Feb 20, 2024 10:22 PM
https://johnhorgan.org/cross-check/is-th...ation-true
EXCERPT: . . . More to Gracie’s point, how real are the equations with which we represent nature? As real as or even more real than nature itself, as Plato insisted? Were the equations of quantum mechanics and general relativity waiting for us to discover them in the same way that gold, gravity and galaxies were waiting?
Physicists’ theories work. They predict the arc of planets and the flutter of electrons, and they have spawned smartphones and H-bombs. But scientists, and especially physicists, aren’t just seeking practical advances. They’re after Truth. They want to believe their theories are correct—exclusively correct—representations of nature. Physicists share this craving with religious folk, who need to believe their path to salvation is the One True Path.
But can you call a theory true if no one understands it? A century after inventing quantum mechanics, physicists still squabble over what, exactly, it tells us about reality. Consider the Schrödinger equation, which allows you to compute the “wave function” of an electron. The wave function, in turn, yields a “probability amplitude,” which, when squared, yields the likelihood that you’ll find the electron in a certain spot.
The wave function has embedded within it imaginary numbers, which consist of the square roots of negative numbers. You can’t find imaginary numbers on the line of negative and positive real numbers; nor do imaginary numbers map directly onto anything in the world. The wave function works, but no one knows why. The same can be said of the Schrödinger equation.
Maybe we should look at the Schrödinger equation not as a discovery but as an invention, an arbitrary, contingent, historical accident, as much so as the Greek and Arabic symbols with which we represent functions and numbers. After all, physicists arrived at the Schrödinger equation and other canonical quantum formulas only haltingly, after many false steps.
Moreover, the Schrödinger equation is far from all-powerful. Although it does a great job modeling a hydrogen atom, the Schrödinger equation can’t yield an exact description of a helium atom. Helium, which consists of a positively charged nucleus and two electrons, poses a three-body problem, which can be solved, if at all, only through extra mathematical sleights of hand.
And three-body problems are just a subset of the vastly larger set of N-body problems, which riddle classical as well as quantum physics. Physicists exalt the beauty and elegance of Newton’s law of gravitational attraction and of the Schrödinger equation. But the formulas match experimental data only with the help of hideously complex patches and approximations.
Maybe the best we can say of any mathematical theory is that it works in a particular context. That is the surprisingly subversive takeaway of Eugene Wigner’s famous 1960 essay “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.”... (MORE - missing details)
EXCERPT: . . . More to Gracie’s point, how real are the equations with which we represent nature? As real as or even more real than nature itself, as Plato insisted? Were the equations of quantum mechanics and general relativity waiting for us to discover them in the same way that gold, gravity and galaxies were waiting?
Physicists’ theories work. They predict the arc of planets and the flutter of electrons, and they have spawned smartphones and H-bombs. But scientists, and especially physicists, aren’t just seeking practical advances. They’re after Truth. They want to believe their theories are correct—exclusively correct—representations of nature. Physicists share this craving with religious folk, who need to believe their path to salvation is the One True Path.
But can you call a theory true if no one understands it? A century after inventing quantum mechanics, physicists still squabble over what, exactly, it tells us about reality. Consider the Schrödinger equation, which allows you to compute the “wave function” of an electron. The wave function, in turn, yields a “probability amplitude,” which, when squared, yields the likelihood that you’ll find the electron in a certain spot.
The wave function has embedded within it imaginary numbers, which consist of the square roots of negative numbers. You can’t find imaginary numbers on the line of negative and positive real numbers; nor do imaginary numbers map directly onto anything in the world. The wave function works, but no one knows why. The same can be said of the Schrödinger equation.
Maybe we should look at the Schrödinger equation not as a discovery but as an invention, an arbitrary, contingent, historical accident, as much so as the Greek and Arabic symbols with which we represent functions and numbers. After all, physicists arrived at the Schrödinger equation and other canonical quantum formulas only haltingly, after many false steps.
Moreover, the Schrödinger equation is far from all-powerful. Although it does a great job modeling a hydrogen atom, the Schrödinger equation can’t yield an exact description of a helium atom. Helium, which consists of a positively charged nucleus and two electrons, poses a three-body problem, which can be solved, if at all, only through extra mathematical sleights of hand.
And three-body problems are just a subset of the vastly larger set of N-body problems, which riddle classical as well as quantum physics. Physicists exalt the beauty and elegance of Newton’s law of gravitational attraction and of the Schrödinger equation. But the formulas match experimental data only with the help of hideously complex patches and approximations.
Maybe the best we can say of any mathematical theory is that it works in a particular context. That is the surprisingly subversive takeaway of Eugene Wigner’s famous 1960 essay “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.”... (MORE - missing details)
