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Determining Longitude: a Brief History

Determining Longitude: a Brief History

case, however, that this entails con- plete that nice piece of . first four satellites in 1610, he real- servation of mass. Although the After ’s ized that comparing their mass of an isolated particle can be 1492 trip to America, ships, mostly with local times at a ship’s po- determined from its four-momentum, Spanish and Portuguese, crossed the sition could be a key component in that connection does not apply to Atlantic Ocean in increasing num- determining . In 1612, and multiparticle states. And since parti- bers. That migration forced a quali- on three occasions thereafter, Galileo cles do interact, and even decay, a tative change in coastal tried unsuccessfully to convince the result that is only valid for single- techniques, since mariners sailed Spanish monarchy of the usefulness particle states does not allow one to without visible land or fixed points of his method. Although his idea draw general conclusions. That is of reference. The determination of proved to be impractical at , it why the many specific manifesta- geographical longitude became an did eventually work on land. For ex- tions of nonconservation of mass urgent need—at sea for navigation, ample, the difference in longitude I discussed in my column can be— and on land for more precise cartog- between Paris and Uranienborg, and are—perfectly consistent with raphy and settlement of territorial Denmark, was calculated on the special relativity in general, and disputes. basis of the eclipse times taken by with the conservation of four- The need led Spanish King Giovanni Cassini, , and momentum in particular. Felipe II (1527–98) to offer a sub- Ole Rømer in 1671. Frank Wilczek stantial reward to the inventor of a Clockmaker won Massachusetts Institute of Technology method to “find longitude.” The re- the British prize by developing, be- Cambridge ward amount was increased tween 1735 and 1764, increasingly later by his successors, and greater precise and practical mechanical rewards were promised by other chronometers, including the one Determining Longitude: countries as they began their own used by James Cook in some of his oceanic . The British gov- expeditions. A Brief History ernment, for example, offered Rømer’s work is probably the first t was a pleasure to read Fokke £20 000 in 1714 to whoever could measured Doppler effect; that is, he I Tuinstra’s letter (PHYSICS TODAY, provide a satisfactory method of discovered that the value observed December 2004, page 16) on Ole finding a ship’s position to within on for the period of Jupiter’s Rømer’s proof that the speed of light half a . moons depends on Earth’s velocity is finite. Perhaps an account of the What has this circumstance to do relative to Jupiter. It is also notewor- reasons that led him and other sci- with the abrupt and almost obses- thy that today’s global positioning entists to study so precisely the sive dedication to the study of system solution to the old problem moons of Jupiter (the system Rømer Jupiter’s moons? of finding longitude requires the use used for his result) would help com- When Galileo discovered Jupiter’s of general-relativistic corrections to

See www.pt.ims.ca/6087-9 See www.pt.ims.ca/6087-10 attain maximum accuracy. If and Tom Powers up to the paragraph quence of discrete energy states in Rømer’s studies are an excellent ex- that refers to the “feeling for en- the form of translations, rotations, ample of how technologically driven tropy.” I drew back at the totally vibrations, electronic excitations, research may provide fundamental misleading analogy in their figure 2. and so forth. basic results, the GPS appli- Molecules, large or small, do not Ludwig Boltzmann demonstrated cation of general relativity also hop over barriers like buffalo in a that in any macroscopic sample of nicely demonstrates complementary stampede. Saying, as many instruc- matter at equilibrium, the popula- feedback in the science–technology tors do, that a particular chemical tion of accessible states follows a system. conversion occurs because the system specific temperature-dependent dis- Jorge Mira-Pérez is “seeking the lowest chemical poten- tribution function. ([email protected]) tial” and in so doing “it must sur- It is useful to consider a feature Salvador X. Bará mount a free energy barrier” gives of the distribution, the density of ac- Universidade de Santiago students no conceptual content, only cessible states, which depends on the de Compostela words to repeat on an examination. total energy and increases rapidly Santiago de Compostela, Spain Furthermore, although the en- with increasing energy. For the con- tropy function developed in a course version of A to B, there must be a se- on conventional thermodynamics is quence of structures that are inter- Statistical-Mechanical fundamental, it resides in a special mediate between the original and mental compartment. It remains un- new species. For the intermediates Viewpoint Needed in connected to molecular and statistical there exist corresponding distribu- concepts that provide students with tion functions characterized by their Teaching Biophysics the basis for constructing models of distinctive densities of states. Gener- o a retired professor of physical the complex processes they will en- ally, the intermediate structures Tchemistry, the proposals outlined counter in biophysical studies. Why have higher electronic energies than in “Teaching Biological Physics” not the molecular and statis- either A or B, so only the higher- (PHYSICS TODAY, March 2005, page tical models early in the program? energy states of A or B are close to 46) concerning the inadequate course - physics and bio- those of the intermediates and thus content for biophysics majors and physics majors have learned the fun- have a high probability of making possible remedies are rational and damentals of quantum mechanics, transitions. Clearly, only if B has a merit implementation to various de- and will not reject the assertion that higher density of states at that level grees. I followed the proposals of au- for each species of molecule, small or does the conversion succeed, since thors Ray Goldstein, Phil Nelson, large, there is a distinctive, huge se- the higher density of accessible

16 October 2005 Physics Today http://www.physicstoday.org