Review
Somewhat interesting point, but perhaps could have been made much briefer.
The verbose writing style makes me wonder if an LLM was used in the writing process?
At an old job I worked on atomic interferometry R&D. We were developing atomic clocks and atomic accelerometers for practical applications. In that field, pretty much every advance is intelligently designed in advance using an analysis involving stereotypical quantum-mechanics analysis (bras and kets and Hamiltonians). For example, here are my former coworkers calculating small correction terms in the scale factor of atomic accelerometers: Analytical framework for dynamic light pulse atom interferometry at short interrogation times (Stoner et al., 2011). Everyone in the field does this type of analysis all the time, and this activity is invaluable for inventing, designing, debugging, and optimizing the instruments.
We don’t have a counterfactual of people trying to invent and design atomic clocks or atomic accelerometers at the modern performance state-of-the-art without knowing anything about quantum mechanics or atomic physics. Seems implausible, right? Well, realistically, if people were messing around in that area without knowing quantum mechanics and atomic physics, they would probably just wind up inventing large parts of quantum mechanics and atomic physics in the course of trying to understand their instruments.
As another example: our understanding of orbital mechanics preceded going to the moon, and I don’t think it’s plausible that people would have made it to the moon without already understanding orbital mechanics, and if people were trying to launch things into space without understanding orbital mechanics, realistically they would just wind up inventing orbital mechanics in the course of trying to solve their engineering problems.
A common defense of theoretical physics goes something like this: "Our engineering works, therefore our physics theories must be true." This argument, while intuitively appealing, contains a fundamental error that reveals something deeper about the nature of knowledge and reality.
The first crack in this argument appears when we examine history. Many of our most significant engineering achievements preceded their theoretical physics explanations. Steam engines powered the Industrial Revolution before thermodynamics explained their operation. Bridge builders developed sophisticated techniques centuries before stress tensors were mathematized. Metallurgists perfected their craft long before quantum mechanics explained material properties.
If engineering success validates physics theories, how do we explain engineering success that predated those theories?
What emerges instead is a fascinating pattern. When we look at successful engineering solutions - whether developed through empirical observation, trial and error, or practical intuition - we consistently find they embody mathematical relationships that were present and operational before being formally recognized.
This suggests a profound truth: mathematics isn't merely a language we invented to describe reality. Rather, it represents fundamental patterns that exist independently of our understanding of them. Engineers, through practical problem-solving, effectively discover and utilize these patterns without necessarily formalizing them. Theoretical physics then comes along later to make explicit what was already implicitly working.
Paul Erdős, the prolific mathematician, spoke of an imaginary "Book" containing the most beautiful mathematical proofs. This metaphor captures something essential about mathematical truth - it exists to be discovered rather than invented. The fact that engineering solutions often work before we understand why suggests we're all reading from this book, just different chapters and with different levels of explicit comprehension.
This perspective challenges standard scientific realism. Rather than viewing physics as the fundamental description of reality that enables engineering, we might better understand both physics and engineering as different approaches to uncovering pre-existing mathematical truths. Engineering often gets there first through practical engagement, while physics provides the explicit theoretical framework later.
None of this diminishes the value of theoretical physics. Rather, it suggests a different role: physics isn't the foundation that enables engineering, but rather a formal system for making explicit the mathematical patterns that engineering has often already discovered implicitly. This helps explain why physics is so useful for optimizing and extending engineering practices - it provides a language and framework for understanding what's already working.
But what about the obvious objection? Engineering deals with messy, imperfect reality while mathematics trades in perfect abstractions. How do we reconcile this?
The answer may lie in the incompleteness of our mathematical knowledge. As Erdős suggested with his Book metaphor, we haven't discovered all mathematical truths. The gap between idealized physics and practical engineering might not reflect a fundamental limitation of mathematics, but rather our incomplete understanding of the full mathematical structure of reality.
The engineering argument for physics' epistemic validity ultimately fails, but in failing it reveals something more interesting: the primacy of mathematical relationships in the structure of reality. Both physics and engineering are different methodologies for discovering these relationships - engineering through practical engagement, physics through theoretical abstraction.
This suggests we need a more nuanced epistemology that recognizes mathematics as primary, with both physics and engineering as complementary approaches to uncovering mathematical truth. The success of engineering doesn't validate physics so much as it validates the existence of underlying mathematical patterns that both disciplines approach from different angles.
This perspective offers a richer understanding of knowledge and reality than the simple "engineering works, therefore physics is true" argument. It suggests that while physics provides powerful and useful descriptions of reality, its true validation comes not from engineering success but from its ability to reveal the mathematical patterns that were always there, waiting to be discovered.
What are your thoughts on the relationship between mathematics, physics, and reality? Leave a comment below.