Physics Problems for Creation Week

It is hard to talk about physics at all during creation week since the UNI-verse was not completed as a complete entity until Day Six. Since space, time, and matter are all interlinked, the universe as a cohesive system was not really functioning until Day Seven. In other words, all the parts and pieces of the universe are connected. The movement of one object--a moon, a planet, a star, a galaxy--is sensed by all the other objects in the ensemble. So how do we talk about the functioning of an incomplete universe one Day at a time? How do we talk about the working of a clock when the gears are not yet in their sockets? Time is a created entity. In the simplest model we consider the universe to possess three spatial coordinates and one time dimension. These four-dimensions are interdependent. Did God hold together all the components of the universe while he was working on them, and only set them in place with all their associated forces on Day Six?

Ordinarily science is limited to talking about the physical world, but the real world is physical-plus-spiritual integrated together. Science is built on physical observations made with the five senses and related sensing instruments. Our observations of the physical are sorted and categorized so as to form rational, understandable patterns from which we infer laws and theories. As discussed elsewhere, we assume in science that the universe is rational and orderly, and we prefer simple "elegant" explanations to complex theories. The latter is actually an argument from aesthetics! We actually have much additional information about the universe which has been given to us by revelation from God. This revealed information tells us a lot about the spiritual realm which we would not have a way of knowing about from observations of the physical world only.

The Bible describes the physical world as a world of "shadows." Many of the artifacts in the physical world have been patterned after more solid, more permanent enduring "objects" which exist in the heavenly realm. One example would be the Tabernacle of Moses, which Moses was told to build "after the pattern which was shown you on the Mount" (Sinai). This means there exists a temple of God "eternal in the heavens."

The entire universe (the physical plus the spiritual) is like a house, a habitation for God, man, the angels, animals and so on. So there is structure and order in the spiritual world which is related to the observed order in the physical world. This suggests that we can hope to do some "integrated" physics which attempts to describe the universe as a whole system. But since we are in a physical realm -- described in Scripure as a realm of "shadows" -- it is difficult for us to infer the nature of the "real" objects that cast those "shadows" which we are attempting to understand.

The Bible teaches that God created the universe during a finite interval of "six days" after which He ceased creating. Since creation God has however unceasingly "maintained" the creation. The theological word is "sustained." God is the Sustainer, as well as the Creator and the Redeemer, so He actually controls everything which takes place in history. (John 1, Colossians 1, Hebrews 1) We assume He does this by constant inputs of force and energy intelligently directed. We can assume that the level of His sustaining power decreased at the time of the Fall.

I believe that the Second Law of Thermodynamics went into effect at the time of the Fall and was probably not a feature of the original creation. (This did not mean energy did not previously flow from hot to cold reservoirs--the Second Law is only about the increasing unavailability of energy to do useful work as time moves forward). The present tendency of the universe to decay and deteriorate (as described in Romans 8) is a result of human evil and/or evil amongst the angels. Likewise it has been suggested there was no radioactivity before the Fall, but that the radioactive decay of certain heavy atoms was switched on at the time of the Fall.

We do not observe God at work in the everyday world of nature because He almost always works within the framework of His own Laws. And also, "His ways are beyond our discovery,"

O the depth of the riches and wisdom and knowledge of God! How unsearchable are his judgments and how inscrutable his ways! "For who has known the mind of the Lord, or who has been his counselor?" "Or who has given a gift to him that he might be repaid?" For from him and through him and to him are all things. To him be glory for ever. Amen. (Rom. 11:33-36)

And the Lord through the prophet Isaiah says,

"Seek the LORD while he may be found, call upon him while he is near; let the wicked forsake his way, and the unrighteous man his thoughts; let him return to the LORD, that he may have mercy on him, and to our God, for he will abundantly pardon. For my thoughts are not your thoughts, neither are your ways my ways, says the LORD. For as the heavens are higher than the earth, so are my ways higher than your ways and my thoughts than your thoughts. "For as the rain and the snow come down from heaven, and return not thither but water the earth, making it bring forth and sprout, giving seed to the sower and bread to the eater, so shall my word be that goes forth from my mouth; it shall not return to me empty, but it shall accomplish that which I purpose, and prosper in the thing for which I sent it. "For you shall go out in joy, and be led forth in peace; the mountains and the hills before you shall break forth into singing, and all the trees of the field shall clap their hands. Instead of the thorn shall come up the cypress; instead of the brier shall come up the myrtle; and it shall be to the LORD for a memorial, for an everlasting sign which shall not be cut off." (Isaiah 55:6-13)

The actual government of the universe, moral and physical, is entrusted to the angels (and especially this has been the case since the Fall of man, according to Hebrews 2:5). What we see as the "laws of nature"--and they appear fixed and inviolate--may, for all we know, simply mean that the angels do an extremely precise job of governing nature. Therefore the Fall of the angels would be expected to disrupt nature. Thus our world is now more chaotic, less controlled, more "uncertain" (as in Planck's constant), and often more "harmful" to man (less benevolent, less bountiful) as one consequence of the Fall of the angels and the Fall of man.

In Genesis, the Observer (God Himself), who apparently wrote Chapter One, begins by describing the creation of the entire universe--"the heavens and the earth." However by the time we reach verse 3 the Observer is clearly telling us things from the vantage point of earth. The creation of the sun, moon and stars is referenced as happening on Day Four but otherwise much of the discussion deals with the earth and its environment. This makes it difficult to do much cosmology unless we look at other descriptions of creation elsewhere in the Bible.

How did God create matter on Day One? We might imagine that God made the parts of the atom, then assembled them into elements and finally into molecules. But, the presence of water (not ice and not steam) right away in Genesis 1:1-2 suggests complete molecules and low temperatures were there from Day One. The statement "Let there be Light" appears to indicate a separate creation of photons (that is, an energy reservoir) for the universe, also taking place as the second act of creation, on Day One. So I find it hard to imagine that temperatures were very high at least until Day Four when God packaged the preexisting light (Hebrew: 'or) into the light-holders, or "light-bearers," i.e., the stars (ma'or). (Incidentally the universe we live in appears to have about one billion times as many photons as protons).

There is nothing in Genesis One to suggest anything like a Big Bang--even the expansion of space on Day two of creation week seems to have been a "cool" process. Presumably the creation of the Stars on Day Four must have been accompanied by the high temperatures we know now exist in the interiors of the stars.

The universe (according to modern astronomy) weighs about 1053 kilograms and contains about 1080 protons. The diameter of the universe appears to be of the order of 1027 meters. The Big Bang age of the universe is about 1018 seconds. The universe contains about 109 more photons than protons.

It is reasonable (but not conclusive) from Genesis 1:1 to assume that all the matter in the universe was created on Day One. The creation of light also on Day One suggests that all the needed energy reservoirs for the universe were also finished on Day One. However much work was done on the universe during the following five days of creation week This would presumably involve more energy input from God and matter organized by God's handiwork so that entropy decreased throughout the week as the universe became more orderly and complex.

What about the relative abundance of the various elements in the universe today? How did this come about if we are skeptical of the secular theory of the heavier elements being synthesized in stellar nuclear reactions. Hydrogen is very abundant, but the relative abundance of oxygen is down by a factor of 104. Not all the oxygen in the universe is tied up in water molecules, but for discussion purposes, one might take the total mass of the water in the universe as 1039 kg. Assembled into a sphere, the diameter of the sphere might be about 1016 meters (0.1 light years). This is of course a wild guess for discussion purposes only.

On Day Two we have that strange statement about God making a firmament in the midst of the waters. Usually the original firmament is thought of as extremely massive and superdense. It is not a substance known to man evidently. The firmament, whatever it is, was then stretched out very thin (raqia)--probably requiring external work to be done to accomplish the stretching (or "hammering thin" like gold leaf-another meaning of the Hebrew raqia). In its final stretched out form the firmament resembles a tent, or a fine fabric, but it is evidently three-dimensional, filling everything. The diameter of the universe is about 1027 meters. If we arbitrarily take the diameter of the spherical shell representing the original firmament to be, say, 1015 meters, then the firmament would have been expanded by about 12 orders of magnitude on the Second Day of creation week. According to the text, the firmament was named "heaven." (Our English word heaven is from the verb "to heave"). If the firmament is the substrate we now call the aether, then it has strange elastic and inertial--properties different from any known material substance--these properties determining the velocity of light c. There is some evidence that the velocity of gravity may be about ten orders of magnitude higher than the present value of c. The suggestion is that c has dropped ten orders of magnitude in the history of the universe, but the speed of gravity has not changed.

If the universe began with all matter inside a sphere then a crude model might be to put the elements (other than water) in the center of a sphere of water. Then the firmament created on Day Two could conceivably occupy a spherical ring. When expanded this ring would be spread very thin to constitute what we call the aether.

The universe may be inherently unstable (prone to collapse), apart from God's constant sustaining work. It seems to be. For instance Peter in his second epistle talks about a future day when the atomic elements will be unloosed and this strongly suggests the nuclear binding forces are externally imposed moment by moment, so the stability of the universe is due to God's constant control.

Peter says,

First of all you must understand this, that scoffers will come in the last days with scoffing, following their own passions and saying, "Where is the promise of his coming? For ever since the fathers fell asleep, all things have continued as they were from the beginning of creation." They deliberately ignore this fact, that by the word of God heavens existed long ago, and an earth formed out of water and by means of water, through which the world that then existed was deluged with water and perished. But by the same word the heavens and earth that now exist have been stored up [reserved] for fire, being kept until the day of judgment and destruction of ungodly men. But do not ignore this one fact, beloved, that with the Lord one day is as a thousand years, and a thousand years as one day. The Lord is not slow about his promise as some count slowness, but is forbearing toward you, not wishing that any should perish, but that all should reach repentance. But the day of the Lord will come like a thief, and then the heavens will pass away with a loud noise, and the elements (stoicheia) will be dissolved (luo) with fire, and the earth and the works that are upon it will be burned up. Since all these things are thus to be dissolved, [unloosed] what sort of persons ought you to be in lives of holiness and godliness, waiting for and hastening the coming of the day of God, because of which the heavens will be kindled and dissolved, and the elements will melt with fire! But according to his promise we wait for new heavens and a new earth in which righteousness dwells. Therefore, beloved, since you wait for these, be zealous to be found by him without spot or blemish, and at peace. (2 Peter 3:3-14)

Peter begins by talking about the terrible disaster of the Flood but then speaks of a future judgment of the earth by what appears to be nuclear fires from within every atom.

Barry Setterfield suggests that constant energy from the vacuum, i.e. from the ZPE, flows in to energize every atom. I think this manifestation of God's sustaining energy and upholdig force comes "from the other side of the vacuum." In Colossians Chapter One we are shown a picture of the Son of God as upholding the universe moment by moment. The work of creation by God occupied just six days, after which God stopped creating. But He went on to sustain the universe. Colossians One and Hebrews One give reason to suppose that the moment-by-moment sustaining of the cosmos involves the input of both force and energy from outside the system, ie., from the spiritual realm in which the material worlds is immersed. The force and energy input would be intelligently applied.

These notes are mostly about physics. Biologically the universe is a house designed to be inhabited by living beings of all kinds. All of life comes from God, God alone has life. He creates not only inanimate objects, but also living cells of all kinds, and from these He has built simple and complex life forms. Some of God's creatures inhabit the spiritual world (the angels). Others inhabit the rivers and seas, the skies and the earth. Life forms all have built-in genetic codes which are of immense complexity. This built-in programming information (categorized as "seed" in the text) gives living things the ability to reproduce and generate new copies (with variation and much variety) without God having to make future generations one individual at a time. Yet this does not remove the Lord from involvement in every step of the development of life-at least human life, as David the Psalmist shows,

O LORD, thou hast searched me and known me! Thou knowest when I sit down and when I rise up; thou discernest my thoughts from afar. Thou searchest out my path and my lying down, and art acquainted with all my ways. Even before a word is on my tongue, lo, O LORD, thou knowest it altogether. Thou dost beset me behind and before, and layest thy hand upon me. Such knowledge is too wonderful for me; it is high, I cannot attain it. Whither shall I go from thy Spirit? Or whither shall I flee from thy presence? If I ascend to heaven, thou art there! If I make my bed in Sheol, thou art there! If I take the wings of the morning and dwell in the uttermost parts of the sea, even there thy hand shall lead me, and thy right hand shall hold me. If I say, "Let only darkness cover me, and the light about me be night," even the darkness is not dark to thee, the night is bright as the day; for darkness is as light with thee. For thou didst form my inward parts, thou didst knit me together in my mother's womb. I praise thee, for thou art fearful and wonderful. Wonderful are thy works! Thou knowest me right well; my frame was not hidden from thee, when I was being made in secret, intricately wrought in the depths of the earth. Thy eyes beheld my unformed substance; in thy book were written, every one of them, the days that were formed for me, when as yet there was none of them. How precious to me are thy thoughts, O God! How vast is the sum of them! If I would count them, they are more than the sand. When I awake, I am still with thee. O that thou wouldst slay the wicked, O God, and that men of blood would depart from me, men who maliciously defy thee, who lift themselves up against thee for evil! Do I not hate them that hate thee, O LORD? And do I not loathe them that rise up against thee? I hate them with perfect hatred; I count them my enemies. Search me, O God, and know my heart! Try me and know my thoughts! And see if there be any wicked way in me, and lead me in the way everlasting! (Psalm 139)

I do not think many people realize how truly unique creation week was! We can not take for granted the physics of today's world and apply it all backwards to creation week. For one thing God was active all week long in creating things and shaping them into their final forms. This implies not only more than one creative act in bringing working matter into existence, but many actions of molding, shaping, forming and organizing matter. This suggests that the overall entropy was lowered in stages during creation week, and that entropy had its lowest value ever on Day Six. (maximum order, maximum available energy). Evidently the physical universe was constantly renewed and its energy reservoirs replenished prior to the fall of the angels, and to a lesser degree after the Fall of man (hence the "curse" on the natural order--Romans 8:19-23). Thus the Second Law of Thermodynamics, and Radioactive decay itself would be artifacts associated with the fall (the ruin) of the old creation, not features of the original creation. If this is so, entropy started increasing after the Fall of man in the garden. But the language of 2 Peter regarding the Flood is so strong, I would not be surprised if there were further disruptions in the basic physical laws of the universe when the Flood took place--these laws of nature being mediated by the angels--Hebrews 2:5.

"In many separate revelations-each of which set forth a portion of the Truth--and in different ways God spoke of old to [our] forefathers in and by the prophets, [But] in the last of these days He has spoken to us in [the person of a] Son, Whom He appointed Heir and lawful Owner of all things, also by and through Whom He created the worlds and the reaches of space and the ages of time-[that is] [He made, produced, built, operated, and arranged them in order]. He is the sole expression of the glory of God-[the Light-being, the out-raying or radiance of the divine],--and He is the perfect imprint and very image of [God's] nature, upholding and maintaining and guiding and propelling the universe by His mighty word of power..." (Hebrews 1:1-4) (Amplified Bible).

Addendum I: In regard to the firmament, Prof. Robert Bob Herrmann, Professor of Mathematics, USNA (ret) says the following,

"The GGU-model yields many modes of "space" expansion. I accept the following type of firmament. It is a predicted notion and its verified predictions yield indirect evidence for its existence.

[1] Compared to our notions of "density," it is composed of an infinitely dense collection of ultimate subparticles. You can remove all of the ultimate subparticles needed to form even an infinite cosmos and it will remain infinitely dense. It is not part of our realized physical world.

[2] This field as a basic entity is NOT defined in any geometric manner. Geometric language only applies when physical realization is being considered. In this case, intuitively, the field can be considered as "spread out" or "stretched out" from a central position near to what would become the earth and its local environment.

[3] This subparticle field yields all realized physical entities and alternations in physical-system behavior.

[4] In my book on the theory of infinitesimal light clocks, various "physical metrics" are derived using only a light propagation theory. These physical metrics also satisfy the Hilbert-Einstein field equations. One, "the linear effect line element," yields all verified Special Theory effects. This line element can be used for a Newtonian-like "constant" gravitational field such as in a shell surrounded by a gravitating mass. It was Humphreys who showed that, in this case, the gravitational field it represents also satisfies the Hilbert-Einstein field equations.

[5] Within each of these metrics is an additional parameter d. Depending upon the application, this d corresponds to the "speed" of expansion relative to the center of expansion. It can also be used for an accelerated expansion if such should be the case. No dark energy is needed for this to occur. In its complex form, it can represent a contraction rather than an expansion of the field if that should ever be the case.

[6] There are different modes for material expansion. For example, the expansion of all physical entities relative to the "center" can occur. But, gravitationally bounded entities can appear to be "moving away" from the center as an entire entity.

[7] Among other possibilities, the expansion can occur in a continuous manner or a discontinuous manner at any moment in primitive time." (added 1/22/09).

Related Study: The Uniqueness of Creation Week

Addendum II:The Origin of the Universe: Standard Model Big Bang Compared to ZPE Model

Matter itself was an ex nihilo creation according to Genesis 1:1. In the Big Bang model, one starts with a singularity, a sort of point of almost infinitesimal smallness, Here is a quote which attempts to explain it:

"According to the standard theory, our universe sprang into existence as "singularity" around 13.7 billion years ago. What is a "singularity" and where does it come from? Well, to be honest, we don't know for sure. Singularities are zones which defy our current understanding of physics. They are thought to exist at the core of "black holes." Black holes are areas of intense gravitational pressure. The pressure is thought to be so intense that finite matter is actually squished into infinite density (a mathematical concept which truly boggles the mind). These zones of infinite density are called "singularities." Our universe is thought to have begun as an infinitesimally small, infinitely hot, infinitely dense, something - a singularity. Where did it come from? We don't know. Why did it appear? We don't know." (From http://www.big-bang-theory.com/).

The initial BB proposal by Gamow started with what he called a 'hot nuclear gas' - in other words, a plasma. There are other ideas about the BB, involving initial radiation (what was radiating is not mentioned) etc. In Steven Weinberg's "The First Three Minutes," he says this: "The process by which matter is produced out of radiation can best be understood in terms of the quantum picture of light. Two quanta of radiation, or photons, may collide and disappear, all their energy and momentum going into the production of two or more material particles." What is interesting is that Weinberg is starting off with radiation, but nothing radiation, and light, but nothing producing the light.

After this point, both models deal initially with plasma - extraordinarily hot matter where atoms are dissociated - and a rapid expansion of space.

Now, the secular plasma model(s) are concerned with extraordinarily long ages, and I (Barry Setterfield) disagree very much with that. I'll try to note where we are different in the following.

In the BB model, the energy for expansion simply 'exists.' There is no determined cause. In the Bible, God says HE stretched out the heavens, so we say the energy came from Him.

In the BB model, there is no energy conversion in the sense of a vast amount of potential energy being converted to kinetic energy or matter. Energy is put into the expansion of matter, but, again, there is no claimed source for that energy that we are aware of.

In our plasma model, God Himself invested enormous potential energy into the fabric of space when He stretched it out. In the BB model, the universe is still expanding, but in the Bible references to the stretching of space almost always occur in the past tense and in connection with creation week. So we are looking at a universe which is no longer stretching out, although it does undergo a slight oscillation, sort of like what you would see with a water balloon when you put it down and it wiggles a bit. The article Barry wrote on this was refused by Chaffin when we submitted it to CRSQ several years ago. It is on the net here: http://www.setterfield.org/000docs/staticu.html

The result of the expansion/stretching is the formation of Planck Particle Pairs (PPP), extraordinarily tiny points of positive and negative charges, much smaller than electrons. Gibson, a leading physicist here in America, has postulated that the actual expansion of space would produce the 'particles.' He has written and presented on this. The article we have here is "Turbulence and Mixing in the Early Universe" as presented to the ICME 2001 conference in Bangladesh. http://arxiv.org/abs/astro-ph/0110012 You will note his paper is evolution/gravitation oriented, but the initial formation of PPP is independent of that.

The standard BB does not deal with any of this. Gibson is trying to point a new way of looking at the BB, but he is still very much on that side.

It is a matter of physics which says the formation of the PPP resulted in the build-up of the electro-magnetic properties of space. The fact that the PPP were positive and negative resulted in movement (swirling about) which resulted in an electric field. The electric field resulted in a magnetic field.

The standard plasma model does not consider the BB in any way. It deals only with the formation of galaxies and stars out of plasma filaments. They do not try to deal with any beginning and often try to consider the universe as being eternal - they don't want any beginning and they don't want any God or Creator.

What Setterfield has done is take a look at the material presented by both sides, used the Bible as a guide for truth, and put together a model which is in accord with all known data. As the potential energy invested by God transferred into the kinetic energy of the PPP, thus forming the Zero Point Energy, space in effect became 'thicker' thus finally impacting (and 'finally' could be a matter of hours, actuallyÉ) the plasma. When the ZPE had built up sufficiently the plasma started to come together to form atoms. With the Bible declaring there was light about twelve hours after the initial moment of creation, we can see these processes were extraordinarily fast.

The Zero Point Energy continued to build through time as the PPP were finished being formed and then started re-combining, releasing the energy when they recombined. This energy then was added to the Zero Point Energy. At the point when the PPP were finished recombining, about 3500 years after creation (or thereabouts), the ZPE finished building and has been maintained on its own feedback cycle ever since. The stabilization of the ZPE is why we do not see quantized red shifts any closer than our local group of galaxies, by the way. The building up of the ZPE caused jerks in energy absorption by atoms, and each time they jerked to a higher energy state, they would produce somewhat bluer, or more energetic light. Plank Particle Pairs are generally accepted in physics and astrophysics. The evidence we have for them (as they no longer exist) is in a slight fogginess we encounter as we look out toward the Cosmic Microwave Background 'fog.' For long distances we can see very clearly, and then things start to get fuzzy. It is this fuzziness which is interpreted as the presence of the PPP.

The primary difference between the two secular models is what happens after the first moments/hours/years (whatever). The BB then depends on gravity to pull things together and the plasma model says no, gravity is much too weak a force to do what we have seen with this initial matter; but plasma filaments, which are seen throughout space, have been the instigators of the objects and formations we see.

2. About gravity. The BB folks do NOT accept gravity as an electro-magnetic manifestation. They are still looking for gravity 'waves.' Einstein considered gravity to be a curving of space itself, and this is still the commonly referred to explanation. On the other hand, SED (stochastic electrodynamics, as differentiated from QED physics, or quantum electrodynamics) physics has been able to explain what mass and gravity are. The mass of subatomic particles arises from the jiggling of the particles by Zero Point Energy waves. As the ZPE built, subatomic particles were jiggled more fiercely and thus took up more space. This resulted in more kinetic energy being imparted to it. Then, on the basis of E=mc^2, this would mean it had more mass. When a charged particle is jiggled, it sends out secondary radiation and, to cut a long story short, this secondary radiation has an attractive property to all charged particles in its vicinity. When the math is done, this attractive property turns out to be the same as what we measure as gravity.

Here, from Bernhard Haisch, Alfonso Rueda and H.E. Puthoff's paper, "Physics of the zero-point field: implications for inertia, gravitation and mass," Speculations on Science and Technology 20, 99-114 (1997) p. 105 quoted here: "If inertial mass, m(subscript)I, originates in ZPF [Zero Point Field]-charge interactions, then, by the principle of equivalence so must gravitational mass, m(subscript)g. In this view, gravitation is a force originating in ZPF-charge interactions analogous to the HRP inertia concept. Sakarov [14] was the first to conjecture this interpretation of gravity. If true, gravitation would be unified with the other forces: it would be a manifestation of electromagnetism.

"Although there were some early attempts to link gravity to the ZPF from a quantum field theoretical viewpoint (by Amati, Adler and othersÉ) as well as within SED [44], the first step in developing Sakharov's conjecture in any detail within the classical context of nonrelativistic SED was the work of Puthoff [15]. Gravity is treated as a residuum force in the manner of Casimir or van der Waals forces. Expressed in the most rudimentary way this can be viewed as follows. The ZPF causes a given charged particle to oscillate. Such oscillations give rise to secondary electromagnetic fields. An adjacent charged particle will thus experience both the ZPF driving forces causing it to oscillate, and in addition forces due to the secondary fields produced by the ZPF-driven oscillations of the first particle. Similarly, the ZPF-driven oscillations of the second particle will cause their own secondary fields acting back upon the first particle. The net effect is an attractive force between the particles. The sign of the charge does not matter: it only affects the phasing of the interactions.

"Unlike the Coulomb force which, classically viewed, acts directly between charged particles, this interaction is mediated by extremely minute secondary fields created by the ZPF-driven oscillations, and so is enormously weaker than the Coulomb force."

Information Source.The references are in Anthony Peratt's "Physics of the Plasma Universe" and Donald E. Scott's "The Electric Sky," as well as others. But those are a good start.

Notes supplied by Barry Setterfield, http://barrysetterfield.org, 1/09/2010

Lambert Dolphin



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March 29, 2000; January 22, 2009. (CV March 22, 2009). December 22, 2022.