D. BLANU

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D. BLANUŠAS FORMULAE FOR HEAT AND TEMPERATURE
TRANSFORMATIONS IN RELATIVISTIC THERMODYNAMICS
AND HIS CORRESPONDENCE WITH W. PAULI IN 1948

• The 22nd ICHS, July 24 30, 2005, Beijing, CHINA
• SS7 Modern Physics an Astronomy, July 26, 2005
• Tomislav Petkovic
• Department of Applied Physics Faculty of
  Electrical Engineering and Computing
• University of Zagreb, CROATIA

DANILO BLANUŠA (1903 1987), Croatian
mathematician and physicist
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I. Blanušas original contributions to STR

• APPLICATIONS OF THE STR IN THERMODYNAMICS
• BLANUŠAS TRANSFORMING FORMULAE (BTF, 1947) FOR
• Q and Q0 T and T0
• Q0 and T0 (in the rest frame) Q and T (for the
  moving frame)
• are quantitatively and conceptually different
  w.r.t.
• Plancks (based on the variational principle),
  and
• Einsteins relations (directly from the Lorentz
  transformation) in 1907.
• W. Pauli claimed Plancks and Einsteins
  expressions were correct, and thus used them
  unaltered in the famous book on the Theory of
  Relativity (1921), and in his later works.

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II. Scientific correspondence with Pauli in 1948

• Unfortunately, Blanuša did not leave his
  Autobiographical Notes like A. Einstein did with
  Autobiographisches (at the age of 67).
• However, Blanuša left his Letters to W. Pauli!
• Unfortunately, Pauli did not encourage Blanuša to
  publish the formulae in the world-known journal.
• This Pauli is a well-oiled head (A. Einstein
  on W. Pauli (1900 1958), Nobel laureate, 1945).
• Despite Les faits ne parlent pas (Henri J.
  Poincaré), I used historical facts from
  scientific letters and achievements obtained
  through local journals, to clarify that Blanuša
  was the first investigator of the relativistic
  relations for heat and temperature.

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Secondary Sources (References) used for research

• W. Pauli, Relativitätstheorie, in Enzyclopädie
  der mathematischen Wissenschaften, Vol. 5, Part
  2, B.G. Teubner, Leipzig, 1921, pp. 539-775.
• Supplementary Notes by the Author, in Theory
  of Relativity, Pergamon Press, Inc., New York,
  1958, pp. 207-232.
• W. Pauli, Theory of Relativity, Translated from
  German by G. Field, Dover Publications, Inc., New
  York, 1958.
• Max Born, Einsteinova teorija relativnosti i
  njezini fizicki osnovi, Einsteins Theory of
  Relativity and its Physical Bases.
• Translated from the 3rd edition, and
  supplemented with Appendix and Comments, by D.
  Blanuša, Scientific Books by the Croatian society
  for natural sciences, Book I, Graphics and
  Publishing Company Tipografija, Zagreb, 1948.
• The first edition in German 1920 English
  translation 1924 Revised edition by Dover 1958.

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Primary Sources (References) used for research

• Blanušas Letter (in German) to the honest
  Professor W. Pauli, dated on March 15, 1948, sent
  from the Tehnical Faculty, Kaciceva street 26,
  Zagreb. Text typed by type writer with Blanušas
  original corrections inserted. Total 7 pages of
  the text including formulae.
• Blanušas Letter (in German) to Paul Urban in
  Graz, Univerzitätplatz 5, dated on June 1, 1948.
  Letter is a draft handwritten by Blanuša. Total 4
  pages of Blanušas writing.
• The correspondence was long, including Urbans
  responses.
• Two scientific colloquia on the occasion of the
  100th anniversary of the birth of academician D.
  Blanuša HAZU, Zagreb, Croatia (the 1st
  colloquium, May 29, 2003) FER, Zagreb, Croatia
  (the 2nd colloquium, July 1, 2003).

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Secondary Sources (References) used for research

• Heinrich Ott, Lorentz-Transformation der Wärme
  und der Temperatur, Zeitschrift für Physik 175,
  70104 (1963).
• H. Arzeliès, Transformation relativiste de la
  température et de quelques autres grandeurs
  thermodynamiques, Il Nuovo Cimento, Vol. XXXV, N.
  3 (1965) 792804.
• I. Derado and E. Ferrari, Temperature
  transformations in relativistic thermodynamics,
  FIZIKA A (Zagreb) 8 (1999) 4, 223-228.
• DANILO BLANUŠA 1903 1987, Remembrance on the
  academicians who have passed away, Vol. 50, The
  Department of Math., Phys., Chem., and Techn.
  sciences, Editor V. Devidé, extraord. member,
  JAZU, Zagreb, 1989.

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Blanušas contributions to relativistic
thermodynamics

• Plancks (i.e. Paulis) formulae for heat and
  temperature for the transition to a moving frame,
  are as follows
• The formulae were derived by combining the
  transforming relations for volume (V and V0),
  pressure (p and p0), total momentum and
  energy (E and E0), the amount of heat dQ
  transferred to the system, and the work dA done
  by the external force on the system.
• The Plancks relations have a general character,
  since they agree with the transformation formulae
  for the Joule heat.

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Blanušas contributions to relativistic
thermodynamics

• The system is given (has) velocity (this can
  be regarded as an adiabatic process).
• Entropy is the Lorentz-invariant quantity!
• If an amount of heat dQ is transferred
  infinitely slowly, we obtain

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Blanušas original papers on the subject,
published in local journals

• Danilo Blanuša, Sur les paradoxes de la notion
  dénergie, Glasnik Mat.Fiz. i Astr., Ser. II 2
  (1947), str. 249 250.
• Danilo Blanuša, O relativistickoj termodinamici
  On the relativistic thermodynamics, Prvi
  kongres mat. i fiz. FNRJ The First Congress of
  Math. and Phys. of the FNRJ, Bled 1949, Naucna
  knjigaScientific Book, Beograd 1951.Belgrade
  1951, str. 235 240.

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Blanušas Letter to W. Pauli (March 15, 1948)

• Blanuša expressed his gratitude to the very
  respected Professor Pauli for his kindness in
  the Letter of the 18th of February, 1948 very
  likely, comm. T.P., and particularly for the
  opinion stated by his collaborator Mr. Schafroth.
• Obviously, Pauli had demonstrated a tendency of
  shifting his scientific responsibility, in
  Blanuša case, to his assistant R. Schafroth.
• Basic statement of Blanuša in his Letter
  Plancks relations are not correct, but presented
  here are those which arose from his (i. e.
  Blanušas) various calculations and thought
  analyses
• (for both expressions)

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Blanušas Letter to W. Pauli (March 15, 1948)

• Blanuša replied to each of the Pauli objections
• In point 1 a) Pauli criticized Blanuša due to the
  transformation relation for the force, where the
  fourth component of the four-vector was not
  included as the heat current. Otherwise, it would
  lead to the Plancks result.
• Blanuša explained his particular concept of the
  force, for that case. That is not force density
  (Kraftdichte), but simply the force by which the
  body A acts on the second body B, in the form

where v is the velocity at the point of action
(Angriffspunkte) or at the joint plane
(Trennfläche) between two bodies, respectively.
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Blanušas Letter to W. Pauli (March 15, 1948)

• Blanuša warned Pauli that in his book (German
  edition) in the formula (219) the factor 1/? was
  mistakenly omitted in the fourth component.
• In the new editions (for ex., by Dover) this
  mistake was fixed, but even though Blanuša was
  the first to notice it, he was never given
  credit.
• For the rest frame (v 0), it follows that the
  components of the questionable four-vector should
  be , which unambiguously would lead
  to Plancks relations.
• Blanuša to Pauli It is not convenient to form a
  four-vector, in this case!

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Blanušas Letter to W. Pauli (March 15, 1948)

• The first fragment from the Letter (on the heat
  transfer between two bodies, A and B)
• Es ist ja auch von vornherein etwas
  überraschend, den Vierervektor zu bilden
  denn was heisst das? Man entnimmt den
  Energieimpulsgrössen des Wärmestroms die drei
  Strömungskomponenten (die im allgemeinen Fall
  alle von Null verschieden sein könnten), bildet
  die Wurzel aus ihrer Quadratsumme und ernennt
  diese Grösse zur vierten Komponente eines
  Vierervektors. Als die ersten drei Komponenten
  nimmt man dann die drei Nullen einer nicht
  vorhandenen Kraft. Es is nicht einzusehen, warum
  das sinnvoll sein sollte.
• Allerdings dürfte die Idee dieser Bildung von
  einer scheinbar ähnlichen herstammen, nämlich vom
  Vierervektor der elektromagnetischen Kraft und
  Leistungsdichte, wenn Joulesche Wärme entwickelt
  wird.

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Blanušas Letter to W. Pauli (March 15, 1948)

• Blanušas tensor Bik
• Quantities in the S0 frame
• energy (heat) current between two bodies
  A and B
• g0 momentum density
• w0 energy density
• p0 momentum current
• Bik Blanušas ?surface? (energy-momentum)
  tensor for the thermodynamics convection (by
  following the Minkowski ?surface? tensor)

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Blanušas Letter to W. Pauli (March 15, 1948)

• It follows the components satisfy conditions (the
  properties of the tensor)
• (symmetry property of tensor)
• velocity of the energy current
• Momentum, which flows per unit area per unit
  time (together with energy current)
• By transforming Bik tensor into the moving frame
  S, Blanuša obtained the corresponding quantities
  in that frame (p, i w).
• In addition, Blanuša had demonstrated to Pauli
  that the velocity of the energy current
  is transforming according to the addition theorem
  for velocities, which had been expected a priori.

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Blanušas Letter to W. Pauli (March 15, 1948)

• Final crucial - proof at the end Assume that a
  part of the total energy current (in Blanušas
  notation the ?-part), flowing through the joint
  plane, would be heat. In that case, the ?-part of
  the momentum current should flow through the
  joint plane as the convection heat momentum
  (p). The rest, according to Blanušas approach,
  has to be realized as the mechanical work and
  momentum transfer, done by the force.
• However, Blanuša had shown by his calculation
  that ? 1. Consequently, both work and momentum
  change (i.e. the force itself) vanish.
• Blanuša concluded, in a scientific part of his
  Letter to Pauli, that he obtained the same result
  he had already shown in his previous Letter.

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Blanušas Letter to W. Pauli (March 15, 1948)

• The second fragment from the Letter
• Es entsteht ein Wärmestrom, der also strömende
  Wärmeenergie darstellt. Ich benütze nun eine der
  Grundvorstellungen der Relativitätstheorie,
  nämlich dass jede mit der Geschwindigkeit v
  wandernde Energie den entsprechenden Impuls
  mit sich führt. Die wandernde Wärmeenergie muss
  also ihren Impuls mit sich tragen und es entsteht
  daher gleichzeitig ein konvektiver Impulsstrom.
  Dass der Wärmestrom impulstragend ist, sagt auch
  Laue und es steht als allgemeine Aussage für
  jeden Energiestrom auch in Ihrem
  Enzyklopädieartikel that is Paulis Book on
  Relativity, Comm. T. P..

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Blanušas Letter to Paul Urban (June 1, 1948)

• The first fragment from the Letter
• U. zw. ist Wärme (pro Zeiteinheit
  gemeint), der Rest ist mechanische
  Arbeit, also die Kraft ist aus
  gleich , was gleichzeitig der
  übertragen Impuls pro Zeiteinheit ist, also der
  gesamte Impuls der ubertragenen Energie.
• Bei mir ist die Wärme, bei
  Planck
• ist nur Wärme.
• Du sichst, die Sache ist nicht so naiv, wie Du
  vielleicht glaubtest.

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Blanušas Letter to Paul Urban (June 1, 1948)

• The second fragment from the Letter

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Conclusions and Outlook

• 1. Blanuša made the fundamental error of not
  publishing his formulae for heat and temperature
  transformation in relativistic thermodynamics in
  the world-known journals of physics in those
  times. His contributions to the STR and
  thermodynamics were left only locally recognized!
• 2. Responsibility of the scientist
  (Verantwortung des Wissenschaftlers) Blanuša
  understood, in this case, that the most prominent
  physicists (founders) in the field of relativity
  had to be first informed, in order to provide
  their agreement and justification for his
  formulae. At that time in Europe it was Pauli,
  rather than Einstein, who was occupied in the USA
  with other problems and questions.
• Despite the fact that Blanuša did not get the
  answers he might had been expecting from Pauli,
  his ethical attitude remained the cornerstone for
  forthcoming young scientist in Croatia, Europe,
  and all over the World.

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Conclusions and Outlook

• 3. Would it be, perhaps, better that Blanuša, in
  his Letter, had referred to the important
  footnote on page 86 of Paulis book Dover ed.
  1958, dealing with Plancks original comment on
  the generalization of the Minkowski tensor Sik to
  other non-electromagnetic forms of energy,
  which can lead to unduly perturbed paradoxical
  situations?
• Should Pauli have behaved in a different way, in
  that case, to recommend the Blanušas work for
  publishing in a world-known journal of physics,
  can only be judged!
• However, it remains open what should had been
  done by ?tremendous Pauli? (der fürchterliche
  Pauli) or by Gods whip (die Geissel
  Gottes)?
• 4. Blanušas motivation for his Letters to Pauli
  was scientific parr excellence. He was deeply
  aiming for the formulae to be included in the new
  project of quantum-mechanical theory of
  thermodynamics De Broglie attempted to develop at
  that time.

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Conclusions and Outlook

• Professor D. Blanuša was one of the most creative
  Croatian mathematicians and physicists of the
  XXth century, who lived and worked in his
  homeland.
• Blanuša deserves an honoured place next to
  Planck, Einstein, and Pauli in the fields of STR
  and relativistic thermodynamics, due to the
  development of transforming relations for heat
  and temperature in 1947, and for the complete
  validity of his reasoning.