Of Big Bangs and Small Fizzes

One of the most amazing aspects of life in the Universe is that the human brain can contemplate the Universe! But this essay is not concerned with philosophy. Although we have learned and are learning a tremendous amount about the Universe, we are engaged in model-making to bridge the gaps between the known and the unknown. This essay reviews three of the many possible models: The Conventional, the Quasi-Steady-State (QSS), and the Continuous-Steady-State (CSS) perspectives.

We first consider the Conventional viewpoint.

According to the latest determination, the Universe began with a Big Bang around 14 billion years ago (that is, 14 followed by nine zeros, or 14,000,000,000). A paltry figure compared to the trillions bandied about nowadays. (One trillion is equal to 1 followed by 12 zeros.) But it is not my purpose here to get caught up in cosmological zerography. I am not concerned with the exact date; eventually, I suppose, it will be 20 followed by nine zeros, and so forth. 

Just how much “stuff” are we talking about? Based upon what we know: There are some 1080 neutrons + protons + electrons in the universe. A neutron or proton weighs 1.67 X 10-27 kilograms, but an electron is much lighter. If we multiply 1080 by 1.67 X 10-27, and somewhat reduce to allow for the light electrons, we get 1053 kilograms as the mass of the Universe.

Before the Big Bang, the 1053 worth of kilograms contracted (via a process known as the Big Crunch, of course) into an unimaginably hot and small “singularity.” We can almost visualize the grand event as it took place; let not familiarity, however, breed contempt! Although cosmologists can be accused of being starry-eyed and they are frequently incredible, they realize that you and I would swallow the Big Bang much more easily if it followed something plausible, such as a Big Crunch.

In any event (it is almost impossible to refrain from a pun, at this point), the hot ball began to expand, with the outer layer going off at the speed of light (almost). The universe has thus been expanding ever since, for 14 billion years. Unfortunately, it continues to expand (perhaps even more rapidly than before) despite heroic efforts by cosmologists to explain how it will stop. 

If it has been expanding, at the speed of light, what is the radius of the universe? The speed of light (300 million meters/sec) multiplied by 14 billion years comes out to 1.3 X 1026 meters, or the diameter is 2.6 X 1026  meters. Not particularly impressive because we can’t appreciate how huge is a value such as 1026.  

Before we proceed, let’s tackle a one-paragraph review of Basic Cosmology: If you take an object that is as large as the sun, and somehow heat it to a few thousand degrees, it will cool off in a relatively short time. What has kept the sun glowing for some 5 billion years? The answer is, that it converts matter (m) into energy (E) in accordance with Einstein’s equation, E = mc2, where c stands for the velocity of light. Yes, the sun has lost a great deal of weight, but there is still a lot left over. Not to worry—it can keep glowing for another 5 billion years. According to the above, therefore, the present-day mass of the universe, 1053 kilograms, could substantially decrease as matter is exchanged for energy (or increase as energy is exchanged for matter).

Because some daunting questions have never been answered, there are some unhappy people out there, and this even includes a few cosmologists. Why did the universe start out at that time? What was there before? How could all of this stuff (1053 kilograms) begin as if it was compressed into a small point called a singularity? The Conventional answer to all of this is “Somehow” and/or “The Laws of Physics were different.” 

A favorite conjecture is that there is some kind of mysterious “Dark Matter” out there. The Dark Matter may stop the expansion by pulling it all together via gravitational attraction. (A sample of Dark Matter has not yet been captured for analysis on Earth.) Then, eventually, all of those kilograms will contract to begin again the never-ending Big Crunch—Big Bang cycle. (New York City, along with the rest of the solar system, would have disappeared long before that happens.) 

If we look out the window, it appears as if the Earth is the center of the universe. But our egos suffered a damaging blow from Nicolaus Copernicus, in the 1500s, when he showed that it is an optical illusion—we are actually rotating around the Sun. Now here are other optical illusions: Why can’t we see where the Big Bang occurred? Why are the galaxies receding from us as if we are the center of the universe? The answers to this are given in Fig. 1:

Fig. 3-1

Fig. 1- Construction used to demonstrate that it is not possible to determine the location of the Big Bang relative to the Earth. (a) Two-dimensional depiction of a simplified “universe.” The Big Bang is located at B, the Earth is at E, and a galaxy that is used as an example is located at P. All galactic objects are receding from B with velocity proportional to distance from B. The lines through each object are vectors representing recession velocity and direction, but vector arrows are omitted for the sake of clarity. (b) Vector components of the recession of P from B. (c) Vector components of the recession of P from E. (d) The universe as seen from E, including the nearest galaxies and B. Although the galaxies are actually receding from B, this information is hidden because they actually appear to be receding from E.
Consider the two-dimensional depiction of a simplified “universe” in Fig. 1(a). The Big Bang occurs at B, the earth is at E, and a galaxy that is used as an example is located at P. In accordance with the expanding universe, all galactic objects are receding from the Big Bang at B with velocity proportional to distance from B. The lines through each object are vectors representing recession velocity and direction (but arrows are omitted for the sake of clarity). (b) shows vector components of the recession of galaxy P from the Big Bang at B, while (c) depicts components of the recession of galaxy P from the earth at E. Finally, (d) shows the universe as seen from the earth at E, including the nearest galaxies and Big Bang at B. Although they are actually receding from the Big Bang, this information is hidden because all of the galaxies, including the Big Bang  itself, actually appear to be receding from the earth at E. Looking in any direction from E (the Earth), we see the expanding universe. (Objects that are receding from us at nearly the speed of light, are invisible to us because their photons never reach the earth.) In other words, don’t expect to find exotic places such as the “center of the universe,” or “ground zero” where the Big Bang occurred. One can easily show, via simple trigonometry, that one part of the universe looks pretty much the same as another, independent of the location of the observer. It makes very little difference whether you are in the Milky Way or Andromeda or wherever; galaxies recede from each observer and from each other, and at the same rate, on average, no matter where you are staring off into space. (This is only approximately true, because the universe is not perfectly uniform. There are clusters in which galaxies are relatively close to each other. The Milky Way is part of the “Local Group” cluster. Also, the heavens may appear to be very non-uniform to “people” that live on a planet near the outer edge of the universe. Perhaps Earth is near the center of the universe, after all!)
There are three reasons for believing in a Big Bang. First, from the speed with which galaxies are receding from us, we can calculate that the ingredients were all together in one “pot” 14 billion years ago. Second, in physics laboratories here on earth, we have determined the characteristics of elementary particles (electrons, neutrons, protons) and atoms, and so forth; the number of neutrons relative to protons is in agreement with what one would expect coming out of a hot primordial plasma. Third, as the hot singularity expanded, it cooled off; after 14 billion years, we expect the outer region to be at a temperature of 2.7 degrees kelvin, and that is exactly what is measured (indirectly, of course). How could the singularity give birth to the 1053 kilograms of matter? The cosmologists can’t explain it. Somehow, it happened with the aid of physics that is different from the everyday physics that we know at lower temperatures. But this is a dangerous proposal, in my opinion, because it is exactly what the “Intelligent Design” people claim—that a deity created the universe by inventing a special physics, and then departed from the scene when his/her work was done.

Regardless of the true situation, the cosmologists have calculated the temperature of the universe, as a function of time, as the hot ball expanded. This is portrayed in Fig. 2. (Quantitative details in the present essay are mostly taken from Principles of Physical Cosmology, by Phillip J.E. Peebles [1].) At time equal to 0.1 second after the Big Bang, the temperature was 3.5 X 1010 kelvins (or 35 billion degrees). Atomic nuclei were disrupted, so that we had free neutrons, protons, and electrons. Temperature corresponds to the average kinetic energy of motion of the neutrons, protons, and electrons; 35 billion degrees has to be visualized as a chaotic soup in which the particles were rushing about at fantastic speed (but which never exceeded the speed of light, 3 X 108 meters/second).

Fig. 3-2
Fig. 2- Temperature versus time during the first few hours of the Big Bang.

The scales of Fig. 2 are logarithmic; therefore, extended to the left, the curve soon reaches the temperature of the upper edge of the plot, 100 X 1010 = 1012 kelvins. But do not be deceived by the logarithmic scales of Fig. 2: there is a tremendous difference between T = 1012 and 1011 kelvins (such as the difference between the normal body temperature of 310 kelvins and a frozen, lifeless form at 31 kelvins).

There appears to be a simple proof that the universe is, indeed, finite like a sphere. Heinrich W.M. Olbers (1758-1840) pointed out that the night sky of an infinite, homogeneous universe should be bright, no different from the daylight sky. This notion is called Olbers’s paradox. Wherever we look, in an infinite universe, we should see nearby stars and galaxies, and farther-away stars and galaxies between the nearby objects, and still more distant stars and galaxies forming a background, until the entire sky is everywhere lit up like a bright, sunlit sky. (It would be a bit blotchy because there are dark clouds of cosmic “dust” that obscure many regions of the galactic structure.) To a first approximation, however, it appears as if our universe is finite, with the earth near the center, because the night sky is uniformly dark, and that lit-up background of stars and galaxies is missing.

There is just one Big Problem—if the universe keeps expanding, if we are to believe the dire predictions of some cosmologists, we are headed for a dismal end; we are, indeed, doomed to terminate like a cinder of coal after the fire goes out. For example, in the November 1999 issue of Scientific American there appeared an article titled “The Fate of Life in the Universe,” by Lawrence M. Krauss and Glenn D. Starkman [2]. Here are some nightmarish excerpts (with gaps eliminated to make for smoother reading):

The culprit is the expansion of the universe. The universe will become so cold and empty that life, no matter how ingenious, will perish. Intelligent beings will need to find new sources of energy, such as cosmic strings; natural processes—such as outbreaks of black holes— will erode linear concentrations of energy. A civilization could use a black hole to convert matter into energy; matter will become so diluted that civilization will not be able to safely build a black hole large enough to collect it. Over time, the amount of matter we can see will decrease, and the number of worlds our starships can reach will diminish. A new era will commence: [there will be] slow evaporation of black holes. After 1033 years or so, the accessible matter will become so concentrated that most of it will collapse into black holes. The universe might be filled with a network of cosmic strings; intelligent beings might try to cut one, congregate around the loose ends and begin consuming it. We still have many billions of years to design new physical incarnations to which we will someday transfer our conscious selves. These new “bodies” will need to operate at cooler temperatures and at lower metabolic rates. If a new form of life could lower its body temperature, [it could not cool] below about 10-13 kelvin. [No misprint — see the accompanying figures.] At 155 kelvins, an equivalently complex organism could think at half the speed but consume a quarter of the power. Consider an alarm clock that consists of two small balls that are taken far apart and then aimed at each other and released; eventually, the clock will run up against constraints from Heisenberg’s uncertainty principle. All organisms would ever do is relive the past, having the same thoughts over and over again. If the quantum mechanics of gravity allows the existence of stable wormholes, life-forms might circumvent the barriers erected by the speed of light, visit parts of the universe that are otherwise inaccessible, or perhaps they could construct “baby” universes.

Is there no hope for us? All of this talk about black holes, cosmic strings, Heisenberg’s uncertainty principle, wormholes, baby universes, and so forth—almost all of it is conjectural. The contortions of these cosmologists are reminiscent of the epicycle models used to “explain” the motions of the sun and planets around the earth. The universe cannot be that complicated! But there is more: If the Krauss-Starkman article is like a main course, then the dessert was served up, two months later, by Lawrence H. Ford and Thomas A. Roman in the January 2000 issue of Scientific American [3]. Now we have also to digest negative energy, warped drives, and space-time bubbles. 

It is frequently said that there is nothing new under the sun (or, in this case, the universe). It so happens that Fred Hoyle and other cosmologists, around 1956, argued that the universe is in a steady state, that the large-scale features of the expanding universe do not change, and that its density is maintained constant by the creation of new matter (hydrogen) [4]. Knowledge gained in the intervening years has somewhat modified their viewpoints; today they advocate a quasi-steady-state (QSS) universe that oscillates with a period of, very approximately, 100 billion years, as depicted in Fig. 3, which is taken from “A Different Approach to Cosmology,” by Geoffrey Burbidge, Fred Hoyle, and Jayant V. Narlikar, in the April 1999 issue of Physics Today [5]. A short editorial comment states that “In this unorthodox assault on mainstream cosmology, three venerable stalwarts argue for a quasi-steady-state universe, with some quasars quite nearby and no Big Bang.” Other people allied with this group include Halton C. Arp and Margaret Burbidge [6]. (Fred Hoyle died on 20 August 2001, at the age of 86.)

Fig. 3-3

Fig. 3- Oscillation of the cosmic scale factor, taken from the quasi-steady-state paper by Burbidge et al. [5]. The period of a single oscillation is 100 billion years.

There is something terribly unbelievable in the above recital by Krauss-Starkman — namely, that our present universe arose out of the ashes of a Big Crunch — Big Bang sequence, but it will simply terminate as if it is a cold cinder of coal. If the Big Bang took place “one day” some 14 billion years ago, why was it a one-time occurrence? Since our present universe will expand forever (according to Krauss-Starkman), why did the previous universe collapse into a Big Crunch? What is the justification for cosmic strings, wormholes, and baby universes? But in cosmology, according to the QSS model, the future should become the past. The QSS cosmologists advocate a universe that will eventually contract to yield the equivalent of a Big Crunch, Big Bang sequence.

In Fig. 3, according to Burbidge et al., it will take 36 billion years more before the “present epoch” reaches the top of the curve. During this period, newly-created hydrogen will add sufficient mass so that, when the Universe arrives at the top, it will stop expanding, and start to contract. This does not answer philosophical questions such as “When did time begin?,” but at least it creates a Big Bang out of something plausible.

The QSS people are paying a price, however, for their minority view that the so-called Big Bang is the recurring feature of a quasi-steady-state universe. According to “Heaven’s Gatekeepers: The Galactic Battle for Telescope Time,” by Tom Scocca in the September 1999 issue of Lingua Franca [7], cosmologists who question the orthodox view have to “battle for telescope time.”

The quasi-steady-state universe presents some severe problems compared to the conventional view in which death gradually takes over.  The greatest challenge is this: How is hydrogen regenerated?  In theory, the answer is obvious:  Replace E = mc2 with m = E/c2 ; that is, reverse the process by which mass is converted into energy.

If a hydrogen atom (proton + electron, or neutron) disintegrates, how much energy is given off? The answer is E = 15.05 X 10-11 joule. This value is rather meaningless to a non-specialist, but we can breathe life into it by remembering that the energy appears as a photon, a minuscule wave packet that travels at the speed of light, and whose frequency is given by f = E/h, where h is Plank’s constant. Substitution into this equation yields, if a hydrogen atom disintegrates, a photon whose frequency is 2.272 X 1023 Hz. Now that is a familiar figure that can be identified: The typical gamma ray has a frequency of 3 X 1021 Hz, so disintegration of a neutron generates a  gamma ray that is 76 times as strong as the typical gamma ray. An impressive, but not impossible, value. (A typical X-ray has a frequency of 6 X 1018 Hz, so the typical gamma ray is 500 times as strong as a typical X-ray.)

If two 2.3 X 1023 Hz gamma ray photons crash into each other, what will happen? Not much, because photons ignore each other; they fly through each other at the speed of light. To give birth to a hydrogen atom or neutron, the gamma ray has to be absorbed by hitting a solid object, such as a relatively heavy atomic nucleus. The nucleus then gains a neutron by converting gamma ray energy into mass, becomes unstable as a result, and then expels the neutron (hydrogen atom).

Is this a fairy tale? Perhaps; to the best of my knowledge, the generation of gamma rays that have a frequency of 2.3 X 1023 Hz, or higher, are beyond the capability of earth-based laboratories. (The Large Hadron Collider that straddles the Franco-Swiss border may soon demonstrate reasonably efficient conversion of energy into matter.) But there are natural laboratories — Black Holes in which high-frequency gamma rays may be commonplace. The philosophy behind the QSS model is that hydrogen is regenerated, and the only facility on the “horizon” that has sufficiently energetic reactions may be Black Holes.

How do the putative hydrogen atoms bubble out of the Black Hole interior and into intergalactic space? It was originally claimed that nothing escapes from a Black Hole, but this condemnation may be weakening. First, the effective mass of a photon is proportional to its frequency; very-low-frequency photons (such as low-frequency radio waves) may be light enough to escape from the gravitational pull of a Black Hole. Second, we now hear of material ejected along the axis-of-rotation (north and south poles) of a spherical Black Hole. (See, also, [8].)

The regeneration and distribution of hydrogen are subjects for nuclear physicists and cosmologists. The paper by Burbidge at al. does not touch upon these matters.

If we are generating hydrogen, there is still one important ingredient missing to complete a steady-state model: it is “entropy.” This romantic-sounding word is shorthand, actually, for the increase in randomness, disorder, and chaos as the universe ages. (But one should not attach any anthropomorphic meaning to these age-related deficits.) How can the chaotic behavior of electrons, neutrons, protons, etc., be reversed?

Entropy is increasing as nuclear reactions, in the interior of stars, are converting matter into energy that, for the most part, ends up as heat. The reversal of E = mc2 has to be accompanied by the reversal of entropy-increase. A familiar refrain is that “the entropy of the universe is increasing”; that is, much of the mass, and nonthermal forms of energy, are degenerating into heat; as Krauss-Starkman imply, we eventually get cold, dark matter. What happens to all of the energy that was converted into heat? It becomes a cosmic background radiation that radiates outward, away from the putative Big Bang center, as the universe continues to expand and cool off. Not a very exciting ending, and considerably less dramatic than the end of the earth, which is scheduled to occur in 5 billion years, when the sun becomes unstable.

It is a common misconception that entropy always has to increase. It has to increase for the system as a whole, but for some sections of the system, the entropy can decrease. A living body, taking in a chaotic assortment of amino acids, assembles them into organized proteins, and so forth, that have less entropy than the original raw materials. Another example is the inside of a refrigerator: The cold foodstuffs have less entropy than they had when at room temperature; but for the system, which includes the entire kitchen, entropy increases because of the heat supplied by the refrigerator’s compressor.

The regeneration of hydrogen, if it proceeds as outlined above, is automatically accompanied by entropy decrease. The 2.3 X 1023 Hz gamma ray, before it strikes the heavy nucleus, has high entropy corresponding to its high frequency; the nucleus, ideally, is standing still, with zero entropy. This scenario is illustrated in Fig. 4. In (a), the gamma ray, traveling at the speed of light, strikes a nucleus. The latter absorbs the ray, converting it into a neutron, which destabilizes the nucleus. In (b), the nucleus returns to its former state by ejecting a neutron. The  newly-generated neutron is, ideally, released “standing still,” with zero entropy. In other words, the entropy of the incoming gamma ray is (ideally, again) wiped out.

Fig. 3-4

Fig. 4 – The idealized conversion of energy into matter. In (a), a gamma ray, of frequency 2.3 X 1023  Hz (or higher), traveling at the speed of light, strikes a nucleus. The latter absorbs the ray, converting it into a neutron, which destabilizes the nucleus. In (b), the nucleus returns to its former state by ejecting a neutron. The latter departs at a relatively slow velocity.

The final problem associated with the Quasi-Steady-State model is the End Points of Fig. 3. If, as Burbidge et al.state, there is no Big Bang, what takes its place? Let’s try to avoid “new physics,” especially any perspective that allows the universe to start out as a point, a singularity. One possibility is that the universe starts out as a sphere consisting of solidly-packed neutrons and protons.

What is the diameter of a neutron? And of a proton? We don’t know exactly, but a uranium nucleus has a diameter of 1.36 X 10-14 meter and contains, fairly closely packed, 92 protons and 146 neutrons, for a total of 238 nucleons. (Protons and neutrons, inside the nucleus, are “nucleons.”) From this, plus the fact that there are 1080 nucleons in the universe, we can calculate that the QSS version of the Big Bang is a sphere with a radius of 5.093 X 1011 meters. Now, finally, we are getting down to earth, because the average radius of the earth’s orbit around the sun is 1.496 X 1011 meters. So my interpretation of the QSS Big Bang is a sphere whose radius is 3.4 times that of the earth-to-sun radius.

This essay ends with a Continuous-Steady-State (CSS) model. It is characterized by a universe that never changes, except for minor deviations from an average. Applied to our universe, which is expanding, the concept requires a return universe that is contracting. Visualize a huge loop, as portrayed in Fig. 5, in which the left-hand branch is expanding while the right-hand branch is contracting. Hydrogen is continuously recreated (as entropy is continuously decreased) in Black Holes.

Fig. 3-5

Fig. 5- Model of a Continuous-Steady-State universe. Matter is recreated in accordance with m = E/c2. Instead of a Big Bang, we have many Small Fizzes, perhaps in Black Holes. A period of 100 billion years is required to traverse the loop.

The major problem with the CSS model is that space has to curve. How can we tell that a space is curved? Launch a photon, say, into a vacuum: if the photon eventually returns to the original starting point, its locus must have included curved space. In “straight” space, if we want an object to follow a curve, we have to give it a lateral shove; in curved space, without a lateral shove, the object may return to its birthplace. In the CSS model, what goes up eventually goes around and comes back to the starting point, neatly compressed into a Big Crunch package. This is but one illustration of curved space. If it is correct, and if we could see the equivalent of 100 billion years into the distance, then we could see “ourselves” as we were 100 billion years ago! But we cannot tell, looking up into the sky, if space is curved; we have to assume that what we see has come to us by traveling along a straight line, more or less. It could be a lot less — in fact, the curvature of space may be a ubiquitous phenomenon. Consider that an electron, moving along a circular path, generates an electromagnetic field. The field, known as synchrotron radiation, has important applications in physics, chemistry, biology, and medicine (and in politics since battles always seem to be going on over the sites for high-powered synchrotron generators). But something mysterious goes on when an electron is captured by an atomic nucleus — it furiously goes around in circles (or ellipses) but does not generate an iota of synchrotron radiation! It is as if the electron “thinks” that it is traveling in a straight line (in which case it generates a magnetic field, but not an electromagnetic field). Aside for “somehow” or “quantum mechanics,” there is no sensible explanation for this weird behavior, yet it is at the heart of every atom.  

The Continuous-Steady-State universe never dies; it is always in transition. But what about time? When did time begin? There is also a conjecture here: The movement of every molecule, atom, electron, proton, neutron, and so forth is governed by four precise laws (yes, “laws,” because there are no exceptions): gravitation, electromagnetic, strong force, and weak forces. When the universe recycles, all of its constituents recycle exactly, fully predetermined by the four basic laws, as they did, say, X billion years previously. Thus time never had a beginning, nor end, but keeps recycling with a period of X billion years. The joy in all this is that man comes alive, again, every X billion years, but let us temper this joy by subtracting the recurrent horror, the endless litany of man’s inhumanity to man.

One final thought: Perhaps you have been wondering about those “Small Fizzes” in the title of this essay. They evolve out of a distaste for the Big Crunch — Big Bang extravaganza every 100 billion years or so. Perhaps rebirth is a continuous process that is taking place in all of those “black holes,” where old and new matter come together in a never-ending stream, forming a plasma at tremendous temperature, which starts life anew like molten iron being poured out of a ladle (and launched into space that is curved). This model is the opposite of a Big Bang; hence, I call it a Small Fizz.

There is something very neat about a steady-state universe. It may be all wrong, but it has a certain philosophical appeal [9].


There are some 1080 neutrons + protons + electrons in the universe. A proton weighs 1.673 x 10-27kilograms, a neutron 1.675 x 10-27kg, and an electron 9.109 x 10-31 kg. As a rough first calculation, 1080 x 1.673 x 10-27  = 1.673 x 1053 kilograms. If this figure is somewhat reduced to allow for the relatively light electrons, we get an approximate value of 1 x 1053 kg. For the purposes of this essay, this is sufficiently impressive. 

To get the radius of the universe, multiply the velocity of light by the age of the universe: There are 9.46 x 1015  meters in a light-year, so 9.46 x 1015 x 14 x 109 = 1.32 x 1026 meters as the radius of the universe. 

Referring to Fig. 1: A galaxy that is used as an example in what follows is located at point P. It is receding from the Big Bang at B with velocity vB = H0r, where r is the distance from B to P, and H0 is the Hubble constant [named after Edwin P. Hubble (1889-1953)]. Velocities are broken up into horizontal (H) and vertical (V) vector components. In Fig. 1(b),
Velocity of P relative to B, the H comp = H0r cos ø,
Velocity of P relative to B, the V comp = H
0r sin ø,
and it turns out that, in Fig. 1(c),

Velocity of P relative to E, the H comp = H0p cos q,
Velocity of P relative to E, the V comp = H0p sin q.
In other words, the velocity of galaxy P relative to E (earth) is only a function of distance to the earth (p) and direction to the earth (q). The velocity is completely independent of distance to the Big Bang (r) and direction to the Big Bang (
ø). An astronomer on earth, looking at P, can only measure p and q, and remains completely ignorant about the “center of the universe.” According to the above, galaxy P is receding from the earth E with velocity H0p. This is depicted in Fig. 1(d). Also shown are several other galaxies that are relatively near the earth in (a). In each case, the velocity vector in (d) has been drawn, to scale, to represent velocity relative to E. This is what our earth-bound astronomer sees.

If a hydrogen atom disintegrates, we substitute in E = mc2 as follows (for the velocity of light, the more exact value, 2.998 X 108  meters/second, is used):
E = 1.675 X 10-27 X (2.998 X 108)2 = 1.505 X 10-10 joule.
To get the photon’s frequency, substitute in f = E/h, where h = Plank’s constant:
f = 1.505 X 10-10 /6.626 X 10-34 = 2.272 X 1023 Hz.

Assuming that the Big Crunch ends with nucleons (neutrons and protons) packed together as they are in a uranium nucleus: The volume of a sphere of radius r is given by V = 4 r3/3, so the volume of a uranium nucleus is
V = 4
(6.8 X10-15 )3/3 = 1317 X 10-45 cubic meters.
Dividing by 238 nucleons, the average volume of a nucleon is 5.534 X 10-45 m3. The volume of the Big Crunch (very approximate, of course) is 5.534 X 10-45 X 1080 = 5.534 X 1035 m3. Substituting in V = 4
r3/3, and solving for r, we get a radius of 5.093 X 1011 meters.


[1] Phillip J.E. Peebles, Principles of Physical Cosmology, Princeton Univ. Press, 1993.
[2] Lawrence M. Krauss and Glenn D. Starkman, “The Fate of Life in the Universe,”  Scientific American, November 1999.
[3] Lawrence H. Ford and Thomas A. Roman, “Negative Energy, Wormholes and Warp Drive,” Scientific American, January 2000.
[4] Fred Hoyle, “The Steady-State Universe,” Scientific American, September 1956.
[5] Geoffrey Burbidge, Fred Hoyle, and Jayant V. Narlikar, “A Different Approach to Cosmology,” Physics Today, April 1999.
[6] Govert Schilling, “New Results Reawaken Quasar Distance Dispute,” Science, 11 Oct 2002.
[7] Tom Scocca, “Heaven’s Gatekeepers: The Galactic Battle for Telescope Time,” Lingua Franca, Sept 1999.
[8] D. Michael Crenshaw, “Mass Outflow in Active Galactic Nuclei,” Science, 25 May 2001.
[9] Sid Deutsch, Return of the Ether: When Theory and Reality Collide, SciTech Publishing, 1999.

(Published in a shorter version in IEEE Engineering in Medicine and Biology Magazine, Nov/Dec 2001.)



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