In their seeking of simplicity, scientists fall into error. They mistake their abstract concepts describing reality – for reality itself. The map for the territory. This leads to dogmatic overstatements, paradoxes and mysteries such as quantum gravity. To avoid such errors, we should evoke the thinking of philosopher Alfred North Whitehead and conceive of the universe as a universe-in-process, where physical relations beget new physical relations, writes Michael Epperson.
When celebrity physicists disagree about some fundamental prediction or hypothesis, there’s often a goofy and well-publicized wager to reassure us that everything is under control. Stephen Hawking bets Kip Thorne a one-year subscription to Penthouse that Cygnus X-1 is not a black hole; Hawking and Thorne team up and bet John Preskill a baseball encyclopedia that quantum mechanics would need to be modified to be compatible with black holes. Et cetera, et cetera. And even as we roll our eyes, we’re grateful because at least some part of us does not want to see these people violently disagreeing about anything.
So when celebrity physicist Lawrence Krauss publicly called celebrity physicist David Albert a “moron” for not appreciating the significance of Krauss’s discovery of the concrete physics of nothingness, it caused quite a stir. In his book, A Universe from Nothing, Krauss argued that in the same way quantum field theory depicts the creation of particles from a region of spacetime devoid of particles (a quantum vacuum), quantum mechanics, if sufficiently generalized, could depict the creation of spacetime itself from pure nothingness. In a scathing New York Times review of Krauss’s book, Albert argued that claiming that physics could concretize “nothing” in this way was at best naïve, and at worst disingenuous. Quantum mechanics is a physical theory, operative only in a physical universe. To contort it into service as a cosmological engine that generates the physical universe from “nothing” requires that the abstract concept of “nothing” be concretized as physical so that the mechanics of quantum mechanics can function. What’s more, if quantum mechanics is functional enough to generate the universe from nothing, then it’s not really nothing; it’s nothing plus quantum mechanics.
This is a familiar maneuver in popular physics books these days—claims of concretizing what is inescapably abstract, usually by way of a purely speculative and untestable assertion costumed mathematically as a testable hypothesis.
This is a familiar maneuver in popular physics books these days—claims of concretizing what is inescapably abstract, usually by way of a purely speculative and untestable assertion costumed mathematically as a testable hypothesis. It is a cheap instrument, as attractive as it is defective, used more often as cudgel than tool for exploration. Fortunately, as we saw with David Albert, few despise its dull edge more than other physicists and mathematicians. During the first years of modern mathematical physics and the construction of its two central pillars, quantum theory and relativity theory, Alfred North Whitehead warned, “There is no more common error than to assume that, because prolonged and accurate mathematical calculations have been made, the application of the result to some fact of nature is absolutely certain.”
Whitehead would later generalize this error as the “fallacy of misplaced concreteness.” It is often oversimplified as merely mistaking an abstract conceptual object, like a mathematical or logical structure (e.g., the number zero, or the concept of “nothingness”), for a concrete physical object. But the fallacy has more to do with what Whitehead argued was the chief error in science and philosophy: dogmatic overstatement. We commit the fallacy of misplaced concreteness when we identify any object, conceptual or physical, as universally fundamental when, in fact, it only exemplifies selective categories of thought and ignores others. In modern science, the fallacy of misplaced concreteness usually takes the form of a fundamental reduction of some complex feature of nature—or even the universe itself—to some simpler framework. When that framework fails, it is replaced with a new reduction—a new misplaced concreteness, and the cycle repeats.
Scientific progress is marked by these cycles because “failure” doesn’t mean the reduction was entirely wrong; it just means it wasn’t as fundamental—as concrete—as previously supposed. Our understanding of nature does increase, just not at the expense of nature’s complexity. In this regard, the reductive mathematization of natural philosophy over the last 500 years has proven to be both its greatest strength and its greatest hazard. The fundamental objects of modern physics are no longer understood as material physical structures but rather as mathematical structures that produce physically measurable effects. The waves of quantum mechanics are not material-mechanical waves; they are mathematical probability waves. The “fabric” of spacetime in relativity theory is pure geometry.
Scientific progress is marked by these cycles because “failure” doesn’t mean the reduction was entirely wrong; it just means it wasn’t as fundamental as previously supposed.
With his “Mathematical Universe Hypothesis,” physicist Max Tegmark has concretized these and other examples of fundamental mathematical objects into a simple reduction: the universe is mathematics. In contemporary mathematical physics, he argues, there is no longer a distinction between a world described by mathematics and a world explained as mathematics. Tegmark characterizes physics as entailing nothing less than a one-to-one correspondence between physical reality and the mathematical structure by which we define this reality. “If our external physical reality is isomorphic to a mathematical structure,” he concludes, “it therefore fits the definition of being a mathematical structure… In other words, our successful theories are not mathematics approximating physics, but mathematics approximating mathematics.”
The artful incoherence of “mathematics approximating mathematics” evinces the misplaced concreteness of the premise it presupposes. The fact that some features of reality are usefully describable as abstract mathematical structures does not necessarily entail that all features of reality are reducible to concrete mathematical structures. What would compel Tegmark to attempt such a leap? What would compel Krauss? “The aim of science,” Whitehead writes, “is to seek the simplest explanations of complex facts. We are apt to fall into the error of thinking that the facts are simple because simplicity is the goal of our quest. The guiding motto in the life of every natural philosopher should be, ‘Seek simplicity and distrust it.’” And then investigate further.
There is no more potent lesson in the history of natural philosophy than this: It is when we make simplicity the end of science rather than its beginning that we doom our fundamental theories to failure. 2500 years after the Pythagoreans had developed their own mathematical universe hypothesis and the Milesians had felt compelled to reduce the four fundamental elements to one, modern physics likewise feels compelled to reduce the four fundamental forces to one—the persistently illusive “Theory of Everything.” After nearly a century, this compulsion has yet to yield a single empirically viable theory, let alone a successful one. What’s worse, the misplaced drive to concretize nature into a single fundamental framework has resulted in two completely incompatible frameworks, each considered equally fundamental: quantum mechanics—the physics by which we understand nature at the small scale—and the general theory of relativity—the physics of the large scale. Given that the large scale is presumed to be reducible to the small scale, this fundamental incompatibility amounts to nothing less than a crisis for physics.