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86

That number, 9192631770, was chosen to make the new definition of the second as close as possible to the less precise old second definition. This meant that except for very precise measurements instruments calibrated before the new second was defined would not have to be recalibrated.


68

It's a definition of a unit, which is an arbitrary choice. In the past we used to define a second as 1⁄86,400 of a solar day and later as "the fraction 1/31,556,925.9747 of the tropical year for 1900 January 0 at 12 hours ephemeris time" but both are pretty poor ways of measuring time because the Earth's movement in the solar system is subject to ...


44

I spent a long time researching this question for Carver Mead (mentioned by Art Brown) in 2008, because we were both curious what Feynman meant. Carver thought Feynman's "better way of presenting electrodynamics" would be something along the lines of his own "Collective Electrodynamics," but that turned out to be only partly true, as I discovered in four ...


33

The two largest contributions that come to mind are both in the realm of general relativity. The first is his contribution to the singularity theorems. These are purely general relativistic results (i.e. no quantum mechanics involved), and they mathematically prove that generically one expects to find singularities in spacetime. That is, except in somewhat ...


31

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 ...


29

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 ...


29

You can check this yourself using this very long link which will give you a list of Hawking's work that has been published in refereed journals, ordered by the number of times they have been cited in other papers (a measure of how influential they are on other scientists). This is a way of providing at least some non-opinion based answer to this question. ...


27

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 ...


27

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 ...


26

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 ...


25

As far as I know, the only clue at the time that the speed of light would be invariant were Maxwell's Equations where "something" shows up as a constant. However, speed of light being invariant in all inertial reference frames is very counter-intuitive. One might rather expect physics to be slightly different in different frames, which is what the MM ...


23

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 ...


23

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 ...


22

Most physical units have to be defined in terms of something measurable, and a good definition of a physical unit is one in which the measurement of the unit is very precisely repeatable. Since prehistory, a day was a very natural way of measuring time, and was highly repeatable, in that the procedure of measuring a day can be performed anywhere on Earth ...


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

It was a completely unexpected result at the time. The principle of the MM experiment hinged on the hypothesis that Maxwell's equations of electromagnetism were valid only in a special frame of reference called the aether frame.The speed of light was equal to its standard value only in this frame and its speed in any other inertial frame had to be given by ...


18

If you assume that one mass does not inhibit the force from any other mass, then the result follows from the multiplicity of all pairwise interactions. Without loss of generality* you can imagine partitioning each object into an integer number of small pieces, all of the same mass. Then the force of each piece in one object on each piece in the other ...


18

The nature of complex numbers in QM turned up in a recent discussion, and I got called a stupid hack for questioning their relevance. Mainly for therapeutic reasons, I wrote up my take on the issue: On the Role of Complex Numbers in Quantum Mechanics Motivation It has been claimed that one of the defining characteristics that separate the quantum world ...


17

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) ...


16

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 ...


16

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. ...



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