Transcript Blanušini doprinosi teoriji relativnosti

D. BLANUŠA’S 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 Petković
Department of Applied Physics
Faculty of Electrical Engineering and
Computing
University of Zagreb, CROATIA
DANILO BLANUŠA
(1903 – 1987), Croatian mathematician
and physicist
I. Blanuša’s original contributions to STR

APPLICATIONS OF THE STR IN THERMODYNAMICS
BLANUŠA’S 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.
Planck’s (based on the variational principle), and
Einstein’s relations (directly from the Lorentz
transformation) in 1907.
W. Pauli claimed Planck’s and Einstein’s expressions were
correct, and thus used them unaltered in the famous book on
the Theory of Relativity (1921), and in his later works.
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.
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 fizički osnovi,
[Einstein’s 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.
Primary Sources (References) used for research

Blanuša’s Letter (in German) to the honest Professor W. Pauli,
dated on March 15, 1948, sent from the Tehnical Faculty,
Kačićeva street 26, Zagreb. Text typed by type writer with
Blanuša’s original corrections inserted. Total 7 pages of the text
including formulae.

Blanuša’s 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 Blanuša’s writing.
The correspondence was long, including Urban’s 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).
Secondary Sources (References) used for research

Heinrich Ott, Lorentz-Transformation der Wärme und der
Temperatur, Zeitschrift für Physik 175, 70–104 (1963).

H. Arzeliès, Transformation relativiste de la température et de
quelques autres grandeurs thermodynamiques, Il Nuovo
Cimento, Vol. XXXV, N. 3 (1965) 792–804.

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.
Blanuša’s contributions to relativistic thermodynamics

Planck’s (i.e. Pauli’s) formulae for heat and temperature
for the transition to a moving frame, are as follows:
dQ  1    dQ 0
2
Q  Q0  1   2
 derived by combining the transforming
The formulae were
G
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 Planck’s relations have a general character, since they
agree with the transformation formulae for the Joule
heat.
Blanuša’s contributions to relativistic thermodynamics


The system is given (has) velocity v (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:
S  S0
dQ  TdS
dQ  dQ0 1   2
T  T0  1   2
Blanuša’s original papers on the subject, published in
local journals

Danilo Blanuša, Sur les paradoxes de la notion
d’énergie, Glasnik Mat.–Fiz. i Astr., Ser. II 2 (1947),
str. 249 – 250.

Danilo Blanuša, O relativističkoj termodinamici [On
the relativistic thermodynamics], Prvi kongres mat. i
fiz. FNRJ [The First Congress of Math. and Phys. of
the FNRJ], Bled 1949, Naučna knjiga[Scientific
Book], Beograd 1951.[Belgrade 1951], str. 235 –
240.
Blanuša’s 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: Planck’s relations are
not correct, but presented here are those which arose from his
(i. e. Blanuša’s) various calculations and thought analyses:
Q
Q0
T

v2
  1 2
c
T0

(for both expressions)
Blanuša’s 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 fourvector was not included as the heat current. Otherwise, it
would lead to the Planck’s 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:
( F1 , F2 , F3 ) 
  1 v / c
2
2
K

L
F4 
c
where v is the velocity at the point of
action (Angriffspunkte) or at the joint
plane (Trennfläche) between two bodies,
respectively.
Blanuša’s 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
1 dQ
questionable four-vector should be 0,0,0, c dt 0 , which
0
unambiguously would lead to Planck’s relations.

Blanuša to Pauli: It is not convenient to form a four-vector, in
this case!
Blanuša’s 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
s0
Vierervektor 0,0,0, c 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”.
Blanuša’s Letter to W. Pauli (March 15, 1948)


Blanuša’s tensor Bik
Quantities in the S0 frame:
dQ0
 s0 
= energy (heat) current between two bodies A and B
dt
 g0 = momentum density
 w0 = energy density
 p0 = momentum current
 Bik = Blanuša’s ˝surface˝ (energy-momentum) tensor for
the thermodynamics convection (by following the Minkowski
˝surface˝ tensor):
 p 0 0 cg 
0
 0

0 0 0 0 
Bik   0 0 0 0 


 s0

0
0
w

0 
c

Blanuša’s Letter to W. Pauli (March 15, 1948)

It follows the components satisfy conditions (the properties of the
tensor):
s
cg 0  0 (symmetry property of tensor)
c
V0 
s0
w0
= velocity of the energy current
Momentum, which flows per unit area per unit time (together
2
with energy current):
p0  g 0V0 

s0
c 2 w0
By transforming Bik tensor into the moving frame S, Blanuša
obtained the corresponding quantities in that frame (p, s  cg i w).
c
In addition, Blanuša had demonstrated
to Pauli that the
s
velocity of the energy current V  w is transforming
according to the addition theorem for velocities, which had
been expected a priori.
Blanuša’s Letter to W. Pauli (March 15, 1948)

Final – crucial - proof at the end: Assume that a part of the
total energy current (in Blanuša’s 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
Blanuša’s 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.
Blanuša’s 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
E
mit
v
wandernde Energie den entsprechenden Impuls
sich
c2
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
Pauli’s Book on Relativity, Comm. T. P.].”
Blanuša’s Letter to Paul Urban (June 1, 1948)


The first fragment from the Letter:
“U. zw. E 2 ist Wärme (pro Zeiteinheit gemeint),
der Rest E 2 ist mechanische Arbeit, also die Kraft
P  E v c 2
Pv  gleich
E 2
ist aus
, was gleichzeitig der übertragen Impuls pro
Zeiteinheit ist, also der gesamte Impuls der
ubertragenen Energie.
Bei mir ist E  E0  die Wärme, bei Planck
ist nur E 2  E0 Wärme.
Du sichst, die Sache ist nicht so naiv, wie Du
vielleicht glaubtest.”
Blanuša’s Letter to Paul Urban (June 1, 1948)

The second fragment from the Letter:
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.
Conclusions and Outlook
3.
Would it be, perhaps, better that Blanuša, in his Letter, had
referred to the important footnote on page 86 of Pauli’s book
[Dover ed. 1958], dealing with Planck’s original comment on
the generalization of the Minkowski tensor Sik to other [nonelectromagnetic] 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 Blanuša’s work for publishing in a worldknown journal of physics, can only be judged!
However, it remains open what should had been done by
˝tremendous Pauli˝ (“der fürchterliche Pauli”) or by “God’s
whip” (“die Geissel Gottes”)?
4.
Blanuša’s 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.
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.