12a Fine tuning of the universe

It has long been recognised that the parameters making up matter in the universe are so incredibly constrained that the universe could never form by natural processes.

The universe is not simple, it is highly defined. I will give lists of some of these quantities below.

These requirements can be due to:

  1. Necessity,
  2. Chance, or
  3. Design.

Because of the incredible degree of constraints, secular scientists have had a severe problem explaining the origin & presence of these. The principle explanation is that of a multiverse, this is also discussed below.

If there was an origin of the universe from a Big Bang scenario, then the logical expectation would be of matter expanding outward in all directions. If all matter/energy was in an ‘cosmic egg’, then the expectations would be:

  1. The complete mass of the universe compressed in a tiny spot, would be the perfect conditions for a mega black hole. There would be no universe as we find it.
  2. The proto-matter is supposed to be an incredible temperature, this would preclude any order, but would have a near infinite entropy, so no order, no possible tuning.

Many physical parameters are integers, for example e = mc2, or F = Gm1m2/r2. There are commonly powers of 2, not 1.965 or 2.001.

Physicists have calculated the limits of ranges in physical parameters.

List of Fine-Tuning Parameters

Cosmic Constants

(1) Gravitational force constant

(2) Electromagnetic force constant

(3) Strong nuclear force constant

(4) Weak nuclear force constant

(5) Cosmological constant

Initial Conditions and “Brute Facts”

(6) Initial distribution of mass energy

(7) Ratio of masses for protons and electrons

(8) Velocity of light

(9) Mass excess of neutron over proton

“Local” Planetary Conditions

(10) Steady plate tectonics with right kind of geological interior

(11) Right amount of water in crust

(12) Large moon with right rotation period

(13) Proper concentration of sulphur

(14) Right planetary mass

(15) Near inner edge of circumstellar habitable zone

(16) Low-eccentricity orbit outside spin-orbit and giant planet resonances

(17) A few, large Jupiter-mass planetary neighbours in large circular orbits

(18) Outside spiral arm of galaxy

(19) Near co-rotation circle of galaxy, in circular orbit around galactic centre

(20) Within the galactic habitable zone

(21) During the cosmic habitable age

Effects of Primary Fine-Tuning Parameters

(22) The polarity of the water molecule

Descriptions:

Cosmic Constants

(1) Gravitational force constant (large scale attractive force, holds people on planets, and holds planets, stars, and galaxies together)—too weak, and planets and stars cannot form; too strong, and stars burn up too

quickly.

(2) Electromagnetic force constant (small scale attractive and repulsive force, holds atoms electrons and atomic nuclei together)—If it were much stronger or weaker, we wouldn’t have stable chemical bonds.

(3) Strong nuclear force constant (small-scale attractive force, holds nuclei of atoms together, which otherwise repulse each other because of the electromagnetic force)—if it were weaker, the universe would have far fewer stable chemical elements, eliminating several that are essential to life.

(4) Weak nuclear force constant (governs radioactive decay)—if it were much stronger or weaker, life-essential stars could not form. (These are the four “fundamental forces.”)

(5) Cosmological constant (which controls the expansion speed of the universe) refers to the balance of the attractive force of gravity with a hypothesized repulsive force of space observable only at very large size scales. It must be very close to zero, that is, these two forces must be nearly perfectly balanced. To get the right balance, the cosmological constant must be fine-tuned to something like 1 part in 10,120. If it were just slightly more positive, the universe would fly apart; slightly negative, and the universe would collapse.

As with the cosmological constant, the ratios of the other constants must be fine-tuned relative to each other. Since the logically-possible range of strengths of some forces is potentially infinite, to get a handle on the precision of fine-tuning, theorists often think in terms of the range of force strengths, with gravity the weakest, and the strong nuclear force the strongest. The strong nuclear force is 1040 times stronger than gravity, that is, ten thousand, billion, billion, billion, billion times the strength of gravity.

Think of that range as represented by a ruler stretching across the entire observable universe, about 15 billion light years. If we increased the strength of gravity by just 1 part in 1034 of the range of force strengths (the equivalent of moving less than one inch on the universe-long ruler), the universe couldn’t have life sustaining planets.

Initial Conditions and “Brute Facts”

(6) Initial Conditions. Besides physical constants, there are initial or boundary conditions, which describe the conditions present at the beginning of the universe. Initial conditions are independent of the physical constants. One way of summarizing the initial conditions is to speak of the extremely low entropy (that is, a highly ordered) initial state of the universe. This refers to the initial distribution of mass energy.

In The Road to Reality, physicist Roger Penrose estimates that the odds of the initial low entropy state of our universe occurring by chance alone are on the order of 1 in 10 10(123). This ratio is vastly beyond our powers of comprehension. Since we know a life-bearing universe is intrinsically interesting, this ratio should be more than enough to raise the question: Why does such a universe exist? If someone is unmoved by this ratio, then they probably won’t be persuaded by additional examples of fine-tuning.

In addition to initial conditions, there are a number of other, well known features about the universe that are apparently just brute facts. And these too exhibit a high degree of fine-tuning. Among the fine-tuned

(apparently) “brute facts” of nature are the following:

(7) Ratio of masses for protons and electrons—If it were slightly different, building blocks for life such as DNA could not be formed.

(8) Velocity of light—If it were larger, stars would be too luminous. If it were smaller, stars would not be luminous enough.

(9) Mass excess of neutron over proton—if it were greater, there would be too few heavy elements for life. If it were smaller, stars would quickly collapse as neutron stars or black holes.

“Local” Planetary Conditions

But even in a universe fine-tuned at the cosmic level, local conditions can still vary dramatically. As it happens, even in this fine-tuned universe, the vast majority of locations in the universe are unsuited for life. In The Privileged Planet, Guillermo Gonzalez and Jay Richards identify 12 broad,

widely recognized fine-tuning factors required to build a single, habitable planet. All 12 factors can be found together in the Earth. There are probably many more such factors. In fact, most of these factors could be split out to make sub-factors, since each of them contributes in multiple ways to a planet’s habitability.

(10) Steady plate tectonics with right kind of geological interior

(which allows the carbon cycle and generates a protective magnetic field). If the Earth’s crust were significantly thicker, plate tectonic recycling could not take place.

(11) Right amount of water in crust (which provides the universal solvent for life).

(12) Large moon with right planetary rotation period (which stabilizes a planet’s tilt and contributes to tides). In the case of the Earth, the gravitational pull of its moon stabilizes the angle of its axis at a nearly constant 23.5 degrees. This ensures relatively temperate seasonal changes, and the only climate in the solar system mild enough to sustain complex living organisms.

(13) Proper concentration of sulphur (which is necessary for important biological processes).

(14) Right planetary mass (which allows a planet to retain the right type and right thickness of atmosphere). If the Earth were smaller, its magnetic field would be weaker, allowing the solar wind to strip away our atmosphere, slowly transforming our planet into a dead, barren world much like Mars.

(15) Near inner edge of circumstellar habitable zone (which allows a planet to maintain the right amount of liquid water on the surface). If the Earth were just 5% closer to the Sun, it would be subject to the same fate as Venus, a runaway greenhouse effect, with temperatures rising to nearly 900 degrees Fahrenheit. Conversely, if the Earth were about 20% farther from the Sun, it would experience runaway

glaciations of the kind that has left Mars sterile.

(16) Low-eccentricity orbit outside spin-orbit and giant planet

resonances (which allows a planet to maintain a safe orbit over a long period of time).

(17) A few, large Jupiter-mass planetary neighbours in large circular

orbits (which protects the habitable zone from too many comet bombardments). If the Earth were not protected by the gravitational pulls of Jupiter and Saturn, it would be far more susceptible to collisions with devastating comets that would cause mass extinctions. As it is, the larger planets in our solar system provide significant protection to the Earth from the most dangerous comets.

(18) Outside spiral arm of galaxy (which allows a planet to stay safely away from supernovae).

(19) Near co-rotation circle of galaxy, in circular orbit around

galactic centre (which enables a planet to avoid traversing dangerous parts of the galaxy).

(20) Within the galactic habitable zone (which allows a planet to have access to heavy elements while being safely away from the dangerous galactic centre).

(21) During the cosmic habitable age (when heavy elements and active stars exist without too high a concentration of dangerous radiation events).

This is a very basic list of “ingredients” for building a single, habitable planet. At the moment, we have only rough probabilities for most of these items. For instance, we know that less than ten percent of stars even in the Milky Way Galaxy are within the galactic habitable zone. And the likelihood of getting just the right kind of moon by chance is almost certainly very low, though we have no way of calculating just how low.

What we can say is that the vast majority of possible locations in the visible universe, even within otherwise habitable galaxies, are incompatible with life.

It’s important to distinguish this local “fine-tuning” is different from cosmic fine-tuning. With cosmic fine-tuning, we’re comparing the actual universe as a whole with other possible but non-actual universes. And though theorists sometimes postulate multiple universes to try to avoid the embarrassment of a fine-tuned universe, we have no direct evidence that other universes exist. When dealing with our local planetary environment, however, we’re comparing it with other known or theoretically possible

locations within the actual universe. That means that, given a large enough universe, perhaps you could get these local conditions at least once just by chance (though it would be “chance” tightly constrained by cosmic finetuning).

So, does that mean that evidence of local fine-tuning is useless for inferring design? No. Gonzalez and Richards argue that we can still discern a purposeful pattern in local fine-tuning. As it happens, the same cosmic and local conditions, which allow complex observers to exist, also provide the best setting, overall, for scientific discovery. So complex observers will find themselves in the best overall setting for observing. You would expect this if the universe were designed for discovery, but not otherwise. So the

fine-tuning of physical constants, cosmic initial conditions, and local conditions for habitability, suggests that the universe is designed not only for complex life, but for scientific discovery as well.

Effects of Primary Fine-Tuning Parameters

There are a number of striking effects of fine-tuning “downstream” from basic physics that also illustrate just how profoundly fine-tuned our universe is. These “effects” should not be treated as independent parameters (see discussion below). Nevertheless, they do help illustrate the idea of fine-tuning. For instance:

(22) The polarity of the water molecule makes it uniquely fit for life. If it were greater or smaller, its heat of diffusion and vaporization would make it unfit for life. This is the result of higher-level physical

constants, and also of various features of subatomic particles.

What About All Those Other Parameters?

In discussing fine-tuned parameters, one can take either a maximal or a minimal approach.

Those who take the maximal approach seek to create as long a list as possible. For instance, one popular Christian apologist listed thirty-four different parameters in one of his early books, and maintains a growing list, which currently has ninety parameters. He also attaches exact probabilities to various “local” factors.

While a long (and growing) list sporting exact probabilities has rhetorical force, it also has a serious downside: many of the parameters in these lists are probably derived from other, more fundamental parameters, so they’re not really independent. The rate of supernova explosions, for instance, may simply be a function of some basic laws of nature, and not be a separate instance of fine-tuning. If you’re going to legitimately multiply the various parameters to get a low probability, you want to make sure you’re not “double booking,” that is, listing the same factor twice under different descriptions. Otherwise, the resulting probability will be inaccurate. Moreover, in many cases, we simply don’t know the exact probabilities.

To avoid these problems, others take a more conservative approach, and focus mainly on distinct, well-understood, and widely accepted examples of fine-tuning. This is the approach taken here. While there are certainly additional examples of fine-tuning, even this conservative approach provides more than enough cumulative evidence for design. After all, it is this evidence that has motivated materialists to construct many universe scenarios to avoid the implications of fine-tuning.

* The Finely Tuned Parameters of the Universe: Barrow & Tipler, in their standard treatment, The Anthropic Cosmological Principle, admit that “there exist a number of unlikely coincidences between numbers of enormous magnitude that are, superficially, completely independent; moreover, these coincidences appear essential to the existence of carbon-based observers in the Universe,” and include the wildly unlikely combination of:
– the electron to proton ratio standard deviation of 1 to 10,000,000,000,000,000,000,000,000,000,000,000,000 (37 x 0’s)
– the 1-to-1 electron to proton ratio throughout the universe yields our electrically neutral universe
– the electron to proton mass ratio (1 to 1,836) perfect for forming molecules
– the electromagnetic and gravitational forces finely tuned for the stability of stars
– the gravitational and inertial mass equivalency
– the electromagnetic force constant perfect for holding electrons to nuclei
– the electromagnetic force in the right ratio to the nuclear force
– the strong force (which if changed by 1% would destroy all carbon, nitrogen, oxygen, and heavier elements)
– all electrons in the universe are identical as are all instances of each fundamental particle
– etc., etc., etc. (including the shocking apparent alignment of the universe with the orbit of the Earth)

Omitting the Cosmological Constant: We have omitted from this list the commonly reported fine tuning of the cosmological constant to one part in 10 to the 120th power. This is so very precise that if the entire universe had as much additional mass as exists in a single grain of sand, it would all collapse upon itself. That is, if a big bang actually formed our universe, and if it created a miniscule additional amount of mass than it is claimed to have created, then no planets, stars, or galaxies could exist. Conversely, if the universe had less mass, by that same quantity, matter never would have coalesced to become planets, stars, and galaxies, and again, we would not exist. So, why doesn’t Real Science Radio include this astoundingly fine-tuned parameter in our list? Well, as physicist John Hartnett points out, the cosmological constant is only a fine-tuning problem for the big bang theory, so it is an argument only against a big bang universe, whereas in our actual universe, it is not a fine tuning issue. So, the cosmological constant does refute big bang cosmology, at least, for anyone who is objective, has common sense, and is not desperately trying to ignore the evidence for the Creator. (By the way, since NASA says that the confirmed predictions of the big bang theory are what validates it, you might want to Google: big bang predictions, and you’ll find our article ranked #1 out of half-a-million, at rsr.org/bbp, presenting the actual track record of the predictions of the theory. Also, if you Google: evidence against the big bang, you’ll find our article on that topic near the top of the first page of Google results!)

* The Whopping Physics Coincidence: NewScientist reports about gravity and acceleration that, “a large chunk of modern physics is precariously balanced on a whopping coincidence” for, regarding gravitational and inertial mass, “these two masses are always numerically exactly the same. The consequences of this coincidence are profound…”

* The Finely Tuned Parameters of the Solar System include:
– The Sun is positioned far from the Milky Way’s center in a galactic goldilocks zone of low radiation
– The Sun is placed in an arm of the Milky Way puts it where we can discover a vast swath of the entire universe
– Earth’s orbit is nearly circular (eccentricity ~ 0.02) around the Sun providing a stability in a range of vital factors
– Earth’s orbit has a low inclination keeping it’s temperatures within a range permitting diverse ecosystems
– Earth’s axial tilt is within a range that helps to stabilize our planet’s climate
– the Moon’s mass helps stabilize the Earth’s tilt on its axis, which provides for the diversity of alternating seasons
– the Moon’s distance from the Earth provides tides to keep life thriving in our oceans, and thus, worldwide
– the Moon’s nearly circular orbit (eccentricity ~ 0.05) makes it’s influence extraordinarily reliable
– the Moon is 1/400th the size of the Sun, and at 1/400th its distance, enables educational perfect eclipses
– the Earth’s distance from the Sun provides for great quantities of life and climate-sustaining liquid water
– the Sun’s extraordinary stable output of the energy
– the Sun’s mass and size are just right for Earth’s biosystem
– the Sun’s luminosity and temperature are just right to provide for Earth’s extraordinary range of ecosystems
– the color of the Sun’s light from is tuned for maximum benefit for our plant life (photosynthesis)
– the Sun’s low “metallicity” prevents the destruction of life on Earth
etc., etc., etc.

carbon atom

* The Finely Tuned Earth includes:
– the Earth’s surface gravity strength prevents the atmosphere from rapidly losing water to space
– the Earth’s just-right ozone layer filters out ultraviolet radiation and helps mitigate temperature swings
– the Earth’s spin rate on its axis provides for a range of day and nighttime temperatures to allow life to thrive
– the atmosphere’s composition (20% oxygen, etc.) provides for life’s high energy requirements
– if Earth’s oxygen content were higher, forest fires would worsen; at 30%-40% the atmosphere could ignite
– the atmosphere’s pressure enables our lungs to function and water to evaporate at an optimal rate to support life
– the atmosphere’s transparency to allow an optimal range of life-giving solar radiation to reach the surface
– the atmosphere’s capacity to hold water vapor provides for stable temperature and rainfall ranges 
– efficient life-giving photosynthesis depends on quantum physics, as reported in the journal PNAS
– organisms do not metabolize lignin (component in soil) for otherwise most all plant life would be impossible
– the water molecule’s astounding robustness results from finely balanced quantum effects. As reported by New Scientist, “Water’s life-giving properties exist on a knife-edge. It turns out that life as we know it relies on a fortuitous, but incredibly delicate, balance of quantum forces. … We are used to the idea that the cosmos’ physical constraints are fine-tuned for life. Now it seems water’s quantum forces can be added to this ‘just right’ list.”
– water is an unrivaled solvent; its low viscosity permits the tiniest blood vessels; its high specific heat stabilizes biosphere temperatures; its low thermal conductivity as a solid insulates frozen-over lakes and as a liquid its high conductivity lets organisms distribute heat; its an efficient lubricant; is only mildly reactive; has an anomalous (fish-saving) expansion when it freezes; its high vapor tension keeps moisture in the atmosphere; and it tastes great too!


– the phenomenally harmonious water cycle (which is one example of astounding functional complexity not explainable by evolutionary theory; another example is the astounding world of quantum physics)
– water permits the passage of the Sun’s life-giving radiation to depths of 500 meters
– the carbon atom’s astounding capabilities. As Cambridge astronomer Fred Hoyle wrote: “Some super-calculating intellect must have designed the properties of the carbon atom, otherwise the chance of my finding such an atom through the blind forces of nature would be utterly minuscule. A common sense interpretation of the facts suggests that a superintellect has monkeyed with physics, as well as with chemistry and biology, and that there are no blind forces worth speaking about in nature. The numbers one calculates from the facts seem to me so overwhelming as to put this conclusion almost beyond question.”
– etc., etc., etc.

* Anthropic Circular Reasoning from Krauss to RSR: Bob quoted Walter ReMine (1993, p. 61) to theoretical physicist (emphasis on the theoretical) Lawrence Krauss that his anthropic principle is as satisfying as a doctor saying, “The reason that your father is deaf is because he can’t hear.” Along with atheists generally, Krauss uses the Anthropic Principle to explain away the extraordinarily unlikely precise values of the many finely-tuned parameters like those listed above, including the one in 10,000 decillion odds against us having a virtually perfect one-to-one electron-to-proton ratio. They make the philosophical argument that it is not surprising that the universe has all the necessary fine tuning for life, for otherwise, we wouldn’t be here to notice. In this way they deflect attention onto the observer and away from the very design of the universe that they are pretending to explain. Meanwhile, Stephen Hawking admits, while faithfully adhering to the anthropic doctrine, “The remarkable fact is that the values of these numbers seem to have been very finely adjusted to make possible the development of life. For example, if the electric charge of the electron had been only slightly different, stars either would have been unable to burn hydrogen and helium, or else they would not have

[supernovaed]

” (Hawking, Brief History of Timep. 160; his next comment is obsolete now that supernovas are rejected as the source of the periodic table’s heavier elements). And in Hawking’s book, The Grand Design, he quotes a famed astronomer, “[Fred] Hoyle wrote, ‘I do not believe that any scientist who examined the evidence would fail to draw the inference that the laws of nuclear physics have been deliberately designed with regard to the consequences they produce…'” with Hawking adding, “At the time no one knew enough nuclear physics to understand the magnitude of the serendipity that resulted in these exact physical laws” (p. 159).

* Fine Tuning Quotes: British astrophysicist Paul Davies wrote, “There is now broad agreement among physicists and cosmologists that the universe is in several respects ‘fine-tuned’ for life. …carbon, and the properties of objects such as stable long-lived stars, depend rather sensitively on the values of certain physical parameters… it is fine-tuned for the essential building blocks and environments that life requires.” And, “There is for me powerful evidence that there is something going on behind it all….It seems as though somebody has fine-tuned nature’s numbers to make the Universe….The impression of design is overwhelming.” An early observer of what has become now this broad agreement was another Brit, astronomer Arthur Eddington, who estimated in 1931, “The picture of the world, as drawn in existing physical theories, shows arrangement of the individual elements for which the odds are mutlillions to 1 against an origin by chance.” Eddington then defined multillions as a general term for numbers of the order of 10 to the 100th power “or larger”. 

* The Astronomer and the Physicist: NASA astronomer John O’Keefe said, “We are, by astronomical standards, a pampered, cosseted, cherished group of creatures.. .. If the Universe had not been made with the most exacting precision we could never have come into existence. It is my view that these circumstances indicate the universe was created for man to live in.” Nobel prize winner physicist Arno Penzias said, “Astronomy leads us to a unique event, a universe which was created out of nothing, one with the very delicate balance needed to provide exactly the conditions required to permit life, and one which has an underlying (one might say ‘supernatural’) plan.” See these and other quotes sourced.

* Hawking’s Circular Argument that Gravity Did It: Famed astronomer Seth Shostak, asking, “Who or what built the universe?” speaks of Stephen Hawking’s claim that, “With gravity in place, the cosmos-as-we-know-it was just a matter of hanging out for a few billion years.” And then Shostak observers:

…this approach inevitably begs the question, “who designed gravity?” Isn’t it remarkable that this gentle force seems so perfectly suited to the job of assembling a grand and habitable universe? And indeed… there are many other physical parameters that seem to be nicely adjusted for our presence. This is frequently referred to as a “fine tuning” of the cosmos. If, for instance, the charge on the electron were of a slightly different value, stars wouldn’t work adequately, and you would be spared both this blog and your existence. Depending on your personal philosophies, you can either credit this custom fitting to the intentions of God, or go for Plan B. The latter posits a multiverse…

And see below for Bob Enyart’s disagreement with physicist Lawrence Krauss who claimed that the multiverse has not been proposed in order to solve the atheist’s fine-tuning problem.

* Fine Tuning of the Make-Believe Big Bang: Known as the flatness problem, if the big bang were true, for the universe to not catastrophically collapse back onto itself under an over density of matter, and for it not to wildly expand beyond the reach of gravity to form galaxies, the initial density of matter had to be tuned to within one part in ten to 57 zeros, i.e., 1 in 10,000,000,000,000,000,000,000,000,000,000,000,000. Conversely, the amount of the hypothetical (anti-gravity) substance dark energy must be similarly tuned, along with a host of other parameters, in order for the make-believe big bang universe to exist. But, since we’re talking about make-believe, we might as well posit an infinite number of universes, a multiverse, in which the most wildly unlikely scenarios, fine-tuned and otherwise, each occur a infinite number of times over, including Boltzmann-Brain universes and ones in which Herbert Hoover created alien worlds filled with sentient creatures who worship him.
Fine-tuning for Actual Life vs. for Abiogenesis: The same distinction should be made between the fine-tuning required for actual life, and for the hypothesis of abiogenesis. By the biological law of biogenesis, life only comes from life. (This is even consistent with biblical teachings regarding the origin of spirit beings.) If life has never arisen naturally from inanimate material, then a list a mile long of the physics and chemistry fine-tuning required for abiogenesis is valuable only as a falsification tool.

* Earth’s Ecosystem Fine Tuned to Use Quantum Mechanics: Until now, the fine tuning of quantum mechanics and the field of biology seemed unrelated. Not any longer! From Science Daily: “Quantum physics and plant biology seem like two branches of science that could not be more different, but surprisingly they may in fact be intimately tied.” And from PNAS as reported by Wired, “More evidence found for quantum physics in photosynthesis.” So, it turns out that The Universe Really is fine tuned for life!

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* Lawrence Krauss Never Heard of Alleged Fine-Tuning Multiverse Solution; Then Proposes It: In our broadcast interview, Dr. Lawrence Krauss rejected Enyart’s observation that materialists were positing multitudes of universes in order to explain apparent design. facie evidence of deistic design. Take your choice: blind chance that requires multitudes of universes or design that requires only one…. Many scientists, when they admit their views, incline toward the teleological or design argument.” Now fast forward to this year when biologist and fellow of both Cambridge University and of the Royal Society, Rupert Sheldrake, wrote, “To avoid a creator God emerging in a new guise, most leading cosmologists prefer to believe that our universe is one of a vast, and perhaps infinite, number of parallel universes…” So beginning at 9 minutes into today’s broadcast Enyart asserted to Krauss that he and other atheists readily accept the notions of trillions upon trillions of universes assuming this gives them a possible explanation for the wildly unlikely finely tuned parameters (rsr.org/fine-tuning) of our universe. At 13:42 in, Krauss denied this. Enyart says, “The reason that so many astrophysicists, cosmologists, have gone to asserting the multiverse, that there are trillions upon trillions of universes, is because they say ours is such that, it is so wildly unlikely, there’s no good reason for it to be here, unless there were septillions.” Krauss “No, that’s not the reason; no, no, that’s not the case.” This prompted Enyart to state, “Let me object, for the record…” And in denying that he had ever heard of the multiverse proposed solution as an answer for the fine-tuning problem, he then claimed that the multiverse is posited only because of string theory, and though he himself rejects string theory, yet he then claimed that there might indeed be an infinite number of universes. What a web we weave. Famed cosmologists John Barrow & Frank Tipler, on the back cover of their standard treatment, The Anthropic Cosmological Principle, “Could there be other universes? How large is the range of conceivable universes that can give rise to living observers?” On page 6 they write, “we are tempted to make statements of comparative reference regarding the properties of our observable Universe with respect to the alternative universes we can imagine possessing difference values [for] their fundamental constraints. But there is only one Universe [no?]; where do we find the other possible universes against which to compare our own in order to decide how fortunate it is that all these remarkable coincidences that are necessary for our own evolution actually exist?” See more RSR multiverse excerpts from this text, by cosmologists whom Lawrence Krauss knows very well. 

* Then Krauss Proposes Multiverse Solution: At 14:40 into their radio broadcast, physicist Lawrence Krauss admitted to Bob Enyart, “something along the lines of what you’re saying, namely, that if [certain fine tuning] were any different… so if [the fine tuning] is a random event, then if it we’re any different, we wouldn’t be here. Now, I should say that that’s a plausible and possible answer, resolution to that problem, and it’s motivated in some sense by the possible existence of many universes, which are predicted by many particle physics theories.” Then at 18 minutes in, Krauss again basically agrees with what he had been rejecting, saying, “There are many physicists who argue that the parameters of our universe are difficult to comprehend and many who predict the existence of many universes… We only exist in the universe with the parameters that allow life.” This is not surprising because:
– Krauss’ own book embraces the multiverse in Chapter 8: A Grand Accident
– Statistician and codger William Briggs noted last year that Krauss himself proposes multiple universes to explain ours.
On RSR, Krauss even stated that there might be infinite universes (which of course could include millions of universes wherein Lawrence was married to Hillary and elected president as Bill Krauss; millions of others wherein he was Chelsea’s brother; and in all of which, atheists spend far too much time thinking about the Physics of Lost in Space). Krauss and his associates were slow to the table though on the multiverse, which was not as supposed invented by physicist Hugh Everett, but a year earlier in 1956 by DC Comics.

 * Atheism, Not Physics, Leads to Belief in Multiverse: However a decade earlier, Stephen Hawking associate and cosmologist George Ellis wrote with co-authors in the Monthly Notices of the Royal Astronomical Society, “The idea of a multiverse — an ensemble of universes — has received increasing attention in cosmology… as an explanation for why our universe appears to be fine-tuned for life and consciousness.” And nearly three decades ago, back in 1985, the consummate astronomer, British cosmologist Ed Harrison, wrote, “Here is the cosmological proof of the existence of God – the design argument of Paley – updated and refurbished. The fine tuning of the universe provides prima

Cosmologists like Lawrence Krauss claim that physics and the study of subatomic particles led to belief in the multiverse. Alternatively, Real Science Radio argues that it is not particle physics but atheism which led to the proposal of, and the current obsession with, the multiverse. Prof. Peter Coveney and Roger Highfield in their popular book, The Arrow of Time, present the “many-worlds interpretation of quantum mechanics” (MWI, aka, the multiverse) as an alternative to the Copenhagen interpretation because whereas the science itself suggested the existence of God, a multiverse was viewed as a way out. At Princeton University in 1957 Hugh Everett working with Prof. John Wheeler proposed that, as in the wave-particle duality double-slit experiment, a photon (electron, etc.) doesn’t pass through one slit or the other, but rather, the entire “universe splits into two” as its wave goes through both, and when an observer sees the collapse of its wave function, we’re merely registering the outcome in our own universe. According to Coveney and Highfield, “Everett’s many-worlds interpretation of quantum mechanics has found favour with many cosmologists because it removes the apparent necessity for an external observer. [For] the only observer who could collapse a conventional wavefunction of the universe must be God.” (pp. 133-134) Incidentally, Everett’s thesis affirms a “psycho-physical parallelism” which rejects the human soul and spirit for a purely physical mechanism, and New Scientist’s review of a Tegmark book asks, has multiverse “cosmology veered towards something akin to religion? … Multiverse champions seem quite happy, even eager, to invoke infinite numbers of other universes as mechanisms for explaining things we see in our own universe. In a sense, multiverse enthusiasts take a ‘leap of faith'”. Famed astronomer Seth Shostak, asking, “Who or what built the universe?” speaks of Stephen Hawking’s claim that, “With gravity in place, the cosmos-as-we-know-it was just a matter of hanging out for a few billion years.” And then Shostak observers:

…this approach inevitably begs the question, “who designed gravity?” Isn’t it remarkable that this gentle force seems so perfectly suited to the job of assembling a grand and habitable universe? And indeed… there are many other physical parameters that seem to be nicely adjusted for our presence. This is frequently referred to as a “fine tuning” of the cosmos. If, for instance, the charge on the electron were of a slightly different value, stars wouldn’t work adequately, and you would be spared both this blog and your existence. Depending on your personal philosophies, you can either credit this custom fitting to the intentions of God, or go for Plan B. The latter posits a multiverse…

Thus the dislike of God is so unquestioned and intense among secular scientists that it motivated the initial proposal (though absurd) of parallel universes. Or, in the slightly veiled terminology of Max Tegmark: “Going from our universe to the Level I multiverse eliminates the need to specify initial conditions.” Exactly. 

For example, for elements as complex as carbon to be stable, the electron– proton mass ration (me ∼ = 5.44617013 × 10−4) and the fine structure constant ( α ∼ = 7.2973530810−3) could not have been more than a few percent from their actual values

The fine-tuning of the Universe is in terms of the following six dimensionless physical constants.

  • N, the ratio of the strength of electromagnetism to the strength of gravity for a pair of protons, is approximately 1036. According to Rees, if it were significantly smaller, only a small and short-lived universe could exist.[12]
  • Epsilon (ε), a measure of the nuclear efficiency of fusion from hydrogen to helium, is 0.007: when four nucleons fuse into helium, 0.007 (0.7%) of their mass is converted to energy. The value of ε is in part determined by the strength of the strong nuclear force.[13] If ε were 0.006, only hydrogen could exist, and complex chemistry would be impossible. According to Rees, if it were above 0.008, no hydrogen would exist, as all the hydrogen would have been fused shortly after the big bang. Other physicists disagree, calculating that substantial hydrogen remains as long as the strong force coupling constant increases by less than about 50%.[10][12]
  • Omega (Ω), commonly known as the density parameter, is the relative importance of gravity and expansion energy in the Universe. It is the ratio of the mass density of the Universe to the “critical density” and is approximately 1. If gravity were too strong compared with dark energy and the initial metric expansion, the universe would have collapsed before life could have evolved. On the other side, if gravity were too weak, no stars would have formed.[12][14]
  • Lambda (λ), commonly known as the cosmological constant, describes the ratio of the density of dark energy to the critical energy density of the universe, given certain reasonable assumptions such as positing that dark energy density is a constant. In terms of Planck units, and as a natural dimensionless value, the cosmological constant, λ, is on the order of 10−122.[15] This is so small that it has no significant effect on cosmic structures that are smaller than a billion light-years across. If the cosmological constant were not extremely small, stars and other astronomical structures would not be able to form.[12]
  • Q, the ratio of the gravitational energy required to pull a large galaxy apart to the energy equivalent of its mass, is around 10−5. If it is too small, no stars can form. If it is too large, no stars can survive because the universe is too violent, according to Rees.[12]
  • D, the number of spatial dimensions in spacetime, is 3. Rees claims that life could not exist if there were 2 or 4 dimensions of spacetime nor if any other than 1 time dimension existed in spacetime.[12]

2.3 x 1039 to 1: The Relative Strength Ratio That Is ‘Fine-Tuned’ For Life. Well, the simple answer is the relative strengths for the four fundamental forces of nature are balanced (equivalent) and fine-tuned for life. More specifically, the relative strengths are balanced because they are mathematically equivalent. Given, the ratio 1.26 x 1036 to 1- the gravitational force verses electrical force between a pair protons, the proton pair will fly apart (outside the nucleus of an atom) with an electrical force that is 1036 times than the gravitational force trying to hold them together. Also given, the ratio 4.1619 x 1042 to 1- the gravitational force verses electrical force between two electrons, like the proton pair, the electron pair will also fly apart, but with a force that is 1836 times squared greater than the proton pair. However, given the ratio 2.29 x 1039

 to 1- the gravitational force verses electrical force between a proton and electron is just right for life or the ‘goldilocks ratio’. The proton-electron pair will bond together, instead of flying apart. The proton-electron bonding allows for the formation of the hydrogen atom – the simplest structure of atomic stability, and the building block of the universe. It is the hydrogen atom, that make the structure of complex atoms, elements, compounds, stars, solar systems, and galaxies – the foundations of life possible. The relative strengths for the four fundamental forces are mathematically equivalent as follows: 2.29 x 1039to 1 / 1.26 x 1036 to 1 = 4.1619 x 1042 to 1 / 2.29 x 1039 to 1. It’s this perfect proportion that makes the product of the extremes (1036) x (1042) equal to the square of the mean or 1039 squared. Notice how nature ‘fine-tuned’ the two extremes with the exact numerical information to make their product equal to precisely the square of the mean. It’s the ratio 2.29 x 1039 to 1 ratio that is just right for the process of hydrogen fusion – a process that produces long-burning stars like our sun, and a life-bearing planet like earth. In summary, the greater / lesser relative strengths are the ‘raw materials’ that are necessary for the origin of life. It appears the mechanism for the creation of life on earth is the product of two extremes that produce the square of a perfect ‘life-giving’ mean. Simply stated: life in the universe is created by the ‘Means of Extremes’.

Q. Does the unimaginably fine tuning of the Cosmological Constant of 1 to the power of 125, suggest the work of a creator?

Extreme Fine Tuning

Sceptics like to say that fine tuning cannot be proven by science, since we have only one universe to study. However, the discovery and quantification of dark energy has puzzled a number of scientists, who realize that its extremely small value requires that the initial conditions of the universe must have been extremely fine tuned in order that even matter would exist in our universe. By chance, our universe would have been expected to consist of merely some thermal radiation.

Rich Deem

How much fine tuning?

How does this discovery impact atheists? Those who favor naturalism had long sought to find the simplest explanation for the universe, hoping to avoid any evidence for design. A Big Bang model in which there was just enough matter to equal the critical density to account for a flat universe would have provided that. However, for many years, it has been evident that there is less than half of the amount of matter in the universe to account for a flat universe. A cosmological constant would provide an energy density to make up for the missing matter density, but would require an extreme amount of fine tuning. The supernovae studies demonstrated that there was an energy density to the universe (but did not define the size of this energy density), and the recent Boomerang study demonstrated that this energy density is exactly what one would expect to get a flat universe. How finely tuned must this energy density be to get a flat universe? One part in 10120,6 which is:

1 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000

Take, for instance, the neutron. It is 1.00137841870 times heavier than the proton, which is what allows it to decay into a proton, electron and neutrino—a process that determined the relative abundances of hydrogen and helium after the big bang and gave us a universe dominated by hydrogen. If the neutron-to-proton mass ratio were even slightly different, we would be living in a very different universe: one, perhaps, with far too much helium, in which stars would have burned out too quickly for life to evolve, or one in which protons decayed into neutrons rather than the other way around, leaving the universe without atoms. So, in fact, we wouldn’t be living here at all—we wouldn’t exist.

5 If the rate of expansion after the B.B. had been smaller by 1 part in a hundred thousand million million the universe would have collapsed in on itself.

6 Likelihood of the forces of expansion & contraction being what they are is like throwing a dart at a dartboard on the other side of the universe and hitting the bullseye.

7 If gravity were altered by a mere 1 part in 1040 (1 in 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000) stars would not exist.

9 A variation of

10 If the oxygen resonance level were 1/2 % higher carbon could never have formed

These numbers represent the maximum deviation from the accepted values,
that would either prevent the universe from existing now, not having matter,
or be unsuitable for any form of life.
Recent Studies have confirmed the fine tuning of the cosmological constant. This cosmological constant is a force that increases with the increasing size of the universe. First hypothesized by Albert Einstein, the cosmological constant was rejected by him, because of lack of real world data. However, recent supernova 1A data demonstrated the existence of a cosmological constant that probably made up for the lack of light and dark matter in the universe. (2) However, the data was tentative, since there was some variability among observations. Recent cosmic microwave background (CMB) measurement not only demonstrate the existence of the cosmological constant, but the value of the constant. It turns out that the value of the cosmological constant exactly makes up for the lack of matter in the universe. (3)

The degree of fine-tuning is difficult to imagine. Dr. Ross gives an example of the least fine-tuned of the above four examples in his book, The Creator and the Cosmos , which is reproduced here:
One part in 10 37 is such an incredibly sensitive balance that it is hard to visualize. The following analogy might help: Cover the entire North American continent in dimes all the way up to the moon, a height of about 239,000 miles (In comparison, the money to pay for the U.S. federal government debt would cover one square mile less than two feet deep with dimes.). Next, pile dimes from here to the moon on a billion other continents the same size as North America. Paint one dime red and mix it into the billion of piles of dimes. Blindfold a friend and ask him to pick out one dime. The odds that he will pick the red dime are one in 1037.
Strong nuclear force constant
if larger : no hydrogen would form; atomic nuclei for most life-essential elements would be unstable; thus, no life chemistry
if smaller : no elements heavier than hydrogen would form: again, no life chemistry Weak nuclear force constant
if larger : too much hydrogen would convert to helium in big bang; hence, stars would convert too much matter into heavy elements making life chemistry impossible
if smaller : too little helium would be produced from big bang; hence, stars would convert too little matter into heavy elements making life chemistry impossible Gravitational force constant
if larger : stars would be too hot and would burn too rapidly and too unevenly for life chemistry
if smaller
: stars would be too cool to ignite nuclear fusion; thus, many of the elements needed for life chemistry would never form Electromagnetic force constant
if greater : chemical bonding would be disrupted; elements more massive than boron would be unstable to fission
if lesser : chemical bonding would be insufficient for life chemistry Ratio of electromagnetic force constant to gravitational force constant
if larger : all stars would be at least 40% more massive than the sun; hence, stellar burning would be too brief and too uneven for life support
if smaller
: all stars would be at least 20% less massive than the sun, thus incapable of producing heavy elements Ratio of electron to proton mass
if larger : chemical bonding would be insufficient for life chemistry
if smaller : same as above Ratio of number of protons to number of electrons
if larger : electromagnetism would dominate gravity, preventing galaxy, star, and planet formation
if smaller : same as above Expansion rate of the universe
if larger : no galaxies would form
if smaller
: universe would collapse, even before stars formed Entropy level of the universe
if larger : stars would not form within proto-galaxies
if smaller : no proto-galaxies would form Mass density of the universe
if larger : overabundance of deuterium from big bang would cause stars to burn rapidly, too rapidly for life to form
if smaller : insufficient helium from big bang would result in a shortage of heavy elements velocity of light
if faster : stars would be too luminous for life support if slower : stars would be insufficiently luminous for life support Age of the universe
if older : no solar-type stars in a stable burning phase would exist in the right (for life) part of the galaxy
if younger : solar-type stars in a stable burning phase would not yet have formed Initial uniformity of radiation
if more uniform : stars, star clusters, and galaxies would not have formed
if less uniform : universe by now would be mostly black holes and empty space Average distance between galaxies
if larger : star formation late enough in the history of the universe would be hampered by lack of material
if smaller : gravitational tug-of-wars would destabilize the sun’s orbit Density of galaxy cluster
if denser : galaxy collisions and mergers would disrupt the sun’s orbit
if less dense : star formation late enough in the history of the universe would be hampered by lack of material Average distance between stars
if larger : heavy element density would be too sparse for rocky planets to form
if smaller
: planetary orbits would be too unstable for life Fine structure constant (describing the fine-structure splitting of spectral lines) if larger : all stars would be at least 30% less massive than the sun
if larger than 0.06: matter would be unstable in large magnetic fields
if smaller : all stars would be at least 80% more massive than the sun Decay rate of protons
if greater : life would be exterminated by the release of radiation
if smaller : universe would contain insufficient matter for life 12 C to 16 O nuclear energy level ratio
if larger : universe would contain insufficient oxygen for life
if smaller : universe would contain insufficient carbon for life Ground state energy level for 4 He
if larger : universe would contain insufficient carbon and oxygen for life
if smaller
: same as above Decay rate of 8 Be
if slower : heavy element fusion would generate catastrophic explosions in all the stars
if faster : no element heavier than beryllium would form; thus, no life chemistry Ratio of neutron mass to proton mass
if higher : neutron decay would yield too few neutrons for the formation of many life-essential elements
if lower : neutron decay would produce so many neutrons as to collapse all stars into neutron stars or black holes Initial excess of nucleons over anti-nucleons
if greater : radiation would prohibit planet formation
if lesser : matter would be insufficient for galaxy or star formation Polarity of the water molecule
if greater : heat of fusion and vaporization would be too high for life
if smaller : heat of fusion and vaporization would be too low for life; liquid water would not work as a solvent for life chemistry; ice would not float, and a runaway freeze-up would result Supernovae eruptions
if too close, too frequent, or too late : radiation would exterminate life on the planet
if too distant, too infrequent, or too soon : heavy elements would be too sparse for rocky planets to form White dwarf binaries
if too few : insufficient fluorine would exist for life chemistry
if too many : planetary orbits would be too unstable for life
if formed too soon : insufficient fluorine production
if formed too late : fluorine would arrive too late for life chemistry Ratio of exotic matter mass to ordinary matter mass
if larger : universe would collapse before solar-type stars could form
if smaller : no galaxies would form Number of effective dimensions in the early universe
if larger : quantum mechanics, gravity, and relativity could not coexist; thus, life would be impossible
if smaller : same result Number of effective dimensions in the present universe
if smaller : electron, planet, and star orbits would become unstable
if larger
: same result Mass of the neutrino
if smaller : galaxy clusters, galaxies, and stars would not form
if larger : galaxy clusters and galaxies would be too dense Big bang ripples
if smaller : galaxies would not form; universe would expand too rapidly
if larger : galaxies/galaxy clusters would be too dense for life; black holes would dominate; universe would collapse before life-site could form Size of the relativistic dilation factor
if smaller : certain life-essential chemical reactions will not function properly
if larger
: same result Uncertainty magnitude in the Heisenberg uncertainty principle
if smaller : oxygen transport to body cells would be too small and certain life-essential elements would be unstable
if larger : oxygen transport to body cells would be too great and certain life-essential elements would be unstable Cosmological constant
if larger : universe would expand too quickly to form solar-type stars References (1) For further information, visit the website of Dr. Edward Wright, Ph.D., Professor of Astronomy at UCLA (2) The amount of light and dark matter is only 30% of that necessary for a “flat” universe (one which contains the critical mass – the amount necessary to stop the expansion of the universe). (3) Sincell, M. 1999. Firming Up the Case for a Flat Cosmos. Science 285: 1831.
http://commonsenseatheism.com/wp-content/uploads/2010/03/hand-galaxy.png

* Another Fun RSR List Show: In Real Science Radio’s List of the Fine Tuned Features of the Universe, Bob Enyart quotes leading scientists and their astounding admission of the uncanny and seemingly never-ending list of the just-perfect finely tuned parameters of the physical features of the Earth, the solar system, and the entire cosmos. This program is brought to you by God, maker of heaven and earth and other fine products!

The Multiverse

Because of the fine tuning in the universe, a term has appeared in cosmological literature: ‘multiverse’. This appeared because of the incredible degree of constraints applying to physical parameters in the universe.

You won’t find it in the dictionary, because it contains a contradiction in terms: multiple universes. By definition, the universe is supposed to include everything. One cannot have multiple ‘everythings’.

The story of how this new word came about reveals the desperation of atheists trying to escape overwhelming evidence for design.

Naturalists want to explain the universe as a necessary outcome of laws and initial conditions, instead of a “roll of the dice.” The Big Bang theory, inflation, and the search for structure in the cosmic background radiation are all part of this tradition.

Everyone knows the universe looks designed because the many features appear to be ordered, rather than change forms.

The design argument took on renewed urgency in the 1930s when quantum physicists realized that certain constants, like the force of gravity and the charge on the electron, could have taken arbitrary values (see above) – yet most values would never produce a universe with atoms, stars, planets, or observers. The universe appears finely tuned for our existence. This is described as the ‘Anthropic principle’. This can be defined as,

“the cosmological principle that theories of the universe are constrained by the necessity to allow human existence”.

To naturalists, this looks disturbingly unnatural.

In its weakest form, it dismissed design by saying that if the laws and constants weren’t what they are, we wouldn’t be here to worry about the question. Of course this doesn’t explain anything.

Stronger forms have asserted that our existence determines the laws of physics, or even that we create the universe by existing to observe it. The phrase, ‘clutching at straws comes to mind’. Needless to say, most naturalists have dismissed such speculations as metaphysical fluff. The Anthropic Principle became a spent fad by the 1990s.

Something was discovered in 1996 that brought cosmologists kicking and screaming back to the Anthropic Principle: the universe is not only expanding, it’s accelerating. The acceleration parameter, or cosmological constant, appears so finely tuned (nearly zero, but slightly positive) that almost any larger value would prohibit the formation of stars and galaxies. Theoretical predictions are off by 120 orders of magnitude.

Some hoped that superstring theory would come to the rescue, but its champions found that their equations permit 10500 different sets of initial conditions—most of them life-prohibiting. The only way our universe could be explained, therefore, was either by a Designer who chose the right values or by luck among untold numbers of alternate universes with random values.

Growing numbers are caving in to his multiverse concept with its anthropic overtones, while others, with no explanation for the fine-tuning of the universe, cling to their faith in naturalism. They argue that multiverse theory relies on alternate realities that are unobservable even in principle.

Occam’s Razor would surely prefer a single Designer to uncountable universes. These are good days for churches to preach out of Isaiah 45, with its winning scientific cosmology: “|He| formed it to be inhabited.”

No secular scientist knows where our universe originated from. To explain the presence let alone origins of a multiverse is (unknown)2. If there was a machine/formation device producing these alternative universes, then its origin would have to be explained.

It has been said that, ‘Evolution is a fairytale for grown ups’. Here you have a fairy story for theoretical physicists.

We are limited to our universe, if the word ‘limited’, is appropriate here. The universe is immense beyond thought, but some people want to imagine multiple others.

http://kgov.com/files/images/science/multiverse-yardstick-for-fine-tuning-argument.png

* What is the Multiverse? (see below). In June of 2016, Fred Williams passed along a question from a listener to his Real Science Radio co-host Bob Enyart.
Q: “What is the Multiverse?”
A: “The multiverse is a yardstick used to measure the strength of the fine tuning argument for God.”
But then…
Q: “Why do so many atheists support the multiverse?”
A: “The degree of acceptance of the multiverse
measures the desperation of atheists.”

Multiverse vs. Bible Verse:

“In the beginning God created” begins the first Bible verse. Krauss’ objections aside, here’s the multiverse alternative as described in the NY Times by Paul Davies:

Imagine you can play God and fiddle with the settings of the great cosmic machine. Turn this knob and make electrons a bit heavier; twiddle that one and make gravitation a trifle weaker. What would be the effect? …there wouldn’t be anyone around to see the result, because the existence of life depends rather critically on the actual settings that Mother Nature selected.

Scientists have long puzzled over this rather contrived state of affairs. Why is nature so ingeniously, one might even say suspiciously, friendly to life? What do the laws of physics care about life and consciousness that they should conspire to make a hospitable universe? It’s almost as if a Grand Designer had it all figured out.

The fashionable scientific response to this cosmic conundrum is to invoke the so-called multiverse theory.

References

Guillermo Gonzalez and Jay Richards The Privileged Planet: How Our Place in the Cosmos is Designed for Discovery (Washington DC: Regnery, 2004).

Robin Collins, “The Teleological Argument: An Exploration of the Finetuning of the Cosmos,” Blackwell Companion to Natural Theology, edited by William Lane Craig and J.P. Moreland, (Oxford: Blackwell Pub., 2009)

John Barrow and Frank Tipler, The Anthropic Cosmological Principle (Oxford: Oxford University Press, 1986).

Roger Penrose, The Road to Reality: A Complete Guide to the Laws of the Universe (New York: Vintage, 2007).

Paul Davies, The Accidental Universe (Cambridge: Cambridge University Press, 1982).

Martin Rees, Just Six Numbers: The Deep Forces that Shape the Universe (New York, NY: Basic Books, 2000.)

References

(1) For further information, visit the website of Dr. Edward Wright, Ph.D., Professor of Astronomy at UCLA

(2) The amount of light and dark matter is only 30% of that necessary for a “flat” universe (one which contains the critical mass – the amount necessary to stop the expansion of the universe).

(3) Sincell, M. 1999. Firming Up the Case for a Flat Cosmos. Science 285: 1831.