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5 Understanding the Universe, and Open-Ended Process

5 Understanding the Universe, and Open-Ended Process

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The Fundamental Physical Forces in the Universe



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in the physical universe or even that we will ever be able to understand

everything. Our observation capabilities are finite, and so are out

capabilities of systematization, as attested by the famous Gödel

theorems.18 A corollary in these theorems holds that in any mathematical

system which is consistent (either “de facto” or assumed to be so) it is

impossible to find the proof of consistency within it. But this does imply

only that the wonderful process of understanding the universe is for us an

open-ended process and will remain so in the future, no matter how large

and how good computers are available.

Some among us may not like it at all, but only God understands

everything. However, this does not detract a bit from the beautiful

intellectual adventure of man understanding the universe. The science of

physics, through the work of a handful of geniuses and a legion of obscure

investigators, has lead us to a most unified and most coherent vision of

the universe, in which hard experimental facts and elegant mathematical

theories are interconnected in an admirable way. Never mind that often

these “hard” facts and theories are almost unavoidably mixed with “soft”

speculations. In the long run, and precisely because the Creator of both

men and universe has endowed us with an intellect, however fallible,

able to detect the true ring of truth, we may be confident that the hard

facts and the good theories will be incorporated in a future better vision

of the cosmos, and the soft speculations will be discarded in due time.

Bibliography

1. L. Dolan, “Unified field theories”, in “Encyclopedia of Physical Science and

Technology”, Vol. 14, pp. 220–30 (New York: Academic Press, 1987).

2. P. Langacker and A.K. Mann, p. 22 “Phys. Today” (December, 1989).

3. R. Eisberg and R. Resnick, “Quantum Physics of Atoms, Molecules, Solids, Nuclei

and Particles”, pp. 685–92 (New York: John Wiley and Sons, 1974).

4. L.A. Ahrens et al. (E734 experiment) Phys. Rev. Lett. 54, 18 (1985); K. Abe et al.,

Phys. Rev. Lett. 62, 1709 (1989).

5. D.J. Gross, p. 39, “Phys. Today” (January 1987).

6. G. Arnison et al. (UAI collaboration), Phys. Lett. B 166, 484 (1986); C. Albajar

et al., Z. Phys. C 44, 15 (1989); R. Ausari et al. (UA2 collaboration), Phys. Lett. B

186, 440 (1987).



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7. J.S. Trefil, “From atoms to quarks”, Chap. 13 (New York: Ch. Schribner’s Sons,

1980).

8. Ibid., Chap. 8.

9. S.L. Jaki, “God and the Cosmologists”, pp. 129–135 (Washington D.C.: Gateway,

1989).

10. J.S. Trefil, “From atoms to quarks”, Chap. 7 (New York: Ch. Schribner’s Sons,

1980).

11. R. Eisberg and R. Resnick, “Quantum Physics of Atoms, Molecules, Solids, Nuclei

and Particles”, p. 708.

12. Fang Li Zhi and Li Shu Xian, “Creation of the Universe”, p. 23 (Singapore: World

Scientific, 1989).

13. R. Loudon, “The Quantum Theory of Light”, 2nd. ed., Chap. 1 (Oxford: Claredon

Press, 1983).

14. Planck used in fact h instead of ħ, introduced later by Dirac, but this is of no

consequence for our purpose.

15. Max Planck, “Physikalische Abhandlungen und Vortráge”, 1:666 (Braunschweig:

Friedr. Vieweg & Sohn, 1958). See also “Planck’s Original Papers in Quantum

Mechanics”, edited by H. Kangro (London: Taylor and Francis, 1972).

16. Max Planck, “Wissenschaftliche Selbstbiographie” (1948), p. 374, in “Physikalische

Abhandlungen”, 3:374 (Braunschweig: Friedr. Vieweg & Sohn, 1958). See also

“Planck’s Original Papers in Quantum Mechanics”, edited by H. Kangro (London:

Taylor and Francis, 1972).

17. S.L. Jaki, “Brain, Mind and Computers”, pp. 214–222, paperback edition (Gateway:

South Bend, Indiana, 1978), and references therein.



Chapter 6



Cosmology and Transcendence



6.1. Towards the Confines of the Universe

As illustrated in the previous chapters, one of the chief achievements of

our century has been to give, for the first time in history, a coherent

quantitative (even if tentative) description of the entire physical universe.

Physicist and astronomers have been amassing a hugh amount of new

facts, and reasonable interconnections amongst these facts, which point

out with increasing evidence to the conclusion that our Universe was

created some fifteen or twenty thousand million years ago in a primordial

event of incredible energy known as the “Big Bang”. According to Prof.

Jastrow,1 founder and director of the NASA Goddard Institute, these

discoveries are truly fascinating “partly because of their religious

implications and partly because of the peculiar reactions of my (scientist)

colleagues before them.”

Jastrow, according to whom scientists did not expect to find evidence

for an abrupt beginning, summarizes succinctly the story of these

remarkable discoveries. In 1913, Slipher, which was looking for solar

systems in formation, discovers that the nebula identified as Andromeda

is an “island universe”, similar to our galaxy, which is receding from it at

a fantastic velocity, as indicated by the Doppler shift of the emitted light.

Later, Hubble and Humason extend their observations to more and more

distant galaxies and confirm that the recession of galaxies is universal

and that the speed of this recession of the galaxies increases

approximately in proportion with their distance to ours. Some years later,

in 1917, Einstein applies to the cosmos as a whole his new theory of



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The Intelligible Universe



general relativity. Because he expects a static cosmos, he includes at first

in his equations a so called cosmological term, which opposes the

universal attraction of the gravitational force. This cosmological term

was later considered by Einstein “the greatest blunder of his life”, but

present day cosmologists, refusing to forget it altogether, have invoked it

again, in connection with “inflationary” cosmological models. Very soon

after Einstein’s equations were set forth, the dutch astronomer de Sitter

finds special solutions which predict an expanding universe, and, a few

years later, the Russian mathematician Alexander Friedmann finds a

complete set of solutions (see Chapter 4) which includes one ever

expanding solution (k < 0), one “marginally” expanding solution (k = 0),

and one oscillating solution (k > 0). By that time news begin to spread

out in the scientific community that the observations of Hubble and

Humason made with the most potent telescopes then available, seem to

support the idea of a non-static, expanding universe.



Fig. 6.1. Slipher.



Einstein travels to visit Hubble in the United States and he appears to

overcome his skepticism about the expansion. While in America, he

meets the Belgian priest George Lamtre, who had worked out a general

and complete set of solutions to Einstein cosmological equations, both

with zero and non-zero cosmological term, and had shown convincingly

that no static solution was stable. His work had deserved the support of



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113



the famous British physicist and mathematician Sir Arthur Eddington,

who was instrumental in giving wide publicity lo Lemtre’s work.



Fig. 6.2. Einstein & Lemtre.



The Second World War and the events preceding it in Germany

distracted the attention of many prominent european and american

physicists away from cosmology and often to matters related to the war

effort. Some years after the end of the war, as mentioned in previous

chapters, G. Gamow’s young collaborators R. Alpher and R. Hermán

predicted the existence of a remnant background radiation provenant from

the “primeval fireball” of incredibly dense energy and elementary

particles, out of which nuclei and atoms, galaxies and stars would later

be formed. It is interesting to note that they were working on the ground

of the “Big Bang” model, somehow implicit in the expanding solutions

of Einstein cosmological equations and explicitly pointed out by



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Lamtre when he spoke of a “primordial egg” of extremely high mass

and energy out of which the material universe evolved. By the late 40’s

and early 50’s there was a rival theory of the “Big Bang” for the origin of

the cosmos, the so called “steady state” theory, in which the universe

remained more or less the same as time went on, but continuous creation

out of nothing had to be assumed to compensate for the expansion. This

non-energy-conserving theory,2 proposed by Bondi, Gold and Hoyle,

somewhat surprisingly, enjoyed considerable favour in wide scientific

circles, until the experimental confirmation of the background thermal

radiation by the American radioastronomers A.A. Pencias and R. Wilson,

in 1965, difficult to explain by the “steady state” theory, inclined the

balance of the scientific consensus in favour of the “Big Bang”

alternative. In the last decade refined experimental observations have

confirmed the blackbody and isotropic character of this radiation, and

astronomical observations by powerful telescopes in the whole range of

radiation have attested to the universal expansion up to the limits of the

observable universe.



Fig. 6.3. Alpher & Herman.



For the “philosophers” of the Enlightenment, as well as for most

nineteenth century scientists following their steps, the universe was



Cosmology and Transcendence



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infinite and eternal, and matter continuous and indefinitely subdivisible,

in contrast with the well known facts of science today. The best available

experimental data seem to be also in contradiction with the ancient

concept of the universe3 as subject to the iron law of “eternal returns”. As

illustrated by the story of the modern development of scientific

cosmology, the conception of the cosmos which it seems to support, often

against the hopes of those who have contributed decisively to shape it,

seems to be more in consonance with the old biblical conception of a

laterally created universe than with the ancient conceptions of past prechristian cultures. In words of Prof. Jastrow: “For the scientist who has

lived by his faith in the power of reason, the story ends like a bad dream.

He has scaled the mountains of ignorance; he is about to conquer the

highest peak; as he pulls himself over the final rock, he is greeted by a

band of theologians who have been sitting there for centuries.”

6.2. Observable Data and Big Bang Model

The Big Bang model is based upon a number of well established

observational facts, which can be summarized as follows:

6.2.1. Approximately isotropic distribution of galaxies in space

From our point of observation (our Earth) the number of observable

galaxies aside from our Milky Way, seems to be more or less the same,

no matter the direction at which we point out our telescope. Recent

investigations of the variation of the density of galaxies with distance to

ours, reported the existence of large local concentrations of galaxies (the

so called “great attractor” and the “great wall”) as well as large voids in

cosmic space. These reports have not been supported by close scrutiny.

At a sufficiently large scale the concentration of galaxies can be

considered roughly homogeneous and isotropic. This means that,

observing from another distant point, the universe would look also quasihomogeneous and quasi-isotropic in galaxy content.



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The Intelligible Universe



It was mentioned before (Chap. 3) that the fact of a dark sky at night

would be contradictory with an infinite universe (Olber’s paradox). From

this fact we are allowed to conclude that the observable universe is finite.

(This is equivalent to say that the farthest away galaxies are escaping

from us at nearly the speed of light, but no more, otherwise they would

not be observable).



Fig. 6.4. Velocity (redshift) vs. apparent magnitude (distance) for a large representative,

sample of galaxies. The upper points, corresponding to brightest cluster galaxies, have

the largest uncertainties.



6.2.2. Universal recession of the galaxies

The observations of Hubble and Humason, abundantly confirmed by

further and more precise observations, lead to the enunciation of

Hubble’s law:

H = R / R ≈ (75 ± 25) km/s ⋅ Mpc

(6.1)

0



0



0



Cosmology and Transcendence



117



where R0 is the recession velocity of a galaxy (determined from the

Doppler shift of its emitted light) and R0 the distance to us (determined

by various methods, f.i., by the apparent luminosity of the brightest stars

of the galaxy, assumed to be approximately the same for all galaxies).

The Megaparsec, as noted previously, is an astronomical unit of distance

which is given by

(6.2)

1 Mpc ≈ 3.26 × 106 light years

This well established fact of the universal expansion allows us,

conceptually, to consider the process in reverse and reach back an instant

at which all mass and energy of the universe would appear concentrated

in a single point. This occurs at the instant of the Big Bang, considered

for some time as an unsatisfactory assumption by many, and generally

accepted now by the scientific community as standard reference model to

describe the time evolution of the universe.

The above value of the Hubble constant allows (see Chap. 4) an

estimate of the time elapsed since the Big Bang event, which would be

roughly

t0 ≈ 1/H0 ≈ 4.2 × 1017 sec ≈ 1.3 × 1010 years,

(6.3)

or somewhere between ten and twenty thousand million years, which is

in acceptable agreement with other independent estimates5 based upon

the ages of globular clusters, the age of the oldest stars in our own galaxy

and radioactive dating. Within our own solar system (and we must

remember that the sun is a second or third generation star) the oldest

rocks, as well as lunar samples brought to Earth by american cosmonauts,

are about 4 to 6 thousand million years old.

6.2.3. Relative abundance of 4He and other primordial light elements

We know that the intermediate and heavy nuclei of the periodic table of

the chemical elements are synthesized in the core of stars, under extreme

conditions of high temperature and pressure, from lighter nuclei, starting

with hydrogen nuclei or protons. The variation in relative abundance of

helium (4He in particular) and other few very light elements, on the other

hand, seems to be more6 or less constant throughout a given galaxy and

more or less the same for different galaxies. This relative abundance is



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The Intelligible Universe



also by far too large to have been produced by the limited number of

successive star-life cycles allowed by the present age of the universe. It

suggests a “primordial” origin for 4He and the other very light elements, in

contrast to what happens with the intermediate and heavy elements. By

“primordial” we mean of early cosmic origin (unrelated to fusion within

stars) or having taken place at an early time in the cosmic expansion. At

this early time the prevalent conditions of very high density and

temperature should have been capable of producing the synthesis of

deuterium nuclei (each with a proton and a neutron), and subsequently the

synthesis of 4He nuclei (with two protons and two neutrons).

The characteristic temperature for deuterium formation is TD ≈ 9.3 ×

109 K. At T > TD the thermal background radiation is sufficient to break

down deuterons into its two components, but at T < TD the background

radiation does not have enough energy to break down deuterons, and

these become stable. The characteristic temperature for 4He formation,

on the other hand, is T4He ≈ 4 × 109 K. It may be assumed that at T > TD

(very early into the universe expansion) the number of free protons and

free neutrons was the same. But the free neutron is unstable7 (it has a half

life of about 700 s) and this implies that if the cooling rate of the universe

between TD and T4He is rapid enough, compared with the neutron half-life,

all available neutrons could have been trapped into 4He nuclei, while if

this cooling rate is too slow, almost no neutron could have been trapped.

The first possibility leads to a universe made up predominantly of helium

(incapable of supporting life as we know it), the second to a universe in

which helium is almost absent (contrary to what is observed). We know

experimentally that the universe contains at present about three times

more hydrogen than helium. This is possible only if the cooling rate of

the universe is properly tuned to the disintegration rate of the neutron to

produce that specific proportion of hydrogen and helium.

Einstein’s cosmological equations and the Big Bang model provide

a connection between the present (T0 ≈ 3 K) expansion rate and the

“primordial” (TD ≈ 9.3 × 109 to T4He ≈ 4 × 109 K) expansion rate in such a

way that the present helium abundance, given by

(6.4)

Y = (4He mass)/(H mass) ≈ 0.25

is reasonably well justified in terms of the half-life of the free neutron.



Cosmology and Transcendence



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6.2.4. Cosmic background radiation

As mentioned in previous chapters (Chaps. 1 and 4), in 1948 R.A. Alpher

and R. Herman, G. Gamow’s collaborators, predicted8 a background

radiation of about 5 K, as a remnant from the very hot state of the early

universe, which was confirmed in 1965 experimentally by A.A. Penzias

and R. Wilson.



DENSITY PARAMETER Ω × (H0/75 km·sec-1·Mpc-1)2

Fig. 6.5. Relative abundance of primordial light elements as a function of Ω0 (ratio of

density t0 critical density) from cosmic nucleosynthesis. (The central band indicates the

range compatible with observations).



These American radioastronomers were looking for something else, and,

after confirming that the observed isotropic 3 K background radiation

was not instrumental noise, they published9 their finding in the

“Astrophysical Journal” with no further comment.

The alternative model competing with the Big Bang model at that

time, the steady-state (continuous creation) model of T. Gold, H. Bondi

and F. Hoyle, was unable to give any reasonable explanation for this

finding, and this fact contributed considerably to tilt the balance within

the scientific community in favor of the Big Bang model. Significant facts



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