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(2002-10-08)   Heliocentric "Copernican" System
Did the idea of an heliocentric system originate with Copernicus?

No.  The idea is actually far more ancient.

Although Heraclides of Pontus (387 BC - 312 BC) deserves great credit for first suggesting that the Earth rotates around an axis, he did not yet place the Sun at the center of the Solar system  (in spite of what some reports are still stating).

Copernicus (1473-1543) credited Aristarchus of Samos (310 BC - c.230 BC) for the idea of an heliocentric system.  This heliocentric idea does not appear explicitly in the only surviving work of Aristarchus, where the distances and sizes of the Moon and the Sun are estimated.  Aristarchus did underestimate the size of the Sun, but he could tell that it was much bigger than the Earth, which may have suggested to him that the smaller body should be revolving around the larger one. However, the actual heliocentric system of Aristarchus is known to us from the summary given in The Sand Reckoner (c.213 BC) by an illustrious younger contemporary of Aristarchus: Archimedes of Syracuse (287 BC-212 BC).

Plutarch (c.45-125) reports that Seleucus of Seleucia (on Mesopotamia's Tigris) championed the heliocentric system shortly thereafter and taught it as an established fact, in the second century BC.  At the exact same time however, Hipparchus of Rhodes (190-120 BC) reverted to the geocentric system, and was instrumental in killing the heliocentric idea [cf. Thomas Little Heath (1861-1940)].

The idea was strongly suppressed by the Church for centuries and it took more than a little courage to revive it on the part of Copernicus and his early followers.

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PJH (2003-10-15; e-mail)     Galileo's Assistants
Who was Galileo's assistant for his famous experiment?

Funny you should ask this...  The legendary experiment, which allegedly took place at the Leaning Tower of Pisa, consisted in dropping two different weights simultaneously from the top of the Tower and supposedly recording their simultaneous arrivals on the ground...  Well, one of Galileo's assistant, Vincenzio Viviani (1622-1703), did play a major role in this, but not in the way you might expect, as Viviani was not even around to witness the event, if it ever occurred!

Some Assistants and/or Noted Disciples of Galileo's

From	To	Who
c. 1605	Nov. 1613	Benedetto Castelli (1578-1643)
c. 1618		Mario Guiducci (1585-1646)
c. 1618		Niccolò Arrighetti (1586-1639)
Oct. 1638	Jan. 1642	Vincenzio Viviani (1622-1703)
Oct. 1641	Jan. 1642	Evangelista Torricelli (1608-1647)

When he became Galileo's assistant in October 1638, Viviani was only a 16-year old youth from Florence, whose promising aptitude for mathematics had earned him the commendation of Galileo's patron, the Grand Duke Ferdinand II of Tuscany.  By that time, the ageing Galileo had already lived under house arrest for 5 years in Arcetri.  He had lost his eyesight in 1637 and he welcomed the live-in presence of the devoted Viviani, who wrote and read for him.

When Galileo died in the evening of January 8 of 1642, he was in the company of only three people:  His own son, Vincenzio Galilei (1606-1649), his aforementioned junior assistant Vincenzio Viviani and his famous new senior assistant, Evangelista Torricelli, who had joined him only weeks before: 

Evangelista Torricelli (1608-1647)   was an orphan who studied at the University of Sapienza under a former student and close friend of Galileo's, Benedetto Castelli (1578-1643).  Torricelli served as Castelli's secretary from 1626 to 1632.  According to Dava Sobel (author of the bestseller "Galileo's Daughter") Torricelli had first written to Galileo in the summer of 1632 to tell him how he had been converted to the Copernican views by reading Galileo's own Dialogue on the Two Chief World Systems, Ptolemaic and Copernican, the very book which would seal the Inquisition's case against Galileo in 1633 (and have him condemned to spend the rest of his life under house arrest).  In 1640, Torricelli wrote a treatise on the motion of bodies (Trattato del Moto) in which he described experimental evidence for the laws of falling bodies expressed by Galileo.  As he was dying and needed help to polish his final scientific thoughts, Galileo made Torricelli his assistant in October 1641.  When Galileo passed away a few weeks later, Torricelli succeeded him as professor at the Florentine Academy and as court mathematician to the Grand Duke Ferdinand.  Torricelli kept working with Vincenzio Viviani, Galileo's younger assistant.  In 1643, the two men invalidated Galileo's own theory about the inability of aspiration pumps to raise water above a certain height [of less than 10 m].  Torricelli and Viviani suspected that the limited tensile strength of water was not at fault, despite what Galileo had conjectured, but that the weight of the liquid column was of crucial importance.  They transposed the effect to mercury and observed that if a mercury-filled glass tube is inverted into a bowl of mercury without letting any air in, then the level of mercury in the tube stabilizes at a height of about 760 mm over the level of the liquid in the bowl.  In 1644, Torricelli correctly stated that the cavity above the mercury in the tube contains "absolutely nothing" and that the mercury is pushed up the tube by the pressure of the air in the atmosphere, which varies slighlty from day to day.  Torricelli is thus remembered as the inventor of the barometer.  (Note that the "Toricellian vaccum" in the tube actually contains mercury vapor at extremely low pressure, but this is largely irrelevant.)

When Torricelli died in 1647, Viviani suceeded him in the position Galileo had occupied only a few years earlier.  In 1654, a dozen years after Galileo's death, Viviani began writing the first biography of Galileo.  He clearly embellished things a little...  In particular, the narration of the experiment at the Leaning Tower of Pisa is usually considered a pure fiction, invented by Viviani:

The Leaning Tower of Pisa and the Alleged "Experiment"

What the Italians call "la Torre pendente di Pisa" is a bell tower, whose seven bells were used until 1950.  The architect Bonnano Pisano began its construction on August 9, 1173 in the Campo dei Miracoli (Pisa's "Field of Miracles").  When the building reached the 3rd level (about 10 years later), its leaning was already pronounced, and construction stopped for 90 years.  The main tower was completed between 1275 and 1284 by Giovanni Di Simone, who compensated for the tilt by giving the building a slight banana shape.  The architect Tommaso Pisano (son of Andrea Pisano) finally added the top belfry between 1350 and 1372.  In Galileo's times, more than two centuries later, the Leaning Tower of Pisa was pretty much what it is today: A building of about 14 700 000 kg rising 58.363 m above its foundations, with a 4 m overhang that would increase steadily (at a rate of about 1.2 mm per year) if it was not for regular heroic countermeasures...

Galileo's "famous experiment" at the Leaning Tower of Pisa probably never took place.  Galileo himself never claimed to have performed the deed, and the fantastic decorum described by Viviani is even more unlikely.  The experiment would have been largely inconclusive anyway, except to disprove the gross misconception [wrongly] attributed to Aristotle, according to which the speed of falling objects ought to be proportional to their weights (this much is easily proven wrong by less dramatic experiments which Galileo did perform).  Galileo may have meant to do the grand experiment, but the idea probably occurred to him at a time when it could not be conveniently carried out, because he no longer lived next to the Tower:  Galileo moved from Pisa to Padua in 1591.  He had began to study falling bodies only two years earlier, in 1589.

For the record, the experiment only "works" properly in a vacuum, where a feather and a ball of lead do fall at the same rate.  (Otherwise, a given shape, size and speed imply a certain value of the air resistance which does constitute a lesser percentage of the weight of an heavier object.)  Astronaut David R. Scott successfully performed Galileo's experiment (using a feather and a hammer) on the lunar surface, on August 2, 1971 [see video].  The same result is routinely demonstrated [at a much lesser cost] with an evacuated sealed tube containing two very different objects, usually a feather and a coin...

Other problems exist when conducting such experiments with the "technology" of Galileo's time, including a curious systematic error (due to muscle fatigue) when people are attempting to release simultaneously balls of different weights.  A tribute to the observational skills of Galileo was that he recorded negative results to similar experiments which could be explained this way...  So much for the simplicity of legendary "experiments".

Weights Make Haste: Lighter Linger  (Dec. 1999)   |   The Legend of the Leaning Tower  (Feb. 2003)

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(2002-10-05) Switching Calendars
Was Newton really born the year Galileo died?

No.  Galileo died 361 days before the birth of Newton.  The death of one and the birth of the other occurred in different Julian years (1641 and 1642) and in different Gregorian years (1642 and 1643).  The year is the same (1642) only when the death of Galileo is recorded in the Gregorian calendar (then prevalent in Italy) and the birth of Newton is recorded in the Julian calendar (still prevalent in England at the time).

Note that there's usually an added complication when comparing both calendars:  The legal year in England under the old [Julian] calendar changed on March 25.  In other words, Newton was 6 days old on December 31, 1641 and clearly 7 days old on the following day, which was legally January 1, 1641.  On the other hand, Gregorian years do change on January 1.  This whole remark is thus entirely irrelevant to our point here, which is fully summarized by the following table:

About calendars...

Primitive Roman calendars evolved into a somewhat variable system which featured 12 short months and, on some years, a thirteenth month (called either Intercalaris or Mercedonius) whose length was ultimately decided politically...  This dubious system was replaced by an early form of the Julian calendar, introduced by Julius Caesar in 45 BC.  After a rough start and too many leap years, the Julian calendar was given its final form by Augustus, and every fourth year was made a leap year starting with the year AD 8.

Our current calendar is only a slight modification of the latter Julian calendar.  It's known as the Gregorian calendar because it was introduced under the authority of Gregory XIII, né Ugo Boncompagni (1502-1585), who was Pope from 1572 to 1585.  The Gregorian reform of the calendar was actually engineered by the astronomer Christopher Clavius to make the seasons correspond permanently to what they were under the Julian calendar in AD 325, at the time of the First Ecumenical Council of the Christian Church, the First Council of Nicea, when rules were adopted for the date of Easter  (usually, the first Sunday after a full moon occurring no sooner than March 21).  10 days were dropped in 1582 (October 15 followed October 4) and new rules were devised to have only 97 leap years in 400 years (instead of 1 in 4).

Various countries adopted the "new" calendar only much later.  In particular, the earliest valid Gregorian date in England (and in what was then known as the American Colonies) is September 14, 1752, which followed September 2, 1752 (the discrepancy had grown from 10 to 11 days by that time, because the year 1700 was not a leap year in the Gregorian calendar).  This happened more than a century after Newton's birth, which was thus still recorded as Christmas day of 1642, although the year in Italy was already 1643.

On the other hand, it is correct to remark that Stephen Hawking was born (January 8, 1942) exactly 300 years after the death of Galileo (January 8, 1642) since both events were recorded in the same Gregorian calendar.

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(2003-11-03)   The Lorenz Gauge   [ not due to H.A. Lorentz ]
The 1867 addendum to Maxwell's equations of electromagnetism (1864)

This is the following relation between the vectorial and scalar potentials A and f, which would otherwise be defined with more leeway.  In a classical context, this equation has some aesthetic appeal, as it makes the d'Alembertians of A and f respectively proportional to the density of current and the density of charge... In a quantum context not anticipated by Lorenz at the time, the potentials have a  real  significance of their own, which is happily consistent with that gauge :

div(A)  +	1		¶ f	=  0       [ In SI units, or Giorgi's MKSA system.]
	c2		¶ t

The thing is very often misspelled  "Lorentz Gauge" (with a "t") because of a fallacious attribution to Hendrik Antoon Lorentz (1853-1928; Nobel 1902). The relation was published by the Danish physicist Ludwig Lorenz (1829-1891) in 1867, when the future great Dutch physicist H.A. Lorentz was only 14...

90% of Internet authors have it wrong  (Lorentz Gauge vs. Lorenz Gauge).

Ironically, it turns out that Ludwig Lorenz is best remembered for the relation he established in 1880, building on earlier work (1878) by the young H.A. Lorentz about the theoretical index of refraction of a dielectric substance.  This result is now known as the  Lorentz-Lorenz  relation...  Spelling bee, anyone?  

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(2002-10-08)   On the Origins of the Special Theory of Relativity
Was Einstein the first to formulate the (Special) Theory of Relativity?

 

The secret to creativity is knowing how to hide your sources.
Albert Einstein  (1879-1955)

What is now known as the Special Theory of Relativity was first completely formulated by the prolific French mathematician  J. Henri Poincaré (1854-1912), who published key results with a relativistic perspective in 1898, 1900, 1904 and on June 5, 1905.  Albert Einstein discovered the whole thing independently and published his original paper on the subject on June 30, 1905.  Einstein later added the adjective "special" to describe this initial theory, in contradistinction to the 1915 theory of  General Relativity,  his relativistic theory of gravitation  (of which Einstein stands as the undisputed sole author).

Neither Einstein nor Poincaré ever quoted each other on the subject.  Both, however, often cite Hendrik A. Lorentz (1853-1928) who put forth the relevant coordinate transform in 1904, incorporating the so-called FitzGerald-Lorentz contraction, which had been proposed by George FitzGerald (1851-1901) in 1889  (and, independently, by Lorentz himself in 1892)  to explain the negative result of the Michelson-Morley experiment of 1887.

In 1887, Woldemar Voigt (1850-1919) came up with a coordinate transform which explained the Michelson-Morley result (and the transverse Doppler shift ) but featured an erroneous overall scale factor implying some asymmetry between the stationary and the moving system, against relativistic principles.  Yet, his idea of involving time as a coordinate was good...  H.A. Lorentz and Voigt were in touch, but it took years for Lorentz to adopt this viewpoint and find a correct transform with the desirable symmetry.  Voigt also introduced modern  tensors  into physics, a key element in Einstein's own General Theory of Relativity.

The symbol "c" for the speed of light (Einstein's constant) was introduced in 1894 by a famous student of Voigt's,  Paul Drude (1863-1906).  Drude used "c" for electromagnetism, but in an optical context he retained the symbol "V" which had been introduced by James Clerk Maxwell.  Einstein himself used "V" until 1907.

The famous equation   E  =  m c ²   has been spotted several times times before Albert Einstein proposed it, in September 1905.  Such reports include:

• 1903:  Olinto de Pretto (1857-1921) in the Italian journal  Atte.
• 1904:  Friedrich Hasenöhrl (1874-1915) a teacher of Erwin Schrödinger.

The Special Theory of Relativity did not take off until 1908, when Max Planck (1858-1947) put his considerable weight in the balance and wrote a paper on the subject.  The same year, Hermann Minkowski expresssed the Maxwell-Lorentz equations [of electromagnetism]  relativistically in  tensor  form, and showed that Newton's theory of gravity was not consistent with Special Relativity.

The whole controversy may have been one of the reasons why Relativity was not mentioned in 1921 when Einstein was awarded the Nobel prize.  Instead, Einstein was officially rewarded for his 1905 explanation of the laws of the photoelectric effect, which may be construed as a discovery of the photon.  In 1912  (the year Poincaré died)  Wien had even proposed that  Lorentz  and  Einstein  share the Nobel prize for Special Relativity, because:

[...]   the merits of both investigators [are] comparable.

Some authors have felt that Einstein's huge fame was not entirely deserved, but calling him a plagiarist  is certainly not fair:  Just like any other genius in history,  Albert Einstein had to build on the work of his elders.  Period.

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Most of Einstein's precursors were about 25 years older than himself.  They were all the heirs of Maxwell (1831-1879)  who died the year Einstein was born...

Maxwell's key contribution was his set of differential equations unifying electricity and magnetism, and predicting electromagnetic propagation at a fixed celerity.  Their mathematical form seemed to make them only valid in some fixed "aether".  Relativity was born with the gradual realization that Maxwell's equations should hold unchanged even for observers in relative uniform motion.  The nontrivial coordinate relations postulated by the Lorentz transform allowed just that.

Before Maxwell, those who paved the road include a few French physicists:

• Augustin Jean Fresnel (1788-1827)  was born on the  de Broglie  estate.  (His mother was the daughter of the overseer.  His father worked for a few years as an architect for the family of the future Nobel laureate.)  Fresnel was educated at Caen and at the Ecole Polytechnique (X) in Paris  [just like this writer, on both counts, incidentally].  Fresnel is best remembered for the type of lenses now named after him  (featuring concentric grooves)  which are used in lighthouses, spotlights, flat plastic magnifiers, etc.  Among other fundamental scientific investigations, Fresnel showed that two light beams polarized in perpendicular planes do not exhibit optical interference, thus establishing the  transverse  nature of lightwaves  (whereas sound in a fluid is a  longitudinal  wave).  Fresnel also investigated light in a moving medium:  In this context, we call Fresnel coefficient of drag  a parameter  f  whose dependence on the refractive index (n) was found empirically by Fizeau and explained by Einstein:

f   =   1 -  ¹/_n²

• Armand Hippolyte Louis Fizeau (1819-1896) discovered the Doppler effect in 1848, independently of Christian Doppler (1803-1853) who wrote on the subject in 1842:  The effect is sometimes called  Doppler-Fizeau, especially in French texts.  In 1849, Fizeau gave the first direct experimental value of the speed of light, by using a rotating toothed wheel  (Fizeau wheel)  and a distant mirror.  In 1851, he used interferometry to investigate how the speed of a moving liquid affects the celerity of light propagating in it.  He obtained a result intermediary between what would be expected of a wave bound to the medium (like sound in a fluid) and something independent of it.  Einstein explained this relativistically. 
• Jean Bernard Léon Foucault (1819-1868)  is still remembered for the  pendulum  experiment named after him, which detects the rotation of the Earth by mechanical means.  In 1851, he first demonstrated this publicly, under the dome of the Panthéon in Paris.  Foucault is on record as the inventor of the  gyrocompass (1852).  Electric currents induced in a metallic mass (eddy currents) were discovered by Foucault; they are now often called  Foucault currents.  He improved on Fizeau's method to measure the speed of light  (using a mirrored wheel instead of a toothed wheel).  Foucault proved the speed of light to be greater in air than in water, as is consistent with an  undulatory  phenomenon.

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(2002-10-05)   The Oil-Drop Experiment [to measure electron charge]
Did Robert A. Millikan (1868-1953) design the famous experiment which helped him earn a Nobel prize?

Not entirely.  Much of the credit should have gone to his graduate student Harvey Fletcher, who was not even named a co-author of the key relevant paper.  Originally, Millikan reproduced an experiment involving drops of water, conceived by J.J. Thompson and E. Regener.  On this subject, let's quote David Goodstein, who is sympathetic to Millikan:

Unfortunately the single-droplet method had a serious flaw. The water evaporated too rapidly to allow accurate measurements. Millikan, Begeman and a new graduate student named Harvey Fletcher discussed the situation and decided to try to do the experiment with some substance that evaporated less rapidly than water. Millikan assigned to Fletcher the job of devising a way to do the experiment using mercury or glycerin or oil. Fletcher immediately got a crude apparatus working, using tiny droplets of watch oil made by means of a perfume atomizer he bought in a drugstore. When he focused his telescope on the suspended oil droplets, he could see them dancing around in what is called Brownian motion, caused by impacts of unseen air molecules. This itself was a phenomenon of considerable current scientific interest. When Fletcher got the busy Millikan to look through his telescope at the dancing suspended droplets of oil, Millikan immediately dropped all work on water, and turned his attention to refining the oil-drop method.
      A couple of years later (around 1910) Fletcher and Millikan had produced two results. One was an accurate determination of the unit electric charge (called e) from observing the rate of fall or rise of oil drops in gravitational and electric fields, and the other was a determination of the product Ne, where N is a separate constant called Avagadro’s number. The product Ne came out of observations of Brownian motion. Millikan approached his student Fletcher with a deal. Fletcher could use a published paper as his Ph.D. thesis, but only if he was sole author. Millikan proposed that Fletcher be sole author on the Brownian motion work and that he, Millikan be sole author on the unit electric charge work. This is the source of the assertion that Millikan mistreated his graduate students. No doubt Millikan understood that the measurement of e would establish his reputation, and he wanted the credit for himself. Fletcher understood this too, and he was somewhat disappointed, but Millikan had been his protector and champion throughout his graduate career, and so he had little choice but to accept the deal. The two men remained good friends throughout their lives, and Fletcher saw to it that this version of the story was not published until after Millikan’s death, and after his own death.

Harvey Fletcher (1884-1981) himself summarized his collaboration with Millikan in the June 1962 issue of Physics Today.  There were in fact 5 papers involved; Millikan is named as sole author of the first (and most important) one, Fletcher is named as the sole author of 2 others (including the one he used as his doctoral dissertation) and the last two appeared with both names as joint authors.

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(2005-08-19)   About Customary Physical Units
Errata about physical units and noteworthy physical quantities.

As we compiled a rather large catalog of physical units over the years, we found a large number of errors throughout the literature.  They propagate at an alarming rate.  We've lost track of most of the sources, but feel compelled to post the following list of errata, as a public service.  (If you must know, this list is sorted alphabetically with respect to the main, unit, scale, quantity, or concept involved.)

These have been thoroughly investigated, so we may hope to avoid the same embarrassment as one author who made a similar claim  (about the rarely-used "poncelet" unit)  and got it wrong!

We did pay particular attention to wrong claims that we found more than once...  At times, it really looks like nobody ever bothers to check mathematical facts.  One particularly startling example is our first entry, about the Beaufort rating of an 18 mph wind, for which we have yet to find a single  correct  table!

• An 18 mph wind should be rated "Force 5" (not  4) in the Beaufort scale.
• A "square centimeter candle" is worth 60 candelas, not  the other way around.
• The mean curvature is the half-sum (not  the sum) of the principal curvatures.
• A clausius is a unit of entropy equal to  1 cal/K  (not  1 kcal/K).
• One gram of radium has an activity of 9 curies (not  just one curie); out of this, 1/9 is from the direct decay of radium nuclei, 8/9 is from subsequent decays of all the decay products of radium (the proportions are exact under "equilibrium" conditions, where the relative concentrations remain constant).
• As a unit, the day remains exactly 86400s, but the "mean solar day" increases.
• The density of the Earth is not  5.2, but 5.52 (a better number is 5.515 kg/L).
• Ordinary screws and corkscrews are dextrorsum (not  sinistrorsum).
• A logarithmic spiral's evolute is congruent but usually not  equal to itself.
• The frigorie (1000 negative gram-calories) is a unit of energy, not  power.
• According to modern tables for the density of water, the old definition of the UK gallon implied measurement at a temperature of about 16.3333°C (61.4°F), not  15.18°C.  (This is a subtle point, due to the fact that the definition was enacted at a time when the liter was not exactly equal to a cubic decimeter: 998.859 g/L "then" is 998.887 g/L "now".)
• The moment of inertia of the Earth is about  8´10 ³⁷ kg×m ²  (not  10 ⁴² ).
• A jansky is not  a W/m²/Hz, it is 26 orders of magnitude smaller!
• The orbital energy of the Earth around the Sun is -2.65´10 ³³ J  (not  10 ⁴⁰ ).
• 39.37 inches are exactly 0.999998 m  (39.37 US Survey inches to the meter).
• Isaac Newton was born in the Gregorian year 1643 (Julian Christmas day 1642).
• The "pascal per square meter" is not  a unit of pressure; the "pascal" is.
• A poncelet is not  100 W, but 980.665 W  (100 kgm/s).
• The spat (whole sphere) is a unit of solid angle, it is  not  a planar angle.
• A torr is  not  quite equal to a millimeter of mercury  (it's 0.14 ppm less).
• As a unit, a year is equal to 31557600 seconds; other "years" are  not  units.
• "Water" units of pressure are conventional units which do  not  depend on the actual density of water (under conditions prevailing during measurement).  A meter of water is defined either as precisely  9806.65 Pa  or roughly  9806.38 Pa  (using a conventional density of either 1 kg/L  or  999.972 g/L).