Chapter 9: Cosmic Fine-Tuning

How accurately has our universe begun, when it was born some 10-15 billion years ago? And how accurately is it working now? Why does the universe not collapse into a chaotic pile of matter? And why does it not explode and fly apart, like an atomic bomb? What have scientists found out now about this?

Roger Penrose is Professor of Mathematics at the University of Oxford, England. He writes in his book The Emperor’s New Mind (1989:328) under the heading "Cosmology and the arrow of time": "The further back in time that it has been possible to see, and the larger the portion of the universe that it has been possible to survey, the more uniform the universe appears. The black-body background radiation provides the most impressive evidence for this. It tells us, in particular, that when the universe was a mere million years old, over a range that has now spread some 10²³ kilometers - a distance from us that would encompass some 10¹⁰ galaxies - the universe and all its material contents were uniform to one part in one hundred thousand (cf. Davies 1987). The universe, despite its violent origin, was indeed very uniform in its early stages. ... Thus it was the initial fire ball that has spread this gas so uniformly throughout space. It is here that our search has led us."

Does the big bang explain the second law?

The second law of thermodynamics show us, how the high-quality energy of the universe is being changed into low-quality energy, while doing work. - Does the big bang explain the second law?

Prof. Roger Penrose: "It is the puzzling fact that the entropy (= disorder) in our universe started out so low - the fact which has given us the second law of thermodynamics - to be ‘explained’ just by the circumstances that the universe started with a big bang? A little thought suggests that there is something of a paradox involved with this idea. It cannot be the real answer. Recall that the primordial fireball was a thermal state - a hot gas in expanding thermal equilibrium. Recall, also, that the term ‘thermal equilibrium’ refers to a state of maximum entropy. ... However, the second law demands that in its initial state, the entropy (= disorder) of our universe was at some sort of minimum, not maximum! ...

"It was a low-entropy constraint at ‘the beginning of time’ which gave us the second law, according to which the entropy of the universe is increasing with time. If this same low-entropy constraint were to apply at the ‘end of time’, then we should find that there would have to be gross conflict with the second law of thermodynamics!" (1989:328, 329).

Singularities

What happened at the initial singularity? And how does it differ from the final singularity of a big crunch, if there ever was such a thing?

Prof. Roger Penrose: "Likewise, using the reverse direction of time, we again find inevitability for a corresponding initial space-time singularity which now represents the big bang, in any (appropriately) expanding universe. Here, rather than representing the ultimate destruction of all matter and space-time, the singularity represents the creation of space-time and matter. It might appear that there is an exact temporal symmetry between the two types of singularities: the initial type, whereby space-time and matter are created; and the final type, whereby space-time and matter are destroyed." (1989:337).

"We see, now, how it is that a recollapsed universe need not have a small entropy (= low disorder). The ‘lowness’ of the entropy at the big bang - which gave us the second law - was thus not merely a consequence of the ‘smallness’ of the universe at the time of the big bang! If we were to time-reverse the picture of the big crunch that we obtained above, then we should obtain a ‘big bang’ with an enormously high entropy (= disorder), and there would have been no second law! For some reason, the universe was created in a very special (low entropy) state with something like the WEYL = 0 constraint of the FRW-models imposed upon it." - Penrose, R. (1989:339).

How accurately has our universe arisen, so that there could be a second law of thermodynamics, and a planet Earth with life on it?

Prof. Roger Penrose: "Try to imagine the phase space of the entire universe! Each point in this phase space represents a different possible way that the universe might have started off. We are to picture the Creator, armed with a ‘pin’ - which is to be placed at some point in the phase space. Each different positioning of the pin provides a different universe. Now the accuracy that is needed for the Creator’s aim depends upon the entropy of the universe that is thereby created. It would be relatively ‘easy’ to produce a high entropy (= highly disordered) universe, since then there would be a large volume of the phase space available for the pin to hit. ...

"But in order to start off the universe in state of low entropy (= low disorder) - so that there will indeed be a second law of thermodynamics - the Creator must aim for a much tinier volume of phase space. How tiny would this region be, in order that a universe closely resembling the one in which we actually live would be the result? ... In order to produce a universe resembling the one in which we live, the Creator would have to aim for an absurdly tiny volume of the phase space of possible universes - about 1/10¹²³ of the entire volume, for the situation under consideration. ... This now tells us how precise the Creator’s aim must have been: namely to an accuracy of

one part in 10¹²³

This is an extraordinary figure. One could not possibly even write the number down in full, in the ordinary denary notation. It would be ‘1’ followed by 10¹²³ successive ‘0’s! Even if we were to write a ‘0’ on each separate proton and on each separate neutron in the entire universe - and we could throw in all the other particles as well for good measure - we should fall short of writing down the figure needed. The precision needed to set the universe on is course is seen to be in no way inferior to all the extraordinary precision that we have already become accustomed to in the superb dynamic equations (Newton’s, Maxwell’s, Einstein’s) which govern the behaviour of things from moment to moment." - Penrose, R. (1989:340, 344).

Paul Renteln is assistant professor of physics at the California State University in San Bernadino. He reports in the journal American Scientist, Nov.-Dec. 1991: 524, 525) under the heading "Quantum Gravity" about electrons and quarks, and photons and gluons, and how precisely they are working together:

"Even though Einstein abandoned it, the cosmological constant still poses a problem for quantum mechanics. As we know, the vacuum is alive with the creation and destruction of virtual particles. These vacuum fluctuations contribute to the zero-point energy of the vacuum, and hence act like an effective cosmological constant. In most field theories, such as quantum electrodynamics, the background is inert. Because of this, the vacuum can be treated as if it had zero energy and hence a vanishingly small cosmological constant.

In general relativity, however, the background is dynamical: the creation and destruction of virtual particles actually warps spacetime, changing the ambient gravitational field. When we consider the gravitational interactions between particles, it is no longer possible to ignore the effects of these virtual fluctuations. Fluctuations in the matter field (such as electrons and quarks) make negative contributions to the cosmological constant, whereas the carriers of forces (such as photons and gluons) make positive contributions to the constant.

"Our observations of the universe suggest that the positive and the negative contributions cancel each other to better than one part in 10¹²⁰! If the particles did not make such nearly equal contributions to the constant, our universe would either collapse upon itself or else expand at a velocity close to the speed of light. In the absence of a physical principle that explains the high degree to which the positive and negative contributions are balanced, the small size of the cosmological constant poses a problem." - Renteln, P. (1991:524, 525).

Cosmological Constant: why so accurate

Why is there a cosmological constant? And why is it so accurate? - We have found out so far: The universe arose with an accuracy of 1 : 10¹²³. The subatomic particles and interacting forces are working together with an accuracy of "better than one part in 10¹²⁰". - Why? - How accurately is the cosmic expanding force working together with the cosmic contracting force, the force of gravitation, so that the universe will not collapse, nor fly apart? What is really behind all this? Is it enough to say, that the small size of the cosmological constant "poses a problem"? If so, for whom is it posing a problem?

John Gribbin states about this: "The Universe today is actually very close to the most unlikely state of all, absolute flatness. And that means it must have been born in an even flatter state, as Dicke and Peebles, two of the Princeton astronomers involved in the discovery of the 3 K background radiation, pointed out in 1979. Finding the Universe in a state of even approximate flatness today is even less likely than finding a perfectly sharpened pencil balancing on its point for millions of years, for, as Dicke and Peebles pointed out, any deviation of the Universe from flatness in the Big Bang would have grown, and grown markedly, as the Universe expanded and aged. Like the pencil balanced on its point and given the tiniest nudges, the Universe soon shifts away from perfect flatness."

"If the density of the universe is now one tenth of the amount needed to make it just closed (a figure that most astronomers would agree is a fair guide on the basis of the visible galaxies), that means that 1 second after the moment of creation the density of the Universe was equal to the critical value to within one part in 10¹⁵. And if we go back to the time just after the GUT era, at 10¹⁴ GeV and 10^-35 second the density must have been only one part in 10⁴⁹ less than the critical value. This is hardly to be a chance occurrence and must mean that the laws of physics somehow require the Universe to be born out of the Big Bang in a state of extreme flatness." - Gribbin, J. (1986:347, 348).

Michael B. Green is an expert on superstrings. He writes in Scientific American Vol. 255, Sept. 1986, p. 56, and asks: "Why is the cosmological constant so close to zero? This constant describes the part of the curvature of the universe that is not caused by matter; its value has been determined to be zero within one part in 10¹²⁰, which makes it the most accurate measurement in all science. If superstring can account for the value, the explanation would be a convincing test of the theory."

10¹²⁰ of what?

The universe started off with an accuracy of 1 : 10¹²³. The subatomic particles and interacting forces - the quarks and electrons, photons and gluons - are working together with an accuracy of better than one part in 10¹²⁰. - But 1:10¹²⁰ of what?

John Barrow, Professor of Astronomy at the University of Sussex, England, says in his book Theories of Everything (1991:104, 105): "What of the cosmological constant today? We know from the effects it would have upon the expansion rate of distant galaxies that if it does exist then its numerical value must be infinitesimal, less than 10^-55 per cm². Such units are not very illustrative. It is more illuminating to compare its size with that of the basic unit of length in the elementary-particle and gravitational worlds. This ‘Planck-length’ is the only quantity with the dimensions of a length that can be build from the three most fundamental constants of Nature: the velocity of light c, Planck’s constant h, and Newton’s gravitational constant G.

= 4 x 10^-33 cm.

This tiny dimension encapsulates the attributes of the world that is at once relativistic (c), quantum mechanical (h) and gravitational (G). It is a standard length that makes no reference to any artifact of man or even of the chemical and nuclear forces of Nature. Relative to this unit of length, the size of the entire visible universe today extends roughly 10^-60 Planck lengths, but the cosmological constant must be less than 10^-118 when referred to these Planck units of length rather than centimetres. To have to consider such a degree of smallness is unprecedented in the entire history of science. Any quantity that is required to be so close to zero by observation must surely in reality be precisely zero. That is what many cosmologists believe. But why?

"What we seem to require is either a ‘set and forget’ principle which sets the cosmological constant small initially in a way that ensures that it stays small, or some new type of principle which ensures that the cosmological constant must be vanishingly small, when the universe has expanded to a large size comparable to its present dimensions of fifteen billion light years." Barrow, J. (1991:105).

So, now we know, what is meant by this "less than 10^-118", and "1 part in 10¹²⁰" and "1 : 10¹²³". It is the accuracy of the cosmological constant, when referring to the Planck-length of 4 x 10^-33 cm. When compared to the size of a square centimeter, it is less than 10^-55 per cm². - Why is there a cosmological constant? And why is it so accurate?

David Gross was Professor of Physics at Princeton University. He says about "The Problem of the Cosmological Constant": "Gravitation, however, is a force, which is directly connected with energy. One often mentions, though, that gravitation is connected with mass, but, as we have learned from Einstein, mass, according to its nature, is nothing but energy. Since gravitation is directly connected with energy, it ‘knows’, so to say, how much energy a certain object contains, and this holds true also for the universe as a whole: Also the universe contains a certain energy-density." (1989:172).

Also when space is entirely empty?

Professor David Gross: "Also when space is empty. One is able to measure empty space, because the universe will contract itself the stronger, the higher its energy-density is. Thus, one is able to determine the background-energy-density of the universe, by determining its global structure. These measurements have been made. One does have here, though, only an upper limiting value, for the exact value seems to lie very close to zero. These measurements are actually the most accurate determinations of a ‘zero-size’, which one has been able to do: Its accuracy is 1:10¹²⁰ in units of the Planck-mass, the natural mass- or energy-scale of gravitation." - Gross, D. (1989:172).

"Let’s assume, for instance, you would be working on a modern physical theory, which includes gravitation. And someone asked you, without knowing the observed results: How high, according to your theory, would you estimate the background-energy-density of the universe? Your estimated value would be then 10¹²⁰ times greater, than the upper limit, resulting from these observation. The observations are given us such small values, so that everyone believes, that its real value is zero.

"But according to this theory, there is no reason for this at all! Actually, its value should be much greater. But that is not all: Even if one manipulated the theory, so that its energy-density would be exactly zero - a bit strong for a physicist, since we are dealing here with an accuracy of 120 decimal places! - and afterwards one finds out, then, that one has overlooked in his calculation a small quantum-mechanical effect. This alone would lead then already to a cosmological constant of measurable size. Since its introduction by Einstein, the small value of the Cosmological Constant has remained a mystery. Again and again it has been found to be zero, zero, and again zero, even, though, no one knows, why." - Gross, D. (1989:172)

Cosmological Constant: How Large

How large is the cosmological constant? What have scientists found out about this?

The universe arose with an accuracy of 1:10^123.. And it is existing now with this accuracy (R. Penrose 1989:344). Electrons and quarks, and photons and gluons "cancel each other to better than one part in 10¹²⁰!" (P. Renteln 1991:524, 525). - "The cosmological constant must be much less than 10^-118, when referred to these Planck-units of length." (J. Barrow 1991:105). - "One does have here, though, only an upper limiting value, for the exact value seems to lie very close to zero. Its accuracy is 1:10¹²⁰ in units of the Planck-mass, the natural mass- or energy-scale of gravitation. ...We are dealing here with an accuracy of 120 decimal places!" (D. Gross 1989:172).

What does this show us? - That the cosmological constant has a value of 1:10¹²³. This is the most accurate value of the cosmological constant we do have so far. - But 1:10¹²³ of what? - Of the Planck-mass and of the Planck-length. First, we must find out, how long the Planck-length and how heavy the Planck-mass really are. Max Planck published them in his book Die Entdeckung des Wirkungsquantums (The Discovery of the Quantum of Action). It was published again in 1969 by Armin Hermann, Professor for natural sciences and technical science at the University of Stuttgart. In his book, on page 70, Max Planck gives the following values:

Planck-length 4.13∙10^-33 cm

Planck-mass 5.56∙10^-5 g

Planck-time 1.38∙10^-43 s

Planck-temperature 3.50∙10³² C.

How long and how heavy is then the cosmological constant quantum?

4.13∙10^-33 cm : 10¹²³ = 4.13∙10^-56 cm = 4.13∙10^-58 m

5.56∙10^-5 g : 10¹²³ = 5.56∙10^-128 g = 5.56∙10^-131 kg.

The cosmological constant quantum is the 10¹²³th part of the Planck-length and the Planck mass: 4.13∙10^-56 cm and 5.56∙10^-128 g.

Cosmic Information

How much information does the cosmological constant contain? How much information was needed, to make it?

1:10¹²³ is a 1 with 123 decimal places behind the comma. Hence, there are at least 10¹²³ yes/no decisions, or 10¹²³ bits of information: The accuracy, with which our universe has begun, and with which is still working. The universe is working close to or with zero-error. Thus, also the amount of information, contained in this figure, is still greater than 1:10¹²³ bits. - How much information is that?

We will understand this a little better, when comparing this figure with the information, which is contained now in all the books, that have been written down till now. Mankind’s total knowledge, written down now in books, is 10¹⁸ bits (Gitt, W. 1986:68). - When dividing 10¹²³ by 10¹⁸, we get 10¹⁰⁵. The information, with which our universe has started and with which it is still working, is therefore 10¹⁰⁵ times as large, as all the information, which mankind has written down till now in its books! - Everything in physics has a cause. Who, then, caused this information of at least 10¹²³ bits to arise? A serious physicist should be able to answer this question.