Transcript O. Lummer & E. Pringsheim
Forgotten experiments and the Planck’s radiation formula.
On the experimenal context at the birth of quantum physics.
Jerzy Karpiuk Photochemistry and Spectroscopy Laboratory, IPC PAS
1
14.12.1900 – birth date
*
of quantum theory
"Das war eine rein formale Annahme, und ich dachte mir eigentlich nicht viel dabei, sondern eben nur das, dass ich unter allen Umständen, koste es, was es wolle (1931) , ein positives Resultat herbeiführen musste.” Max Karl Ernst Ludwig Planck (1858 –1947) „It was a purely formal assumption and I really did not give it much thought except that no matter what the cost , I must bring about a positive end.” (1931) * A. Sommerfeld, Atombau und Spektrallinien , 1919, p. 4
2
Traditional point of view
and it is universally true that the formation of the quantum theory is his alone.” „Planck’s unique position is best illustrated by what is in my opinion the singular fact that he had no precursors or competitors whose thoughts moved in a similar direction.”
E. Segrè, Phys. Bl. 23 (1967) 62
„Did Planck create them out of nothing?”
H. Kangro, Early History of Planck’s Radiation Law (1976) p. 1 3
Planck’s opinion ...
M. Planck on the nomination for the Nobel Prize in physics for 1908:
„It was not so that theoretical work paved the way for the experimental studies; more correctly is to say it was just the opposite."
The Prize was then to be shared by
„a leading theoretician and a leading experimentalist, in this case perhaps Lummer"
.
R. Torge: Otto Lummer, Fritz Reiche, Mieczysław Wolfke: Szkice biograficzne. Postępy Fizyki 53 (2002) 201
„It seems as if the formula , once put in mathematical form, survived quite well , whereas the experiments on which it was first founded have relatively rapidly fallen into oblivion .”
H. Kangro,
Early History of Planck’s Radiation Law
, 1976, p. 2 4
„Rosencrantz i Guildenstern are dead”
One of the great anticlimaxes in all of literature occurs at the end of Shakespeare’s Hamlet. On stage strewn with noble and heroic corpus —Hamlet, Laertes, Claudius, and Gertrude — the ambassadors from England arrive and announce that “Rosencrantz and Guildenstern are dead”. No one cares. A similar reaction might be produced among a group of physicists, or even among historians and philosophers of science, were someone to announce that “Lummer and Pringsheim are dead” .
Jeden z największych zawodów w całej literaturze występuje pod koniec „Hamleta” Szekspira. Na scenę usłaną ciałami bohaterów – Hamleta, Laertesa, Klaudiusza i Gertrudy wkraczają ambasadorowie z Anglii I zawiadamiają, że “Rosenkranz i Guildestern nie żyją”. Nikt się tym nie przejmuje. Podobna reakcja mogłaby wystąpić wśród fizyków lub nawet historyków i filozofów nauki, gdyby ktoś zawiadomił, że “Lummer i Pringsheim nie żyją” .
Allan Franklin, The Neglect of Experiment , 1986
5
u
( ,
T
) 6
Kirchhoff’s problem – 1860
u
( ,
T
)
e
(
a
( ,
T
) ,
T
) G. Kirchhoff: Über das Verhältnis zwischen dem Emissionsvermögen und dem Absorptions vermögen der Körper für Licht und Wärme, Annalen der Physik 19 (1860) 275.
7
Kirchhoff’s black body definition: a(ν,T) = 1
-
Experimental problems: radiation source detector method of spectral measurements
u
( ,
T
)
e
(
a
( ,
T
) ,
T
) When a space is surrounded by bodies of the same temperature, and no rays can penetrate through these bodies, every ray in the interior of the space is so constituted, with respect to its quality and intensity, as if it proceeded from a perfectly black body of the same temperature, and is therefore independent of the nature and form of the bodies, and only determined by the temperature.
” G. Kirchhoff, Annalen der Physik 19 (1860) 275.
8
Radiant heat: in the search
for
u(ν,T)
Frederick William Herschel (1738-1822 ) 1800 – discovery of infrared radiation
9
John Tyndall (1820- 1893)
Shift of the maximum with temperature
F. W. Herschel, 1800: prism (glass) + thermometer J. H. Müller, 1859: rock salt prism + thermopile
Refraction spectra
André P. P. Crova (1833- 1907) Light sources in order of increasing temperature:
stearin candle, coal gas flame, electric arc light, sun
invisible radiation visible radiation red blue J. Tyndall, 1864: rock salt prism + thermopile electric carbon arc light spectrum 10
Thermo-electric pile (1860-s)
antimony bismuth "My assistant stands several feet off. I turn the thermopile towards him. The heat from his face, even at this distance, produces a deflection of 90 degrees [on the galvanometer dial]. I turn the instrument towards a distant wall, judged to be a little below the average temperature of the room. The needle descends and passes to the other side of zero, declaring by this negative deflection that the pile feels the chill of the wall."
J. Tyndall, Heat considered as a mode of motion , 1864 , Six lectures on light , 1872-3
Stefan-Boltzmann law
J. Stefan (1879) + L. Boltzmann (1884) = Stefan-Boltzmann law
U
(
T
) 0
u
( ,
T
)
d
T
4
Deduced by J. Stefan from J. Tyndall’s experiments
L. Boltzmann derived theoretically the law studying a heat engine with light as a working matter „From weak red heat (about 525 C) to complete white heat (about 1200 C) the intensity of radiation increases from 10.4 to 122, thus nearly 12-fold (more precisely 11.7). The ratio of the absolute temperature 273 + 1200 and 273 + 525 raised to the fourth power gives 11.6.
”
J. Stefan, Über die Beziehung zwischen der Wärmestrahlung und der Temperatur,
Mathemat.
–Naturwiss. Classe Abteilung 2 79 (1879), pp. 391 –428. 12
Samuel P. Langley’s bolometer - 1878
Bolometer 1880:
T
improved resistance thermometer 10 -5 °C, ± 1%
Two platinum strips, covered with lampblack, one strip was shielded from the radiation and one exposed to it. The strips formed two branches of a Wheatstone bridge which was fitted with a sensitive galvanometer and connected to a battery.
„Langley's bolometer was so sensitive that it could detect thermal radiation from a cow a quarter of a mile away.”
13
Bolometer in the service of photometry
0°C 100 °C – 10
m – 7.5
m
I
( )
B
1
T
3 / 2 exp
c
2
T
6
Michelson equation (1887) described well Langley’s results.
In the derivation Michelson used Maxwell’s velocity distribution law.
„...we are facing a big problem, awaiting for solution. I mean the relationship between the temperature and radiation, as we do know virtually nothing about the issue, but once we know it, we will have a new view on almost all the processes occurring in nature.”
S. P. Langley, 1889 (S. Barr, Am. J. Phys.
28 (1960) 42) W. Michelson, J. de Phys. 6 (1887) 467.
14
A search for reliable luminosity standard Competition between electrical and gas lighting
Platinum plate 1 cm 2 with T m Pt (2042 K) ( 1884 ) Hefner candle, standard in Germany (1883 – 1947) (amyl acetate, PTR) sensitive to fluctuations in air humidity Carcel lamp, standard in France (rapeseed oil - 42 g/h)
Light sources of that time (incandescent lamp [1879] of gas lamp radiated a lot of energy in the invisible part of the spectrum – radiometry must have been developed .
15
The place of birth of quantum physics: Physikalisch-Technische Reichsanstalt
1887 H. von Helmholtz PTR Observatory (clock hall) and not the lecture room of the Physical Institute at Berlin’s University
16
We Wilhelm, by the grace of God German
1898 Act on electrical units
The Ohm is a unit of electrical resistance. It is equal to the resistance of a mercury column at a temperature of melting ice, with a length, at consistently identical cross section of 1 mm 2 , of 106.3 cm, and a mass of 14,4521 gram.
PTR, 1898
17
Radiation Laboratory at PTR Lummer-Broduhn spectral bolometer surface bolometer
18
Development of detection techniques
Lummer’s bolometr :
T
10 -7 °C, ± 1% PTR Report 1899/1900: The purpose of optical studies is to confirm the fundamental laws of heat and light radiation.
19
Microstructural detectors (1890-s)
20
Ferdinand Kurlbaum 1857 - 1927 Otto Lummer 1860 - 1925 Ernst Pringsheim 1859 - 1917 Heinrich Rubens 1865 - 1922 Friedrich Paschen 1865 - 1947 Wilhelm Wien 1864 - 1928 21
Radiation laws
J. Stefan (1879) + L. Boltzmann (1884) = Stefan-Boltzmann law
W. Wien (1893) Wien displacement law
U
(
T
) 0
u
( ,
T
)
d
T
4
u
( ,
T
) 3
f
( /
T
)
W. Wien (1896) - Wien law (until mid 1900 in agreement with experimental data) Stefan-Boltzmann law confirmed up to ± 1% (surface bolometer)
u
( ,
T
) 8 3
c
3 exp
T
Wien displacement law confirmed (linear bolometer)
22
Wien law - 1896
u
( ,
T
) 8 3
c
3 exp
T
W. Wien, Annalen der Physik 58 (1896) 662.
23
Should black body be black?
Initially the importance of „blackness” of the bodies for emitted radiation was neglected.
(„man hat überhaupt außer acht gelassen”)
As black bodies blackened metal plates were used that can be used as black bodies only in a limited T range (Ch. Christiansen, 1880) Wien i Lummer (1895):
blackened plates”: „we have to abandon these artificially
(“man muß überhaupt von den künstlich geschwärzten Blechen absehen” und stattdessen “
die Strahlung eines schwarzen Körpers als den Zustand des
Wärmegleichgewichts aufzufassen...
man einen Um hierauf auch eine praktisch brauchbare Methode zu gründen, durch die man die Strahlung eines schwarzen Körpers in beliebiger Annäherung herstellen kann, muss
Hohlraum auf gleichmässige Temperatur bringen und
durch die Öffnung seine Strahlung nach aussen gelangen lassen”.)
24 W. Wien, O. Lummer, Annalen der Physik 56 (1895) 453.
O. Lummer & E. Pringsheim: 1895 - 1898
liquid air boiling water boiling niter hot gas -188°C 680°C 1200°C 100°C Cavities:
- cylindrical and spherical, metal - double-wall, spherical, porcelain - surface blackened with lampblack, FeO
or UO 2
D. Hoffmann,
On the Experimental Context of Planck’s Foundation of Quantum Theory
, 2000 25
Electrically annealed black body (Lummer & Kurlbaum, 1898)
4 cm 40 cm Black body: platinum plate 0,01 mm 100 A / 1500°C graphite - 2100°C (1903) Lummer:
Betriebsblindheit
professional blindness
W. Wien, O. Lummer, Annalen der Physik 56 (1895) 453.
26
H. J. Kostkowski, R. D. Lee, Theory and methods of optical pyrometry, NBS Special Publication 300: Precision measurements and calibration. Temperature, Washington 1968, p. 361
27
Precision measurements of black body spectrum
Tests of Wien energy distribution law (since 1899 Wien-Planck e.d.l.
)
u
( ,
T
) 8 3
b
exp
c
3
a
T
Spectrobolometer
28
Deviations from Wien distribution
Feb. 1899: measurements up to 6
m, T: 800 - 1400°C „indicate small deviations from Wien Planck distribution ”
O. Lummer, E. Pringsheim, Verh. Deutsch. Phys. Gesell. 1 (1899) 36.
29
Deviations from Wien distribution
Nov. 1899: measurements up to 8,3
m, T up to 1650°C: „the discrepances between the theory and experiment are of systematic nature”
O. Lummer, E. Pringsheim, Verh. Deutsch. Phys. Gesell. 1 (1899) 226.
30
Wien law is not generally valid, but … justified
Feb. 1900: in mesurements up to 18
m, T up to 1772°C: „the differences between the theory and experiment reached 50%” Feb. 1900: being aware of the above, Planck publishes justification of Wien law using a non-mechanistic, purely thermodynamic approach to the radiation field
O. Lummer, E. Pringsheim, Verh. Deutsch. Phys. Gesell. 2 (1900) 163.
M. Planck „Entropie und Temperatur strahlender Wärme”, Annalen der Physik 1 (1900) 719.
31
Entropy and energy of a system of n „resonators”
dS n U n
dU nU n
U n f
(
U n
)
ndU
Uf
(
U
) 2
U S
2
a U
S U
1 ln(
U
/ )
S U
1
T U
exp(
T
)
S
U
ln(
U
)
u
( ,
T
) 8 3
c
3 exp
T
,
f
( ) M. Planck „Entropie und Temperatur strahlender Wärme”, Annalen der Physik 1 (1900) 719.
32
Wien
(PTR, 1896)
Thiesen
(PTR, Feb. 1900)
Lummer
&
Pringsheim
(PTR, Feb. 1900)
Planck
(Oct. 19, 1900)
Equations
33
Deviations from Wien distribution
H. Rubens i F. Kurlbaum, Oct. 1900 Reststrahlen-method: measurements up to 50
m. Clear divergences from Wien distribution. (die Abweichungen lassen sich nicht wegdiskutieren)
34
19 Oct. 1900
u
( ,
T
) 8 2
c
3 exp
T
1 35
Planck, 19 Oct. 1900
dS n U n
dU nU n
U n f
(
U n
)
ndU
Uf
(
U
)
Feb. 1900 U n , dU n and ΔU n are not sufficient to calculate dS n U is needed!
2
U S
2
U
2
S
U
2
U
(
U
)
u
( ,
T
) 8 3
c
3
Wien
exp
T u
( ,
T
) 8 2
c
3 exp
Planck
1
T
h
h
/
k
M. Planck „Über eine Verbesserung der Wien’schen Spektralgleichung”, Verh. Deutsch. Phys. Gesell. 2 (1900) 202.
36
Planck, 19 Oct. 1900
«…
at last I reached the point of constructing an
absolutely arbitrary expressions for entropy
which, though more complicated than the Wien’s expression, seems to satisfy with the same perfection every requirement of the thermodynamic and electromagnetic theories.
» 2
S
U
2
U
(
U
) M. Planck „Über eine Verbesserung der Wien’schen Spektralgleichung”, Verh. Deutsch. Phys. Gesell. 2 (1900) 202.
37
Planck, 14 Dec. 1900 Discretization procedure
M. Planck „Zur Theorie des Gesetzes der Energieverteilung im Normalspectrum”, Verh. Deutsch. Phys. Gesell. 2 (1900) 237.
38
Es wäre erhebend, wenn wir die Gehirnsubstanz auf eine Waage legen könnten, die von den theoretischen Physikern auf dem Altar dieser universellen Funktion hingeopfert wurde; und es ist dieses grausamen Opfers kein Ende abzusehen! Noch mehr: auch die klassische Mechanik fiel ihr zu Opfer, und es ist nicht abzusehen, ob. Maxwells Gleichungen der Elektrodynamik die Krisis überdauern werden, welche diese Funktion f mit sich gebracht hat.
A. Einstein, 1913
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