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A K Peters/CRC Press eBooks

The Physics of the Twentieth Century

Károly Simonyi, David Kramer

Published Feb 7, 2025• 0 citations
Publisher

Abstract

“But this is dreadful,” Grete Hermann said. “On the one hand, you claim that your knowledge of the Radium B atom is incomplete inasmuch as you cannot tell when and in what direction the electron will be emitted, while, on the other hand, you tell me that your knowledge is complete because, if there were further determinants, you would get into trouble with other experiments. But our knowledge cannot possibly be complete and incomplete at the same time. The whole thing is sheer nonsense… I was wondering why our inability to discover the causes of, say, the emission of an electron means that we must stop searching further. Admittedly, you don’t forbid this search, but you claim that it is futile since no further determining factors can be found. Indeed, you contend that, if only it is formulated in precise mathematical language, the indeterminacy allows a definite prediction in another experiment. And this, too, you claim is borne out by the results. If you argue like that, you turn uncertainty into a physical reality, with an objective character, while, normally speaking, uncertainty is a synonym for ignorance, and as such something purely subjective.”

DOI
10.1201/9781032697697-6

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“But this is dreadful,” Grete Hermann said. “On the one hand, you claim that your knowledge of the Radium B atom is incomplete inasmuch as you cannot tell when and in what direction the electron will be emitted, while, on the other hand, you tell me that your knowledge is complete because, if there were further determinants, you would get into trouble with other experiments. But our knowledge cannot possibly be complete and incomplete at the same time. The whole thing is sheer nonsense… I was wondering why our inability to discover the causes of, say, the emission of an electron means that we must stop searching further. Admittedly, you don’t forbid this search, but you claim that it is futile since no further determining factors can be found. Indeed, you contend that, if only it is formulated in precise mathematical language, the indeterminacy allows a definite prediction in another experiment. And this, too, you claim is borne out by the results. If you argue like that, you turn uncertainty into a physical reality, with an objective character, while, normally speaking, uncertainty is a synonym for ignorance, and as such something purely subjective.”
Quantum mechanics is our most successful physical theory. It predicts the behavior of atoms, molecules, and light to ten decimal places. No experiment has ever contradicted it. It also contains a crack at its foundation. The theory’s central equation—the Schrodinger equation—describes a smooth, continuous, perfectly predictable evolution of the quantum state. But whenever anyone performs a measurement, they get a single, definite result. Which result they get appears to be random. The transition from smooth evolution to random outcome is called the “collapse of the wavefunction,” and after nearly a century of analysis, there is no agreed-upon explanation for what causes it, when it occurs, or whether it occurs at all. This is the measurement problem. The measurement problem is not a minor puzzle at the margins of the theory. It is a failure to explain the most basic operation in science: looking at the result of an experiment. Around it cluster other puzzles. Light behaves like a wave in some experiments and like a particle in others—two contradictory descriptions. Two particles that have interacted remain correlated across arbitrary distances, as though communicating faster than light. The probabilities that govern measurement outcomes appear as a postulate—the Born rule—inserted by hand with no deeper justification. And the theory offers no unified picture of reality: quantum mechanics, general relativity, and the standard model of particle physics speak incompatible mathematical languages. A century of effort has produced many interpretations of quantum mechanics. Copenhagen. Many-worlds. De Broglie-Bohm. Objective collapse. Quantum Bayesianism. None has achieved consensus. The measurement problem remains. This document proposes that the source of these puzzles is not quantum mechanics itself. It is a single, invisible assumption made at the very beginning of the theory in 1900—an assumption so deeply embedded that nobody noticed they were making it. Change that assumption, and the puzzles do not get solved. They dissolve. They stop being puzzles. They become predictable consequences of geometry.
Schrödinger’s equation and the “wave function” that satisfies it are the first bold brushstrokes of a new portrait of Nature that physicists gradually filled in during the middle half of the twentieth century. The emerging pattern was strange, but not entirely alien to science. It was drawn, to paraphrase Galileo, in a mathematical idiom “without some knowledge of which it is humanly impossible to understand.” While nonmathematical accounts are conceivable, I would rather at this point say more about the mathematics because it will deepen our view of the whole enterprise of modern physics. Most people never get beyond the “math is numbers and numbers are boring” barrier that hides behind it a limitless universe of beautiful things. So let us delve briefly into the nonboring side of mathematics.
Introduction When I was a student I had much difficulty with quantum mechanics. It was comforting to find that even Einstein had had such difficulties for a long time. Indeed they had led him to the heretical conclusion that something was missing in the theory: ‘I am, in fact, rather firmly convinced that the essentially statistical character of contemporary quantum theory is solely to be ascribed to the fact that this (theory) operates with an incomplete description of physical systems.’ More explicitly, in ‘a complete physical description, the statistical quantum theory would … take an approximately analogous position to the statistical mechanics within the framework of classical mechanics …’. Einstein did not seem to know that this possibility, of peaceful coexistence between quantum statistical predictions and a more complete theoretical description, had been disposed of with great rigour by J. von Neumann. I myself did not know von Neumann's demonstration at first hand, for at that time it was available only in German, which I could not read. However I knew of it from the beautiful book by Born, Natural Philosophy of Cause and Chance , which was in fact one of the highlights of my physics education. Discussing how physics might develop Born wrote: ‘I expect … that we shall have to sacrifice some current ideas and to use still more abstract methods. However these are only opinions.
When metaphysicians pay attention to theories in fundamental physics, they are usually interested in their implications for fundamental metaphysics: they want to know what the theories imply or suggest concerning the ultimate structure of reality. This essay, by contrast, is concerned with the “derivative metaphysics” of quantum mechanics. I will be considering a certain hypothesis about the fundamental structure of reality, which I will call H. I am interested in H because it strikes me as embodying the most obvious, flat-footed way to read an account of the fundamental structure of reality off the mathematical apparatus of elementary quantum mechanics. But I won’t be defending this claim here, or trying to argue that the members of H are more plausible than other accounts of the fundamental structure of reality inspired by quantum mechanics. Instead, my question is: if H were true, could there be (non-fundamentally speaking, of course) such ordinary objects as plants, planets and people? More specifically: could there be such ordinary objects as ourselves and the things we are familiar with, having more or less the ordinary properties we take them to have? And more generally: given that the fundamental structure of a possible world is such as to make H true, what is its correct description in ordinary terms? Of course, I care about these questions in part because I want to explore the extent to which we might have good reason to believe H, or something akin to it. But even if H turned out to be consistent with our ordinary knowledge about the world of ordinary objects, it would obviously take a lot more work to show that it has any serious claim on our credence. At a minimum, one would have to say something about how likely we should regard our evidence as being, given H; one would want to make some sort of survey of alternative hypotheses; and one would want to take into account our specialised scientific knowledge as well as our ordinary knowledge, including the facts that make trouble for elementary quantum mechanics and force us to look beyond it to quantum field theory and ultimately towards some kind of theory of quantum gravity.
The new physics just described was still based largely on Newtonian ideas. Indeed, in its theoretical aspects, it might not unfairly be described as a final attempt to explain the world in materialistic terms—as particles being pushed and pulled about in space and time. Nevertheless, the new physics had found it necessary to abolish most of the forces of pushing and pulling, replacing the gradual changes of motion of the particles under these forces by sudden and unpredictable jumps. These appeared to involve violations of the law of causality, both in the disintegration of radioactive atoms and also in the internal changes of ordinary atoms. We seemed to see Fate defying this law as she picked out certain atoms for disintegration or collapse and, by her apparently capricious acts, sent the universe along one path or another according to her whim. On such lines the new physics had explained many phenomena which had hitherto seemed inexplicable, but it had by no means met with complete success. For instance, while it gave a perfect interpretation of the simplest spectrum of all, namely that of the hydrogen atom, it failed with more complex spectra. This was not necessarily a fatal objection; a few emendations and possibly a few new ad hoc assumptions might have effected a complete reconciliation, although this seems improbable.
Bohr is said to have remarked that anybody who is not shocked by quantum theory has not understood it. No physicist, however, challenges its practical usefulness in predicting experimental results and providing an explanatory framework for an enormous range of study. Nevertheless, more thoughtful physicists have been astonished and disturbed by what is implied when attempts are made to interpret its meaning. As a result a variety of ingenious, and sometimes bizarre, schemes have been devised since its inception in order to make these implications more acceptable to the scientific mind. Some of these schemes have resulted in proposals which appear stranger than the problems they have been designed to resolve. After some sixty years there is no consensus of opinion upon the solution of the epistemological problems posed. Indeed the debate keeps on resurfacing in the scientific literature and continues to generate library shelves of books. Some progress, however, has been made and the late John Bell himself and the experimental work of Alain Aspect have demonstrated that some epistemological positions cannot be sustained.