Far out cosmology: a complaint about theoretical math (Introduction)

by David Turell , Tuesday, June 15, 2021, 18:44 (1255 days ago) @ David Turell

The use of math at times clouds issues:

https://www.realclearscience.com/2021/06/15/the_universe_is_not_made_of_mathematics_781...

"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,

"So when Lawrence Krauss publicly called 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 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.

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"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 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), 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.

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“'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.

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"When viewed through the lens of the fallacy of misplaced concreteness, the root of this crisis is clear: the general theory of relativity concretizes spacetime as a continuum. The problem with this, as Zeno famously demonstrated, is the infinite divisibility of a finite interval—the finite containing the infinite—which is fine if you’re thinking about numbers alone, but highly problematic for physics.

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"Quantum mechanics was explicitly designed to immunize physics against such concretized infinites and their associated paradoxes, and this is the heart of its incompatibility with the general theory of relativity. It avoids the misplaced concreteness of a fundamental continuum by instead describing physical systems as serial “physical histories” of discrete, physical states. But quantum mechanics is not without its own misplaced concretizations... Quantum mechanics contains no physical “mechanism” to explain this; it only contains mathematical structures that describe the process.

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"It is not surprising that it took a mathematician and philosopher as brilliant as Whitehead to emphasize the fallacy of misplaced concreteness and its hazards, or that the most promising solutions to our current problems in fundamental physics would be those that explicitly aim to avoid that fallacy. Deconstructing the “simple” and “self-evident” concretized categories by which we habitually (and often dogmatically) coordinate our thoughts and experiences of the world…this, for Whitehead, was the only route to progress. “If science is not to degenerate into a medley of ad hoc hypotheses,” he writes, “it must become philosophical and must enter upon a thorough criticism of its own foundations.” While it’s true that the strongest foundations are often concretized, it is equally true that this strength always begins and ends with what lies beneath."

Comment: This is why we have crazy string theory that won't work and won't die.