# Tag Info

19

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 ...

19

Unlike Einstein, Planck did not quantize electromagnetic waves themselves, only the exchanged energies, and even them only statistically. So the other two questions have no satisfactory answer because he was not dealing with specifics of emission/absorption at the level of individual quanta. The quanta were meant as mathematical fictions for the purposes of ...

19

It is not random. These names are of Greek origin, and -ic or -ics are Anglicizations of the Greek suffix -ikos, which meant "pertaining to". In other languages it can be rendered as -ika or -ica, Wolfram's "Mathematica" uses such a version. From the Online Etymology Dictionary: "-ics in the names of sciences or disciplines (acoustics, aerobics, ...

16

Bose derived the black body radiation formula in early 1924 by considering the ideal gas of light quanta. Nothing could be further from Planck's mind in 1900. The idea of light quanta did not appear until Einstein's 1905 photoeffect paper, in 1908 he thought of them as vortices in EM field rather than localized energy packets, and in 1911 remarked that the ...

16

One can only speculate what Hawking will be remembered for, but according to NYT in 2002 he apparently expressed a wish to have what he saw as his biggest accomplishment engraved on his tombstone (following the tradition that goes back at least to Archimedes):"Perhaps in imitation of Boltzmann, Dr. Hawking declared at the end of the meeting that he wanted ...

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 ...

14

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 ...

14

Max Planck, Scientific Autobiography and Other Papers (Westport, CT: Greenwood, 1949), pp. 33-34:A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it.as quoted in:• M. López Corredoira and C. Castro Perelman, ...

12

Sounds like we're all on the same page. But FWIW: In all my research for that Planck book (2015), I found no evidence that he was commissioned, contracted or paid by light bulb (or similar) companies in the 1890's for his theoretical work. Please note I'm not a proper historian, but I did, for instance, go through a number of German historical works on the ...

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

The wave and the particle (or corpuscular) theories of light go back to the 17-th century and are often associated with Huygens and Newton, respectively, as their founders. What preceeded them was called geometric optics, where light consisted of rays connecting an eye to an object. There were two theories in geometric optics too. According to the emission ...

11

I do not agree with the statement, that the lack of mathematical rigor is a major reason for not teaching the path integral formalism in quantum mechanics. The common physicist is normally not interested in complete mathematical rigor, as long as the concepts make sense from a physical point of view and produce the right results. A good example of this is ...

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 $\sigma_1, \sigma_2,\sigma_3,$ ...

10

I wonder why the insistence on the (English) word rule, especially as German wikipedia translates / redirects it to interpretation. Isn’t it enough for your purposes to see it stated, named and credited as Born’s Deutung (Jordan 1927, p. 811), assumption (Dirac 1927, p. 257), Interpretation (Hilbert et al. 1928, p. 29), or Auffassung (Schrödinger 1927, p. ...

9

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 ...

9

It is a good question, how such a weird theory could be invented:-) In its present form the theory was developed by Dirac (physicist) and von Neumann (mathematician). von Neumann essentially developed the mathematical operator theory which is needed. They both wrote books on quantum mechanics which explain the motivation for operators. (You may prefer one ...

9

This is a very good question, I wish it got more attention. My answer will only be partial for I had difficulty finding early details on gyromagnetic effect and ratio. The concept comes up every time we have a rotating system of charged particles, because it has angular momentum and creates a magnetic dipole field, and it played an important historical role ...

9

It was Dirac's paper The Lagrangian in Quantum Mechanics. He gave more than just a remark about $\exp{iS/\hbar}$, he described the general structure of the path integral expression for the transition amplitude, see Dirac's remark that inspired Feynman when formulating path integral on Physics SE. But he did not come up with the suggestive intuition of ...

8

See How did Planck derive the black body radiation formula without using the Bose statistics? for general circumstances of Planck's discovery. Specifically, Planck was trying to reproduce the expression for entropy of an ideal oscillator involved in the original derivation of the black body radiation law. To do so, he had to assume that energy is split into "...

8

From where did the concept of operator in quantum mechanics came, historically? This was a gradual development started by Heisenberg's insight. He invented (infinite) matrices (without any prior knowledge of matrix multiplication). This was followed by by Born, Jordan and Dirac. Dirac's book Principles of quantum mechanics (1930) explains in great detail ...

8

The notion of Hilbert space comes from Hilbert's theory of integral equations. Of course, it was partially motivated by physics, by the theory of oscillations in classical mechanics, but this theory was developed much earlier than quantum mechanics: the main work Grundzuge einer allgemeinen Theorie der linearen Intergalgleichungen (Foundations of the general ...

8

It came to physics a bit earlier than quantum mechanics. The homomorphism $SU(2)\to SO(3)$ was discovered by Cayley (1843), Hamilton (1847), and Klein (1875) in their pure mathematical studies, and came to the attention of physicists through the theory of rigid body rotation (classical mechanics). It was Klein who brought it to the attention of physicists. ...

7

Actually what Einstein proposed was not a perpetual motion machine but was an experiment design to take down the Uncertainty principle. So Einstein design an experiment known as "Einstein's box". It was a thought experiment. He said that consider a box (ideal one) lined up with mirrors so that it contains light indefinitely. Also there is a shutter (ideal ...

7

The turn to operators occurred in Heisenberg's 1925 paper, and it was a compromise between positions taken by Bohr and Born. Bohr wanted minimal modifications to classical mechanics, like his quantization rules for the hydrogen atom, while Born wanted a new discrete mechanics governed by difference equations. Heisenberg's idea was to keep equations of motion ...

7

"Serious" in the OP sense is probably too high a bar. In 1900-s the situation was very much in flux as to what classical physics could and could not explain. Even Planck's and Einstein's ideas, that we now associate with quantum mechanics, were incorporated into seemingly classical approaches at the time. But what dominated the scene were ...

7

I would like to add a slightly more technical answer to supplement the other (although it is a bit late). It may be helpful, I think, and it touches a broader issue which interesting. It's a conflict of history of teaching versus history of the mathematical prerequisites for the material. First of all, supposing the topic material is taught early on, how ...

7

It is more accurate to say that Hamilton anticipated some of the ideas of mathematics and heuristics of quantum mechanics, that would later inspire Schrödinger to produce his formulation of wave mechanics. The reason he was able to anticipate those ideas is that the quantum wave-particle duality had a classical predecessor, the optico-mechanical analogy. ...

7

Some centuries before Mermin, Leibniz in the 17th century was seeking a solution to some of the denominational quarrels that were plaguing his generation by envisioning a calculus ratiocinator that would make it possible for the quarreling parties to "sit down and calculate". A hypothetical science he envisioned was called Mathesis Universalis and included ...

7

Mermin has a thorough analysis[1] and traces the phrase to himself in a 1989 Physics Today column [2] & makes a strong case that the numerous attributions to Feynman are mistaken. [1] Could feynman have said this? / Mermin, Physics Today, 2004 [2] What's Wrong with this Pillow? / Mermin, Physics Today, 1989

7

After looking into more reputable sources it seems that the "commissioned by electricity companies" is a confabulation, and the "commissioned by the German Bureau of Standards" is closer to the truth but still a huge stretch. In Kuhn's Black-Body Theory and the Quantum Discontinuity, 1894-1912, which devotes two chapters to Planck's ...

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