Müller I. A history of thermodynamics. The doctrine of energy and entropy (Müller I. A history of thermodynamics. The doctrine of energy and entropy.pdf), страница 12

Indeed, both equations – the one for x1(t) and thosefor x2(t), x3(t) – may be combined in one asÈØdxidm„ÉÙdt ÉÊ 1 12 ( dxdt1 ) 2 dt ÙÚcFiso that there is only one velocity-dependent mass m which is related to them„rest mass mƍ by m. That formal simplification of the new1 dx1 21c2(dt)equation of motion – which amounts to a momentum balance – was75The notions of transverse and longitudinal mass had already been introduced by Lorentz inhis paper: “Electro-magnetic phenomena …” (1904) loc.cit. which Einstein later said hehad been unaware of, see above.422 Energysuggested by Planck. Says Einstein in a later footnote:76 The definition offorce here given [in his 1905 paper] is not advantageous, as was first shownby M.

Planck. It is more to the point to define force in such a way that thelaws of momentum and energy assume the simplest form.Transverse and longitudinal massesThe invariance of the Maxwell equations implies, of course, the invariance of thespeed of light as a corollary, but it implies more: Namely the transformation lawsfor the electric field components, cf.

Insert 2.3E 1cE 2cE1,E 2 VB13E 3 VBE 3c,V 2c212V 2c2.On the other hand, if a mass is momentarily at rest in Kƍ, – that is the simple caseunder consideration – its accelerations in Kƍ and K are dictated by the Lorentztransformation and it is a simple matter to calculate the relation. It readsd 2 x1cdt c 2111c2( dxdt1 ) 23d 2 x1 d 2 x 2c,dt 2 dt c 2d 2 x 2 d 2 x 3c1,1 c12 ( dxdt1 ) 2 dt 2 dt c 2d 2 x31.1 c12 ( dxdt1 ) 2 dt 2Insertion into Newton’s lawmc1mcd 2 xicdt c2eEic provides1c2dx1 2dt( )mc11c2( dxdt1 ) 23d 2 x1dt 2d 2 x2dt 2mc11c2( dxdt1 ) 2F1F2d 2 x3dt 2F3 ,so that the inertial mass is different in the direction of the relative motion of theframes and perpendicular to that direction.

Einstein speaks of transverse andlongitudinal masses. One can avoid this unfamiliar concept when one rephrasesNewton’s law from“mass·acceleration = force” to “rate of change of momentum = force.”Insert 2.476In A. Einstein: “The principle of relativity, ...” Dover Publications. loc.cit.Annus Mirabilis43So what about the law of energy? Multiplication of the 1-component ofdxthe momentum balance by dt1 provides an expression for the power of theforce on the moving mass, viz.dmc 2dtF1dx1,dtand, since the power is known to produce a rate of change of energy inmechanics, we must interpret mc2 as energyEmc2m „c 22m „ È dx ؝ m „c É 1 Ù .dx22 Ê dt Ú1 c12 ( dt1 )2Of course, the first term of the approximate formula is huge compared tothe second one, but it is also constant, so that we obtain the familiar energybalance of classical mechanics: The rate of change of the kinetic energymc dx1 22 ( dt ) equals the power of the force.Special relativity – the theory of frames of reference related by theLorentz transformation – says nothing about mass and potential energyexcept by implication: Indeed, if a body has a big mass because it movesfast, that movement may be due to a fall from a great height.

And if mass,or energy is conserved, the body must have had the big mass before it fell,simply by resting in a high place.77 Considerations like these have led to anextrapolation of the formula E = mc 2 to all types of energy other thankinetic energy; for example to the binding energy in nuclei which manifestsitself in the mass defect.Annus MirabilisThe year 2005 – when I write this – has been declared the Einstein year byphysicists all over the world in order to celebrate the centenary of the annusmirabilis when Einstein published three salient papers, of which we havejust discussed one.

The other two concern thermodynamics as well, andthey will be discussed below, cf. Chaps. 7 and 9.It is quite unusual that the anniversary of a scientific achievement likethis should be celebrated in this manner. Occasions of such type are morecommon for the feats of politicians, or generals or, perhaps, football playersand sports coaches.

But now it is upon us, the annus mirabilis. In Germany,where Einstein was born and where he spent some of his productive years, –not 1905 though! – the centennial is taken seriously to the extent that mostpublic buildings in Berlin carry words of wisdom from Einstein. On the77Einstein’s general relativity – the theory of accelerated frames and gravitation – makessuch arguments explicit.442 Energychancellery it says in huge bright red letters: The state must serve thepeople, not people the state. And buses, trains, trams and moving vans carrythe slogan: If you wish to have a happy life, set yourself a destination.It is true that some of these maxims are somewhat trite, but Einstein wascapable of pregnant wise-cracks, like when he discarded the probabilisticaspects of quantum mechanics by saying God does not throw dice.

Or whenhe expressed doubt about Heisenberg’s uncertainty principle: Our Lord maybe subtle, but He is not malicious. Incidentally, on both occasions Einsteinwas wrong, at least according to current wisdom. He was indubitably right,however, when he advised physicists that their theories should be as simpleas possible, but not simpler.Despite the present-day fanfare, the fact is that Einstein could not get aprofessorship until four years after the annus mirabilis – and not because hewas not trying! It was eight years before a special position was created forhim at the Kaiser Wilhelm Institute in Berlin – at the instigation of MaxPlanck.

In 1916 Einstein published his paper78 on General Relativity – asopposed to Special Relativity – and that is perhaps his greatest achievement.Einstein became world-famous in 1919 when his prediction, made in1911,79 about light rays being deflected by gravitational fields wasconfirmed by an observation during a solar eclipse.Einstein anticipated the loss of his position and the impendingbanishment from Germany by not returning from a trip to the United Stateswhen Hitler came to power in 1933.

From then on he lived and taught inPrinceton until his death.The above-mentioned mass-defect occurs not only in the fusion of lightelements but also in the fission of heavy ones like uranium. And in 1939Otto Hahn (1879–1968) and Lise Meitner (1878–1968) reported that theyhad achieved fission. The collateral conditions were such that a chainreaction of fission could conceivably occur, and that provided the feasibilityfor nuclear explosions.The possibility of a chain reaction had been conceived by Leo Szilard(1898–1964), an admirer of the science fiction stories by H.G. Wells (1866–1946),80 in one of which the term atomic bomb is first used.81 Szilard,himself an able physicist, knew of Hahn’s and Meitner’s work, and hefeared that Germany might develop and use a fission bomb in theimpending second world war. He convinced Einstein – then an absolutelegend as a scientist and a public figure – to sign a letter to President78A.

Einstein: “Die Grundlagen der allgemeinen Relativitätstheorie” [On the foundation ofthe general theory of relativity] Annalen der Physik 49, (1916).79 A. Einstein: “Über den Einfluß der Schwerkraft auf die Ausbreitung des Lichtes” [On theinfluence of gravitation on the properties of light]. Annalen der Physik 35, (1911).80 Herbert George Wells (1866–1946) was a scientific visionary and social prophet, bestknown for his classic short story: “The time machine” first published in 1895.81 According to I.

Asimov: “The finger of God.” In: “The sun shines bright.” Avon Books(1981).Annus Mirabilis45Roosevelt, in which an American crash program for the development of thebomb was recommended. The letter succeeded and on December 6th,1941 – the eve of the Japanese attack on Pearl Harbour – PresidentRoosevelt signed Project Manhattan into existence.As is was, German scientists never worked more than half-heartedly on afission bomb, and the Manhattan project was successfully concluded toolate, shortly after Germany’s capitulation.

But there was still Japan, andtwo bombs were available, incongruously called thin man and fat boy. Sothey were dropped on Hiroshima and Nagasaki on August 6th and August9th, 1945 when 300.000 civilians died.Unlike other scientists who lent their support to scientific warfare,Szilard, and Einstein, and the physicists of the Manhattan project – amongthem Compton, Fermi, and Bohr – are largely excused, or even praised fortheir commitment. One might say that the theory of relativity asserts itselfhere in one of its more popular versions: Everything is relative, or else: It isimperative to be on the winning side.Maybe, however, it is fair to say that a fair number of the scientists, whohad promoted the bomb project, had second thoughts afterwards, andcampaigned for the decommissioning of the atomic arsenal.

Among themwere Einstein, Fermi, and Bohr. The politicians brushed their initiativeaside and, when Bohr would not give up, Winston Churchill (1874–1956)threatened to put him in jail.82After the second world war nuclear fission was employed as an energysource in power plants, and now a growing proportion of the humandemand for energy is covered in this way.83 The mass defect inherent infusion of light elements has been utilized in the hydrogen bomb – so far notused in war.

Despite energetic – and vastly expensive – research in thefield, controlled fusion for the conversion of nuclear energy into usefulpower could not so far be realized. The problem is that enormoustemperatures must be reached before the charged nuclei can overcome theirrepulsive electric forces so as to be able to fuse.84 The centre of the sun isthe only place in our planetary system where such temperatures areavailable and, indeed, nuclear fusion is the process that supplies the energyof the sun, cf. Chap. 7.In the 1990’s two physicists from Provo, Utah, USA claimed to haveachieved fusion – on their laboratory table and at room temperature – bysomehow overcoming the repulsion catalytically, as it were, inside metals.82According to I.