¹ The formula is actually labeled (21.22) in the published version of von Laue, M.'s book, Relativitätstheorie, Braunschweig, 1952, B i, 161Google Scholar. The first edition of the book was published in 1911 in one volume, i.e. von Laue, M., Relativitätsprinzip Braunschweig, 1911Google Scholar, which only deals with the special theory of relativity. The new edition which appeared in 1952 consists of two volumes, the first deals with special relativity and the second with general relativity. There appeared several editions of the book before the one in 1952; the 3rd edition in 1919 announces the coming of the second volume, and the second volume first appears with the 4th edition in 1921.

² In fact, the only place where this episode was discussed is in an unpublished paper by Earman, J. and Glymour, C., ‘Abraham's heat force and relativistic thermodynamics: a strange chapter in the history of modern physics’ (preprint).Google Scholar

³ This feature of special relativity was characteristic in the early years after its emergence, since it was thought of as a meta-theory or a theory of principles. It provides general constraints on laws or theories of whatever nature in physics (as long as it has something to do with conceptions of space and time). Relativistic thermodynamics was certainly among the ‘established’ classical theories at the time. Electrodynamics of continua was another branch of physics whose relativization was accomplished by Minkowski (see Minkowski, H., ‘Die Grundgleichungen für die elektromagnetische Vorgänge in bewegten Körpern’, Nachichten von der Königlichen Gesellshaft der Wissenshaften zu Güttingen, Berlin, 1908, 53–111).Google Scholar

⁴ Planck was, in 1905, one of the editors for Annalen der Physik and was responsible for the publication of Einstein's famous 1905 paper on the special theory of relativity. During the years 1906–10, Planck published several papers defending and further developing this theory: Planck, M.: (a) ‘Das Prinzip der Relativität und die Grundgleichungen der Mechanik’, Verh. Deutsch. Phys. Ges. (1906), 8, 136–41Google Scholar; (b) ‘Die Kaufmannschen Messungen der Ablenkbarkeit der β-Strahlen in ihrer Bedeutung für die Dynamik der Elektronen’, Phys. Zs. (1906), 7, 753–61Google Scholar; also in Verh. Deutsch. Phys. Ges. (1906), 8, 418–32Google Scholar; (c) ‘Nachtrag zur Besprechung der Kaufmannschen Ablenkungsmessungen’, Verh. Deutsch. Phys. Ges. (1907), 9, 301–5Google Scholar; (d) ‘Zur Dynamik bewegter Systeme’, Sitzungsber. Preuss. Akad. Wiss. (1907), 867–904Google Scholar; also in Ann. Phys. (1908), 26, 1–34Google Scholar. All these articles can also be found in Planck, 's Physikalische Abhandlungen und Vorträge, 3 vols., Braunschweig, 1958.Google Scholar

⁵ Planck, (a), op. cit. (4).Google Scholar

⁶ Planck, (d), op. cit. (4).Google Scholar

⁷ Planck's version of the principle of relativity reads as follows.

The principle of relativity says that one can use, besides the heretofore used reference frame (x, y, z, t), also the following reference frame:

for the fundamental equations of mechanics, electrodynamics and thermodynamics with exactly the same correctness, and therefore, designate it as being at ‘rest’. We will in the following discussion characterize all quantities measured in the new reference frame with a stroke on their symbols and correspondingly also call the two reference frames the ‘primed’ frame and the ‘unprimed’ frame. Then the content of the relativity principle can also be so expressed: All equations of the primed, the unprimed quantities or of even those of both kinds remain correct, when one substitutes in them the primed quantities with the unprimed ones of the same quantities and, at the same time, the unprimed quantities with the primed ones of the same quantities. Moreover, let c′ = c and v′ = – v. (see Planck, (d), op. cit. (4), 551.)Google Scholar

Although this construal of the principle differs significantly from Einstein's own construal (which only requires the equivalence of inertial frames with respect to observers moving with the system of interest), it is in fact practically equivalent to Einstein's version of the principle together with the principle of the constancy of light. The construal was actually quite prevalent at the time (von Laue, (1911), op. cit. (1)).Google Scholar

⁸ In the expression, v is the velocity of the system and dG its momentum change caused by the heat transfer.

⁹ It has something to do with his project for the general dynamical theory of the entire physics. What he in fact did in his paper was first to derive the Lorentz transformation for temperature through the special case of black-body radiation, and went on to find the Lorentz transformation of the general Lagrangian of a mechanicothermal system, and finally the Lorentz transformation of heat was derived from that of the Lagrangian. (see Planck, (d), op. cit. (4).)Google Scholar

¹⁰ Those established branches of theoretical physics at the time were: Newtonian theory of gravitation, electrodynamics of continua, mechanics of continua (fluid mechanics) and thermodynamics. The relativization of gravitation theory, as is well known, led to Einstein's discovery of the general theory of relativity. Relativistic electrodynamics of continua was single-handedly completed by Minkowski (see Minkowski, , op. cit. (3))Google Scholar, and from that to relativistic mechanics of continua is only a small step. We saw a full treatment of it in von Laue's book in 1911.

¹¹ There were minor improvements of Einstein's derivation later in several comprehensive treatises on relativity theory. M. von Laue used a pure mechanical medium instead of a charged one as Einstein had used, and the four-dimensional tensoral language was used instead of Einstein's three-dimensional one. (See von Laue, (1911), op. cit. (1), sections 22, 28Google Scholar; and also Pauli, W., Theory of Relativity, Dover, 1958, 134–5Google Scholar; a translation of ‘Relativitätstheorie’, Encyklopädie der Mathematischen Wissenschaften, (ed. Teubner, B. G., Leipzig, 1921, xix.)Google Scholar

¹² Einstein, A., ‘Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen’, Jahrb. Radioaktivität und Elektron (1907), 5, 411–62Google Scholar. Section 15 is where relativistic thermodynamics is discussed.

¹³ Ibid., 414.

¹⁴ Karl von Mosengeil was one of Planck's students. Planck had supervised von Mosengeil, during the years 1904–07, on a dissertation dealing with black-body radiation of a moving cavity. In his study, von Mosengeil obtained formulae for magnitudes such as pressure and energy density of the radiation of a moving black body, which were in fact Lorentz transformations for those magnitudes, without explicitly using the principle of relativity. Also, for the purpose of studying the thermal properties of moving black bodies, von Mosengeil had to define the temperature of a moving cavity, which was what Einstein had referred to as the definition of moving temperature. Von Mosengeil died in 1907 before the final version of his dissertation was ready. Planck edited the work and saw to its publication (see von Monsengeil, K., ‘Theorie der stationären Strahlung in einem gleichförmig bewegten Hohlraum’, Ann Phys. (1907), 22, 876–904Google Scholar; also reprinted in Planck, (1958), op. cit. (4), ii, 138–75Google Scholar.) In his original work on relativistic thetmodynamics, Planck also used results from von Monsengeil's dissertation, such as the Lorentz transformation of pressure of black-body radiation.

¹⁵ von Mosengeil, (1907), op. cit. (14), 160–1.Google Scholar

¹⁶ Einstein, , op. cit. (12), 451.Google Scholar

¹⁷ Planck, (d), op. cit. (4), 552.Google Scholar

¹⁸ Einstein, , op. cit. (12), 452Google Scholar. Einstein actually quoted Planck's argument verbatim.

¹⁹ Planck, (d) op. cit. (4), 552.Google Scholar

²⁰ As to how those Lorentz transformations in electrodynamics of continua are derived by Einstein, I refer the readers to Einstein's original paper (Einstein, op. cit. (12)Google Scholar). The crucial sections are sections 7, 9, 11 and 12, and the equations used are (5) and (6); and then (13) and (15); and then (16), (16a), (16b), (18), (18a) and (18b); and the final results are (16c) and (18c).

²¹ von Laue, (1911), op. cit. (1)Google Scholar and Pauli, (1921), op. cit. (11).Google Scholar

²² See Tolman, R. C., Relativity, Thermodynamics, and Cosmology, Dover, 1987Google Scholar; it was originally published by Oxford University Press in 1934; and van Dantzig, D., ‘On the phenomenological thermodynamics of moving matter’, Physica (1939), 6, 673–702.CrossRefGoogle Scholar

²³ The set of letters I will study in this section are contained in the Einstein Papers in Boston University. It contains the correspondence between Einstein and von Laue during the period 1952–53. They are numbered ‘Max v. Laue(x)’, where x is the sequence number of the letter. This set contains letters from Max v. Laue(48) to Max v. Laue(57), or from 23.1.1952 to 27.3.1953. The letters will be referred to in the text by ‘Max v. Laue(x) date.month.year’.

²⁴ For the original content of the letter, see appendix (letter I).

²⁵ von Laue, (1911), op. cit. (1), 173–5Google Scholar; and Tolman, (1932), op. cit. (22), 159–61.Google Scholar

²⁶ To derive this equation one needs only the following well-known equations:

G = (E + pV)v and W = pdV-(v·dG), see equation (3).

²⁷ It is a puzzle as to who wrote that final paragraph in the letter, as seen in the quotation, which recorded von Laue's response to Einstein's argument. The handwriting is distinctly different from Einstein's, at least, different from the one Einstein had in composing that letter; nor do we known when that paragraph was written. The only thing we are certain is that it is a record of the main point of von Laue's letter of 1.2.52.

²⁸ This is contained in the next letter von Laue sent to Einstein on the latter's birthday, see Max v. Laue(51), 14.3.52.

Du vergisst bei Deinem Kreis-Prozess einen Arbeitsbetrag, nämlich den, welcher notwendig ist, um den bewegten Körper bei konstanter Geschwindigkeit Wärme zu entziehen. Dabei änder sich bekanntlich sein Impuls. Zur Aufrechterhaltung der Geschwindigkeit ist also eine Kraft notwendig, die auch Arbeit leistet. Du findest diesen ganzen Kreis-Prozess durchgerechnet auf Seite 169–171 meines Buches.

²⁹ von Laue, (1952), op. cit. (1), i 169–71.Google Scholar

³⁰ In this case,

A = W₂ + W₃ + W₄ = (1–v²) (E_e–E_d)–G₀, hence, A = [√(1–v²/c²)–1]G₀. But, G – G₀ = A = [√(1–V²/c²) – 1]G₀, hence, G = √(1–v²/c²)G₀.

And this is the Planck–Einstein formula.

³¹ Max v. Laue(52), 17.3.52.

Wenn nämlich zwischen einem Reservoir und einer ‘Maschine’ – beide in relative Ruhe und beschleunigungsfrci – ein Wärme-Austausch stattfindet, so bedarf dieses Vorgang keiner Arbeitszufuhr. Dies gilt unabhängig davon, ob die beiden relativ zu dem benutzten Koordinatensystem in Ruhe oder in gleichförmigen Bewegung sind. Auch hier genüg es mir, dies deutlich gesagt zu haben.

³² For a detailed discussion, see Tolman, (1934), op. cit. (22), 79–80.Google Scholar

³³ Max v. Laue(53), 22.3.52.

³⁴ See Clark, R. W., Einstein: The Life and Times, Avon Books, New York, 1971, 735–64Google Scholar; and Pais, A., Subtle is the Lord…, Clarendon Press, Oxford, 1982, 325–56Google Scholar, for a detailed account of Einstein's struggle for the unified field theory.

³⁵ For the original letter, see appendix (letter II).

³⁶ Max v. Laue(55), 9.3.53.

Beides finde ich viel ‘schlimmer’, als den Verzicht auf Invariant der Wämemenge und der Temperatur. Ich mochte annehmen, auch empfändest wenig Freude bei dem Versuch, eine andere Thermodynamik in Einzelheiten auszufiihre, obwohl man dabei zweifellos nirgends auf logische Schwierigkeiten stisse.

³⁷ See Kellerman, , Found. Phys. (1980)Google Scholar; Neugebauer, G., Relativistische Thermodynamik, Berlin, 1980CrossRefGoogle Scholar; Ammiraju, P., Lettere at Nuovo Cimento (1984), 39, 17.Google Scholar

³⁸ Ott, H., ‘Lorentz-Transformation der Warme und der Temperatur’, Z. Phys. (1963), 175, 70–104.CrossRefGoogle Scholar

³⁹ Arzeliés, H., ‘Transformation relativiste de la température et de quelques autres grandeurs thermodynamiques’, Nuovo Cimento (1965), 35, 792–804.CrossRefGoogle Scholar

⁴⁰ After Arzeliés, scores of articles appeared in Nuovo Cimento, debating a technical problem which was not directly related to the problem of relativistic thermodynamics. For the details of this initial exchange of criticism, see Gamba, A., Nuovo Cimento (1965), 37, 1792CrossRefGoogle Scholar; Kibble, T. W. B., Nuovo Cimento (1966), 41B, 72–8 (Immediately following this paper (pp. 79–85)CrossRefGoogle Scholar, there are two short comments on Kibble's work by Gamba and Arzeliés, and then two rejoinders from Kibble.) Penny, R., Nuovo Cimento (1966), 43A, 911CrossRefGoogle Scholar; Rohrlich, F., Nuovo Cimento (1966), 45B, 76CrossRefGoogle Scholar. It was in this exchange of opinions that Ott's work was first discovered and defended.

⁴¹ See Landsberg, P. T., Nature (1966), 212, 571 and (1967), 214, 903CrossRefGoogle Scholar; Fremlin, J. H., Nature (1967), 213, 277CrossRefGoogle Scholar; Williams, I. P., Nature (1967), 213, 1118 and 214, 1105.CrossRefGoogle Scholar

⁴² See Moller, C., ‘Thermodynamics in the Special and the General Theory of Relativity,’ in Old and New Problems in Elementary Particles (ed. Puppi, G.), Academic Press, 1968Google Scholar; Landsberg, P. T., ‘Concepts in special relativistic statistical thermodynamics,’ in Essays in Physics (ed. G. T. Conn and G. N. Fowler), 1970, iiGoogle Scholar; Yuen, C. K., Am. J. Phys. (1970), 38, 246–52CrossRefGoogle Scholar; Schmid, L. A., ‘Effects of heat exchange on relativistic fluid flow,’ in A Critical Review of Thermodynamics (ed. Stuart, E. B., Gal-Or, B. and Bainard, A. T.), Mono Book Corp. 1970, 161–201.Google Scholar

⁴³ van Kampen, N. G., Phys. Rev. (1968), 173, 295.CrossRefGoogle Scholar

⁴⁴ Landsberg, P. T. and Johns, K. A., Nuovo Cimento (1967), 52B, 28CrossRefGoogle Scholar; Landsberg, P. T., in A Critical Review of Thermodynamics (ed. Stuart, E. B., Gal-Or, B. and Bainard, A. T.), Mono Book Corp., 1970, 253–72.Google Scholar

⁴⁵ Anderson, J. L., ‘Relativity principles and the role of coordinates in physics’, in Gravitation and Relativity, (ed. H-Y. Chiu and W. F. Hoffmann), 1964.Google Scholar