The End of Time: The Next Revolution in Physics

The Aims of Machian Mechanics (1) (p. 71) In creating the beautiful diagrams that form such an important part of this section, Dierck Liebscher was able to draw on initial data devised by Douglas Heggie (University of Edinburgh), using software written by Piet Hut (Institute for Advanced Study), Steve McMillan (Drexel University) and Jun Makino (University of Tokyo). Dierck has written a very interesting book (alas, as yet published only in German) on the connection between different possible geometries and Einstein’s relativity theory (Liebscher 1999). It contains many striking computer-generated diagrams.

(2) Poincaré’s discussion is contained in his Science and Hypothesis, which, along with the writings of his contemporary, Mach, became a popular-science best-seller. In fact, in this book I am actually revisiting many of the themes discussed by Poincaré and Mach, but with the advantage of hindsight. How are the great issues they raised changed by the discovery of general relativity and quantum mechanics? I have adapted Poincaré’s discussion somewhat to match the requirements of a timeless theory (he considered only the possibility of eliminating absolute space).

(3) Since writing Box 3, which draws attention to the present unsatisfactory use of absolute dislance in physics, I have discovered a way to create dynamical theories in which distance is not absolute. This is achieved by a very natural extension of the best-matching idea described later in the book. The new insights that I mention in the Preface are in part connected with this development. One of the most exciting is that, if such theories do indeed describe the world, gravitation and the other forces of nature are precisely the mechanism by means of which absolute distance is made irrelevant. Since this work is still in progress, I shall make no attempt to describe it in detail, but I shall keep my website (www.julianbarbour.com) up to date with any progress (see also p.358).

CHAPTER 6: THE TWO GREAT CLOCKS IN THE SKY

The Inertial Clock (p. 99) Tait’s work, which I feel is very important, passed almost completely unnoticed. This is probably because two years later the young German Ludwig Lange introduced an alternative construction for finding inertial frames of reference, coining the expression ‘inertial system’. Lange deserves great credit for bringing to the fore the issue of the determination of such systems from purely relative data, but Tait’s construction is far more illuminating. Lange’s work is discussed in detail in Barbour (1989) and Tait’s in Barbour (forthcoming).

The Second Great Clock (p. 107) A very nice account of the history of the introduction of ephemeris time was given by the American astronomer Gerald Clemence (1957).

CHAPTER 7: PATHS IN PLATONIA

Nature and Exploration (p. 109) For physicists and mathematicians who do not know the book, a wonderful account of the variational principles of mechanics, together with much historical material, is given by Lanczos (1986).

Developing Machian Ideas (p. 115) Translations of the papers by Hofrnann, Reissner and Schrödinger, along with other historical and technical papers on Mach’s principle, can be found in Barbour and Pfister (1995).

Exploring Platonia (p. 115) The special properties of Newtonian motions with vanishing angular momentum were discovered independently of the work of Bertotti and myself by A. Guichardet in the theory of molecular motions and by A. Shapere and E Wilczek in the theory of how micro-organisms swim in viscous fluids! A rich mathematical theory has meanwhile developed, and is excellently reviewed in the article by Littlejohn and Reinsch (1997), which contains references to the original work mentioned above. All mathematical details, as well as references to the earlier work by Bertotti and myself, can be found in Barbour (1994a).

CHAPTER 8: THE BOLT FROM THE BLUE

Historical accidents (p. 123) Poincaré’s paper can be found in his The Value of Science, Chapter 2. Pais’s book is in the Bibliography.

Background to the Crisis (p. 124) The best (moderately technical) historical background to the relativity revolution that I know of is the book by Max Born. It is available in paperback.

The Forgotten Aspects of Time (p. 135) My claims about the topics that somehow escaped Einstein’s attention are spelled out in detail in Barbour (1999, forthcoming). I have tried to make good the gap in the literature on the theory of clocks and duration in Barbour (1994a).

CHAPTER 10: THE DISCOVERY OF GENERAL RELATIVITY