# Tag Info

22

Hamilton and Klein, Klein was more explicit about it. Hamilton in Lectures on Quaternions (1853) realized that his representation of rotations of rigid bodies by the unit quaternions was not $1$-$1$, but $2$-$1$. Klein in Lectures on the Ikosahedron and the Solution of Equations of the Fifth Degree (1888) replaced the unit quaternions by $2 × 2$ unitary ...

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, ...

15

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

It was "solved" by Huygens in Horologium Oscillatorum (1673). The scare quotes are there because he never wrote down the equation, and even Newton's laws were not yet explicitly formulated. Huygens considered the motion of pendula, and for simple cases knew the "law of the conservation of living force" (mechanical energy), as Bernoullis later called it, see ...

11

There are lots of different ways of stating the equivalence principle, and they're not all logically ... er ... equivalent to each other. Names that come up in this connection, from before Einstein, are Galileo and Eotvos. Experiments that test the equality of gravitational and inertial mass are called Eotvos experiments. Einstein's version of the ...

10

${\def\Target#1{\rlap{\smash{\label{#1}\phantom{\tag{#1}}}}}} {\def\BackUp{\raise{0.25em}{\Tiny{\boxed{\boldsymbol{\Uparrow} \hspace{-2px}}}}}}$tl;dr- It's unclear. The symbol $ \hbar "$ itself wasn't anything new. Paul Dirac used it defining $\hbar \equiv \frac{h}{2 \pi}$ in a 1926 paper, but didn't explain the choice of the symbol. It might still be ...

9

Ancient Greeks painstakingly avoided negative numbers, although they could have come handy in astronomical calculations and number theory, among other places. Brahmagupta in Correctly Established Doctrine of Brahma (c. 630 AD) uses the language of "fortunes" and "debts", which suggests the merchant origin of the negative number concept, but that remains a ...

9

There was an opposition. The reasons were mainly philosophical. The main thing which was hard to accept was "action at a distance" through the void space. For example Huygens did not accept this. It contradicted Descartes theory which was prevalent at that time. So the question had too be decided by observations and experiments, as it always happens in ...

9

Before Hamilton (1847) one should cite Euler (1771), Gauss (1819), Rodrigues (1840), and Cayley (1845). Detailed references in e.g. Pujol, J., Hamilton, Rodrigues, Gauss, quaternions, and rotations: a historical reassessment, Commun. Math. Anal. 13, No. 2, 1-14 (2012). ZBL1268.01010. Specifically, to four numbers $p,q,r,s$ with $pp+qq+rr+ss=u$, Euler (1771,...

9

The status of scientific education in the 19th century is a very complicated mess, especially for the fact that every country worked different than the others. I know of no book or article that tackles this problem in general, so I'll attempt an answer based on various readings, majorly biographies. 1) Basic Education in the 19th century To understand what ...

8

I suggest that the baseless suggestion offered in this question can best be answered by Einstein's own words about Newton, written in 1919. The background was the now-well-known eclipse expedition of 1919, in which the amount of deflection of light from stars close to the sun's limb had been observed during the eclipse. The results gave a probable ...

7

Going by Wikipedia's definition, a physical constant is a number "generally believed to be both universal in nature and have constant value in time". The significance of these constants began to be recognized in the late 19th century, partly as a result of the standardization of the measurement system. But their modern prominence is due to Eddington's semi-...

7

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

In a way everyone knew that it was heat that is flowing and coldness is absence of heat. But how did they know it? The answer, quite simply, is that they didn't know it. Coldness was frequently measured in degrees just as heat was, and terms like degrees of frost were in common use even into the early 20th century. Alternative temperature scales like the ...

6

Newton proved that if the attraction obeys the inverse square law, then the force inside a uniformly charged sphere is zero. It follows from the description that you give that Cavendish used the converse statement. In fact this converse statement is true though I doubt that Cavendish had a proof of it in full generality. It is very common for physicists (...

6

The use of reduced mass in spectroscopy goes back to Bohr's planetary model of the atom. Nasri explains the context in his notes on quantum mechanics: "In 1912, Alfred Fowler showed that similar lines can be produced in a laboratory mixture of hydrogen and helium gas. Bohr noticed that they have the same spectrum of spectral lines as of hydrogen but with ...

6

It is hard to prove that answer is negative, but I suspect that that's the case. That sentence looks familiar. In fact, in his book Relativity: The Special & the General Theory, Einstein wrote “Without it the general theory of relativity […] would perhaps have got no farther than its long clothes.” But here Einstein is talking about ...

6

In a now-deleted comment, Consigliere ZARF listed a number of papers published in Zeitschrift für Physik in the late 1920's that used this notation. The earliest was Pascual Jordan's 1927 "Über eine neue Begründung der Quantenmechanik", using the notation on pp.816-817; with about 10 other papers published in the following few years, all in the ZfP, all ...

5

“In Copenhagen again! The brothers Bohr fetched me at the pier, and now I’m established in Niels Bohr’s private palace. I had numerous conversations with the Bohrs and Mrs. Bohr, of course mostly political—but we even managed to talk an hour and a half on ‘the interpretation of quantum mechanics.’ I’m sure we were showing off, the both of us: giving an ...

5

I've always liked logarithms because of their properties, and for some time I wondered who got the idea in the first place and how were the tables computed. It turns out logarithms were developed and computed simultaneously and independently by John Napier and Joost Bürgi. Both of them calculated huge logarithm tables by hand: Napier computed almost ten ...

5

Another example of a "remarkable achievement of hand calculation" was in the field of mathematical astronomy. During 1758, Alexis Clairaut and his collaborators in Paris worked to refine Edmond Halley's prediction (published in 1705) of a return in about 1758 of the comet that now carries Halley's name. Halley's original prediction had been for 1758, ...

5

Newtonian mechanics was resisted throughout its history, all the way until it was replaced by relativity and quantum mechanics. But the criticism did not so much concern the specifics of his laws of motion, there were few Aristotelians around, and, after all, they were pretty well confirmed by experiments, as their interpretations and "metaphysical" ...

5

Gibbs, the father of vector analysis in physics, or his student Edwin Bidwell Wilson, seems to have established the tradition of using the word speed for the scalar, and the word velocity for the vector. It seems to me that using these two different names was meant to be helpful when introducing vectors, rather than to confuse and complicate. Gibbs's ...

5

Trigonometric functions became "mainstream" since the publication by Ptolemy (II AD) of trigonometric tables. To be sure he did not use our modern sine and cosine, but a single trigonometric function, the chord ($=2\sin(t/2)$). Modern definitions of sine and cosine were introduced by Indian mathematicians (Surya Siddhanta (V century AD), and reached Europe ...

5

It makes no difference for either measuring temperature, or calculating heat flow, what flows there, if anything. So experimental basis for measuring temperature was established long before the nature of what was measured became clear. As Fowler writes in Early Attempts to Understand Heat: "By the late 1700’s, the experiments of Fahrenheit, Black and ...

4

This quite difficult question seems to place the mathematization of nature in the 18th century, but a substantial body of scholarly opinion writes of it as developing earlier than that, in the 17th -- although there can of course be no doubt that its further development in the 18th century was very extensive indeed. Sources on the 17th century earlier ...

4

Paul Krugman's research was caused by Isaac Azimov's Foundation novels. (For this answer, you have to accept economics as a science and you have to accept "caused scientists to do real research" in the sense of motivating them to do it.) From his interview, December 2008, on the Nobel website. (Yes, yes, I know, the Sveriges Riksbank Prize in Economic ...

4

Arhytas made the first known steam powered toy in the shape of a pigeon, see The steam-powered pigeon of Archytas. Priestley put a mint plant in a closed container with a burning candle. The candle flame went out after using up the oxygen, but after 27 days Priestley re-lit the candle, demonstrating that mint produces oxygen of its own. Kekulé claimed, 25 ...

4

There's "Buridan's ass" in logic, which says that a "hungry donkey" will not be able to decide "between two completely alike bales of hay" (Duhem 2018 p. 13) and thus will starve. It's attributed to medieval physicist John Buridan (1295-1360), but a physics (not logic) version of it can be found in Aristotle's De Caelo 295b32 [375.]: the man who, though ...

4

Contribution of Newton to optics is enormous. He is considered a founding father of physical optics. I can only give some examples. His main discovery was that the sunlight can be dissolved into colors (spectrum). The discovery which lead to spectroscopy, and eventually to quantum mechanics. He also analysed what is called "Newton rings" (discovered by Hooke ...

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