Computing Reviews

Mechanistic explanations in physics and beyond
Falkenburg B., Schiemann G., Springer International Publishing, New York, NY, 2019. 220 pp. Type: Book
Date Reviewed: 10/01/21

This book provides an overview of the mechanistic approach to science from historical, philosophical, computational, and other viewpoints. This approach arises from the fact that, in real life, most objects remain the same (at least locally) almost all the time: objects move, parts may break off, rubber objects may change shape, but local properties mostly remain the same. There are exceptions--water boils, wood burns--but these are relatively rare. We can break most objects into smaller and smaller pieces until we cannot, so it is reasonable to imagine the world as a collection of not-further-divisible parts--what Greeks called atoms.

Interaction between objects is also usually local: to move my desk, I need to stand next to it and either push it or lift it. There are exceptions, like magnetism, but they are rare. So, it is reasonable to conclude that atoms interact only when they happen to be next to each other, that is, when they collide. Such a description of the world as several (possibly moving) particles is the original mechanistic description (see chapter 2). The main advantage of such a description is that mechanical motion and mechanical collisions are ubiquitous; we have developed intuition about such processes, which helps us to make predictions based on such models. Also, from numerous observations, we can deduce equations of motion for such interacting particles, and this allows us to apply standard algorithms for solving these equations, and thus for extracting numerical predictions from such mechanical models.

Success of this approach led to the idea of representing seemingly action-at-a-distance processes, like magnetic attraction or gravity, in the same way, that is, as caused by an exchange of special particles. Until Newton, this was the usual explanation for gravity, for optical phenomena, and so on.

This naive mechanistic model of the world was broken by Newton (see chapters 2 through 5). Newton came up with explicit formulas and algorithms for describing action-at-a-distance. Thus there was no longer any need for a mechanical model. Physicists still used mechanistic atom-based models, for example, in statistical physics, but these models were perceived as a useful way to derive observable equations, not as a description of physical reality.

Somewhat surprisingly, a revival of the mechanistic approach came in the 20th century with the emergence of relativity and quantum mechanics (see chapters 2 through 5). Relativity (discussed in chapter 7) showed that immediate-action-at-a-distance is impossible; all interactions have to be local. For simple particles, relativity made predictions somewhat more complicated, since relativistic equations of motion are more complex than Newtonian ones. However, as a whole, the fact that all interactions are local means that all the processes can be described by differential equations-- and for differential equations, known feasible algorithms can provide moment-by-moment predictions of the future states (at least for some time).

Quantum physics, in its turn, concluded that, crudely speaking, everything is discrete and consists of quanta: light consists of photons; normal matter consists of protons, neutrons, and electrons; and seemingly action-at-a-distance interaction is indeed an exchange of the corresponding quanta (photons for electromagnetic interactions, gravitons for gravity, and so on). From this viewpoint, modern physics came back to a mechanistic model (see chapters 4 through 6)--of course, on a different level: interaction between quantum relativistic particles is described by much more complex formulas than in the traditional mechanics. Such a particle representation underlies Feynman diagram techniques--one of the main algorithmic schemes for making predictions about quantum systems.

Similar mechanistic physics-type models are successfully used beyond physics, for example, in biology (chapter 7), in economics (econophysics, chapter 10), and so on. This does not mean that, for example, economic processes, for some mysterious reason, exactly follow Schrödinger’s equations of quantum mechanics: the physics-type models are usually approximate. The beyond-physics success of mechanistic models can be naturally explained by the fact that, according to theoretical computer science, all complex (NP-hard) classes of problems are reducible to each other. So, one way to solve a practical problem from a difficult-to-solve class is to use one of such reductions, and reduce this problem to a problem from a class for which many good algorithms are known. From this viewpoint, physics, with its centuries of solving many practical problems, provides a perfect class of such problems to which to reduce.

Warning to the reader: the book has several computation-related chapters and sections (most of this material is in chapters 9 and 11), but overall most of its ideas are on a more philosophical level and not yet on the level of actual computations. These ideas may be raw, but they are also very interesting and thought provoking, so I strongly encourage everyone interested to read this book.

Reviewer:  V. Kreinovich Review #: CR147367

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