Can and Can't versus Did or Didn't

kw: book reviews, nonfiction, physics, constructor theory, counterfactuals

When I saw the title of The Science of Can and Can't: A Physicist's Journey Through the Land of Counterfactuals, by Chiara Marletto, I was intrigued. I wondered whether it would be a diatribe against pseudoscience (where we most frequently encounter the word "counterfactual") or an explanation of something new. Thankfully, it is the latter.

Dr. Marletto is a disciple of Dr. David Deutsch, and together they are trying to reformulate physics. That's a tall order, but it's about time. A couple of generations have passed since the clash between the General Theory of Relativity and Quantum Theory became evident…perhaps it is better to say, the best explanations of these two theories definitely clash. It is not known whether the General Relativistic principles and Quantum principles indeed clash, or somehow mesh. If they clash, one must eventually be superseded, or both.

Studying the subject on the side I found that Dr. Deutsch presented his earliest ideas on the subject under the title Constructor Theory. I suggest reading the Wikipedia article Constructor Theory before reading the book, to get a grounding there. Then the book will be easier going. For a deeper dive, see the Constructor Theory web site.

Strangely, the words "constructor theory" do not appear in the book. Instead, the subject that previously had less emphasis has taken center stage: "Counterfactuals." I hope a better term can be found, but it may not be possible. Here is why I think so.

As an adjective, counterfactual refers to something that is not true, it is "contrary to fact." As a noun, a counterfactual is a conjecture about what might happen if something were changed, "Could a kangaroo jump if its tail were removed?" Whether the animal can still jump, you don't have a kangaroo any more, but a ruined kangaroo.

As used in the book, "counterfactual" partakes of the latter meaning, but does not extend it to "ruined" systems. Rather, a counterfactual is a statement about what is provably possible and what is provably impossible about a system, and Dr. Marletto calls it the Science of Can and Can't. Though this is never stated, it is placed in apposition to physics theory as a Science of Did and Didn't. We develop hypotheses by doing experiments and making observations about what Did happen and what Didn't happen. One or more hypotheses can be tested until we have a sufficient collection of happenings, or failures to happen, to enable us to propose a theory, or an explanation for the successes and failures of our experiments and observations. Based on the theory we can make predictions about the outcomes of experiments not yet done. Doing those experiments, assuming we have the means to do so, will either tend to confirm or refute the theory.

How does this relate to a counterfactual (or whatever it will eventually be called)? The counterfactual states what is possible or not possible for the system. It goes beyond the observations. Therefore, "counterfactual" is taken to mean, "Facts to be discovered in the future are expected to conform to this." It is a more powerful idea than it sounds at first. However, because of the on-the-street connotation of "counterfactual = false", I hope a different term can be devised. I tried to think of terms including the Latin root "potens-", for potential, because a counterfactual expresses the potential range of effect for a system, and sets its limits also. I didn't get far. Don't hold your breath; it isn't easy to find a euphonious term for this powerful concept.

This concept, that "Can and Can't" goes beyond "Did and Didn't" leads to the key focus of the book. Systems that have been considered outside the realm of "good physics", such as information theory and thermodynamics, can be analyzed using counterfactuals. The author claims that, using counterfactuals, exact statements can be propounded, while using traditional physics, the statements are approximations. Info theory and thermo and a few other systems larger than quanta are analyzed in the book, to discern the qualities that make them unique. For example, what was earlier called a Constructor is called in the book a Catalyst, generalizing the chemical term to mean any system that induces a change to another system and is either not changed or is returned to its initial condition afterward. Thus a thermodynamic engine can transform heat energy into motion but is not changed in the process; it is, in the most general terms, a catalyst for such a conversion.

The simplest system (in one view) treated is Information. A system such as a switch, or transistor, or coin (to be flipped) can carry information, and larger aggregates of such items can carry more information. Information has two counterfactual properties, Set and Copy. Turning a lamp on or off, or setting a coin to show heads or tails, is a Set operation. Information transfer refers to performing a Copy operation, so that the information is duplicated. When you see a lamp's light appear it causes a change in your brain: When the lamp was the steeple lantern and the brain was Paul Revere's, he began his ride to announce, "The British are coming!" (and if a second lamp was on it indicated a coastal invasion). The information system of the lamps was Set to send a certain signal, and the information was Copied to Paul, who further copied it by announcing it, loudly, as he rode.

Why does this have anything to do with counterfactuals? Because there is nothing in particle physics, quantum mechanics, and so forth, that delimits information. Set and Copy are characteristics of systems bigger than the particles dealt with the the Standard Model and the Modern Synthesis.

One way I began to think about "standard physics" related it to the gears on a bicycle. If you have a 3-sprocket cluster at the pedal and a 6-sprocket cluster at the wheel, you can choose among 18 gears. That's a lot more than the single-speed bicycle I used as a child, or the 3-speed bicycle I used as a teen. But it still has limitations. If you want to study bicycle locomotion, your observations will be limited to the gears available.

Then, suppose you think, what kind of versatility could I have if there were many gears, thousands, perhaps? Keep thinking along those lines and you begin to wonder about a continuously variable "gear" system.

This Evans Cone Drive, patented in 1880 and used in machine shops for some decades thereafter (a few are still in use; this one is in Delaware at the Hagley Museum machine shop. I used it when I was a docent there), has a range of speeds of 16:1. The effective ratio is set by moving the leather belt right or left. This idea is behind the CVT transmissions used in Toyota Corollas, some BMW models, and a few other autos, plus many snowmobiles. This Drive has the counterintuitive quality that it yields an essentially infinite number of "gears" by doing away with the gears! Dear author, if you run across this review, and you like this example, you are free to use it.

It is early days for Constructor Theory. Drs. Deutsch and Marletto are just getting their feet wet. Perhaps a revolution in physics is on the horizon. They think so. This book might be the infant's cry of a new take on physics.