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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 ...


22

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 ...


20

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

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 ...


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 ...


16

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 ...


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

First, a historical subtlety: Schrödinger has actually stolen the idea of the cat from Einstein. Second, both men – Einstein and Schrödinger – used the thought experiment to "explain" a point that was wrong. They thought it was absurd for quantum mechanics to say that the state $a|{\rm alive}\rangle+b|{\rm dead}\rangle$ was possible in Nature (it was ...


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. ...


14

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 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) ...


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 ...


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

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

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, ...


10

Here is a pdf file with the letter in both German and English. Screenshot:


10

There's no such thing as verifying a theory "to complete exclusion." One of the key principles of the scientific method is that theories can't be proven by experiment, only supported (or disproven as the case may be). The scientific reality is that quantum mechanics, like any other theory of its caliber, has been supported by countless experiments, so we ...


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 ...



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