*The Comprehensible Cosmos: Where Do the Laws of Physics Come from? *

Victor Stenger

Prometheus Books, New York, 2006, ISBN 1-59102-424-2.

After the backlash comes the return to orthodoxy. In *A Brief History of Time*, Stephen Hawking suggested that physics was on the verge of solving the final puzzles of creation: the marriage of quantum physics and gravity and the origin of the universe. Since then, there has been a general sense of disappointment at the progress made by pretenders such as string theory. A number of works have suggested that mankind is still scrabbling around in the foothills of understanding, and that the universe may not even be ultimately explicable by our scientific and mathematical tools. Now, in a new magisterial account of the state of modern physics, Stenger reasserts the original optimistic outlook: physics has explained almost all that is and has been, and the few remaining pockets of resistance must soon fall.

He argues that the measure of the success of physics is that it can be encapsulated in a set of succinct equations which account for almost all human experience. In the first half of the book, he guides the reader through the historical development of physics, passing through special and general relativity and then dealing with particle physics, embarking on a brief excursion through statistical thermodynamics, before reaching the standard model and finally cosmology. He shows that this historical development can be seen as the expression of two principles: the principle of objectivity – that the laws of physics should be independent of our formulation of them and of our position in the universe – and the principle of symmetry. He shows that, in many cases, our theories are the simplest that can result from “point of view invariance” and symmetry. Thus, the universe is comprehensible.

Given the centrality of invariance to the thesis of the book, and the enormous power of his approach, it is unfortunate that Stenger does not spend more time introducing it to the reader, as he does, for instance, with the concept of symmetry later in the book. He explains that “point of view invariance” means that the laws of physics must look the same wherever you are – an experiment will have the same result whether it is carried out in England or France, say, and can be explained using the same theories in either place. In mathematical terms, this means that vectors must be unchanged by a co-ordinate transformation. This is accompanied by an obscure diagram (p47). But he does not say, in simple terms, that it is not the expression of the vector in the transformed co-ordinate system that is unchanged. In fact, the expression of that vector will be changed. It is the vector itself, as a point in space, that does not actually move when the co-ordinate system is changed. It is still the same point, although its expression in the new co-ordinate system is different. A little more time explaining and demonstrating co-ordinate transformations would remove the risk that an uninformed reader might be led astray, and would make the deductions that follow from invariance even more breathtaking.

The first half of the book almost entirely eschews equations (even E=mc^{2} is avoided by referring to Einstein’s “familiar formula” (p49)). Stenger calls on his own profound understanding to digest relativity and quantum physics in language accessible to the lay reader, communicating some of the beauty and logic of these theories with the passion of the practitioner. The second half of the book contains all the equations that were excised from the first half. It is not a tutorial in the mathematics of relativity and quantum physics, nor is it a reference work for those already familiar with these areas. Rather, it is like a guided tour through a mathematical museum displaying the most beautiful and important exhibits. You can tour a natural history museum and admire all the skeletons of dinosaurs without already having or aspiring to have a deep understanding of paleontology. In the same way, the second half of *The Comprehensible Cosmos* will show you the mathematical landmarks of modern physics and make you gasp with their simplicity and beauty, even if you only grasp a tiny proportion of their meaning. It is no criticism to say that the second half of the book fails to identify a target readership, because that is effectively impossible given the task it has set itself. It is perhaps suitable for a student familiar with differential geometry, including covariant derivatives and the curvature tensor, but not relativity and who is familiar with functional analysis, including operators on Hilbert spaces, but not quantum physics. Towards the end, Stenger can only refer the interested reader to relevant “textbooks” (pp305, 306) to fill in the yawning chasms of logic that he spans in a few lines. The second half of the book is, nevertheless, a valiant attempt to introduce the reader to some of the beauty of the underlying mathematics and makes an intriguing guided tour.

The optimism of Stenger’s judgment on physics follows from his philosophy of science, which he sets out at the start of the book. He takes an operational view of measurement – the definition of a particular measure is the set of operations that are used to make it. He sets out, by way of example, the various ways in which the “metre” has been defined by a particular canonical measurement – as the length of a particular metal bar at a particular temperature, a certain percentage of the wavelength of a part of the cadmium spectrum and most recently as the distance light travels in a certain time. This raises an obvious question: if the “metre” is defined purely operationally, then these different operational definitions must refer to different measures. Why are they all called the “metre”, unless there is some additional concept underlying the operations which unifies them all and justifies using the same name? Leaving this difficulty to one side, Stenger builds his scientific theories on top of operationally defined measurements. He eschews the culturally laden word “theory”, preferring to use the word “model”. His models take these empirical measurements and provide a description of them. Models are useful if and to the extent that they are consistent with the measurements – the larger the number of measurements that are explained by a theory, the better it is.

This approach provides a clear empirical basis to physics and allows models to be easily compared. If two different models explain the same facts, then they are equal in value and either can be used (although an appeal to parsimony may be used to choose between them in this case). It serves well as a philosophical background to the historical narrative in *The Comprehensible Cosmos*, showing how each model builds on its predecessors by explaining slightly more of the sum of human experience and measurement. Above all, it is to be preferred to the complete absence of any philosophical background found in many similar popular physics books.

However, there is a problem with this approach. To begin with, there is an ambiguity in the use of the word “model”. A model can be a description of a set of facts, such as a description of the position and velocity of the Earth at points in its orbit. This description might consist of a large number of different measurements at different times, but a more parsimonious model would consist of a few measurements together with rules to calculate new positions and velocities at times other than those explicitly set out. We might describe this as a “model of the Earth’s orbit”. But a model, in the sense of a scientific theory adopted by Stenger, also means a set of laws that can be used to develop a model, in the narrower sense. For instance, we might create a “model of gravity” (to employ the rather infelicitous phrase used by Stenger at p26) that embodies an inverse square rule, which could then be used to create a model of the Earth’s orbit. Stenger wants to elide these two meanings, because he does not want to deal with the metaphysical questions raised by the existence of laws within scientific models – he just wants to concentrate on the empirical facts. This accords with his narrative view of a progression of scientific theories each having a slightly better empirical basis than the previous one.

Unfortunately, this elision misses out something essential to scientific theories. It eliminates the laws that stand behind the physical models. Stenger rightly points out that so-called “laws” do not themselves force material objects to obey them, and in that sense are different from the laws that apply to humans. However, jurisprudential laws do not “force” human action either. Jurisprudential laws are normative statements: they say that a human should do something at some point in the future. They do not predict that the person will actually do that thing – humans break human laws all the time. But, whether obeyed or not, the law of jurisprudence does correctly assert that a normative obligation will apply to a person in certain circumstances. A scientific law is not a jurisprudential law. It does not say that a particle will be “obliged” to move at some point, it simply predicts that it will move in certain circumstances. The common element is prediction. By downgrading scientific laws, Stenger downgrades the importance of prediction in science.

Laws are not necessary for models that describe what has already happened. A set of measurements can be a correct model in these circumstances – although not particularly interesting – and it need not contain any laws. But laws are essential when making predictions. A law predicts what will happen in certain sets of circumstances. It cannot simply be a descriptive list. An essential difference between scientific theories is in the qualities of the predictions that they make and the sets of circumstances that their predictions cover. This is why Einstein’s theory of relativity cannot simply be characterized as Newton’s theory plus a minor tweak to correct some observed wobbles in the orbit of Mercury. It imposes a new paradigm consisting of a new, enhanced set of predictions that follow from a new set of laws.

Stenger’s comparison of scientific theories on the basis of quantity of correct descriptions, minimizing the role of laws and prediction, need not stop at downgrading Einstein. What are Newton’s laws but a minor refinement of the law that planets move in ellipses, which fit the data well to a lesser approximation? And why stop there? Let’s just agree that the planets move in circles – a far more parsimonious theory that still fits a good proportion of the data. This reductio ad absurdum is only possible because Stenger’s philosophy of science fails to capture something central to physical theories – that they contain laws that make statements about the future – and it is exactly this failure that provides the temptation to subscribe to an excessively optimistic view of physics.

Nevertheless, Stenger’s optimistic view based on the high proportion of data fit by modern scientific theories serves to propel the reader through Newton, Einstein and into quantum physics and cosmology. The extraordinary depth of theory that follows from an axiomatic reliance on “point of view invariance” and symmetry do convince the reader that the cosmos is comprehensible, and why. It must be admitted that there is a slight letdown when it is revealed that current theories only explain about 3.5% of the matter and energy in the universe, and for the rest we rely on some dubious appeals to “dark matter”, “dark energy” and, even worse, “quintessence”. Similarly, the upper reaches of particle physics become less satisfying when the symmetries start to break down and the number of observed parameters starts to multiply. But these are minor quibbles compared to the total breadth of explanation.

*The Comprehensible Cosmos* is an entertaining and stimulating tour of the upper reaches of modern physics, driven by the unifying themes of “point of view invariance” and symmetry. It demonstrates how much of the universe is comprehensible as a result of a few basic principles. It is a welcome reminder how far physics has come, whatever your opinion on how much further physics still has to go.

Adam Sanitt