In Lecture 20 we saw how science of the 16th century had moved the Earth from the centre of the universe into an orbit around the Sun, and how this led to the scientific revolution of the 17th century that redefined mechanics as the physics of forces between gravitational bodies. Lecture 28 discussed how the concept of gravity was changed by the theory of relativity.
Within years of the publication of Einstein's papers astronomers undertook experiments to verify predictions of the theory. Since then new astronomical observations have moved the solar system from the centre of the universe into just one of many galaxies somewhere in space. The idea was not new. Giordano Bruno formulated it in the 16th century, and 200 years later Immanuel Kant expressed it in his theory of the formation of the solar system.
The history of modern astronomy is another example of the close link modern science has forged with technology. Our present understanding of star formation, evolution and decay rests entirely on observations made with equipment that was not available to 19th century scientists. A discussion of our present view of the universe therefore requires a brief introduction into astronomical instrumentation and techniques.
Modern astronomy forms the basis of cosmology, the science that investigates the evolution of the universe, in other words its past, present and future. It will lead us to such questions as whether the universe is of finite or infinite extent, questions that seem to blur the boundaries between science, philosophy and religion. It is important to remember that science can describe how the world works but will never be able to explain why it exists.
Some astronomers distinguish cosmology, the description of the structure of the universe and its dynamics, from cosmogony, the study of how the universe first received its characteristic features. (Roy and Clarke, 1989) Cosmogony should not be mistaken for an attempt to explain the existence of the universe; science has to leave such considerations to religion. Cosmogony as a scientific endeavour is restricted to the investigation of the early history of the universe. But the early history is part of its evolutionary history, too, and should logically be part of its dynamics, ie part of cosmology. Most books on astronomy therefore avoid the term cosmogony altogether.
It should also be kept in mind that science describes how the world works through models of the world, not through a description of its true self. As we have seen in Lectures 27 and 28 science uses two models to describe light, wave theory and particle theory. Neither of the two describes the nature of light, but both lead to useful and correct predictions of the behaviour of light. When we now turn to a discussion of elements of the universe we should likewise accept that science can describe the behaviour of the universe but does not claim to have discovered its true nature.
Accepting the inability of science to discover the true nature of objects does of course not mean that we cannot distinguish between true or false. It is false that the Sun "is" a solid object and true that it "is" a ball of gas, because its evolution and dynamics are correctly described by the theory of gases and not by the theory of flying stones. Whether the Sun really consists of protons, electrons, neutrons and other particles, or whether it only behaves in the way described by the theory of nuclear particles, is impossible to tell.
Before Newton's formulation of the concept of gravity any ideas about the structure of the universe belonged to the realm of philosophy. The discovery of gravity allowed scientists to develop ideas about the stars that were based on scientific principles, and the problem shifted from lack of physical understanding to lack of means for verification.
First cosmological ideas after Newton concentrated on the origin of the solar system. In 1644 Descartes suggested that it developed from a vortex of material. (Roy and Clarke, 1989) A century later, in 1745, George Buffon proposed that an obliquely striking comet (thought in his time to be comparable in size to stars) could have hit the Sun and removed chunks of material that made the planets, resulting in the rotation of the planets and the Sun in the process. His suggestion was refined by others, until 20th century astronomy showed that such a collision would increase the temperature to such a degree that the gas could not solidify but fly out into space or collapse back into the original star.
Immanuel Kant published a theory of the formation of the solar system in 1755. He assumed that initially the universe was filled with gas of slightly varying density and that the denser regions would attract material through gravity, forming clouds known as nebulae. In his model conservation of angular momentum forces the nebulae to rotate faster and faster and flatten in the process. The Milky Way was the result of one such process, and in Kant's theory the
Kant's mechanism cannot work in all its aspects, but its central hypothesis that stars are formed by condensation of interstellar dust and gas is close to the astronomical ideas of today.
Half a century later, in 1796, Laplace in his Exposition du système du monde (Explanation of the System of the World) suggested his own mechanism, which does not stand up to modern quantitative analysis. In his model a nebular disk cools and contracts in the process, forming a sun in its centre. The increased rotation from contraction allows some gas to escape into an equatorial ring around the still shrinking disk. The process then repeats itself, creating a planet each time it is repeated. (Roy and Clarke, 1989) In the same work Laplace discussed objects - he called them "dark bodies" - with such high gravity that light cannot escape from them, an idea raised 13 years earlier by the Cambridge University professor John Mitchell. (Abell et al., 1991) Such objects are today known as black holes.
Although these and other suggestions were based on physical principles they were barely better than the ideas of the ancient Indian, Egyptian, Greek and other astronomers - there was no way to prove or disprove them at the time. The first modern astronomer who tried to establish a cosmology based on observations was William Herschel, who designed and built his own telescopes for the purpose of viewing objects in the sky beyond the planets. His instruments allowed him and his sister Caroline Herschel to resolve nebulae into large numbers of stars. By counting all stars he could see he came to the conclusion that the universe contains many "island universes" (now called galaxies) of a structure similar to our Milky Way.
Just before the end of the 19th century Henri Poincaré published Les méthodes nouvelles de la méchanique céleste (The New Methods of Celestial Mechanics). It contained a mathematical analysis of the theory of equilibrium of rotating fluid masses with an application to binary stars. A decade later he and Albert Einstein independently arrived at the theory of special relativity.
Herschel's decision to improve his instrumentation before speculating on the structure of the universe foreshadowed later development. Today's astronomy has much more powerful - and much more diverse - means of observation at its disposal.
The first commercially available telescopes were produced around the beginning of the 17th century. When Galileo Galilei heard about its principle in 1609 he built one himself. It had a magnification of three. Within a year his telescopes had a magnification of 30, which allowed him to resolve the Milky Way into individual stars, discover four of the many moons of Jupiter and show that Venus goes through phases like the Moon.
Galilei's telescopes used convex lenses. Such telescopes are called refracting telescopes. Newton built the first successful model of a reflecting telescope, in which the image is produced by reflection from a concave mirror. Mirrors are sheets of metal backed by a thin layer if silver. Producing large concave mirrors is much easier than producing large lenses, and almost all modern telescopes are reflecting telescopes.
Today, observations using telescopes are rarely if ever made by a human observer. Through most of the 20th century images of the sky were recorded photographically. Light strikes photographic plates as a stream of particles called photons, and at least 100 photons are required to produce a measurable imprint. Modern telescopes use so-called photoconductive detectors in which an impacting photon releases an electron, ie produces an electric charge. Such detectors are about 50 times more sensitive than photographic plates. As a result the number of objects that can be detected has increased tremendously, and images of known objects have improved in resolution.
The capability to resolve celestial objects from observatories on Earth is limited by the atmosphere. To avoid light contamination from cities and natural haze observatories are located in remote regions with a particularly dry and clear atmosphere. Even better resolution is achieved when the observatory is set up in space.
Moving the observatory into space has other advantages as well. As we have seen in Lecture 28, light is only one form of electromagnetic radiation. There is no reason why stars should emit electromagnetic radiation only at the wavelengths of visible light. Making observations of the sky at other wavelengths can reveal information not accessible in the visible wavelengths. Unfortunately the Earth's atmosphere absorbs much of the incoming electromagnetic energy. It is transparent only to optical wavelengths and to the wavelengths used for radio transmission.
First observations of electromagnetic radiation were made at wavelengths of radio waves. Instruments used for such observations are called radio telescopes. Radio waves have wavelengths of centimetres to several metres and reflect from a wire mesh provided the grid size is smaller than the wavelength. Radio telescopes are therefore easier to build than optical telescopes, which require very accurately designed mirrors. They can also be built to much larger size.
A disadvantage of radio telescopes is their reduced resolution of objects. To improve resolution radio telescopes can be arranged into interferometer arrays, which use the different arrival times at different radio telescopes to pinpoint the location of transmission sources in space.
Observing the sky from space opens the possibility of measurement at all wavelengths of the electromagnetic spectrum. The USA launched the first space-based telescope IRAS, the Infrared Astronomical Satellite, in 1983. It operated for ten months. The first space-based telescope of the USSR was installed in the KVANT module of the Mir space station 1987 and is still operational. The Hubble telescope is designed as a permanent, regularly serviced space observatory. Other satellite telescopes are now operated by the USA, Europe and Japan. These "high-energy astronomy" instruments allow observations in the ultraviolet, x-ray and gamma-ray wavelengths.
That the Sun is not a solid body was first convincingly shown in 1859 by the amateur astronomer R. C. Carrington. Carrington observed that different parts of the Sun separated by solar latitude rotate at different speed. Not much later the Irish physicist Thomas Andrew showed that there is a critical temperature above which gases could not turn into liquids at any pressure. The fact that the Sun was gaseous was thus clearly established by the 1860s. (DeVorkin, 1984)
A central question of 19th century astronomy was how the Sun can maintain its luminosity (the rate at which it radiates electromagnetic energy into space) without exhausting its energy store. It was generally accepted that solar energy is heat energy and that as a consequence the Sun would have to cool unless it receives new amounts of energy. First attempts at an answer to the question were based on mechanical energy replenishment by gravitational attraction of meteorites: Since a meteor that traverses the Earth's atmosphere shines as intensely as stars, scientists assumed that the Sun's luminosity was kept up by immense continuous bombardment with meteorites.
William Thomson (Lord Kelvin) concluded, however, that such a scenario would also expose the Earth to continuous bombardment, sufficient to make the atmosphere glow. He therefore accepted meteorite bombardment only for the initial heating up of the Sun and assumed that the Sun is now cooling and contracting. This led him to conclude that the age of the Sun could not be as large as required by uniformitarian geology. (Lecture 31)
The final answer to the question had to await the discovery of radioactivity in 1896. But the basic principle of the balance of forces that operate in stars was established some 20 years before that time, when A. Ritter, Professor of Mechanics at the Polytechnical School in Aachen, developed a theory of stellar evolution based on equilibrium between gravity and pressure: Gravity acts to compress a star, while pressure in its interior acts to expand it. (DeVorkin, 1984)
During the first two decades of the 20th century knowledge of the gaseous character of stars, the discovery of transformation of matter in nuclear reactions, the development of models of the atom, an understanding of the properties of blackbody radiation, the study of the electromagnetic spectrum (Lecture 28) known as spectroscopy, and chemical analysis of meteorites combined into a general understanding of the history of stars. It allowed the determination of a star's surface temperature, distance from Earth, size and stage of development between birth and death. This sequence is based on the works of Ejnar Hertzsprung and Henry Russell, who independently of each other discovered the main star sequence of the so-called Hertzsprung-Russsel diagram in 1905 and 1909.
During the first thousands or millions of years when a star is formed from accumulating gas it shrinks under gravitational contraction and undergoes convective motion. When its core becomes dense enough to bring convection to a halt its temperature (expressed in Kelvin) increases to a level that nuclear reaction sets in. This establishes a state of balance between energy loss through radiation and energy gain through nuclear reactions, and the contraction of the star is arrested.
In the Hertzsprung-Russell diagram stars in this state of equilibrium are found on a nearly straight line, known as the main sequence, which relates the star's surface temperature to its luminosity. The exact point where a star finds itself on the main sequence depends on its initial mass; the larger its mass, the hotter and more luminous is its equilibrium state.
Stars on the main sequence are fusion reactors. They convert ("burn") four hydrogen atoms into one helium atom, a process during which 4 percent of the mass is converted into energy. (The Sun burns 600 million tons of hydrogen per second, which converts 4 million tons of matter into energy.) They remain in the main sequence until all hydrogen in their core is burnt. Large stars are the most luminous; they burn their hydrogen fast and cannot stay in main sequence equilibrium longer than a few million years. Smaller, fainter stars burn slowly and remain on the sequence for billions of years.
Once the hydrogen of the core is depleted the energy source to maintain the core in equilibrium is gone and the core contracts under gravity. This releases gravitational potential energy, which is transferred to the outer layers, causing them to expand enormously. The falling pressure causes the outer star to cool, which shifts its appearance towards longer wavelengths in the red part of the spectrum. In this state the star is known as a red giant.
In a red giant hydrogen conversion into helium occurs in the layer immediately surrounding the core; its luminosity is therefore similar or even greater than during the time before it evolved into a red giant. This means that the luminosity - surface temperature relationship of the main sequence no longer holds; red giants are found in the low temperature - high luminosity region of the Hertzsprung-Russel diagram.
While hydrogen is burnt in a layer around the core, the core itself does not contain a source of energy and continues to contract. Its density increases enormously, and with it its pressure, temperature and luminosity.
When the core temperature has reached 100 million K helium begins to "burn" through fusion of three helium atoms to a single carbon atom. This releases energy in a runaway nuclear reaction known as the helium flash. The core expands rapidly, and the star's luminosity is reduced. Continued burning of helium produces a carbon-oxygen core.
When all nuclear energy is exhausted the star can only contract under gravity. Its density increases enormously to more than 1 million kg m-3 (one teaspoon full of its material would weigh nearly 50 tons) and its size shrinks into a white dwarf. (A star of one solar mass shrinks into a white dwarf of the size of the Earth.) At such high density not all electrons can find allowable positions on an atom shell and move around as so-called degenerate electrons. They resist that situation by trying to expand the star, creating tremendous outward directed pressure. The balance of forces in a white dwarf is therefore no longer provided by a balance between gravity and gas pressure (which depends on the temperature) but by a balance between gravity and degenerate electron pressure (which depends on the density).
The temperature in a white dwarf exceeds 10 million K. Lacking a source of energy a white dwarf cools gradually, which means that its luminosity and temperature both decrease. Eventually it will no longer be visible and float through space as a cold mass of degenerate gas.
Observations show that many stars exist in pairs, so-called binary stars. If a white dwarf has a binary companion its extreme density creates enough gravitational pull to transfer some material from the companion to the white dwarf. This material, which contains potential nuclear fuel, accumulates on the surface of the white dwarf and heats up until its temperature is high enough to ignite the nuclear process. Hydrogen burns in a nuclear explosion seen as a nova or new star on the sky. The white dwarf then settles down but continues to gain mass from its companion, and after a while another nova outburst occurs.
Massive stars of many solar masses develop a white dwarf as their core, while nuclear burning continues around it. The products of the nuclear burning accrete on the core, increasing its mass until the degenerate electrons are forced to fuse with the protons inside the atom nuclei into neutrons. This removes the degenerate electron pressure from the balance of forces that kept the white dwarf core stable, and the core collapses almost instantly. Within less than a second a core of the diameter of the Earth is reduced to a diameter less than 100 km.
When the core has reached the density of an atomic nucleus the collapse comes to an abrupt halt. This sends shock waves outwards through the star and causes it to explode in an intense flash of light known as a supernova. Much of its material is dispersed through space as an expanding ring of gas.
The material left after the explosion consists exclusively of neutrons packed into an object nearly as dense as an atomic nucleus. Such objects are known as neutron stars. Their existence and their generation from supernova explosions were suggested within a few years after the discovery of neutrons in 1932. A neutron star of one solar mass would have a diameter of about 20 km and a density of 1017 - 1018 kg m-3. According to the theory of general relativity the gravitational field associated with such extreme densities produces a curvature of space. While this effect deflects light passing the Sun by about 1.75 seconds of arc, light that passes neutron stars is deflected by about 30°.
Bodies with even greater density can have a gravitational field in which the lift-off velocity to overcome gravity exceeds the speed of light. Photons that try to radiate into space cannot leave the object. If the density of the object is extreme, light and other matter that passes is deflected into the object and can never leave it again. Such objects are called black holes.
The existence of black holes is difficult to verify, not only because they cannot be seen but also because they are extremely small. A black hole of one solar mass has a diameter of 6 km, and light or other matter has to come to within 1.5 km of its surface to become trapped. Theory suggests that largest black holes cannot exceed three solar masses.
Stars that display the typical movement of a binary star but have no visible companion suggest that their companion may be a black hole. It could also be a star so faint that present observation methods do not resolve it. If the black hole attracts matter towards it this matter accelerates to a sizeable fraction of the speed of light. Friction will then create intense heat, of 100 million K or more. Under such conditions matter produces x-ray radiation. The binary star system Cygnus - Cygnus X-1 contains one visible star and one x-ray source and is believed to be an observation of a black hole.
This very compressed and schematic summary of stellar evolution can of course not replace a proper scientific treatment of astronomy. It serves here to answer the question: How do we know all these things? Do astronomers just speculate about these things, as the scientist-priests of early civilizations speculated about the universe, or is the description of stellar evolution the result of observation and experiment?
Experiments in stellar evolution are difficult to perform for creatures with a life span of less than 100 years. But the universe is not static, it is dynamic. New stars are formed every day - in our own galaxy a new star is formed every 500 - 1000 years. The stars we see consist of stars of all ages, and a careful star count and analysis of their spectral lines allows us to see similarities and differences, extract commonalities and develop theories that can be tested against other stars. Meteorites provide evidence that the theoretical sequence of conversion from hydrogen to helium to carbon etc. to iron as the final state of evolution is correct.
Astronomers acknowledge that much still has to be learnt before the evolution of stars is fully understood. But when we place known stars on a Hertzsprung-Russel diagram and compare their position with their known development the result makes sense.
Until the 19th century the universe was considered static; its stars were believed to exist forever. Astronomers of the late 19th and early 20th century showed that the universe is dynamic, that stars are born and disappear. Cosmology addresses the question of the dynamics of the universe as a whole: Does the universe evolve, or is it in an ever-lasting steady state? If it evolves, did it have a beginning? Does it have an end?
It is important to remember in such a discussion that if science is to address such questions it has to answer them scientifically. Assumptions are acceptable if they can lead to verification. The method of verification may not yet exist, but unless a way can be seen to find such a method it is futile to propose the assumption.
This is also the time to repeat what we said at the beginning, that it is not the role of science to explain why the universe exists or to discover its true essence. Science can describe the history of stars and predict their future development, just as it can describe and predict the digestive process in the human body. It has to leave to religion the question whether humans have a soul. Does the universe have a soul? Is it conscious of itself? Some religions believe so. Science does not address such questions.
What do astronomers know about the universe? In the 1930s Edwin Hubble took 1,283 sample photographs of the entire sky and counted the galaxies he could find. He counted about 44,000 and found that they are uniformly distributed in space; in other words, the distribution of galaxies in the universe is "isotropic." This is the first fundamental fact about the universe. It is usually called the cosmological principle.
By multiplying up from his selected regions to the entire sky Hubble concluded that with his telescope he would be able to see about 100 million galaxies. Today's more sensitive telescopes should thus be capable of seeing about one billion galaxies. It is obviously impossible to study their history and movement by performing a full spectral analysis for all of them, so sample analysis will have to do.
The second basic fact about the universe was recognized some 40 years before Hubble's survey of galaxies: The universe is expanding. All spectra taken from galaxies outside our own "local group" to which the solar system belongs show a redshift, indicating that all galaxies are moving away from us. Hubble compared the redshift of many galaxies with their distance from our own galaxy and discovered what is now known as the Hubble Law: Galaxies move away from us with a speed proportional to their distance from us.
A moment of reflection will show that the Hubble Law means that the universe is expanding uniformly and that the law applies not only to our galaxy but to all: Regardless from which galaxy the universe is viewed, the more distant galaxies move away faster than the closer ones.
An expanding universe must have once been much smaller than it is today. Did it have a beginning? There are several theories, and there is no definite answer. The most widely accepted theory, known as the "Big Bang", which is in agreement with all known observations, suggests that it did. Some people find it hard to accept that time had a beginning (although in my own view the idea of infinite time and space is equally hard to grasp) and prefer alternative models. A "steady-state model" gained some support during the mid-20th century but was found to contradict newer observations.
Newton realized already one consequence of the Law of Gravity: A finite universe cannot be static; even if all galaxies were initially stationary, gravity would inevitably pull them together. He pondered the question whether an infinite universe could be static but was unable to find the answer. Einstein revisited the question as part of his theory of general relativity and concluded that even infinite universes cannot be static. Unhappy with the result he introduced a "cosmological constant" to express the principle of repulsion to balance gravity, an idea he later described as "the biggest blunder of my life." (Abell et al., 1991)
A theory that can be reconciled with all observations is the "pulsating universe" that expands and contracts regularly. Such a universe would be a "closed universe" in which the space-time coordinates are unbounded but finite. Light cannot leave a closed universe, so communication with other universes beyond its borders is impossible. An alternative model is the open universe in which the space-time coordinates are curved but connect to everywhere in space and time.
It is futile to speculate about the past and the future of the universe unless we find ways to verify model predictions. The "Big Bang" model was first proposed as a cosmological philosophy by the Belgian priest Georges Lemaître (1894 - 1966), who suggested that the universe originated from a "primeval atom" and that
Today the model is based on principles verified through observation:
It leads to an estimated age of the universe of 10 - 15 billion years and can trace its history back to within fractions of a second from the Big Bang. The finite and fixed speed of light helps us to look back: Light from remote galaxies takes so long to reach us that we see them today in the state in which they were millions or even billions of years ago. (Light from the most distant galaxy known in the mid-1990s, the galaxy 4C41.17, left that galaxy when the universe had reached 20 percent of its present age.)
The so-called "standard model" of the Big Bang uses general relativity to explain the known properties of the universe. If it is used to go back to the moment of the Big Bang it is found that it cannot penetrate further towards that moment than a very, very small fraction of a second (10-43 s). If the model is pushed back beyond that moment it moves towards a universe of zero volume and infinite density. The same conditions are found in the centres of black holes. Mathematically such a situation is called a singularity.
A mathematical singularity is usually a sign that the theory is missing an essential element of the physics. A very simple example is given by the case of mechanical resonance. If someone swings a pendulum back and forth its movement can be described by a balance between gravity and the forced acceleration imposed by the person. If the movement is very fast (the pendulum is wiggled back and forth much faster than its resonance period) the pendulum remains close to stationary. If the movement is very slow the entire pendulum will simply follow the movement but not swing. With a little bit of trial and error it is easy to find a period at which the pendulum responds with a very large swing; this is its resonance period.
A mathematical theory of pendulum movement based on the described balance of forces will predict the pendulum's swing amplitude very accurately except in the vicinity of the resonance period, where it predicts that the swing amplitude will become infinite. This has of course never been observed, and the singularity at the resonance period indicates that a force is missing in the balance. In the case of the pendulum this force is friction. If friction is included in the theory the resulting predictions for the swing amplitude are accurate for all periods including the resonance period.
The singularity at the centre of black holes and at the very earliest stage of the Big Bang has also to be seen as an indication that the theory of general relativity is missing a force. Just as the theory of relativity is not required to explain the behaviour of bodies that move very slowly when compared with the speed of light (Newtonian mechanics work well in such situations), this unknown force is not required to explain the behaviour of the universe under conditions of normal star densities. It has to be taken into account in situations of extreme densities. What this force is, we do not yet know.
Singularities are annoying aspects of theories, but at least we know what they tell us - we are missing a force. Other aspects of modern science are just as annoying but do not have such an easy answer. The dualism of light, already discussed in Lecture 28, is all-pervasive in astrophysics. We describe photons as particles but use wave spectra to analyse the properties of stars. Another dualism is provided by relativity theory and quantum theory. In relativity theory
Observations from the solar system and other parts of the universe show that relativity theory is an appropriate way to describe the universe at the macroscale. In quantum theory, on the other hand
Its predictions have been verified with experiments at the microscale.
Many theoretical physicists are dissatisfied with this state of affairs and try to find a unifying theory that describes the behaviour and properties of matter on all scales. Such theories invariably take the form of complex mathematical equations that allocate a new property to time. Solutions that have been proposed are imaginary time (Hawking, 1988), negative time, quantized time (Oeckl, 2003) and an 8-dimensional complex space-time geometry (Buers, 2004).
All such models have in common that they aim at a mathematical description of the world, preferably an elegant one. In that sense it can be said that we have returned to the ancient Greek philosophers, who used the elegant mathematics of perfect circles when they speculated about the solar system without the slightest hope of verification of their ideas. But history does not repeat itself, and science has learnt how to proceed. Any mathematical model is only worth as much as it points towards new experiments or observations that can prove or disprove its predictions. Without the possibility of verification mathematical models remain mere intellectual exercises.
Whether a mathematical model will bring new insight or new observations will point the way, the fact remains that cosmology is dealing with laws of nature that are far outside our everyday experience. Understanding the universe will require new ways of thinking. Maybe time does come in quanta. The pre-Columbian civilizations (Lecture 18) would not have found that at all difficult to comprehend.
Abell, G. O., D. Morrison and S. C. Wolff (1991) Exploration of the Universe 6th ed. Saunders College Publishing, Philadelphia.
Buers, A. J. (2004) Antigravity in a composite space-time model. In: Faculty of Physics and Nuclear Sciences, Amirkabir University of Technology (ed.): International Conference on Physics Proceedings, Teheran, 171 - 177.
DeVorkin, D. (1984) Stellar evolution and the origin of the Hertzsprung-Russell diagram. In: Gingerich, O. (ed.): The General History of Astronomy volume 4: Astrophysics and twenthieth-century astronomy to 1950: Part A. Cambridge University Press, Cambridge, 90 - 108.
Hawking, S. (1988) A brief history of time. Bantam Books, New York.
Oeckl, R. (2003) A "general boundary" formulation for quantum mechanics and quantum gravity. Physics Letters B 575, 318 - 324, hep-th/0306025.
Roy, A. E. and D. Clark (1989) Astronomy: Structure of the universe 3rd ed. Adam Hilger, Bristol.
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