Chapter 2: The ball-shaped Universe

Has the universe been made from nothing? If so, how? Does the whole Universe rotate around its own axis? Is there also an outside? What shape does our Universe have? Is it round like our planet Earth? If so, what scientific proof is there?

John D. Barrow, Astronomy Centre, University of Sussex. In Between Inner Space and Outer Space (1999) Oxford, under the heading, "Getting something from nothing": "The fact that the laws of Nature are the same in every direction of space and from one time to another are equivalent to the conservation of the total momentum of rotation (called angular momentum) and the conservation of total energy in any physical process. These two qualities, together with the total amount of electrical charge, are observed to be conserved in all physical processes and their status as conserved quantities is deeply entwined with the entire superstructure of physics.

"If one proposes giving a scientific account of a universe coming into being out of nothing then an immediate objection seems to be that one would indeed be trying to get something out of nothing because one would have to suddenly bring into being a universe that possessed the laws of Nature, which enshrine the conservation of these quantities and so the creation of the Universe out of nothing cannot be a consequence of those laws.

"There is nothing wrong with this argument and it is really quite persuasive until one starts to inquire what the energy, angular momentum, and electric charge of the Universe seem to be. If the Universe possesses angular momentum then on the largest scales the expansion will possess rotation. The most distant galaxies would be moving across the sky as well as receding directly away from us. In practice, the lateral motion will be too slow for us to detect even if the Universe has a significant level of rotation. However, there are more sensitive indicators of this rotation. If we consider the effects of the Earth's rotation we see that it causes a slight flattening at the poles so that the radius of the Earth is greater at the equator than at the poles.

"A similar thing would occur if the Universe were rotating on its largest scales. Directions along the rotation axis would expand more slowly than others. Consequently, the microwave background radiation would be hottest if it came from the direction of the rotation axis and coolest from directions at right-angles to that. The fact that the radiation temperature is the same in every direction to a precision of one part in a hundred thousand means that if the Universe does have large-scale rotation then it must be rotating more than one trillion times more slowly than it is expanding in size. This is so small that it suggests that the Universe might well have zero net rotation and angular momentum."

Comment: This also proves, that the Universe has the shape of a ball, of a sphere. The Universe is rounder, than our planet Earth.

J. D. Barrow: "Similarly, there is no evidence that the Universe possesses any overall net charge. If any cosmic structures contain a charge imbalance between, say, the number of protons and electrons (which have equal but opposite electric charges) then this imbalance would have a dramatic effect since electricity is so much stronger than the force of gravity holding these structures together. In fact, it is a remarkable consequence of Einstein's theory of gravitation that if a universe is of the 'closed' sort, which will eventually contract to a future singularity, then it must have zero net charge. All the matter it contains, whether the individual elementary particles of which it is made have positive or negative charges, must total to give zero overall charge.

"Finally, what about the energy of the Universe? This is the most intuitively familiar example of something that we cannot produce from nothing. But remarkably, if the Universe is 'closed' then it must also necessarily have zero total energy. The reason can be traced to Einstein's famous E = mc² formula which reminds us that mass and energy are interchangeable and so would be thinking about the conversation of mass-energy together rather than energy or mass taken alone. The important point is that energy comes in positive and negative varieties. If we add up all the masses in a closed universe they contribute a large contribution to the total energy. But those masses also exert gravitation forces upon each other. Those forces are equivalent to negative energies that we call potential energy. If we hold a ball in our hand it has potential energy of this sort which, if the ball is dropped to the ground, will become positive energy of motion. The law of gravitation ensures that the negative energy of gravitation between the masses of the Universe must always be equal in magnitude but opposite in sense to the sum of the mc² energies. The total is always exactly zero.

"This is a remarkable state of affairs. It seems that the three conserved quantities that prevent us getting something from nothing may well all be equal to zero. The full implications of this are not clear. But, curiously, it does appear that the conservation laws do not present a barrier to creating a universe out of nothing (or, for that matter, to having it disappear back into nothing).

Cosmological Constant

"Theorists have been ambitiously pushing back their reconstructions of the Universe's past history towards the first instants of its expansion about 15 billion years ago. ... We can reconstruct its past history and predict what fossil relics should remain today of conditions billions of years ago. Our searches have been remarkably successful. They show that we have a reliable picture of what the Universe was like just one second after its expansion began. We know this because the abundances of the lightest chemical elements in the Universe are determined by the detailed behaviour of the expansion at this early time. Remarkably, the predictions of the theory match the observed abundances. By this process of predicting what we should find in the Universe today, and searching for it with our telescopes, cosmology has become a rigorous observational science.

"Despite the success of the theory of the expanding Universe in supplying a consistent description of the Universe today, puzzles remain about some of the distinctive features of the cosmic expansion. Why does it proceed at a rate that is so tantalising close to the great divide that separates a future of eternal expansion from one in which the expansion will eventually be reversed into contraction? Expanding universes veer steadily away from this critical divide for billions of years, so it must have begun at a speed that was fantastically close to the divide at the beginning. Why? There are other puzzles of this sort. Why is the Universe so similar in the way it expands, from one direction to another, and from place to place? On the face of it, these remarkable uniformities we see in its properties - good to one part in a thousand - are very unlikely to have fallen out just by chance. Moreover, the small variations that do exist have a special pattern, one that enables them to form galaxies and clusters of galaxies with the distribution and special shapes that we see with out telescopes. ...

"The first satellite to look found fluctuations consistent with expectations but could only observe variations between points separated by more than about 10 degrees on the sky. This story is told in 'What COBE saw'. But there is a lot more of it to come: in 2000 and 2005, two new satellites (MAP and Planck Surveyor) will be launched to look at the pattern of temperature variations over far smaller angular separations on the sky. What they see will be a decisive test of our theories about the Universe's past." - Barrow, J. D. (1999:228).

"A simple picture might be to think of specks of dust on the surface of an inflating balloon. The balloon will expand and the dust specks will move father apart, but the individual dust specks will not themselves expand in the same way. They will act as markers of the amount of stretching of the rubber that has occurred. Similarly, it is best to think of the expansion of the Universe as the expansion of the space between clusters of galaxies. What is intriguing about the concept of an expanding Universe is that it must have expanded from something smaller.

"The discovery of cosmic microwave background marked the beginning of serious study of the Big Bang model. Gradually, other observations revealed further properties of background radiation. It had the same intensity, or 'brightness', in very direction to at least one part in a thousand. And, as its intensity was measured at different frequencies, it began to reveal characteristic variations of intensity with frequency - the signature of pure heat. Such radiation is called 'black-body' radiation. ... This was finally done by Nasa's Cosmic Background Explorer (COBE) satellite in 1992. The instruments on board the satellite measured the most perfect black-body spectrum ever seen in Nature. It was striking confirmation that the Universe was once hundreds of thousands of degrees hotter than it is today.

"Another key experiment to confirm that the background radiation did not have a recent origin nearby in the Universe was carried out by the high-flying U2 aircraft. These former spy-planes are extremely small with large wing spans, which makes them very stable platforms for making observations. On this occasion, they were looking up rather than down, and they detected a small but systematic variation in the intensity of the radiation around the sky, a variation that had been predicted to arise if the radiation originated in the distant past.

"The microwave background radiation is like an ocean through which all heavenly bodies are moving. Each is moving within its own system - for example the Earth and planets around the Sun - and each system is moving within another - for example the Sun's motion around the Milky Way and the Milky Way's motion around the Sun, and so on. This means that we are moving through radiation in some direction. The radiation intensity will appear greatest when we look in that direction and least intense 180 degrees away, and should display a characteristic variation in between. It is rather like running in a rainstorms. You get wettest on your chest and stay driest on your back. This is precisely the sort of variations in microwave intensity that the U2s detected.

"The microwave background radiation found everywhere in the Universe fitted the Big Bang theory perfectly. Moreover, subsequent observations of the abundance of the lightest elements in the Universe matched the predictions of the Big Bang model and confirmed the idea that they were produced by nuclear reactions during the first three minutes of the expansion." - Barrow, J. D. (1999:236).

"When the COBE satellite's observations were made they revealed the most perfect spectrum of heat radiation ever observed in Nature. No distortions were present down to a limiting accuracy better than one part in a hundred. The unblemished spectrum tells us that the early history of the Universe was quiescent and eliminates from consideration an array of violent scenarios for the origin of galaxies.

"COBE's second great discovery was to measure the first variations in the intensity of the microwaves from one direction in the sky to another. If the Universe is expanding slightly faster in one direction than in another then the radiation intensity from the first direction will be slightly reduced with respect to the second. Likewise, galaxies arise from regions of the Universe with slightly more material in them than the average. When the radiation passed though these regions it would cool differently than if it had passed them by. A map of how the microwave intensity varies around the sky gives a picture of how the gravity field of the Universe looked in the distant past; it helps us to determine the sizes of the precursors of galaxies and clusters of galaxies and to discover whether the overall expansion of the Universe is asymmetrical in any other way." (1999:238, 239):

"COBE was the first observatory to see these tiny microwave fluctuations: they are among the smallest effects measured in astronomy - variations in radiation intensity of just a few parts in one hundred thousand. ... The COBE satellite ... has taken a photograph in radio waves of the Universe when it was about a million years old. Today it is about fifteen billion years old. COBE's microwave photograph shows the Universe before galaxies formed when their embryos were merely blips on the cosmic landscape." - Barrow, J. D. (1999:239).

Michael Rowan-Robinson

Michael Rowan-Robinson is Professor of Astrophysics and Head of the Astrophysics Group at Imperial College, London. He is an internationally recognised expert on observational cosmology. He says in his book, The Nine Numbers of the Cosmos (1999:32): "In 1965 Arno Penzas and Bob Wilson, two young radio-astronomers working at the Bell Telephone Laboratories, made a discovery which was to transform cosmology. Using a huge communications antenna at Holmdel, New Jersey, to study the Milky Way at microwave frequencies, they discovered a general background radiation, which was the same no matter which direction they looked. ... The radiation they were detecting had travelled for almost the whole age of the universe before it hit their antenna. ...

"As the accuracy of the measurements improved it became clear that the radiation was extremely isotropic (the same). ...The universe is homogenous and isotropic. ... This implied that we are looking back to an era when matter and radiation were locked together in thermal equilibrium." (1999:32, 34).

"The COBE team measured the average fluctuations in temperature or intensity of the microwave background radiation, ... which they found to be 1 part in 100 000, or 10^-5. ... From COBE we can say that the universe was isotropic and homogenous on these scales to this accuracy, 1 part in 100 000, at a time a few hundred thousand years after the Big Bang. This is a very strong statement about the smoothness of the universe and the degree with which it satisfies the cosmological principle. The universe we live in has evolved from an earlier state extremely close to homogeneity and isotropy. This is a very deep fact about the universe." (1999:35-37).

The Hubble constant = 65 km s. (1999:56). What does one mean by the "critical density" of the Universe?

"For omega = 1, the socalled critical density case, the universe keeps on expanding but the rate of expansion gets ever slower and slower. The density parameter omega can be thought of as the ratio of the density of the universe to the critical value. It can also be interpreted as the ratio of the gravitational energy of a volume of the universe to the kinetic energy, or energy of motion of the same volume. Over the months that they had been studying the microwave background radiation, Penzas and Wilson found that it had the same intensity in whichever direction they looked. They also soon found that the temperature of the radiation was the same whatever wavelength they observed at." (1999: 57, 74).

"The whole universe is bathed in this radiation at a temperature of 2.728 K, so apart from regions shielded from the radiation this represents the minimum temperature that matter in the universe can have. As we go back in time the radiation temperature satisfies the law, discovered by Tolman, that the temperature increases inversely proportionally as the size of the universe gets smaller. When the universe was ten times smaller, the temperature was 27.28 K and so on." - Michael Rowan-Robinson (1999:75)

"When the universe was 1000 times smaller than at present, the temperature was about 3000 K. An important change to the matter occurs at this point, because the most abundant element, hydrogen, can no longer hold on to its electron at this temperature. The gas becomes 'ionized' and consists of electrons moving around freely, and nuclei (mainly protons, with a few helium nuclei). The free electrons have a dramatic effect on the radiation. Whereas after this phase the photons that make up the background radiation travel through the whole universe rarely encountering any matter, before it they are scattered by the electrons very frequently...

"The recombination era occurred about 300 000 years after the beginning of the Big Bang. When we look outwards at the microwave background radiation today we are looking back to this moment in the history of the universe. It is the limit of our observable universe using light and defines a kind of horizon for our observations with telescopes." (1999:77).

"At very early epochs the number of electrons and positrons is about the same as the number of photons and all are in 'thermal equilibrium' together; that is, each electron and position carries about the same amount of energy. The photons of radiation also each have about this same amount of energy, which is determined by the temperature. Once the radiation cools below 10 billion degrees, the photons no longer have enough energy to make an electron-positron pair and so most of these pairs start to annihilate. If there had been exactly the same number of electrons and positrons, they would all have annihilated and there would be no matter in the universe today, just radiation (protons and neutrons), or more precisely their constituent quarks would also have annihilated with their antiparticles at an earlier time. For reasons that we do not yet know for certain, the universe happened to have a small excess of matter (electrons) over antimatter (positrons), so when all the positrons had been annihilated there were still some electrons left (and an equal number of protons) so that the universe has a net electric charge of zero - otherwise electrostatic forces would be overwhelmingly stronger than gravity)." - Michael Rowan-Robinson (1999:79).

How heavy is the vacuum? The cosmological constant lambda: what is that?

Prof. M. Rowan-Robinson: "The cosmological constant tells us how heavy the vacuum is. It may seem strange to think of the vacuum as possessing energy but in modern particle physics the vacuum is a seething mass of pairs of particles and antiparticles which come into existence for a fleeting instant and then annihilate, so-called 'virtual' particle pairs. When particle physicists estimate what is a 'natural' value for the energy density of the vacuum, they come up with a value equivalent to lambda = 10¹²⁰, 1 followed by 120 zeros, a mind-boggling number. In the actual universe it is clear that lambda could be about 1 but it certainly is not as big as 10, let alone 10¹²⁰. At present, particle physicists can not explain why the observed lambda is so small. So they tend to argue that there must be some fundamental principle which they have not yet discovered that forces the cosmological constant to be exactly zero in the present-day universe." (1999:122

The Anisotropy of the Universe

The estimate from COBE for the anisotropy on large scales, ... is 1 part in 100 000, that is 1. X 10^-5, to an accuracy of 25%. Following MAP and PLANCK the accuracy with which this is known will improve slightly to about 10%. On the other hand the accuracy of the anisotropy on small scales (at present not really known at all), will, particularly from PLANCK, be known to very high accuracy, to about 1%.

The Hubble constant H₀ = 65 km s Mpc, with an uncertainty of about 12%. For the age of the universe, I have adopted the value = 12 billion years, with a total uncertainty of 2 billion years either way. This is a 20% reduction from the value of 15 billion years, which was believed only a few years ago. ...The temperature of the microwave background: COBE has already determined the temperature of the microwave background, as 2.728 degrees Kelvin to an accuracy of 0.1%. This is the one cosmic number, which we really do know accurately. - Michael Rowan-Robinson (1999:153, 154).