 120.

[36] Rees, page 122.

[37] Rees, page 122.

[38] Kaku, page 56.

[39] Kaku, page 62 – emphasis on IF is mine.

[40] Rees, page 50.

[41] Rees, page 50.

[42] Rees, page 50.

[43] Rees, page 50.

[44] Kaku, page 67.

[45] Rees, page 56.

[46] Genesis 1: 7.

[47] Rees, page 119 – emphasis in bold is mine.

[48] Greene, page 308.

[49] Rees, page 119.

[50] Rees, illustration at page 132.

[51] Rees, page 139 – emphasis in bold is mine.

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