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Episode Link: https://share.snipd.com/episode/baee47c5-4d10-480f-b6c3-d8cdc4e8af42 Episode publish date: August 31, 2025 12:42 PM (PDT) Last edit date: September 21, 2025 8:39 AM Last snip date: September 21, 2025 8:37 AM (PDT) Last sync date: September 21, 2025 8:38 AM (PDT) Show: The Man from the Future: The Visionary Life of John von Neumann Snips: 11 Warning: â ïž Any content within the episode information, snip blocks might be updated or overwritten by Snipd in a future sync. Add your edits or additional notes outside these blocks to keep them safe.
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Part 3 of 10 of The Man from the Future: The Visionary Life of John von Neumann
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[02:20] Quantum Theory
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Quantum Theory
Bohr’s quantum model, though brilliant, raised numerous questions about electron behavior.
Physicists sought a more coherent theory, leading Heisenberg to formulate matrix mechanics.
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Brilliant though it was, Bohr’s model was a jury-rigged affair that raised as many questions as it answered. What held electrons in their special orbits? How did they hop from one to another in an instant? The more success the quantum theory enjoys, the more stupid it looks, said Einstein, who realized early on that the shotgun wedding of classical and quantum concepts could not last. Physicists soon wanted an amicable divorce. In 1925,
[11:39] Schrödinger’s Discovery
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Schrödinger’s Discovery
Schrödinger worked intensely during a two-week rendezvous with an ex-lover in an alpine resort.
He returned with a wave equation applicable to key problems in atomic physics.
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Anxious to make his name with a big discovery, Schrodinger worked through a two-week tryst with an ex-lover in an alpine resort that Christmas, returning to Zurich in January to apply His new wave equation to some of the key problems that were being thrown up by atomic physics. A late erotic outburst was how Hermann Weill, a close friend of Schrödinger, and his wife’s lover, would describe the deluge of academic papers that were to follow. Among them was a complete description of the hydrogen atom spectrum based on his theory, and a version of his equation that how the
[13:53] Two Atomic Theories
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Two Atomic Theories
Within a year, two atomic physics theories emerged, both seemingly valid.
Heisenberg rejected Schrödinger’s wave mechanics, disturbed by its physical depiction of atoms and invisible waves.
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Less than twelve months later, were two. Both theories seemed to do the job, but were so different that many physicists wondered if they could both really be correct. Schrödinger confessed he was repelled by the instantaneous quantum jumps of Heisenberg’s theory. When electron transitions took place in Schrodinger’s theory, the wave function describing the atom changed smoothly from one form to another. Heisenberg was even blunter about the failings of Schrodinger’s wave mechanics. It’s crap, he wrote to Pauli. He was particularly disturbed by the physical picture that Schrödinger was trying to paint of the atoms in the workings. Heisenberg,
[15:49] Reconciling Quantum Theories
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Reconciling Quantum Theories
Scientists sought a deeper connection between Heisenberg’s matrix mechanics and Schrödinger’s wave mechanics.
Both von Neumann and Hilbert had expertise in the underlying mathematics of quantum theory.
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There had to be some deeper connection, they reasoned, between Heisenberg’s infinitely large arrays of numbers and Schrödinger’s strange, formless waves of undulating probabilities. But what could it be? At Göttingen, von Neumann heard about matrix mechanics firsthand. He was keen to help Hilbert extend his programme of axiomatization to physics. By sheer coincidence, both he and his hero were experts in the underlying mathematics of quantum theory. In mathematical terms, Schrodinger was applying a mathematical operator, the energy operator known as the Hamiltonian, to his wave function to extract from it information about The energy of the system. Crudely speaking, operators are mathematical instructions. The solutions, i.e. The wave functions, to equations like Schrodinger’s are eigenfunctions. The answers, i.e. The energy levels of an atom that pop out of the equation after Eigenfunctions are substituted in, are Eigenvalues. Hilbert himself had come up with these terms in 1904, based on the German word Eigen, meaning characteristic or inherent.
[19:56] Heisenberg vs. Schrödinger
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Heisenberg vs. Schrödinger
Heisenberg’s matrices and Schrödinger’s continuous wave functions occupy different types of space.
Von Neumann warns that relating the two theories involves difficulties and violence to mathematics.
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Heisenberg’s matrices, with their countable elements and Schrödinger’s continuous wave functions, are said to occupy different types of space. Every attempt to relate the two, von Neumann warns, must run into great difficulties and cannot be achieved without some violence to the formalism and to mathematics. One person who nonetheless tried to do exactly that was the taciturn British theoretical physicist Paul Dirac, whom novelist Ian McEwan describes as a man entirely claimed by science, Bereft of small talk and other human skills. His Cambridge colleagues even named a unit of speech after him. A Dirac amounted to a single solitary word per hour.
[21:15] Dirac’s Quantum Theory
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Dirac’s Quantum Theory
Dirac merged Heisenberg’s discrete space and Schrödinger’s continuous space in his 1930 book.
He used a mathematical device called the Dirac delta function.
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Dirac began to expound his version of quantum theory in 1925. In his 1930 book, The Principles of Quantum Mechanics, he set out an ingenious trick to merge the discrete space of Heisenberg’s matrices and the other continuous space of Schrödinger’s Waves. The key to Dirac’s approach was a special mathematical device that is now named after him, the Dirac delta function.
[33:26] Quantum Mechanics Interpretations
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Quantum Mechanics Interpretations
Physicists have struggled to understand the meaning of quantum mechanics since its beginning.
There’s still no agreement on its meaning, despite the practical applications of quantum theory.
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Physicists have wrestled with what quantum mechanics is really telling us about the nature of the physical world since its early days. The failure to come up with an acceptable interpretation of the theory even led students at Schrodinger’s University to make up a ditty, gently ribbing their great professor. Erwin with his psi can do calculations quite a few, but one thing has not been seen. Just what does psi really mean? The existence of GPS, computer chips, lasers, and electron microscopes attest that quantum theory works beautifully. But nearly a hundred years after Heisenberg published his paper on matrix mechanics, there is still no agreement on its meaning. In the interim, a plethora of exotic ideas have been put forward to make sense of what quantum physics is saying about reality. All have their passionate advocates, but none have yet been proven. Physicists ruefully joke that though new interpretations of quantum physics arrive with astonishing none ever go away. For many, that joke is turning sour. It is a bad sign, theoretical physicist Stephen Weinberg noted recently, that those physicists today who are most comfortable with quantum mechanics do not agree with one another About what it all means.
[40:04] Observer’s Role in Quantum Measurement
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Observer’s Role in Quantum Measurement
Von Neumann argues that any quantum measurement sequence must end with someone perceiving the events.
Therefore, we must always divide the world into the observed system and the observer.
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But no matter how many steps we add, von Neumann argues, the sequence of events must end with someone perceiving these events. That is, he says, we are obliged always to divide the world into two parts, the one being the observed system, the other the observer. But what about the steps in between? The most straightforward interpretation of quantum mechanics would seem to require that any number of such steps would lead to the same result, at least as far as the observer is concerned.
[43:04] Quantum Entanglement
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Quantum Entanglement
Measuring one entangled object instantly collapses the wave function of the entire system, even across vast distances.
Einstein called this consequence of entanglement ‘spooky action at a distance,’ but von Neumann was more relaxed about it.
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This means that measuring some property of one of the pair instantly collapses the wave function of the whole system, even if the objects are separated by some vast distance after their Initial interaction. Einstein, who was probably the first to fully appreciate this consequence of entanglement and did not like it one bit, called it spooky action at a distance. Von Neumann was always rather more relaxed about the weirder aspects of quantum physics than Einstein.
[55:28] Princeton’s Recruitment Strategy
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Princeton’s Recruitment Strategy
Oswald Weblen at Princeton poached European mathematicians, including von Neumann and Wigner, with lucrative salaries.
He used Rockefeller Foundation money to build Fine Hall and wanted top talent to fill it.
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Towards the end of October 1930, Wigner had received, out of the blue, an offer of a one-term lectureship from Princeton University. If that were not enough, the telegram quoted a salary so high, more than seven times what Wigner was earning in Berlin, he thought there must have been a mistake during the message’s Transmission. He quickly learned that von Neumann had received a letter from Princeton a couple of weeks earlier with the offer of even more money. It was clearly Yanchi that Princeton really wanted, said Wigner. Unbeknownst to him, von Neumann’s letter asked if Wigner should be invited too. Luckily for Wigner, von Neumann agreed this would be a good idea. He added that there would, however, be a short delay before he could take up the post because he wanted to fix a family matter. Von Neumann was going to Budapest to get married. The scheme to entice the two Hungarians had been cooked up by Oswald Weblen, a distinguished Princeton professor of mathematics. America was an intellectual backwater, and Weblen wanted to change that by poaching some of Europe’s most brilliant mathematicians with the offer of huge American salaries. He had secured millions of dollars from the Rockefeller Foundation and wealthy private donors to erect grand new building named Fine Hall for the Mathematics Department. Now he just needed the mathematicians to fill it. Veblen came under pressure from the wider faculty to hire a physicist.
[01:16:55] Many Worlds Interpretation
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Many Worlds Interpretation
Hugh Everett III introduced the many worlds interpretation which was ignored initially, but re-emerged later in science fiction.
Everett started in game theory, a field von Neumann helped found, before moving to quantum mechanics.
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While Bohm’s theory struggled to win widespread acceptance, though Bell continued to champion it, another was to be ignored altogether, only to spawn countless science fiction Stories and half-baked mystical philosophies and more than a few research papers it re-emerged over a decade later. The progenitor of the many worlds interpretation was a young American theorist named Hugh Everett III, who began his graduate studies at Princeton University in the mathematics Department. By coincidence, he spent his first year working on game theory, a field which von Neumann had helped found with his