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First edition, very rare offprint, of Heisenberg's proposal of a 'universal length'. "In the early 20th century, with the advent of quantum field theory, it was widely believed that a fundamental length was necessary to cure troublesome divergences. The most commonly used regularization was a cut-off to render integrals finite. It seemed natural to think of this pragmatic cut-off as having fundamental significance, though this caused problems with Lorentz-invariance. In 1938, Heisenberg wrote "Über die in der Theorie der Elemtarteilchen auftretende universelle Länge" (On the universal length appearing in the theory of elementary particles), in which he argued that this fundamental length, which he denoted r0, should appear somewhere not too far beyond the classical electron radius. This idea seems curious today, and has to be put into perspective. Heisenberg was very worried about the non-renormalizability of Fermi's theory of beta-decay. He had previously shown that applying Fermi's theory to the high center of mass energies of some hundred GeV lead to an "explosion," by which he referred to events of very high multiplicity. Heisenberg argued this would explain the observed cosmic ray showers. We know today that what Heisenberg actually discovered is that Fermi's theory breaks down at such high energies. Heisenberg then connected the problem of regularization with the breakdown of the perturbation expansion of Fermi's theory, and argued that the presence of the alleged explosions would prohibit the resolution of finer structures: 'If the explosions actually exist and represent the processes characteristic for the constant r0, then they maybe convey a first, still unclear, understanding of the obscure properties connected with the constant r0. These should, one may expect, express themselves in difficulties of measurements with a precision better than r0 . . . The explosions would have the effect . . . that measurements of positions are not possible to a precision better than r0.' In hindsight we know that Heisenberg was, correctly, arguing that the theory of elementary particles known in the 1930s was incomplete. The strong interaction was missing and Fermi's theory indeed non-renormalizable, but not fundamental. But lacking that knowledge, it is understandable that Heisenberg argued gravity had no role to play for the appearance of a fundamental length: 'The fact that [the Planck length] is much smaller than r0 gives us the right to leave aside the obscure properties of the description of nature due to gravity, since they - at least in atomic physics - are totally negligible relative to the much coarser obscure properties that go back to the universal constant r0. For this reason, it seems hardly possible to integrate electric and gravitational phenomena into the rest of physics until the problems connected to the length r0 are solved.' Today, one of the big outstanding questions in theoretical physics is how to resolve the apparent disagreements between the quantum field theories of the standard model and general relativity. But the same is true for Fermi's theory that Heisenberg was so worried about that he argued for a finite resolution where the theory breaks down - and mistakenly so since he was merely pushing an effective theory beyond its limits." (Sabine Hossenfelder, On the universal length appearing in the theory of elementary particles - in 1938, BackReaction blog, September 28, 2011). Miller, Source Book in Early Quantum Electrodynamics, 10. 8vo, pp. 20-33. Original printed wrappers. Seller Inventory # ABE-1677945443692
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