Phlogiston and caloric

Before we look at Einstein's famous equation, we had better set the scene by describing how scientists had arrived at the concepts of energy and mass – the ‘E’ and ‘m’ in the equation. The gradual evolution of our present understanding of energy began with two ideas at least as curious as the infamous aether – ‘phlogiston’ and ‘caloric’. It provides us with some insight into the way that science progresses to look at why these two theories were invented and subsequently discarded.

Phlogiston was introduced towards the end of the seventeenth century by Georg Stahl, a German professor of medicine and chemistry, in an attempt to understand fire. Even in the latter part of the eighteenth century, many scientists still regarded fire as an element. Combustible materials were supposed to be made up of two parts -the calx, or ash, and the ‘phlogiston’. It was thought that, when a substance burned, the phlogiston was liberated, leaving the ash behind.

Prologue

In this chapter, we shall explore the application of special relativity to atomic physics. In order to make accurate quantitative predictions for the atomic structure underlying both physics and chemistry, it turns out to be essential to take into account ‘relativistic corrections’ to the standard quantum mechanical picture of the atom. Such applications of relativity form an important part of the experimental evidence supporting Einstein's theory, and to ignore them would give a distorted impression of its success. Thus, although this is a book about relativity, in order to appreciate this area of applied relativity, it is necessary to give a brief overview of our present understanding of atomic physics. A companion volume, The Quantum Universe, gives a fuller account of the development of quantum theory and its application to the modern world.

We begin our overview with an account of the great debate about the existence of atoms. In 1905, the same year that he published his paper on special relativity, the young Einstein made a crucial contribution to the debate with an atomic explanation of Brownian motion. At the same time as this debate was raging, the first discoveries about radioactivity were being made by Roentgen, Bequerel and the Curies. A major puzzle of the era was the origin of the energy released in radioactive decays.

Prologue

In this chapter, we explore me application of special relativity to nuclear physics. As in chapter 6, the reader need only read the following overview to gain an impression of the impact Einstein's theory has had on our understanding of nuclear structure and nuclear reactions. The story of Einstein's development of the theory of general relativity is taken up in chapter 8: the rest of this chapter is not essential for an understanding of the remainder of this book.

The story begins with Ernest Rutherford and Frederick Soddy quantifying the amount of energy released in radioactive decays and their joint realization that such a huge energy source could be a mixed blessing for humanity. Francis Aston, working in Cambridge with Rutherford, invented the ‘mass spectrograph’ and was able to separate different ‘isotopes’ of many elements. There was much confusion about the nature of ‘isotopes’ until James Chadwick discovered the neutron in 1932. Aston had also realized that the neutrons and protons when bound in the nucleus weigh less than in their free state. The difference arises from the nuclear binding energy, which results from the strong nuclear forces holding the nucleus together. This is a direct example of Einstein's mass-energy relation.

The scope of this review

Ever since the 1930s, it has been conventional wisdom in cosmology that the Friedmann (1922, 1924)–Lemaître (1927, 1931)–Robertson (1929, 1933)–Walker (1935) (FLRW) models describe the large-scale properties of our observed Universe faithfully. At the same time, it has been conventional wisdom in relativity theory that finding exact solutions of the Einstein equations is extremely difficult and possible only for exceptionally simple cases. Both these views were challenged repeatedly by lone rebels, but a few generations of physicists and astronomers have been educated with these conventional wisdoms solidly incorporated into their minds. As a result of this situation, a large body of literature has come into existence in which exact solutions generalizing FLRW have been derived and applied to the description of our observed Universe, but most of it remains unknown to the physics community and is not being introduced into textbooks. This book is intended to achieve the following two objectives:

1. To list all the independently derived cosmological solutions of the Einstein equations and to reveal all the interconnections between them.

2. To compile an encyclopaedia of physics in an inhomogeneous Universe by gathering together all physical conclusions drawn from such solutions.

An exact solution of the Einstein equations is termed “cosmological” if it can reproduce a FLRW metric when its arbitrary constants or functions assume certain values or limits. This requirement will be discussed in Section 1.2. The solutions are organized into a few families.

This appendix contains a list of papers which, in the opinion of this author, played a crucial role in the development of inhomogeneous cosmological models. It must be stressed that, except for a few, the papers listed below have never been properly appreciated, and many of them are virtually unknown even today. The list is thus a call for historical justice (based on a personal assessment by this author) rather than a presentation of development of the field.

Lemaître (1933a) – the pioneering paper, and probably the most underappreciated one. The author introduced the Lemaître–Tolman model, and in addition presented or solved a few problems commonly associated now with names and papers younger by a whole generation. Examples: the definition of mass for a spherically symmetric perfect fluid, a proof that the Schwarzschild horizon is not a singularity (by a coordinate transformation to a system of freely falling observers), a preliminary statement of a singularity theorem illustrated by a Bianchi I model.

McVittie (1933) – presented a superposition of the Schwarzschild and FLRW metrics which is a perfect fluid solution. A remarkably bold and early entry, but the solution has still not been satisfactorily interpreted.

Dingle (1933) – a preliminary investigation of spherically symmetric shearfree perfect fluid solutions, later completed by Kustaanheimo and Qvist (1948). The paper is remarkable for the author's strong criticism of the cosmological principle and an explicit call for inhomogeneous models (see Appendix C).

Every review article or book raises the obvious question about its completeness. In order to give the readers an idea about the degree of completeness of this review, the method used to compile the bibliography is described briefly below. These were the essential steps:

1. The author has been interested in the subject since about 1980. Until 1988, when systematic compilation was begun, I studied every newly published research or review article on inhomogeneous cosmological models, and followed each reference whose context of citation suggested that it might contain more of the relevant material. The latest publications included are those that reached my hands in September 1994.

2. I looked through the subject indexes to all volumes of Physics Abstracts, beginning with the 1915 volume, and studied the sections on cosmology, general relativity, gravitation, gravitational collapse and spacetime configurations. Whenever any keyword of title or abstract suggested that the paper might be relevant for the review, I added the reference to the list of papers to look up. The last index so surveyed was Part I of the 1994 volume.

3. While reading or looking through the papers, I added every reference that seemed relevant to the list.

Stage 3 produced more than 1000 references in addition to about 1000 found in stage 2 (but about two-thirds of the total number of papers were discarded according to the criteria listed in Section 1.1).

For most physicists, sufficient reason to consider the Universe as being inhomogeneous is the intellectual challenge to explore the unknown. A mathematical argument in favour of inhomogeneous models was given by Tavakol and Ellis (1988). The authors demonstrated on examples that including new parameters (or changing values of parameters) in a set of ordinary differential equations may drastically change the behaviour of solutions, for example, from periodic to chaotic. This shows that the set of cosmological models is most probably structurally unstable. Tavakol and Ellis emphasized the importance of studying models without symmetry.

Several physicists were already able to see in the 1930s that the “cosmological principle” was not a summary of any kind of knowledge, but just a working hypothesis leading to the simplest models that were yet acceptable. A sample of early reservations about the cosmological principle is given in Appendix C. Unfortunately, the astronomical community was largely unconvinced. The discoveries of large inhomogeneities in the 1970s and 1980s were met with surprise. By the present day, those same discoveries could be sufficient argument for considering inhomogeneous models, and the idea seems to be gaining still wider acceptance (see an interesting proposal by Melott, 1990, to measure the topology of large-scale matter distribution in the Universe). However, over the years, astrophysical and philosophical arguments have been given by several authors in favour of generalizations of the FLRW models, and they are briefly recalled here. The collection does not pretend to be complete.

Afterthoughts

In addition to justifying the two messages from Section 1.1, the main purpose of this book was to draw together and bring to the readers' attention all those fine and illuminating contributions to relativistic cosmology that do not fit into the “standard model”, while still not negating its applicability as a first approximation. Hopefully, the book has proved that these contributions are not phantasies of isolated individuals, but that, taken together, they do tell us about interesting processes that might be going on in the Universe – processes that we would not even suspect using the FLRW models alone. The results presented highlight several problems in the current system of education and research in physics.

The first problem is the highly dogmatic approach of astronomers towards the “standard model” and other “standards”. It seems that the hypothetical, provisional character of the assumptions that lead to the FLRW models has not been given sufficient emphasis in astronomy courses. As a result, the homogeneity and isotropy of the Universe are treated by many (most?) astronomers as a revealed truth, never to be questioned. This author has sometimes experienced outright aggression during seminars and conference talks, while presenting the various ideas that now appear in this book. Physicists do not seem to suffer from this problem, but astronomers would be well advised to treat the “current knowledge” in a more relaxed way, especially in view of the still highly unsatisfactory reliability and precision of most observations and the numerous changes in the apparently well-established results.

In this chapter, those papers will be described which discuss physical and astrophysical implications of the various properties of inhomogeneous cosmological models. A great majority of the papers are based on the L–T model. Those considerations which are not based on any explicit solution are described in Section 3.9. Some more cosmological considerations, based on the McVittie (1933) solution, will be presented in Section 4.7. The papers are sorted by the subjects they discuss; each section is devoted to one subject; the sections are ordered in chronological order of the earliest contributions.

Formation of voids in the Universe

The first predictions that voids should form in an inhomogeneous Universe were formulated by Tolman (1934) and Sen (1934) on the basis of the L–T model. Tolman predicted it in just a casual remark (see quotation in Section 2.12), while Sen made a thorough study of stability of the static Einstein and the FLRW models with respect to the L–T perturbation, and concluded explicitly that “the models are unstable for initial rarefaction”.

In a follow-up paper, Sen (1935) considered the influence of pressure on the stability. That investigation is based on the Einstein equations in a spherically symmetric perfect fluid spacetime, without invoking any explicit solution. Depending on the spatial distribution of pressure, stability may be restored or instability enhanced, but this observation is not developed further.

Bondi (1947) predicted the formation of voids in just one phrase: “… if originally there is a small empty region round O and if the matter nearest to O does not move inward at first … then it will never move inwards”.