Synge, talking about relativity: 50 years on

A Review of Synge’s Talking About Relativity – is it still as relevant as it was 50 years ago?

It is an oft-cited aphorism that intelligence is best displayed in the process of aptly simplifying the complex for general understanding. Though a passionate and rather frequent reader of physics-related literature, I frequently find my desire to (though verily only at an abstract level) grasp the varying intricacies of the field constrained by time and my largely incompatible law degree. I can already feel the curl of contempt on the lips of first-year law students: how can I even attempt to devote time to reading science? But before you pour the phials of your spitefulness unto my unasking soul, know that the answer is both sad but simple: insomnia. I find the recourse to insomnia, however, justified. There is nothing more abhorrent than the restriction of thought (a saying I attribute principally to Jack Henry Abbott’s In The Belly of the Beast). Unfortunately, I would fain concede that this dislike frequently renders me insane. Fortunately for me, however, to calm my irascibility exist authors that possess the solemn ability to delve into the penetralia of scientific esotericisms and condense them into material that is, for all practical purposes, readily understandable. 

In 1972, Synge (after whom the brutalist-looking Art’s Block Synge Lecture Theatre is named) set out to do just that. Having described the religion of modern man to be “understanding,” Synge opens up his short, pristine Talking About Relativity with the notion that it be used as a guide to the field of general and special relativity for all non-experts thereon. In his own words: “[s]cientific communication is the most exciting when it succeeds, and the most depressing when it fails.” Except for two complex, equation-filled chapters which – through no fault of his own – he found indispensable, the book remains in its entirety comprehensible and, to my admittedly unsophisticated understanding, relevant.

“Indeed, this puts forth a fine, oft-trodden line, as the purpose of physics is to explore the “R-World” via the hand and the brain. Though I confess, one must give play to the imagination in order to understand reality!”

Chapter I, a mise en abyme entitled “Talking About Concepts”, sets out a preliminary distinction that will thereafter serve as a lynchpin to his explanation of both relativistic theories; that is, a distinction between what he terms the “Real World” (“R-World”) and the “Model/Mathematical Worlds” (“M-Worlds”). The former is self-explanatory; the latter, contrarily, relates to that invented by ‘the mind of man’. Their distinction is sacrosanct: intermingling both would lead to what he terms the “Pygmalion syndrome” – indeed a satisfactory reference to Pygmalion’s becoming infatuated with his own sculpture. Germanely, infatuation with one’s own creation would be similarly pernicious: it leads scientists to erringly believe they have proved something in the “R-World” by proving the same in the “M-World”. Indeed, this puts forth a fine, oft-trodden line, as the purpose of physics is to explore the “R-World” via the hand and the brain. Though I confess, one must give play to the imagination in order to understand reality!

Furthering this distinction, he subdivides the ‘M-World’ into two subscripts, wherein “M1” pertains to Newtonian physics, and “M2” pertains to the novel world of scientific relativism. To better explain this distinction, Synge attempts to exemplify this schism in Chapter II with geometry. Simply put, a conviction without reason (e.g., the drawing of bisectors) relates to a mere observance of the “R-World.” When one takes these bisectors, however, and rids them of a corresponding size & shape, after which we are left to concentrate purely on its position, then we have entered the “M-World” (e.g., the non-Euclidean discovery that the angle-sum is greater than or less than two right angles; in fact, “M-Geometry” is only to be applied in relativism with great circumspection). In Chapter III, Synge calls algebra to his succour to further concretise this distinction, which he deemed still vague in principle. Therein, we left the “R-World”, Synge argues, once we – driven by a conviction that algebraic solutions abound – began using integers and symbolised what was previously worded (e.g., using symbols such as =, ÷, and utilising negative numbers). To pertinently quote Kronecker: “God created the positive integers, and man created all the rest”.

Having laid out this preliminary groundwork, Synge then goes on to argue that “M2” serves as a better model to understand our universe than “M1” does. The correctness of such a statement remains trite. It has been the very purpose of the Einsteinian revolution to better those Newtonian doctrines. However, this is not to take away from the fact that numerous Newtonian ideas remain largely applicable. In fact, I am presently reminded of a passage in Daniel Dennett’s Darwin’s Dangerous Idea, in which he states that (at least as of 1995), NASA still used Newtonian mechanics when projecting their spatial trajectories. Two important forks nonetheless universally lie on the “M” road: (1) the concept of simultaneity and (2) the concept of rigidity. Though Newton accepts those two concepts, Einstein doesn’t. In the following eleven chapters, Synge attempts to lay out how that is so. And, unsurprisingly, this is where things get a tad bit tricky: what was hitherto as clear as day suddenly becomes fuscous and – at times – unfathomable (to the poor mind of a law student, that is).

In order to understand Einstein’s rejection of these two core concepts, further groundwork needs to be laid. Foremostly, one must understand what actually happens in physics. All throughout my perusals of scientific literature, I have come across no better and more succinct explication than this: physics is the science of “matter in motion” (Tim Maudlin, Philosophy of Physics: Quantum Theory: p. 1). Synge actually omits a definition of physics, so I thought I thought it fit to resolve this forlorn omission with an easily understandable definition. This being said, the proper study of such matter demands the finding of an appropriate leading operator (a question of theoretical physics and is often supplanted with the inventions of Einstein, Schrödinger, and Dirac) and a finding of a subsequent operator (a question of mathematical physics); the ne plus ultra of which is to solve the following “M-World” equation: BAx = Cx, in which “x” is the variable, “B” and “C” are known operators (“B” being however leading), and “A” is to be found. This formulaic arrangement, Synge declaimed, was – at his time of writing – the most used equation in his field. Such a statement, I believe, stands to this day (at least in matricial form). A final piece of groundwork is then laid out in Chapter V and may be summarily dealt with as follows: space-time is four-dimensional; one coordinate does not suffice to describe an event. In effect, it is what Synge coins the “fourness” of the operation that is important, not the way it is carried out. 

Chapter VI, humorously titled “The Queen and the Captain of the Guard”, proffers the purest demonstration of Synge’s mastery of digesting the complex. In a tale of supposed adultery between the King’s wife and the Captain of the Guard, the King summons the President of the Royal Academy of Sciences to conjure up a plan that would permit him to spy on his wife’s daily doings. The President tasks the King with assembling four groups (one for each dimension) for each person, the purpose of each being to note her and the Captain’s daily activities in numerical form, thereafter transcribing them into twelve curves (six for each person), so that if both respective curve groupings coalesced for some distance, such would serve as proof of their having been together. The excess in notation (i.e., groupings of six instead of four) the President surreptitiously demands of the King so as to prove the four-dimensionality of space-time: ideally (for the President, that is!), the first eight curves would coalesce, whereas the remaining wouldn’t.

The idea of ascribing to each succession of acts a curve, Synge later terms “world line.” Once applied to the notion of a particle, he explains that we can better understand the idea of particle signalling, the process of which could be understood – for Synge, at least – as a succession of events. This is where Einstein rejects simultaneity: for him, the best signal is the light signal in vacuo (the notorious “c” in E=mc2, where the world-line of a free particle is a geodesic [that is, the shortest path between two points]); whereas for Newton, “it would be better to shake a massive fist, and this would cause an instantaneous gravitational effect, which could be returned immediately,” – whence comes his acceptance of simultaneity. 

In Chapter IX, labelled “Time”, Synge – in a fashion reminiscent of his awesome sixth chapter – tells the story of two skippers who, on different boats, seek to record the times at which both have breakfast, their aim being to eat synchronously. After multiple failed attempts, both are, by some deux-ex-machina-type revelation, made aware of the concepts of “relative distance” and “relative time.” Accordingly, if one sends out a light signal at time ‘t1’ to record the world-line of that very signal by having it reflect at an event on that same world-line, and returning to the observer at time “t2”, we are left with:

D  (cm) = 12 c (t2t1)

Applying this idea of world-lines to that of curvatures of space-time, Synge explains Reimann’s curvature as a “deviation of geodesics representing the histories of free particles and photons.” Planets are made up of these free particles, and the light by which we see them is made up of photons. Recall now BAx: the operator “B” is gravitation – or what Reichmann coined the “curvature tensor.” The operator is determined by the energy tensor “Mx” (matter) and is composed of twenty different functions, and Ax itself demands a twofold differentiation and a subsequent algebraic addition. There is no way in hell that I will even attempt to further explain. 

Up until now, Synge’s discussion of theoretical physics has remained utterly enjoyable, relevant to present-day physics, and – for the most part – fathomable. However, in opening up the final chapter, “Particles in Collision”, we are suddenly reminded of the book’s age”

It is at this juncture that Synge sub-subdivides “M2” between the general and special theories of relativity. For the latter, gravity is tritely trivial (space-time being not curved, but instead flat). From the latter also springs the rejection of the fork’s second prong: rigidity. Recall that relativity rejects the idea of simultaneity. Given that a rigid body transmits information instantaneously (think of yourself swinging a stick left-to-right: the opposite part wouldn’t lag behind), rigidity is ipso facto rejected. As such, special relativity allows only for “clock-clouds”, the distance between them being measured in an elaborate manner involving light signals. 

Synge closes his book with a comparatively thorough discussion of particle collision. Up until now, Synge’s discussion of theoretical physics has remained utterly enjoyable, relevant to present-day physics, and – for the most part – fathomable. However, in opening up the final chapter, “Particles in Collision”, of his book with the following: “[p]roblems about the collision of particles stand in the forefront of present-day research in theoretical physics,” we are suddenly reminded of the book’s age. Not to discount the discovery of, say, the Higgs boson, and other discoveries made by the Large Hadron Collider and Stanford’s Linear Collider (both of which I have had the pleasure of seeing with my very own eyes!). But, theoretical physicists now grapple with a myriad of other, fascinating issues: e.g., dark matter, dark energy,  early universe theories, interplay between quantum mechanics and gravity, unified theory (within the framework of string theory) – the list goes on… Scientific progress notwithstanding, Synge’s book remains an incredibly enjoyable, informative, and relevant account of theoretical physics, and I would recommend it to anyone who seeks a more thorough understanding of the field. To anyone looking for a more contemporaneous (and thus expounded) account on the matter, I would emphatically recommend Brian Greene and Lawrence M. Krauss, with the former’s works (all of which I can absolutely guarantee are worth a read) being the closest to Synge’s.

Sébastien Laymond

Sébastien Laymond is the Editor of the 'SciTech' column for Trinity News, and is currently in his Junior Sophister Year reading law.