Newton contra el movimiento perpetuo

Alejandro Jenkins

24 horas de física Escuela de física, UCR

15 de diciembre del 2014

“Tampoco funcionan los aparatos de movimiento continuo cuyos dibujos dan misterio a las páginas de las más efusivas enciclopedias; tampoco funcionan las teorías metafísicas y teológicas que suelen declarar quiénes somos y qué cosa es el mundo. Su pública y famosa inutilidad no disminuye su interés.”

— Jorge Luis Borges, “La máquina de pensar de Raimundo Llull” (1937)

Antecedentes• Cultura clásica griega solo alcanza

a desarrollar la estática

• En el s. XII d.C., astrónomo indio Bhāskara II propone rueda de movimiento perpetuo

• Idea llega a Europa en el s. XIII, mediante manuscrito árabe

• Rápidamente captura atención de mecánicos y “filósofos naturales”

Villard de Honnecourt, MS Fr 19093, ca. 1230

H.-P. Gramatke

Imposibilidad• A partir del s. XV, da Vinci,

Cardano, Stevin y Galileo adoptan imposibilidad del movimiento perpetuo como postulado teórico

• Ver E. Mach, Mechanik in ihrer Entwicklung (1883); P. Duhem, Origines de la statique (1905)

• Argumento análogo usado por Sadi Carnot al fundar termodinámica (1824)

Simon Stevin, clootcrans

— I. Newton, “Remarks upon the Observations Made upon a Chronological Index…”, Phil. Trans. 33, 315 (1724)

— I. Newton, “Questiones quædam Philosophiæ”, MS Add. 3996, p.102r. Cambridge U. Library

— I. Newton, “Questiones quædam Philosophiæ”, MS Add. 3996, p.121v. Cambridge U. Library

Bessler/Orffyreus• Johann Ernst Elias Bessler (ca.

1680-1742), empresario alemán oriundo de Alta Sajonia, alias Orffyré o Orffyreus

• Demuestra ruedas de movimiento perpetuo en Gera (1712), Draschwitz (1714) y Merseburg (1715)

• Testimonios favorables de Leibniz, Johann Bernoulli y otros

• Protegido del príncipe de Hesse-Kassel a partir de 1716 Das Triumphirende Perpetuum mobile

Orffyreaneum, (Kassel, 1719)

Das Triumphirende Perpetuum mobile Orffyreaneum, (Kassel, 1719)

• Cuatro referencias positivas a Bessler en Acta Eruditorum (Leipzig) y Mathematisches Lexikon de Christian Wolff (1715-18)

• Leibniz muere en 1716; Wolff mantiene apoyo a Bessler

• Demostración en castillo Weissenstein, 1717-18

• Argumento de imposibilidad publicado en 1720 por J. T. Desaguliers (Royal Society)

• Bessler exige £20 000 por revelar mecanismo.

• Demostración en 1721 convence a ’s Gravesande (U. de Leiden), pero Bessler luego destruye su rueda

• Hatzfeld invoca a Bessler en diatriba contra Newton, 1724

• Zar Pedro I interesado en pagar por mecanismo, antes de morir en ’25

• Demostración anunciada en ’27 no se concreta

• En cartas a Clairaut en ’42, Euler argumenta que Bessler podría haber construido máquina sin equilibrio

— J. C. F. de Hatzfeld, The Case of the Learned, (Londres, 1724)

Leibniz a Carolina (nov. 1715)

• “Newton y sus seguidores tienen una opinión muy curiosa del trabajo de Dios. Según ellos, el reloj de Dios, el Universo, dejaría de funcionar si no le diera cuerda de vez en cuando. No tuvo suficiente previsión para hacerlo un movimiento perpetuo. La maquinaria que ha construido es tan imperfecta que necesita limpiarla de tiempo en tiempo por una intervención milagrosa, e inclusive repararla, como un relojero repara su aparato.” Retrato de J. Amigoni (1735)

Fuente: Wikipedia

“Query 31” (1706)• “Mientras que los cometas se mueven

en órbitas muy excéntricas y en toda clase de posiciones, el mero azar no hubiera hecho que los planetas se movieran todos en órbitas concéntricas, exceptuando algunas pequeñas irregularidades, que pueden haber sido producidas por las acciones mutuas de los cometas y planetas y que bien podrían tender a aumentar, hasta que el sistema requiera una reforma.”

• Problema de estabilidad dinámica del sistema solar

VI. THE END OF THE AFFAIR

The record of how and when Orffyreus’s hoax wasexposed is hazy, probably because of the natural disinclina-tion on the part of the Hessian authorities and of the savantswho had vouched for the machines to acknowledge howfar they had been duped. In a letter dated 18 May 1727,the Landgrave’s Superintendent of Works informed’s Gravesande that Orffyreus was building a new wheel thatwould soon be ready for testing, but no news of themachine’s progress followed.

A few months later, Orffyreus’s maid, Anne RosineMauersbergerin, ran away from her employer’s home andrevealed that the wheels had always been turned from an ad-jacent room, sometimes by her, sometimes by Orffyreus’swife or by his brother Gottfried, sometimes by Orffyreushimself. She produced a written oath that Orffyreus hadthreatened her into signing, in which she had sworn underpain of damnation not to reveal what she knew of themachine’s operation. It also emerged that Orffyreus’s wifehad already informed a government official of her husband’sdeception, but had been angrily instructed to keep quiet.

It is not possible now to determine with certainty howOrffyreus’s wheels turned. Mauersbergerin’s testimony, asquoted in Ref. 24, is unclear on the mechanical details, but itagrees with Borlach’s earlier allegation that one of the postswas hollow and contained a coupling of the axle to a humanforce acting from an adjacent room [see Fig. 3(a)].’s Gravesande dismissed the maid’s claims on the grounds thatthey were inconsistent with what he had seen of the wheel andthat he paid “little attention to what a servant can say aboutmachines.”40 ’s Gravesande and others reported seeing theends of the axle turning freely in the exposed bearings, but thisdoes not really rule out the presence of a turning mechanismhidden inside the post. With enough cleverness, Orffyreuscould even have made the mechanism so that the axle could bedismounted and exhibited without giving away his secret.41

During Orffyreus’s time in Kassel, he also tried unsuccess-fully to establish an Orffyrean church, which he hoped would

transcend the differences between Catholics and Protestants.Prince Karl died in 1730 and Orffyreus was questioned andarrested in 1733, though by 1738 he was again free and liv-ing in his estate in Karlshafen, where he advertised outland-ish new inventions and schemes. In 1745, he fell to his deathwhile constructing a windmill in F€urstenberg.

VII. LEIBNIZ AND MIXED PERPETUAL MOTION

Why did Leibniz, who in his controversies with theCartesians had dismissed gravity-powered perpetual motionas an absurdity, advertise Orffyreus’s wheel in a letter to theTsar’s physician? It might be significant that that letter waswritten in 1716, during the last months of Leibniz’s life, at atime when the priority dispute with Newton over the inven-tion of calculus had negatively impacted his internationalreputation and when he had fallen out of favor with hisemployer, Prince Georg Ludwig of Hanover, who hadacceded to the British throne in 1714 and moved to aLondon in which Newton dominated the scientific commu-nity as president of the Royal Society.42 Leibniz might there-fore have been eager to gain favor with the Tsar and otherprinces by calling attention to a potentially revolutionaryGerman invention.

Furthermore, Johann Bernoulli, a close associate ofLeibniz and an ally in his controversies with Newton, hadlong claimed that some sort of perpetual motion had to bepossible, because otherwise the Universe would not keeprunning on its own.43 Bernoulli argued that microscopic“natural” processes (such as fermentation) could be used topower a macroscopic motion and replenish mechanicallosses, as demonstrated by the continual motion of wind,water, and living creatures.44 In 1722, Bernoulli wrote to’s Gravesande that Orffyreus’s wheel was probably an imple-mentation of a “mixed” perpetual motion, in which theaction of gravity (which could not, on its own, maintain acyclic motion) was complemented by some other “activeprinciple.”45

Fig. 3. (a) Detail of an accusatory image published by engineer Johann Borlach after witnessing Orffyreus’s exhibition at Merseburg.32 (b) Version given byOrffyreus in Ref. 35, accompanied by a brief text dismissing Borlach’s interpretation as absurd. Suspiciously, Orffyreus altered the image in significant ways,adding handles to the axle and obscuring the crank that Borlach thought coupled the wheel to the lever.

424 Am. J. Phys., Vol. 81, No. 6, June 2013 Alejandro Jenkins 424

Fraude• Artículo de 1795 por F. W. Strieder

(archivista de Hesse-Kassel) revela que Bessler fue denunciado por su criada y otros en 1727

• Borlach ya había argumentado que un poste era hueco y contenía manivela

• ’s Gravesande descalificó testimonio de criada

• Bessler arrestado en ’33; en ’38 vivía libremente en Karlshafen

• Muere en ’42, tras caer de molino en construcción

J. Borlach, Gründlicher Gegenbericht von dem Perpetuo oder per se Mobili,

(Leipzig, 1716)

— Christian Wolff, Meletemata mathematico-philosophica, (Bibliopoleo Rengeriano, 1755), p. 69

“La supuesta máquina de Orffyreus, (cuyos fraudes ocultos aún eran desconocidos).”

Interpretación• Leibniz rechaza gravedad newtoniana y

propone modelo neo-cartesiano, con planetas arrastrados por torbellinos en el éter cósmico

• Ver: D. Bertoloni Meli, Equivalence and Priority (Oxford, 1993)

• Apoyo a Bessler vino principalmente de leibnizianos

• Posiblemente esperaban que sirviera de modelo para sistema solar en movimiento perpetuo, mantenido por circulación de un “fluido sutil”

• Último intento de montar demostración en 1727 podría conectarse a muerte de Newton dos meses antes

R. Descartes, Principia Philosophiæ, parte III, 53 (Amsterdam, 1644)

Algunas referencias• R. T. Gould, Oddities, ed. rev. (Londres, 1944)

• S. Schaffer, “The Show that Never Ends: Perpetual Motion in the Early Eighteenth Century”, Brit. J. Hist. Sci. 28, 157 (1995)

• AJ, “The mechanical career of Councillor Orffyreus, confidence man”, Am. J. Phys. 81, 421 (2013). arXiv:1301.3097

• S. Dumas-Primbault, “Les Roues d’Orffyre: Mouvement perpétuel et processus de légitimation du savant dans l’Europe des Lumières”, tesis de maestría en historia de las ciencias, técnicas y sociedades, EHESS, París, 2014