Review of Martin Rees’ Book “Just Six Numbers: The Deep Forces That Shape the Universe”

Synopsis: How could a single “genesis event” create billions of galaxies, black holes, stars and planets? The nature of our universe is remarkably sensitive to just six numbers, constant values that describe and define everything from the way atoms are held together to the amount of matter in our universe.  If any of these values was “untuned,” there would be no stars and life as we know it in our current universe.  This realization offers a radically new perspective on our place in the universe, and on the deep forces that shape, quite simply, everything.

About the book author:
Martin Rees is a famous astrophysicist and cosmologist from England.  He is currently Professor of Cosmology and Astrophysics at Cambridge University; he is also the President of the Royal Society in England. The book is published by Basic Books in 2000.

Book Review

We will begin this book review with an introduction providing some background information on several key astrophysical and cosmological concepts that are used by the author in this book.  The review is presented in layman’s terms.  However, since the reader may not be familiar with some of the complex concepts discussed in the book, the reader may not be able to follow everything discussed in this review.  That is perfectly okay, because it is not that important that the reader must understand everything that is discussed in this review.  What is important is that the reader understands the gist of the conclusions drawn from this book, which I will try to explain clearly and plainly.

I want to mention that I am not an expert on astrophysics or cosmology. If someone with more expertise finds errors or unclear explanations, I would greatly appreciate receiving some comments.

I.   Some basic background concepts

  1. What is cosmology? Cosmology (from Greek word “kosmos” meaning universe and Greek word “logia” meaning study) is the study of the universe in its totality, and by extension, humanity’s place in it.
  2. Determining distances in astronomy: There are many methods, such as the geometric method of parallax, the spectroscopic method, comparing apparent luminosity with absolute luminosity, standard candle method using variable Cepheid stars. For our discussion, we do not need to understand any of these methods; we only need to accept that there are methods of measuring distance.
  3. Doppler Effect: The frequency or pitch of a sound signal varies depending on the speed and direction of the source of the sound. If the source is moving toward you, you hear a higher pitch (larger frequency), and if the source is moving away from you, you hear a lower pitch (smaller frequency). Similarly, the frequency of a light signal (or more generally speaking any electromagnetic signal) varies depending on the speed and direction of the source of the light. If the light source is moving toward you, the frequency increases or the light is shifted toward the blue color, and if the light source is moving away from you, the frequency decreases or the light is shifted toward the red color. Therefore, by measuring the amount of red shift of a light source allows one to determine the velocity of a distant astronomical object. If the light source is moving at speeds close to the speed of light, then one also needs to include relativistic corrections.
  4. Hubble’s Law: Hubble’s 1929 fundamental experimental observation (he also made use of other people’s astronomical observations from the previous decade): Astronomical objects are moving away from us, and the speed an astronomical object is moving away from us is proportional to its distance from us, i.e., an object that is twice as far away is moving away from us at twice the speed. The relation between speed and distance can be expressed as V=H0xD, where H0 is the Hubble constant which is a constant at any particular time, but it could vary with time. H0 is currently approximately 20 kilometers per second per million light years. Note: Hubble’s Law in this simple form needs to be modified when the speeds involved are close to the speed of light to avoid speeds that are faster than the speed of light which is forbidden by Einstein’s Theory of Relativity. From the measured velocity of the most distant objects in our universe and the independently measured distance of these objects, one can then determine the age of the universe (when all galactic matter were essentially at the same location) to be approximately 15 billion years.
  5. Cosmological Principle: Due to the belief that our galaxy (Milky Way) is nothing special in the universe, Hubble’s Law is generalized to state that the universe should look the same (on a macroscopic scale) to observers in all typical [1] galaxies, and in whatever directions they look, i.e., on a macroscopic scale the universe is homogeneous and isotropic. This is known as the Cosmological Principle. This means that from any object at any spot in the universe, the other objects are all moving away from this object and the speeds of these objects are directly proportional to the distance of separation. [2]  Note: If Hubble had found some other relationship between the speed and distance, e.g., if the speed is proportional to the square of the distance, then it will not be consistent with the Cosmological Principle. Therefore, even though the Cosmological Principle is not necessarily a consequence of Hubble’s Law, it is at least consistent with it.
  6. Expanding Universe: Hubble’s Law and the Cosmological Principle cause us to conclude that the universe is expanding like a balloon being blown up or a loaf of bread rising up while being baked. For example, take three points A, B, and C on a “straight line” on the surface of a balloon that is being blown up, with the distance between A and B the same as the distance between B and C. As the balloon is being blown up, the distance between A and B will increase with time and the distance between B and C will also increase with time. Then the distance between A and C will increase twice as much, just as according to Hubble’s Law. If the universe has been expanding, then looking back in time, the universe must have been a very small entity at the beginning of the expansion. The beginning of the expansion is known as the “Big Bang”, when matter began flying apart from each other. What caused this expansion and will this expansion continue forever are two of the biggest and most important astrophysical, as well as philosophical, questions facing mankind.
  7. Cosmic Microwave Background Radiation: We don’t really know what caused the Big Bang and what happened immediately after the Big Bang. However, we do know that after the first few minutes of the Big Bang, if there wasn’t an intense background electromagnetic radiation present, then nuclear reactions would have proceeded so rapidly that a large fraction of the hydrogen present would have interacted with each other to form heavier elements, in contradiction to the fact that three-quarters of the present universe is hydrogen. If the universe was filled with radiation at the then high temperature, then the radiation could have blasted the heavier nuclei apart as fast as they could be formed. As a matter of fact, such electromagnetic radiation is expected as the “heat” radiated off from this primordial mixture, in the form of a black-body radiation. This radiation would survive the expansion of the universe except that as the universe expands, the temperature corresponding to the radiation would fall in inverse proportion to the size of the universe. Furthermore, the radiation should be homogeneous and isotropic anywhere in the universe.

    Therefore, we should be able to observe this radiation, called the Cosmic Microwave [3] Background Radiation. Various theoretical calculations before its discovery estimated that the temperature corresponding to this radiation ranged from a few degrees Kelvin to a few dozen degrees Kelvin (the lowest temperature possible is zero degree Kelvin).

    This radiation was discovered in 1965 by the Bell Labs scientists Arno Penzias and Robert Wilson working at the Crawford Hill Lab in Holmdel, NJ. They found that the cosmic microwave background radiation corresponds to a temperature of 2.7 degree Kelvin, i.e., less than 3 degrees above absolute zero. Their discovery was sort of an accident, because they were not specifically looking for this remnant radiation from the Big Bang. At first they didn’t realize what they had discovered; at one point they even thought that the radiation was statics from the droppings of two pigeons who nested on their 20-foot radio antenna. But the radiation remained even after they had cleaned their antenna of the droppings and got rid of the pigeons. They learned of the significance of their discovery only after another physicist (Bernard Burke of MIT) referred them to several physicists at Princeton University (Robert Dicke, Jim Peebles, P. G. Roll, and David Wilkinson) who were then also doing an experiment to detect this radiation as the remnant radiation from the Big Bang.

    The discovery of this Cosmic Microwave Background Radiation provided strong support to the Big Bang Expanding Universe theory of the origin and evolution of the universe. Penzias and Wilson were awarded the Physics Nobel Prize in 1978.

  8. Inflationary Universe: Although an expanding universe can explain Hubble’s Law and the Cosmic Microwave Background Radiation, there were other experimental observations that the expanding universe alone didn’t seem to be able to explain, e.g., why on a grand scale the universe was more or less homogeneous instead of having more graininess, why there were no or so few magnetic monopoles. In 1981, a young American physicist Alan Guth proposed that almost immediately after the Big Bang, the universe underwent an extremely rapid expansion so that the size of the universe quickly increased by many, many orders of magnitude. This is known as the Inflationary Universe theory. Current formulation of this theory is that cosmic inflation occurred between 10-36 to 10-32 second, and during this brief period, the size of the universe increased by a factor of 1026! Although this theory may seem strange and ad hoc, the results of many experiments in the last 20-30 years seem to support such a theory, even though it is not clear what caused the inflation. Due to lack of time, we will not elaborate on the Inflationary Universe.

II.   Just Six Numbers

We now discuss the main contents of Martin Rees’ book Just Six Numbers: The Deep Forces That Shape the Universe. The main thesis of this book is that the evolution (both physical and biological) of our universe is remarkably sensitive to the values of six numbers. If any of their values was ‘untuned,” there would be no stars and life as we know it in our current universe.

We will now discuss these six numbers, and the next section will discuss several interpretations based on the conclusions of this section.

  1. N = Relative strength of electrical force over gravitational force (e.g., electrical force between 2 protons/gravitational force between 2 protons) = (approximately) 1036, i.e., the gravitational force is extremely weak compared with the electrical force.

    Matter is made up of atoms and molecules which in general are neutral because they are made up of equal numbers of protons (positively charge) and electrons (negatively charge), and some neutrons (neutrally charge). Therefore, even though the electrical force is so much larger than the gravitational force, the aggregate force governing the macroscopic structure of matter is the gravitational force, and not the electrical force. This self gravitational force will pull the matter inward into smaller and smaller spheres. When they get smaller and smaller, its temperature gets hotter and hotter, because temperature is due to the collision of atoms with each other within the matter, and there will be more collisions if the spheres are smaller. When the interior temperature gets hot enough, nuclear fusion reactions can occur as in our sun. These nuclear fusion reactions release energy and therefore outward pressure which can counteract the inward pressure from gravitation. That keeps the matter from continuous collapse and allows stars like our sun to shine from the released energy.

    However, If the gravitational force were larger, e.g., a million times larger, i.e., if N=1030, then the matter spheres would collapse much faster into smaller spheres when they reach the temperature which can generate the nuclear fusion reactions and stabilize the matter. Under these circumstances, galaxies would form much more quickly and would be much smaller in size (due to less time for the universe to expand). Instead of the stars being widely dispersed, they would be so densely packed that close encounters would be frequent, thus precluding stable planetary systems, which are a prerequisite for life. Furthermore, when gravity is so strong (relatively speaking), no animals could get much larger than very tiny insects, because gravity would cause any larger living organism to collapse.

    We can conclude that instead of having 36 zeros after 1 in the value of N, if there were only 30 zeros after 1, then the universe would be very much different from the current universe, and life as we know it would not be able to exist. Note: On the other hand, if the gravitational force were even weaker, i.e., if N is even larger (having more than 36 zeros after 1), then it would take longer to form galactic structure, and galactic structures would be less densely populated, and larger and perhaps more complex life organisms, different from current life organisms, could exist.

  2. = nuclear efficiency, defined as the % of the mass of the nuclear constituents that is converted to heat when the nuclear constituents react via nuclear fusion to form a heavier nuclei = 0.007.

    The force governing nuclear fusion is called the strong force, and is one of four forces known in nature, with the other three being the electromagnetic force, the weak force (a repulsive short-range force governing radioactive decay), and the gravitational force. The strong force is the strongest of the four forces and is about 100 times stronger than the electromagnetic force. However, its force is very short range, i.e., the force falls off very rapidly with distance. The number € is a measure of the strength of the strong force; a larger € means a stronger strong force.

    As explained below, if € were smaller than 0.006 or larger than 0.008, then the universe and life as we know it would not exist.

    When two protons and two neutrons react to form a helium nucleus, the reaction does not go in one step. Instead, it occurs in two steps. The first step is that one proton and one neutron would react to form a deuterium nucleus, i.e., an isotope of hydrogen consisting of one proton and one neutron. Similarly, the other proton and the other neutron would react to form another deuterium nucleus. Then the two deuterium nuclei would react to form a helium nucleus consisting of two protons and two neutrons.

    If € = 0.006 or smaller, the strong force is not strong enough to fuse a proton and a neutron into a stable deuterium. Without stable deuterium, helium cannot be formed. Then our universe would be composed of hydrogen only, and no heavier elements could be formed to make rocky planets and carbon-based living things. This means no chemistry and therefore no life organisms as we know it can be formed.

    In our actual universe with € = 0.007, the strong force is not strong enough for two protons to overcome their electrical repulsion to fuse together. It requires one or more neutrons which provide additional strong force but no additional electrical repulsion to fuse together into a heavier element.

    If € = 0.008 or greater, then the strong force is strong enough to overcome the electrical repulsion of two protons, and two protons can fuse together. This would have happened early in the life of the universe, so that all the hydrogen (i.e., protons) would have been used up very early on, and there is no hydrogen remaining to continue to provide the fuel to produce light in ordinary stars as in our sun. Furthermore, water, H2O, could never have existed, and therefore no life as we know it.

    Therefore, any universe with complex chemistry and life would require € to be in the range of 0.006 – 0.008.

  3. Ω and dark matter

    When a rocket, is launched upward from the surface of a galactic object, e.g., the earth, whether it will escape from that galactic object, or whether it will be pulled back by gravity to the surface of that galactic object, depends on the velocity of the launch and the strength of gravity for that galactic object. The critical velocity that is required to cause that rocket to escape from that galactic object is known as the “escape velocity”. In the case of the earth with its known gravitational field, the “escape velocity” is 11.2 kilometers per second, or about 25,000 miles per hour.

    In an expanding universe, galactic matters are moving apart from each other. Will this expansion continue forever, or will these motions eventually reverse, so that the universe will eventually re-collapse to a “Big Crunch”? Since we know the expansion speed of our expanding universe, the answer to the above question depends on whether there is enough matter in the universe so that gravity from all these matters is strong enough to slow down the expansion and then cause the collapse to a “Big Crunch”. The matter density in the universe that is necessary to cause this reversal is called the galactic “critical density”. Knowing the expansion speed, we can calculate and determine this critical density to be approximately five atoms [4] per cubic meter.

    If we calculate the masses of all known matter in our universe, we can determine the average mass density of all known matter in our universe, which turns out to be about 0.2 atoms per cubic meter, or about 25 times smaller than the critical density.Ω = ratio of actual density in galactic matter to the galactic critical density = 0.2/5 = 0.04. We see that the known matter in the universe is only about 4% of the critical mass (i.e., about 25 times smaller) than the amount of matter needed to keep the universe from expanding forever.

    Is there any other indication for the existence of dark matter? By observing the motions of various stars and galaxies, it seems that their motions cannot be completely explained by the gravitational pulls of other stars and galaxies that are known to exist today. It seems that there are other matters in the universe, called dark matter (because we cannot see/detect their electromagnetic radiation), that are nevertheless affecting the motions of stars and galaxies. The assumption of the existence of dark matter is actually not so ad hoc or unreasonable. Such inference is actually the same line of reasoning used to explain the unexpected motion of some stars by assuming that these stars must be orbiting around a “black hole” that does not emit any radiation and therefore cannot be directly seen or detected. It is also similar to the reasoning used in the 19th century to infer the existence of the planet Neptune in order to explain the observed motion of the planet Uranus.

    Even with generous account of the possibility of such dark matter, based on current information the value of Ω can at most be raised to approximately 0.3, not quite the critical value of 1, but not extremely far from it. At first sight, such large abundance of dark matter may seem strange, but why most of the matter in the universe must emit radiation so that they can be seen or directly detectable? There are various theories for what constitutes dark matter, but it remains as one of the most important unsolved questions in astrophysics and cosmology.

    What is the significance of the value of Ω with respect to the existence of our universe and life as we know it? If Ω were significantly smaller than 1, then not only that the universe would expand forever, the gravitational pull would be so small that expansion would occur so rapidly that galactic matters would be so far apart and galaxies would not be able to be formed, with a corollary that planets and life as we know it would not be able to exist. On the other hand, if Ω were significantly larger than 1, then the universe would quickly collapse before there was time for any interesting evolution of galaxies, planets, and life as we know it.

  4. λ: When Einstein first formulated his field equation in general relativity in 1916 to describe the universe, he found that the solutions of his field equation would lead to a non-static universe, i.e., the universe would either contract or expand. Since the general thinking at that time (in the latter part of the 1910 decade or the early part of the 1920 decade) was that the universe should be static (remember that this period was before Hubble’s observations that the universe was expanding), Einstein introduced an extra term in his equation, called the cosmological constant term containing the cosmological constant λ. By adding this term and with the proper choice of the value of λ, his equation could lead to a static universe.

    However, in 1922, the Russian mathematician Alexander Friedman showed that Einstein’s fix is unstable, like balancing a pencil on its point, and therefore really doesn’t lead to a static universe.

    When in 1929 Hubble discovered Hubble’s Law that the universe is expanding, Einstein regretted that he ever introduced the cosmological constant term and called that action the “biggest blunder” of his life. [Note: Since without the lamda term, Einstein’s equation can also lead to an expanding universe, so why do we need to introduce the lamda term in an ad hoc way. That was why Einstein thought that doing that was a big blunder.]

    The common belief in the 1970s and 1980s was that the expansion of the universe should slow down with time due to the continued pull of gravitation from all the matter in the universe. In the decades of the 1990s and 2000s, a series of observations of very bright stars called supernova was carried out to try to show that. [One of the leaders of this research was a physicist from the Lawrence Berkeley Laboratory of the University of California at Berkeley.] It was a great surprise that these observations found that not only that the universe is expanding, but its expansion is accelerating, i.e., the expansion speed is increasing instead of decreasing with time. The magazine Science rated this as the number-one scientific discovery of 1998 in any field of research. This led to a revival of the need for the cosmological constant term, with this term representing perhaps a new form of matter or energy that is gravitationally repulsive, unlike the dark matter of the previous section. Adding such a term could lead to an accelerating expanding universe. Such explanation is very tentative and much more work remains to elucidate this mystery!

    From other astronomical observations, the current estimated value for λ is around 0.7, which is also consistent with the supernova observations of an accelerating expanding universe. A much larger value for λ would mean that the universe would have expanded rapidly even in its early stages. Therefore, there would not be sufficient time for stars, galaxies, planets to form, and therefore would have precluded life as we know it. On the other hand, a much smaller value for λ would not lead to catastrophic consequences in terms of the formation of stars, galaxies, planets, and life; it only means that the expansion of the universe will slow down.

  5. Q: After the Big Bang as the universe expanded, matter was randomly distributed in space, which means that there were areas which were more densely populated and areas which were less densely populated. In the more densely populated areas, there would be stronger gravitational attractions between various matters. So over time, these clusterings of matter would become bigger and bigger and would eventually form stars, galaxies, and clusters of galaxies, all are held together by gravity.

    How tightly these structures are bound together is tied to the physical and biological evolution of the universe. If they were very tightly bound, i.e., it would take a lot of energy to break them up and disperse them (or Q as defined two paragraphs later is very large), then clustering would occur earlier and more likely to stay together. This would mean that it would take less time for the universe to evolve to the current structure. Stars and galaxies would be more closely packed, and they would more likely collide with each other, thus decreasing the chance to retain stable planetary systems and therefore less likely for life as we know it to exist.

    On the other hand, if they were very loosely bound, i.e., it would not take a lot of energy to break them up and disperse them (or Q as defined in the next paragraph is very small), then clustering would be less likely to occur or to stay together. This would mean that it would take more time for the universe to evolve to the current structure. There would not be sufficient time for stars, galaxies, and planets to form, and then for life as we know it to develop and evolve.

    The measure of the strength of these bonds among galactic matter to form clusters (stars, galaxies, and clusters of galaxies) is called Q = the amount of energy, as a proportion to their rest mass energy, needed to break up and disperse the clusters. For our universe, Q is estimated to be 10-5. As explained in the two previous paragraphs, if Q were much larger or smaller than 10-5, then life as we know it would not exist.

  6. D = the number of dimensions in our universe = the number of physical dimensions plus the dimension of time.

    We are used to thinking that we live in a world of four dimensions, with three spatial directions and one time dimension with an arrow. But why are there only three spatial dimensions?

    One consequence of a three-dimensional spatial world is that forces like gravity and electricity obey an inverse-square law, such that the force from a mass or charge is four times weaker if you go twice as far away. This can be illustrated by a graphical method (first pointed out by Michael Faraday, a pioneer in the study of electricity). If you envisage lines of (electrical or gravitational) force emanating from every charge or mass and the strength of the force is proportional to the concentration of the force lines. At a distance r, the force lines are spread over an area of (π x r2). At a distance 2r, the force lines are spread over an area of [π x (2r)2] = 4πr2. Since in both cases, the number of force lines is identical, the force at a distance of 2r is thus four times weaker than the force at a distance of r. However, in a four-dimensional spatial world, the force lines would now be spread over the volume of a sphere (instead of the area of a circle) which is proportional to r3, thus the force at 2r would be eight times weaker than at r, and not consistent with the physical electrical and gravitational forces we observe in nature.

    The author Rees provides another reason for a three-dimensional world: “Another reason for a three-dimensional spatial world is the stability of orbits in our solar system, in the sense that a slight change in a planet’s speed would only nudge its orbit slightly. But this stability would be lost if gravity followed an inverse-cube (or steeper) law rather than one based on inverse squares. An orbiting planet that was slowed down – even slightly – would then plunge ever faster into the sun, rather than merely shift into a slightly smaller orbit, because an inverse-cube force strengthens so steeply towards the center; conversely, an orbiting planet that was slightly speeded up would quickly spiral outwards into darkness.

    ”Are there arguments against a world with fewer than three spatial dimensions? In a two-dimensional spatial world, it is impossible to have a complicated network without the wires crossing. This would make it essentially impossible to create communication networks or physiological circulatory networks. Similarly, you cannot have a channel through an organ (e.g., a digestive tract) without dividing the organ into two. The restrictions are even more severe in a one-dimensional spatial world.

    Can we live in a universe where the fundamental physical laws at the time of the Big Bang have more dimensions than four, and then these physical laws “simplify” to our current four-dimensional world shortly after the Big Bang? To address this question, we will first discuss the grand unification of the forces of nature. Almost 150 years ago, Maxwell was able to provide a unified description of the electric force and the magnetic force into a single set of equations that describe both forces, now called the electromagnetic force. The introduction of quantum mechanics and especially the advances in the last 60 years seem to have led first to a quantum mechanical unified field theory of the electromagnetic force, called Quantum Electrodynamics. Then it led to a quantum mechanical unified field theory of the electromagnetic force and the weak force, called the Standard Electroweak Theory. Similar type of field theory may also have the potential to provide a quantum mechanical field theory of the strong force, called Quantum Chromodynamics, thus leading to the hope that such field theories may be able to provide a unified description of the electromagnetic force, the weak force, the strong force, and perhaps also the gravitational force.

    Einstein’s theory of relativity is a classical theory of gravitation, in the sense that it did not include quantum mechanics. To date, we still don’t have a satisfactory quantum gravitational theory. Furthermore, we don’t have a grand unified theory that can provide a unified description of all four forces of nature: the electromagnetic force, the weak force, the strong force, and the gravitational force (and there could be a new force associated with a new type of matter/energy that is gravitationally repulsive that was discussed earlier with the cosmological constant λ). Because the strength of the strong force and the weak force fall off rapidly with distance and because of the electrical neutrality of atoms and molecules, the gravitational force, in spite of its being so weak in comparison with the other forces, becomes the dominant force in the celestial realm of planets, stars, and galaxies where very large distances are involved. However, at the time of the Big Bang when we had very large masses concentrated in very small spaces and where we might have exotic objects like black holes where our current laws of physics might not be applicable, we really need a quantum gravitational theory and a grand unified theory of all the forces.

    Many (but definitely not all) physicists are pinning their hopes on the superstring theories, sometimes called “the theory of everything.” In superstring theories, the fundamental entities in our universe are not points but tiny string loops, and that the various subnuclear particles are different modes of vibration – different harmonics – of these strings. The strings are very small, about 10-19 times smaller than the proton. Furthermore, these strings are vibrating not in our (3+1)-dimensional space, but in a space of 10 (9+1) or 11 (10+1)-dimensions, depending on the specific superstring theory. At the time of the Big Bang, the four forces of nature were unified and actually more or less equal in strength. Very shortly after the Big Bang, the four forces transformed into their current forces with tremendous differences in their strengths. Furthermore, during this short period, the six or seven extra spatial dimensions collapsed into extremely small dimensions, which become essentially invisible to us. This is analogous to a long two-dimensional sheet when rolled up into a very tight cylinder may look like a one-dimensional line from far distances. The superstring theories not only claim to provide a unified description of the strong, electromagnetic, and weak forces, it also yields quantum gravity almost as a bonus, i.e., quantum gravity is an essential ingredient of the theory, rather than an extra complication.

    Superstring theories are currently one of the most actively research areas in both elementary particle/high energy physics and astrophysics/cosmology. Although many physicists believe that superstring theories will lead us to the ultimate theory, many other physicists are very skeptical of it, and believe that it is more of a mathematical theory, instead of a physics theory. Many superstring advocates call superstring theories or the eventual superstring theory “The Theory of Everything.” Personally, I think that is more for posturing to help get research grants and to make their important research to sound even more important. I think that if we look back into history, we will find that major discoveries only showed us that there are more unknowns to be discovered or solved.

    One reason for the merging of these two areas of research, high energy physics and astrophysics, is because the extremely high energies that are involved in these grand unified theories are many, many orders of magnitude larger than the energies that can be reached by the world’s largest accelerators that can be built in the foreseeable future. The only way to have such high energies is to look at the initial period around the Big Bang.

    Therefore, there also seems to be fine tuning of the number D. If D is not equal to 4 shortly after the Big Bang, our physical world and life as we know it would not exist. If D is not equal to 10 or 11 during the short period around the Big Bang, then we may not have a grand unified theory (assuming that superstring theories will turn out to be correct).

III.   Interpretation

The above six numbers provide a recipe for a universe. They govern the outcome of the recipe, i.e., the formation and evolution of a universe, including the existence and type of life in that universe. It seems that the outcome is remarkably sensitive to the values of these six numbers. It seems that these six numbers were tuned so that our current universe and life can exist. If any of these six numbers was untuned, there would be no stars or life as we know it in our current universe.

There are at least three interpretations of the fine tuning of these six numbers.

Interpretation A: These numbers just so happen to take these values. They could have taken other values, then the universe and life as we know it will not exist. But another type of universe, perhaps without life, could exist.

Interpretation B: There is a Creator who purposely designed the universe in this way so that we could exist, i.e., there is intelligent design. It is important to point out that this type of intelligent design is not the same as those intelligent design advocates who claim that Darwin’s evolution theory cannot be correct.

Interpretation C: There could actually be many universes, with each having a different set of values for these numbers. This is the viewpoint of the “multiverse” advocates. Depending on the particular multiverse theory, the different universes may or may not interact with each other, and it is not clear how these different universes were created. The multiverse (or many-world) concept actually has existed for more than 50 years. It was first formulated in 1956 as the Many-World Interpretation of Quantum Mechanics in Hugh Everett’s Ph.D. thesis at Princeton (under Professor John A. Wheeler). In quantum mechanics, we cannot predict the exact outcome of any experimental observation; but we can predict only the probability distribution of multiple outcomes. For example, in the famous double slit experiment when electrons (or photons) pass through two slits, the only way to explain the interference pattern obtained is that the waves associated with the electrons went through both slits, and not just one slit. However, when you try to experimentally detect the electrons, you will always find that the electrons end up in one spot and not two or multiple spots, or saying it in another way, you don’t find part of an electron. So it seems that when you make an experimental observation to determine the location of the electron, you end up in one particular universe (out of many possible universes), i.e., you are put in the universe in which the electron ended up on the spot on the right or the spot on the left. [5] Both universes exist, but the different universes do not interact with each other. I should add that even if this could be a possible interpretation of quantum mechanics, most physicists do not accept this interpretation, including Professor Wheeler later in his life.

Martin Rees, the author of this book, believes in the multiverse interpretation of the fine tuning of these six numbers. Personally, I do not agree with his interpretation. I favor Interpretation B.

Final Comments: A lot of progress has been made in high energy physics, astrophysics, and cosmology during the last 50 years. Many people claim that we are on the verge of discovering a theory of everything. Personally even though I agree that we have made tremendous progress, we are far from discovering a theory of everything. Just on the topic of this article, there are still too many fundamental issues that we either do not understand or do not have an adequate explanation, e.g., what caused the Big Bang, what was before the Big Bang, what caused the universe to expand, what caused the universe to inflate, what is the dark matter, what is the potentially new unknown repulsive force that seems to be required to explain the accelerating expansion of the universe, what are the extra dimensions, why there is not a symmetry between the amount of matter and anti-matter, etc.


[1] The label “typical” is to indicate galaxies that do not have any large peculiar motion of their own, but are simply carried along with the general cosmic flow of galaxies.
[2] For more discussion of the Cosmological Principle, see, e.g., Figure 1 “Homogeneity and the Hubble Law” in the book The First Three Minutes by Nobel Prize physicist Steven Weinberg, Basic Books, 1988.
[3] It is called microwave radiation because the wavelength of this radiation is in the microwave range.
[4] The atoms are mostly hydrogen, with a smaller amount of helium and much smaller amounts of other heavier elements.
[5] This is known as the collapsing of the probabilistic wave function into a definite state.

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4 Responses to “Review of Martin Rees’ Book “Just Six Numbers: The Deep Forces That Shape the Universe””

  1. Sylybillie says:

    Dear Mr. Don,

    I am thoroughly impressed by your notes of Rees’6 numbers and thank you deeply for the uncomplicated explanation in layman’s terms.

    I am also surprised that at the end of it, you are in favor of “interpretation B.” Maybe you will write about the “why” of it, so common people like me will have a new window to look into, to explore and question and understand.

  2. MRobsn says:

    Wonderful article! – By the way, I don’t need for you to tell me why you believe Interpretation B: I believe the exact same thing you do, that there is Intelligent Design but not as it is presented in the community. / Sylybillie, there is a Book you can read in order to explore that new window, to question and understand — Jeremiah 33:3. I hope that you listen to the Creator as He guides you to that Book, for He wrote it. – from MRobsn

  3. Sandro says:

    I just discover now the book and your article … Am not not a scientist … Just an engineer …and I did enjoy …but don’t we like more the B interpretation because otherwise our lives will have no sense !? When the rest is so well organized and ruled !?

  4. Rene says:

    I agree. I am also deeply impressed with your review of Rees’ book! But I am also curious why you favor “interpretation B”. I have a nagging feeling that any environment which supports the existence of an intelligent creator requires the existence of the six described numbers before the creation of our universe. Which leaves the origins of these six values unexplained (the same is true of the origins of the creator).

    The multiverse interpretation states that all possible values of these numbers can/do exist in some universe. But only universes with ‘our’ life-supporting values produce intelligent life. I prefer “interpretation c” because its explanatory power is the biggest of the three options.

    BTW, “interpretation c” technically does not rule out interpretation B. It just does not need the hypothesis of a creator.

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