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28

1915 On November 25, nearly ten years after the foundation of special relativity, Einstein submitted his paper The Field Equations of Gravitation for publication, which gave the correct field equations for the theory of general relativity (or general relativity for short). Actually, the German mathematician David Hilbert submitted an article ...


23

The list of topics can be found here (in Russian, of course). Nowadays students are examined by collaborators of Landau Institute for Theoretical Physics. Each exam, as it was before, consists of problems solving. For every exam there is one or several examiners with whom you are supposed to contact with to inform that you're willing to pass this particular ...


21

in the late 1960s, the strongly interacting particles were a jungle. Protons, neutrons, pions, kaons, lambda hyperons, other hyperons, additional resonances, and so on. It seemed like dozens of elementary particles that strongly interacted. There was no order. People thought that quantum field theory had to die. However, they noticed regularities such as ...


21

In the following arXiv article Landau's Theoretical minimum, the author details personal experiences on being one of 42 students ever who passed it, as well as some details of the examination. He also mentions some questions in passing, from which I gather most of them were similar to the exercises and examples of his famous books. Quote: Landau gave ...


20

which experiment gave scientists the reason to believe nuclear fission/fussion existed Fusion was first. Francis William Aston built a mass spectrometer in 1919 and measured the masses of various isotopes, realizing that the mass of helium-4 was less than 4 times that of hydrogen-1. From this information, Arthur Eddington proposed hydrogen fusion ...


19

As you probably know, Newton thought that energy is linearly proportional to velocity. The second law's original formulation reads: "Mutationem motus proportionalem esse vi motrici impressae" = "any change of motion (velocity) is proportional to the motive force impressed". This law, which nowadays is wrongly interpreted as: $F = ma$ (there is no ...


19

Newton's 1st and 2nd laws weren't particularly revolutionary or surprising to anyone in the know back then. Hooke had already deduced inverse-square gravitation from Kepler's third law, so he understood the second law. He just could not prove that the bound motion in response to an inverse square attraction is an ellipse. The source of Newton's second law ...


18

The first estimate of Avogadro's number was made by a monk named Chrysostomus Magnenus in 1646. He burned a grain of incense in an abandoned church and assumed that there was one 'atom' of incense in his nose at soon as he could faintly smell it; He then compared the volume of the cavity of his nose with the volume of the church. In modern language, the ...


17

Poincaré was confused on several points. (See the discussion on Wikipedia regarding "mass energy equivalence".) He could never get the mechanical relations straight, since he could not figure out that $E=mc^2$. Einstein followed Poincaré closely in 1905, he was aware of Poincaré's work, but he derived the theory simply as a geometric symmetry, and made a ...


16

There was no problem with electromagnetism. The problem was that Maxwell's equations are invariant under Lorentz transformations but are not invariant under Galileo transformations whereas the equations of classical mechanics can be easily made invariant under Galileo transformations. The question was: how to reconcile both in a universe in which Maxwell's ...


15

There have only been 3 recorded deaths that occurred in space (that is, greater than 60 miles above the Earth). The crew of the Russian capsule Soyuz 11, died when their capsule depressurised during preparations for re-entry. It wasn't known they had died until the re-entry capsule was opened on Earth as communications had been lost with the capsule during ...


15

The complex numbers in quantum mechanics are mostly a fake. They can be replaced everywhere by real numbers, but you need to have two wavefunctions to encode the real and imaginary parts. The reason is just because the eigenvalues of the time evolution operator $e^{iHt}$ are complex, so the real and imaginary parts are degenerage pairs which mix by rotation, ...


15

I did not do more than read Newton, and a few commentators, so my insight on this is probably meager. But I am sure that you are right that the inertial frame interpretation of the first law is only a modern ex-post-facto justification for making it separate from the second law. Newton certainly never used the first law to define an inertial frame, he just ...


15

First of all, it would be preposterous to think that there was a simple recipe that Newton followed and that anyone else can use to deduce the laws of a similar caliber. Newton was a genius, and arguably the greatest genius in the history of science. Second of all, Newton was inspired by the falling apple - or, more generally, by the gravity observed on the ...


14

The excitement behind various claims is somewhat excessive. First, the Mayan astronomers, see e.g. Mayan astronomy at this page, didn't use any armillary spheres or sextants as others did. Their observations were made with naked eye and they were depicting positions of planets with crosses. The accuracy of the Venus' position after a synodic 584-day cycle ...


14

The wording of the question suggests that the electrons were the first objects or particles whose charge required the people to establish the sign convention. But that's obviously not the case. The electron was discovered by J. J. Thomson in 1897 but for much more than a century before that moment, people had already been studying electric (and magnetic) ...


14

If you don't like complex numbers, you can use pairs of real numbers (x,y). You can "add" two pairs by (x,y)+(z,w) = (x+z,y+w), and you can "multiply" two pairs by (x,y) * (z,w) = (xz-yw, xw+yz). (If don't think that multiplication should work that way, you can call this operation "shmultiplication" instead.) Now you can do anything in quantum mechanics. ...


13

I googled a little bit a while ago, and found him. I didn't get any insights into the history of this discovery, he didn't respond to my email. The person I contacted in order to reach him was eventually so offended by my rude email questions that he told me to buzz off. I am only posting this because the guy obviously wants his privacy, and one should ...


13

Gugg's answer is thorough (+1 :-), and the answer to your question is probably "yes". However Hilbert acknowledged that he had merely added the last step to a long process and therefore that he had no claim to have invented General Relativity. It's tempting to think of GR being revealed to the world in a single stunning paper, but this isn't the way it ...


12

I will exaggerate a bit, but in physics, proof in the sense of mathematical proof is irrelevant. Even if all of Einstein's deductions of the formula were wrong, it still turns out that empirical evidence supports $E=mc^2$. Now, without the exaggeration, mathematical deduction is important in physical theories because it shows us how conclusions and ...


12

The Dirac equation implies negative energies as well as positive. This is due to energy-momentum relation $E=\pm \sqrt{m^2+p^2 }$. If we replace $E$ and $p$ by operators $E\to i\frac{\partial }{\partial t}$ and $p\to -i\nabla$ we get the Klein-Gordon equation $(\Box+m^2)\phi=0$ for scalar (spinless) fields $\phi$. The problem with this equation is that it ...


12

There were many models overturned throughout history, I will list some of the most salient ones. I will ignore the ones that predate modern science, the most prominent one being the geocentric model of the solar system, and I will confine myself to wrong ideas that were scientifically accepted as probably true at some point in history. Phlogiston: This is ...


12

As far as I know, nuclear fission was already understood at the time, so was all the competition between the american team and the german team to develop the bomb first, a mere matter of engineering? Only some very, very basic knowledge about the physics of nuclear fission was available at this time. I'll give a few details about this below. Also, ...


11

First of all, this is not true that noble gases do not form any compounds -- it can be done with some chemical tricks, usually using fluorine and some hell conditions. Yet, you don't need any chemistry to detect a new element -- helium was for instance first spotted in the sunlight spectrum. The isolation can also be made by physical means only; the most ...


11

The idea of the existence of galaxies is certainly not new, and quite a bit older than the field of modern astrophysics. In 1750, Thomas Wright, an English astronomer correctly speculated that the Milky Way was a flattened disk of stars and that some of the nebulae astronomers viewed in their telescopes were separate "Milky Ways". In 1755 Immanuel Kant ...


11

The first undeniably reliable measurements of Avogadro's number came right at the turn of the twentieth century, with Millikan's measurement of the charge of the electron, Planck's blackbody radiation law, and Einstein's theory of Brownian motion. Earlier measurements of Avogadro's number were really only estimates, they depended on the detailed model for ...


10

Ladder operators are usually constructed to form a Lie algebra (we want them to have specific conmutation relations). The mathematical basis is weight theory. The important thing of Lie algebras is that they are a vector space and their elements, which are called generators obbey this conmutation rule: $$[X_i,X_j]=f_{ijk}X_k$$ Where we have used the ...


10

(Attn: non-seriousness ahead.) Since Helen, whose face could launch a thousand ships is the unit of beauty (as in a millihelen is a face that could launch one ship), perhaps Edison could be the unit of jerkishness. I base this, of course, on an entirely unbiased source.



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