If you could soar high in the sky, as red kites often do in search of prey, and look down at the domain of all things known and yet to be known, you would see something very curious: a vast class of things that science has so far almost entirely neglected. These things are central to our understanding of physical reality, both at the everyday level and at the level of the most fundamental phenomena in physics—yet they have traditionally been regarded as impossible to incorporate into fundamental scientific explanations. They are facts not about what is—“the actual”—but about what could or could not be. In order to distinguish them from the actual, they are called counterfactuals.
Suppose that some future space mission visited a remote planet in another solar system, and that they left a stainless-steel box there, containing among other things the critical edition of, say, William Blake’s poems. That the poetry book is subsequently sitting somewhere on that planet is a factual property of it. That the words in it could be read is a counterfactual property, which is true regardless of whether those words will ever be read by anyone. The box may be never found; and yet that those words could be read would still be true—and laden with significance. It would signify, for instance, that a civilization visited the planet, and much about its degree of sophistication.
To further grasp the importance of counterfactual properties, and their difference from actual properties, imagine a computer programmed to produce on its display a string of zeroes. That is a factual property of the computer, to do with its actual state—with what is. The fact that it could be reprogrammed to output other strings is a counterfactual property of the computer. The computer may never be so programmed; but the fact that it could is an essential fact about it, without which it would not qualify as a computer.
The counterfactuals that matter to science and physics, and that have so far been neglected, are facts about what could or could not be made to happen to physical systems; about what is possible or impossible. They are fundamental because they express essential features of the laws of physics—the rules that govern every system in the universe. For instance, a counterfactual property imposed by the laws of physics is that it is impossible to build a perpetual motion machine. A perpetual motion machine is not simply an object that moves forever once set into motion: It must also generate some useful sort of motion. If this device could exist, it would produce energy out of no energy. It could be harnessed to make your car run forever without using fuel of any sort. Any sequence of transformations turning something without energy into something with energy, without depleting any energy supply, is impossible in our universe: It could not be made to happen, because of a fundamental law that physicists call the principle of conservation of energy.
We cannot bring about transformations that laws of physics declare to be impossible.
Another significant counterfactual property of physical systems, central to thermodynamics, is that a steam engine is possible. A steam engine is a device that transforms energy of one sort into energy of a different sort, and it can perform useful tasks, such as moving a piston, without ever violating that principle of conservation of energy. Actual steam engines (those that have been built so far) are factual properties of our universe. The possibility of building a steam engine, which existed long before the first one was actually built, is a counterfactual.
So the fundamental types of counterfactuals that occur in physics are of two kinds: One is the impossibility of performing a transformation (e.g., building a perpetual motion machine); the other is the possibility of performing a transformation (e.g., building a steam engine). Both are cardinal properties of the laws of physics; and, among other things, they have crucial implications for our endeavors: No matter how hard we try, or how ingeniously we think, we cannot bring about transformations that the laws of physics declare to be impossible. But by thinking hard enough, we can come up with more and better ways of performing a possible transformation—for instance, that of constructing a steam engine—which can then improve over time.
In the prevailing scientific worldview, counterfactual properties of physical systems are unfairly regarded as second-class citizens, or even excluded altogether. Why? It is because of a deep misconception, which, paradoxically, originated within my own field, theoretical physics. The misconception is that once you have specified everything that exists in the physical world and what happens to it—all the actual stuff—then you have explained everything that can be explained. Does that sound indisputable? It may well. It is easy to get drawn into this way of thinking without ever realizing that one has swallowed a number of substantive assumptions that are unwarranted. You can’t explain what a computer is solely by specifying the computation it is performing at a given time; you need to explain what the possible computations it could perform are, if it were programmed in possible ways. More generally, you can’t explain the presence of a lifeboat aboard a pirate ship only in terms of an actual shipwreck. Everyone knows that the lifeboat is there because of a shipwreck that could happen (a counterfactual explanation). And that would still be the reason even if the ship never did sink!
Despite regarding counterfactuals as not fundamental, science has been making rapid, relentless progress; for example, by developing new powerful theories of fundamental physics, such as quantum theory and Einstein’s general relativity; and novel explanations in biology—with genetics and molecular biology—and in neuroscience. But in certain areas, it is no longer the case. The assumption that all fundamental explanations in science must be expressed only in terms of what happens, with little or no reference to counterfactuals, is now getting in the way of progress.
Let’s consider one of the most rare and important properties in our universe: resilience. Most things in our universe are impermanent. Rocks are inexorably abraded away; the pages of books tear and turn yellow; living things—from bacteria, to elephants, to humans—age and die. Notable exceptions are the elementary constituents of matter—such as electrons, quarks, and other fundamental particles. While the systems they constitute do change, those elementary constituents stay unchanged. Entirely responsible for both the permanence and the impermanence are the laws of physics. They put formidable constraints on everything in our universe: on all that has occurred so far and all that will occur in the future.
The laws of physics decree how planets move in their orbits; they govern the expansion of the universe, the electric currents in our brains and in our computers; they also control the inner workings of a bacterium or a virus; the clouds in the sky; the waves in the ocean; the fluid, molten rock in the glowing interior of our planet. Their dominion extends even beyond what actually happens in the universe to encompass what can, and cannot, be made to happen. Whatever the laws of physics forbid cannot be brought about—no matter how hard one tries to realize it. No machine can be built that would cause a particle to go faster than the speed of light.
The misconception is that once you have specified everything in the physical world, you have explained everything.
The laws of physics are the primary explanation for that natural tendency for things to be impermanent. The reason for impermanence is that the laws of physics are not especially suited for preserving things other than elementary components. They apply to the primitive constituents of matter, without being specially crafted, or designed, to preserve certain special aggregates of them. Electrons and protons attract each other—it is a fundamental interaction; this simple fact is the foundation of the complex chemistry of our body, but no trace of that complexity is to be found in the laws of physics. Laws of physics, such as those of our universe, that are not specially designed, or tailored, to preserve anything in particular, aside from that elementary stuff, I shall call no-design laws. Under no-design laws, complex aggregates of atoms, such as rocks, are constantly modified by their interactions with their surroundings, causing continuous small changes in their structure.
From the point of view of preserving the structure, most of these interactions introduce errors, in the form of small glitches, causing any complex structure to be corrupted over time. Unless something intervenes to prevent and correct those errors, the structure will eventually fade away or collapse. The more complex and different from elementary stuff a system is, the harder it is to counteract errors and keep it in existence. Think of the ancient practice of preserving manuscripts by hand-copying them. The longer and more complex the manuscript, the higher the chance that some error may be performed while copying, and the harder it is for the scribe to counteract errors—for instance, by double-checking each word after having written it.
Given that the laws of physics are no-design, the capacity of a system to maintain itself in existence (in an otherwise changing environment) is a rare, noteworthy property in our universe. That’s what I call resilience. That resilience is so hard to come by has long been considered a cruel fact of nature, about which many poets and writers have expressed their resigned disappointment. Here is a magisterial example from a speech by Prospero in Shakespeare’s The Tempest:
Our revels now are ended. These our actors
(As I foretold you) were all spirits, and
Are melted into air, into thin air,
And like the baseless fabric of this vision,
The cloud‐capp’d tow’rs, the gorgeous palaces,
The solemn temples, the great globe itself,
Yea, all which it inherit, shall dissolve,
And, like this insubstantial pageant faded
Leave not a rack behind. We are such stuff
As dreams are made on; and our little life
Is rounded with a sleep.
Now, those lines have such a delightful form and rhythm that, on first reading, something important may go unnoticed. They present only a narrow, one-sided view of reality, which neglects fundamental facts about it. If we take these other facts into consideration, we see that Prospero’s pessimistic tone and conclusion are misplaced. But those facts are not immediately evident. In order to see them, we need to contemplate something more than what spontaneously happens in our universe (such as impermanence, occasional resilience, planets, and the cloud-capped towers of our cities). We have to consider what can, and cannot, be made to happen: the counterfactuals—which, too, are ultimately decided by the laws of physics.
The most important element that Prospero’s speech neglects is that even under no-design laws, resilience can be achieved. There is no guarantee that it shall be achieved, since the laws are not designed for that; but it can be achieved because the laws of physics do not forbid that. An immediate way to see this is to look around a bit more carefully than was possible in Shakespeare’s time. There are indeed entities that are resilient to some degree; even more importantly, some are more resilient than others. Some of them very much more. These are not, contrary to what proverbs and conventional wisdom might suggest, rocks and stones, but living entities.
Living things in general stand out as having a much greater aptitude to resilience than things like rocks. An animal that is injured can often repair itself, whereas a rock cannot; an individual animal will ultimately die, but its species may survive for much longer than a rock can.
The laws of physics, expressed as counterfactuals, offer a chance for improvement.
Consider bacteria. They have remained almost unchanged on Earth for more than 3 billion years (while also evolving!). More precisely, what has remained almost unchanged are some of the particular sequences of instructions that code for how to generate a bacterium out of elementary components, which are present in every bacterial cell: a recipe. That recipe is embodied in a DNA molecule, which is the core part of any cell. It is a string of chemicals, of four different kinds. The string works exactly like a long sequence of words composed of an alphabet of four letters: Each word corresponds roughly to an instruction in the recipe. Groups of these elementary instructions are called genes by biologists.
It is the particular structure, or pattern, of bacterial DNA that has remained almost the same over such a long time. In contrast, during the same period, the arrangement and structure of rocks on Earth have profoundly changed; entire continents have been rearranged by inner movements taking place underneath the Earth’s crust. Suppose some aliens had landed on Earth early in prehistory, collected DNA from certain organisms (say, bluegreen algae), and had also taken a picture of our planet from space; and that they were to come back now to do the same. In the pictures of the planet, everything would have changed. The very arrangement of continents and oceans would be utterly different. But the structure of the DNA from those organisms would be almost unchanged. So, after all, certain things in our universe, like recipes encoded in DNA, can achieve a rather remarkable degree of resilience.
The other element that Prospero’s speech disregards is that living entities can operate on the environment, transform it, and (crucially) preserve the ability to do so again and again, thus leaving behind much more than “a rack.” The Earth still bears the signs of bacterial activity from a billion years ago (for instance, in the form of fossil carbon). Plants have caused a dramatic change in the composition of the atmosphere by releasing gaseous oxygen as a side effect of converting the sun’s light into chemical energy via photosynthesis. Humans, too, are capable of transforming the environment in a wide set of conditions. Contrary to Prospero’s view, palaces, temples, and cloud-capped towers can achieve resilience—because they are products of civilization. Humans can restore them by following a blueprint—or rather, again, a recipe—of how they were initially built, guaranteeing that they will endure much longer than their constituent materials. In principle, a 3-D printer provided with such a recipe could reconstruct from scratch any ancient palace that happened to be completely destroyed.
The human life span may be still constrained, but technology has already extended it well beyond that of our ancestors. By changing the naturally occurring environment, human civilization is tentatively improving and growing. We now have the knowledge to produce warm (or cooled) houses, powerful medications, efficient transport on Earth and even into space, and tools to save ourselves labor, to lengthen our lives and make them more enjoyable. We have majestic works of art and literature, music, and science. Those very words in Prospero’s speech are an example of our literary heritage, and they have survived—together with countless other wondrous outputs of human intellectual activity. So, rather than fading away, this pageant we have set up, which sustains us, has been under way for centuries. The rest of life’s show on Earth has endured even longer, for billions of years.
Of course, the resilience of our civilization is constantly threatened by severe problems, which crop up as we try to move forward. Some of them, such as global warming and fast-spreading pandemics, are in fact a byproduct of the very progress I have described. These problems present considerable challenges and could easily wipe out several aspects of the progress we have made.
But it is possible to take steps to solve those issues, no matter how serious they appear; and the laws of physics do not forbid still greater improvement. They do not guarantee improvement or resolution, but nor do they forbid it: Resilience and further progress, by addressing problems such as the climate crisis, are both possible. The laws of physics, expressed as counterfactuals, offer a chance for improvement. By contemplating what is possible in the universe, in addition to what happens, we have a much more complete picture of the physical world. Prospero’s gloomy conclusion is partial and profoundly misguided. It was nothing more than an unreal nightmare.
Chiara Marletto is the author of The Science of Can and Can’t: A Physicist’s Journey Through the Land of Counterfactuals. She is a research fellow at Wolfson College, University of Oxford. She holds degrees from the universities of Oxford and Turin. Her main research focus is in theoretical physics, and she also pursues interests in theoretical biology, epistemology, and Italian literature.
From The Science of Can and Can’t by Chiara Marletto, published by Viking, an imprint of Penguin Publishing Group, a division of Penguin Random House, LLC. Copyright © 2021 by Chiara Marletto.
Lead image: MJgraphics / Shutterstock
This article first appeared online in our “Hidden Truths” issue in June, 2021.