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Phase transitions in three dimensional ferromagnets

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Lieb and Thirring clean up my matter stability proof

Freeman Dyson
Scientist

Views | Duration | ||
---|---|---|---|

101. One-dimensional ferromagnets | 1076 | 02:32 | |

102. The ground state energy of a hard-sphere Bose gas - Elliot Lieb | 1080 | 02:06 | |

103. Energy levels of complex systems: background | 1072 | 03:50 | |

104. Inviting Mehta to work on circular ensembles | 1065 | 02:13 | |

105. My work with Mehta is now more relevant | 1007 | 04:49 | |

106. A bottle of champagne to prove the stability of matter | 1369 | 03:40 | |

107. Lieb and Thirring clean up my matter stability proof | 1561 | 03:24 | |

108. Phase transitions in three dimensional ferromagnets | 874 | 03:00 | |

109. Could gravity vary with time? | 1292 | 06:09 | |

110. Work by Dyson and Alex Shlyakhter on the fine-structure constant | 1001 | 04:08 |

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So we worked on this and it ended up with two very long papers which nobody reads in... in the *Physical Review*, first proving it in the case where the... both the positives and negatives both have an exclusion principle, which is the easier case.

[Q] *The exclusion principle stating that no two particles can be at the same place at the same time*...

Right, which is the case for electrons; but it's not always true, of course, for nuclei. Ideally if they have integer spin and they have... they obey Bose statistics, they don't have an exclusion principle. But it... anyway, the much more difficult case is where the electrons have an exclusion principle but the positive charges don't. So the second paper which proved that was even more complicated and opaque than the first paper. And we finally proved the energy is not... the binding energy is not greater than a constant times the number of particles, but the constant was absurdly large, in fact it was something like 10^{14}, and this 10^{14} was just a piling up of sloppy factors from the many, many steps in the argument. It had nothing to do with physics. Well, then... it turned out actually fairly soon after this - after Lenard and I had earned the bottle of champagne, and we did in fact drink the champagne - but fairly soon afterwards Elliot Lieb and Walter Thirring found a good proof of stability of matter which was based on physics, which did the whole job in four pages, which was infinitely more useful than our proof, and it led to understanding and not just to a proof. And they also got a reasonable constant. So the Lieb-Thirring is the way to do it, and as usual, I mean, I think it was Littlewood who said that you can tell a great mathematician by the number of bad proofs that he publishes. The first proof is usually bad, and then somebody else cleans it up.

[Q] *The... but it's fair to say that your solution, or your indication, was the stimulus for the further activities. *

Yes, that's the good thing, if you publish a bad proof then of course it's a challenge to other people to find a good proof and that certainly worked in this case. But, I might mention that Elliot Lieb has just published a whole volume of... papers on the stability of matter which is an absolute treasure house and so he's the world expert on this subject and he has proved a very large number of difficult theorems which are all collected in this volume.

Freeman Dyson (1923-2020), who was born in England, moved to Cornell University after graduating from Cambridge University with a BA in Mathematics. He subsequently became a professor and worked on nuclear reactors, solid state physics, ferromagnetism, astrophysics and biology. He published several books and, among other honours, was awarded the Heineman Prize and the Royal Society's Hughes Medal.

**Title: **Lieb and Thirring clean up my matter stability proof

**Listeners:**
Sam Schweber

Silvan Sam Schweber is the Koret Professor of the History of Ideas and Professor of Physics at Brandeis University, and a Faculty Associate in the Department of the History of Science at Harvard University. He is the author of a history of the development of quantum electro mechanics, "QED and the men who made it", and has recently completed a biography of Hans Bethe and the history of nuclear weapons development, "In the Shadow of the Bomb: Oppenheimer, Bethe, and the Moral Responsibility of the Scientist" (Princeton University Press, 2000).

**Tags:**
Physical Review, Elliot Lieb, Walter Thirring, JE Littlewood

**Duration:**
3 minutes, 25 seconds

**Date story recorded:**
June 1998

**Date story went live:**
24 January 2008