Episode #125 of the Stack Overflow podcast is here. We talk Tilde Club and mechanical keyboards. Listen now
39

It's not exactly the war, but the Nazi regime more generally that caused the decline of Göttingen. When the Nazi's came to power in 1933, they started implementing antisemitic measures quite quickly. An important step in the Nazi policy was what is now dubbed 'the great purge of 1933', which (basically) aimed to expel all Jews from positions in government or ...


26

Not quite. Minkowski had the idea of representing special ralativity as geometry in 1907 under the direct influence of Einstein's 1905 paper, and he developed it in Raum und Zeit (1907) and Zwei Abhand lungen über die Grundgleichungen der Elektrodynamik (1909). See Minkowski on MacTutor. Before that only classical "spacetime" appeared, and only superficially....


21

A good account is Weinstein, Max Born, Albert Einstein and Hermann Minkowski's Space-Time Formalism of Special Relativity. They did no have much of a relationship, what it was is well-summarized by Sommerfeld: "Strangely enough no personal contacts resulted between his teacher of mathematics, Hermann Minkowski, and Einstein. When, later on, Minkowski ...


20

Einstein himself told the story in his Kyoto address of 1922, which I quote from Pais's biography titled Subtle is the Lord: "If all systems are equivalent, then Euclidean geometry cannot hold in all of them. To throw out geometry and keep laws is equivalent to describing thoughts without words. We must search for words before we can express thoughts. ...


18

The general question is difficult to answer. Why were the British and Dutch scientists of 17-th century so impressive? Why was French science of the 18-th and 19-th century so impressive, especially in the early part of 19-th century ? The only thing which is clearly seen, is the correlation of these periods with vigorous economic development of these ...


18

The "movement" against relativistic mass was started by Adler in 1987 with Does Mass Really Depend on Velocity, Dad? (his answer, "actually no, but don't tell your teacher"). It got a boost from Okun's two 1989 papers. In 1990 American Journal of Physics solicited Okun's contribution on the relativistic mass to be published alongside Sandin's, who defended ...


16

I will focus on the history before the Yang-Mills paper. The first harbinger was the introduction of the scalar potential for the gravitational field by Lagrange in 1773. In 1864 Maxwell introduced vector potential for the magnetic field, which can be interpreted as a connection form, making magnetic theory the first gauge theory in hindsight. In the famous ...


16

I'll focus on the geometry of Yang-Mills theories specifically, but as Conifold's answer points out, gauge theories were studied geometrically long before the work of Yang and Mills. The foreward to volume 5 of Atiyah's collected works (on gauge theories) contains some historical comments on this from the mathematics side. You can read it here. This is ...


15

The basic answer is yes, he was dependent on a few nurses and a research assistant or two. From Wikipedia - the article you brought forth: Nurses were hired for the three shifts required to provide the round-the-clock support he required. One of those employed was Elaine Mason, who was to become Hawking's second wife. For his communication, Hawking ...


15

From Pais's book Inward Bound, chapter 13: Wigner had become interested in $n>2$ identical particle problem. He rapidly mastered the case $n=3$ (without spin). His methods were rather laborious; for example, he had to solve a (reducible) equation of degree six. It would be pretty awful to go on this way to higher $n$. So, Wigner told me, he went to ...


15

A case from this year is that of Aubrey de Grey. Aubrey de Grey, a biologist known for his claims that people alive today will live to the age of 1,000, posted a paper to the scientific preprint site arxiv.org with the title “The Chromatic Number of the Plane Is at Least 5.” In it, he describes the construction of a unit-distance graph that can’t be ...


13

This seems a bit of a naive question to me. Einstein had been working on this problem for several years (starting as early as 1907), and had developed much of the physics by 1912. He greatly struggled to find the correct mathematical formulation of his theory, finally discovering the necessary tools from differential geometry during a collaboration with the ...


13

Einstein made a number of contributions of momentous importance to quantum theory in the 'early days'. In 1905, his famous annus mirabilis, he published a paper on the photo-electric effect that laid the basis for the modern understanding of photons (i.e. quantized wavepackets). This was twenty years before the foundations of quantum mechanics were ...


13

It seems not. See: A.Douglas Stone, Einstein and the quantum: The quest of the valiant Swabian (2013): [page 6] Planck was the first major figure to recognize Einstein’s seminal 1905 work on relativity theory, and he became Einstein’s greatest champion in the world of science and one of his closest personal friends. [page 83] [Einstein's 1905 paper ...


11

It's not true that Einstein rejected quantum mechanics completely. He acknowledged that it gave numerically accurate predictions in a wide variety of cases, as did any competent physicist by 1935. In that year, he introduced the EPR paradox, which shows that quantum mechanics doesn't respect locality in special relativity. In particular, if one considers an ...


11

"Simply modifying" Newtonian gravity to have it spread at finite speed does not work if the finite speed is the speed of light. It was attempted by Laplace in his Celestial Mechanics (1799), who found that the planets will promptly fly off their orbits and the Solar system will disintegrate in seconds, unless the propagation speed is $7×10^6$ times greater ...


10

It's worth noting that we can't just pin it down to "The Nazi regime" and we may have to just say "The Nazis." Take for instance the case of Landau. He could not be purged as such but when he tried to teach in Fall 1933 he faced a student boycott led by Oswald Teichmuller. A letter from Landau sets the scene. On 2 November, about 11.15, as I wished to ...


10

One routinely speaks of the Dirac operator as a square root of the Laplacian (or Dalembertian as the case may be), and Dirac himself rather supports this heuristic in his Recollections of an exciting era, History of twentieth century physics, Academic Press 1977, pp. 109-146: I was playing around with the three components $\sigma_1, \sigma_2,\sigma_3,$ ...


9

Let's talk about special relativity (1905) first, then general relativity (1915). The motivation for special relativity is stated clearly in the first sentence of Einstein's paper "On the Electrodynamics of Moving Bodies": It is known that Maxwell's electrodynamics -- as usually understood at the present time -- when applied to moving bodies, leads to ...


9

There seems to be enough evidence to believe that people were joking around about Stueckelberg's notes in 1965, when the Nobel prize was awarded to Feynman, Schwinger and Tomonaga, but I do not see how that implies conclusions in the last paragraph. If Schwinger or Coleman took it seriously they wouldn't be privately joking about it with Feynman, they'd be ...


9

According to a slide deck I found, it was Willis Lamb. Quote from said deck: In 1955, Willis Lamb started his Nobel Prize acceptance speech by saying that “maybe physicists discovering a new particle ought to be fined 10 000$”


8

Given the historical circumstances the German education system might or might not have played a significant role in the formation of these scientists. In his collection of essays entitled "Brocas Brain", Carl Sagan gives some excellent insight into Einsteins biography: (I think this an accurate reprint of the original piece) Einstein dropped out of school ...


8

Curiously, Kepler thought that gravity falls as $1/r$, and he had a peculiar ether vortex theory borrowed from Gilbert's work on magnetism, to support it. But he argued that the intensity of light falls as $1/r^2$ along the same lines that others later applied to gravity: "there is as much light in the narrower spherical surface, as in the wider, thus it is ...


8

What we learned so far belongs to the realm of mathematics, or more generously formal side of theoretical physics, rather than knowledge of nature in the narrow sense. Namely, what effects different unification constructions can produce and account for, and what in them is problematic. Many tricks originally introduced trying to unify gravity and ...


8

I think this covers the actual question: While working to receive his Ph.D. and make a name for himself at [Oxford], Stephen proved himself able to handle great levels of theoretic equations in his head Then later Most of his [most famous work on black holes and space time] was done while working with Roger Penrose, a mathematician who wrote the ...


8

The history is well-described in Wikipedia's article on string theory. There have been many books written about string theory. Two that I found helpful regarding the history are Davies and Brown's Superstrings: a Theory of Everything?, published in 1988 (which may provide some indication as to the answer to your question), and Smolin's The Trouble with ...


8

The anecdote you have in mind concerns Max Planck and his advisor Philipp von Jolly who, in 1874, told the young Planck that it was probably not a great idea to study theoretical physics, since there was not much left to do. With the power of hindsight this is of course extremely ironic since Von Jolly was addressing the man who would personally (though ...


8

Minkowski space time was considered by mathematicians before Einstein and before Minkowski. Of course the name "space-time" was not used. The reasons were purely mathematical, not physical. The most important application was the Klein model of the hyperbolic geometry (non-Eucludean geometry of Bolyai and Lobachevski). More presicely, Klein considered the ...


8

To not be measured is not to have any behavior. No dynamic is induced on any other system in the universe by this object (Rosen 1978). Objects without behavior do not exist. Their behavior is that which makes some perceptions objective not subjective things (Hutton 1794). What is measured but not found different is double counted; it does not exist in ...


8

Ampère did. Ampère's force law (not to be confused with one of Maxwell's equations, "Ampère"'s circuital law, which Ampère never wrote down, as Ampère didn't deal with the field concept), written in modern vector notation, gives the force that current elements $I_1 d\vec {\ell }_1$ and $I_2 d\vec {\ell }_2$ exert on one another to be: $$d^2\vec{F_{21}^A} = -...


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