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Transcript of Fresnel, 1818 Fizeau, 1851 - home.fnal. stancari/Carpi/Carpi2005_relativita_   ¥Gli...

Lelettrodinamica deicorpi in movimento:

appunti di relativit speciale

ITIS da Vinci, Carpi (MO), 1 marzo 2005

Giulio Stancari

Istituto Nazionale di Fisica NucleareSezione di Ferrara

1

Basi sperimentali ed evoluzione delle idee

Gli articoli di Einstein del 1905

Commenti su relativit ed elettromagnetismo

Esempi dalla fisica nucleare

Note sulla didattica

2

Le Nazioni Unite, attraverso lUNESCO, hanno proclamato il 2005 Anno Mondiale della Fisica

Celebriamo il centenario dellanno mirabile di Einstein (1905), durante il quale vengono pubblicati alcuni articoli fondamentali:

moto browniano

quanti di luce

relativit speciale

Approfondiamo contenuti e conseguenze degli articoli sulla relativit speciale

3

Nel 1905 Einstein pubblica due articoli sulla relativit speciale

Zur Elektrodynamik bewegter Krper, Ann. Phys. (Leipzig) 17, 891 (giugno 1905).Lelettrodinamica dei corpi in movimento, nel quale vengono gettate le basi della teoria e ricavate le principali conseguenze

Ist die Trgheit eines Krpers von seinem Energiegehalt abhngig?, Ann. Phys. (Leipzig) 18, 639 (settembre 1905).Dipende linerzia dei corpi dal loro contenuto energetico? Viene mostrato che se un corpo cede energia E sotto forma di radiazione, la sua massa m decresce di E / c2

Come si giunse a questa teoria?

4

Basi sperimentali edevoluzione delle idee

5

Contesto

Galileo aveva mostrato che le leggi della meccanica sono le stesse per osservatori in moto relativo rettilineo uniforme (principio di relativit). Estensione naturale a tutte le leggi fisiche.

Le radici della relativit einsteniana provengono dallo studio della natura corpuscolare (Newton) o ondulatoria (Huygens) della luce e dallintroduzione delletere

Una questione fondamentale nasce nel XIX secolo: si pu estendere il principio di relativit a tutti i fenomeni fisici, comprendendo ottica, elettricit e magnetismo?

6

x=x vty=yz=zt =t

Il principio di relativit pu essere formulato matematicamente dicendo che le leggi fisiche devono mantenere la stessa forma (essere covarianti o invarianti in forma) nel passaggio tra due osservatori inerziali. Esempio:

F = ma F = ma

seconda leggedella dinamica

seconda leggedella dinamica

trasformazionigalileiane*

*battezzate da Philipp Frank nel 1909

7

Bradley, 1729

Alla ricerca della parallasse come prova del sistema eliocentrico, Bradley osserva il fenomeno dellaberrazione: langolo tra stelle lontane varia nel corso dellanno di circa 20 = 1 E-4 rad in maniera incompatibile con la parallasse.

Nel 1729 attribuisce il fenomeno alla velocit finita della luce.

Esiste una velocit della luce universale anche nella teoria corpuscolare?

8

D

R

Parallasse

!

Aberrazione

"

tan = RD

< 106

sin = VTerrac

(rel.)

tan = VTerrac! 104 (class.)

indistinguibilisperimentalmente

non osservatada Bradley

9

Arago, 1810

Rifrazione della luce stellare a ore diverse e in differenti periodi dellanno. Nessun effetto.

Fallimento della teoria corpuscolare o limitazione dellocchio?

Chiede a Fresnel se il risultato sia spiegabile con la teoria ondulatoria...

Arago (1810): the first experimental result against the ether 199

MARCH OCTOBER

18:00

21:00

0:00

3:00

6:00

6:003:00

0:00

21:00

18:00

Castor

Hydra

Leo

Virgo

Arcturus

Antares

Orion

Aquila

Aquarius

Cetus

RigelAldebaran

EARTHEARTH

SUN

Figure 1. This diagram shows the light from different stars and the Earths orbital motion whenAragos measurements were made on 27 March and 8 October 1810. Wavy lines representlight from stars (projected on Earths orbital plane), and the open arrows correspond to the Earthsorbital velocity. The different Galilean compositions of motions were expected to result in differentstarlight deviations by the prism.

could easily be understood in the context of the wave theory of light by accepting that the Earthimparts its motion to the surrounding ether. In that case, the prism would be at rest in the localether, and no differences of velocities would appear (the speed of light is a property of theether). However, in spite of its simplicity, this hypothesis would hinder the understanding ofthe starlight aberration: so far I could not conceive this phenomenon [the starlight aberration],apart from supposing that the ether freely passes through the globe, and that the velocityimparted to this subtle fluid is nothing but a small part of the one of the Earth, which does notexceed the hundredth for example [14]6. Although the Earth should be pervaded by an etherflow, Fresnel says that light, which is an ether vibration, does not propagate inside the Earthdue to an interference of secondary waves. Concerning the transparent media, Fresnel says:it is evident that the placing of water among the particles, which favours the propagation ofluminous vibrations, must be a little obstacle to the establishment of an ether flow [14]. So,Fresnel thought that the way the ether flows through a body depends on the properties of thebody.

In contrast to the corpuscular model, Snells law implies for the wave theory of light that,the bigger the refractive index of a transparent substance, the slower the light propagates in itsinterior7. Fresnel considered the ether as an elastic material. It is well known that the velocityof waves propagating in an elastic material is proportional to 1/2, where is the densityof the material (the ether, in our case). This means that the density of the ether should bebigger in water or glass than in air. At this point, Fresnels hypothesis about the dragging ofether enters the scene: only a part of this medium [the interior ether] is dragged by our globe,

6 Since the rays are perpendicular to the wavefront in the ether frame, the starlight aberration should be understoodas a complicated process where the wavefronts change their orientation when passing from the universal ether to thelocal terrestrial ether. A model of this kind was built by Stokes [15], but Lorentz found it mechanically inconsistent[16]).7 The speed of light in water was only measured by Foucault in 1850 [17], confirming the value c/n (n is the refractiveindex) of the wave theory.

10

Fresnel, 1818

In risposta ai risultati di Arago, Fresnel ipotizza che, in un mezzo trasparente (indice di rifrazione n) in moto rispetto alletere con velocit v, la luce venga parzialmente trascinata e la sua velocit sia

Lipotesi spiega i risultati nulli sulla rifrazione di Arago (1810) e viene confermata da Fizeau (liquidi in movimento, 1851) e Airy (aberrazione con telescopio pieno dacqua, 1871)

Meccanismo microscopico misterioso

c =cn

+ v (

1 1n2

) coefficientedi Fresnel

11

The Optics and Electrodynamics of Moving Bodies

13

instance, by Lorenzo Respighi (18241889) and by Martinus Hoek (18341873) in the 1860s.

George Biddell Airy (18011892), in an experiment first suggested by Rudjer Josep Boskovic

(17111787) in 1776 in the context of the particle theory, confirmed that filling the tube of a

telescope with water does not affect the measured angle of aberration. Fresnel had explicitly noted

this consequence of the dragging coefficient in his 1818 letter to Arago, and our introduction of

the Fresnel coefficient was inspired by this celebrated experiment.

What all such explanations of these experimental results have in common is that the Fresnel

coefficient compensates some otherwise detectable effect of the earths motion through the

presumed immobile ether, thus nullifying the effect. There is one important exception to this rule.

In 1851, shortly after he and Jean Foucault (18191868) had shown that it is possible to determine

the velocity of light in the laboratory (rather than as previously from astronomical observations),

Fizeau devised a method for putting Fresnels predicted value for the velocity of light in moving

media directly to the test. The experiment is illustrated in Fig. 7.

Figure 7: The Fizeau Experiment

Fizeau examined the effect of a water flow on the interference pattern produced by

light travelling with the flow (AB) and counter to the flow He observed a shift in the

interference pattern of roughly the size one would expect on the basis of the Fresnel coefficient for

water. Fizeaus result strongly supported the theory of an immobile ether as emended by the

Fresnel coefficient. To account for it, Stokes rival theory of a dragged-along ether also had to

incorporate the Fresnel coefficient, whereas one of its chief attractions had been that the

coefficient was not needed to explain the results of terrestrial refraction experiments. Another way

to turn Fizeaus result into an objection to Stokes theory can be found in Einsteins writings (see,

e.g., Einstein 1915, p. 704): according to the Fresnel coefficient a non-refractive medium

(a medium for which n = 1), such as the earths atmosphere, does not drag along the ether.

Despite the undeniable success of the Fresnel coefficient in accounting for the observed

phenomena, the physical mechanism underlying the effect was unclear. When Fresnel introduced

his coefficient, he also propose