4 hours ago
https://iai.tv/articles/new-theory-argue..._auid=2020
INTRO: Quantum mechanics works perfectly in experiments, but Oxford physicist Tim Palmer argues it rests on a mathematical fiction: building the theory on the continuum of real numbers, including irrational numbers like v2. Palmer’s radical alternative abandons the continuum of real numbers and eliminates quantum mysteries that aren't actually physical—from Schrödinger's cat, to Einstein’s “spooky action at a distance.” The theory makes a testable prediction: quantum computers will fail beyond 400 qubits, hitting a fundamental limit set by the discrete structure of nature itself. The coming quantum computing race will determine whether Palmer has identified a basic mistake in our most successful theory.
EXCERPTS: I refer to this theory, where the continuum has been banished, as Rational Quantum Mechanics (RaQM)
The existence of the mathematical continuum goes back to the fifth century BCE, when Hippasus of Metapontum showed that not all numbers can be described as the ratio of two whole numbers. [...] Until Newton and Leibniz invented the calculus, one could view Hippasus’s irrational numbers simply as an oddity. But the calculus required us to make sense of these irrational numbers not just here and there, but everywhere.
[...] But weird stuff lies just under the hood. As the twentieth-century mathematicians Stefan Banach and Alfred Tarski showed, if you take the continuum seriously, it is possible to take a solid sphere, divide it into five pieces, and reassemble the pieces to make a sphere twice as big. Clearly this is not physical! Something goes wrong if you take the continuum too seriously. But for physicists, the calculus was a boon, and its utility far outweighed any weirdness that resulted from embracing the irrationals...
[...] The continuum became hard-baked into the mathematical formalism of quantum mechanics a few years after Heisenberg and Schrödinger’s papers when John von Neumann formulated his famous axioms of quantum mechanics.
[...] I find Von Neumann’s naming of the state space of quantum mechanics as “Hilbert Space” deeply ironic because Hilbert famously asserted “the infinite is nowhere to be found in reality.” In his 1925 lecture “On the Infinite,” he argued that while infinity is a necessary, non-contradictory concept in mathematics, it is a theoretical “idea” rather than a physical reality. And yet here was von Neumann proposing Hilbert Space, where the infinitesimal—the number one divided by infinity—plays a vital role as an element of physical reality!
[...] In RaQM I have developed an approach to quantum physics which eschews the continuum. Here the double-meaning behind the word “rational” is deliberate. RaQM is, on the one hand, based on rational numbers, and on the other hand, its interpretation is totally comprehensible. Not only that, RaQM is a much simpler theory than quantum mechanics...
[...] In recent months, there has been much excitement about the development of quantum computers and quantum algorithms to break modern encryption codes in the coming decade. I can’t wait for such computers to be built and for computer scientists to try to break such codes. Their expectations assume quantum mechanics remains valid for large-dimensional Hilbert Spaces. My prediction, based on RaQM, is that quantum mechanics will fail in such a regime, and quantum computers will never be able to break such codes. If this happens, it will be the first time quantum mechanics has ever failed—and I guess that would be quite a red-letter day!
[...] RaQM is not just another interpretation of quantum mechanics (like Copenhagen, Many Worlds, Pilot Wave Theory, the Subjective QBist interpretation, and so on). It is a new theory—one where the continuum of Hilbert Space has been banished... (MORE - missing details)
INTRO: Quantum mechanics works perfectly in experiments, but Oxford physicist Tim Palmer argues it rests on a mathematical fiction: building the theory on the continuum of real numbers, including irrational numbers like v2. Palmer’s radical alternative abandons the continuum of real numbers and eliminates quantum mysteries that aren't actually physical—from Schrödinger's cat, to Einstein’s “spooky action at a distance.” The theory makes a testable prediction: quantum computers will fail beyond 400 qubits, hitting a fundamental limit set by the discrete structure of nature itself. The coming quantum computing race will determine whether Palmer has identified a basic mistake in our most successful theory.
EXCERPTS: I refer to this theory, where the continuum has been banished, as Rational Quantum Mechanics (RaQM)
The existence of the mathematical continuum goes back to the fifth century BCE, when Hippasus of Metapontum showed that not all numbers can be described as the ratio of two whole numbers. [...] Until Newton and Leibniz invented the calculus, one could view Hippasus’s irrational numbers simply as an oddity. But the calculus required us to make sense of these irrational numbers not just here and there, but everywhere.
[...] But weird stuff lies just under the hood. As the twentieth-century mathematicians Stefan Banach and Alfred Tarski showed, if you take the continuum seriously, it is possible to take a solid sphere, divide it into five pieces, and reassemble the pieces to make a sphere twice as big. Clearly this is not physical! Something goes wrong if you take the continuum too seriously. But for physicists, the calculus was a boon, and its utility far outweighed any weirdness that resulted from embracing the irrationals...
[...] The continuum became hard-baked into the mathematical formalism of quantum mechanics a few years after Heisenberg and Schrödinger’s papers when John von Neumann formulated his famous axioms of quantum mechanics.
[...] I find Von Neumann’s naming of the state space of quantum mechanics as “Hilbert Space” deeply ironic because Hilbert famously asserted “the infinite is nowhere to be found in reality.” In his 1925 lecture “On the Infinite,” he argued that while infinity is a necessary, non-contradictory concept in mathematics, it is a theoretical “idea” rather than a physical reality. And yet here was von Neumann proposing Hilbert Space, where the infinitesimal—the number one divided by infinity—plays a vital role as an element of physical reality!
[...] In RaQM I have developed an approach to quantum physics which eschews the continuum. Here the double-meaning behind the word “rational” is deliberate. RaQM is, on the one hand, based on rational numbers, and on the other hand, its interpretation is totally comprehensible. Not only that, RaQM is a much simpler theory than quantum mechanics...
[...] In recent months, there has been much excitement about the development of quantum computers and quantum algorithms to break modern encryption codes in the coming decade. I can’t wait for such computers to be built and for computer scientists to try to break such codes. Their expectations assume quantum mechanics remains valid for large-dimensional Hilbert Spaces. My prediction, based on RaQM, is that quantum mechanics will fail in such a regime, and quantum computers will never be able to break such codes. If this happens, it will be the first time quantum mechanics has ever failed—and I guess that would be quite a red-letter day!
[...] RaQM is not just another interpretation of quantum mechanics (like Copenhagen, Many Worlds, Pilot Wave Theory, the Subjective QBist interpretation, and so on). It is a new theory—one where the continuum of Hilbert Space has been banished... (MORE - missing details)