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II. Untitled Fragment
11. UNTITLED FRAGMENT FROM FOLDER LABELLED COMO LECTURE II (1927) DANISH TEXT, TRANSLATION AND FACSIMILE
See Introduction to Part I, sect. 3.
P A R T I: T H E E M E R G E N C E O F T H E C O M P L E M E N T A R I T Y A R G U M E N T
“COMO LECTURE 11” The folder “Como Lecture 11”, 1927, contains a large number of drafts and notes, comprising 181 sheets, a few of which have notes on the reverse, making a total of 195 written pages. Most of them are handwritten, in pencil or ink, in Klein’s, Bohr’s, Mrs Margrethe Bohr’s and an unidentified hand. There are a few typed pages and carbon copies. The languages are English, Danish and German. Many sheets are dated, carrying dates between 2 July 1927 and 13 September 1927 (except for 2 pages, dated 1926, apparently by mistake). The main titles are: “Atomteori og Berlgemekanik” (“Atomic Theory and Wave Mechanics”), “Philosophical Foundations of the Quantum Theory”, ‘‘Fundamental Problems of the Quantum Theory”, “Uber die Wellentheorie des Lichts und der Materie” (“On the Wave Theory of Light and Matter”), and “Zur Frage des begrifflichen Aufbaus der Quantentheorie” (“On the Question of the Conceptual Structure of the Quantum Theory”). We have here (as document 11) reproduced 3 pages in Danish written in ink in Bohr’s handwriting with an amendment in pencil in Klein’s handwriting at the end. The first two pages are numbered and are dated 10 July 1926 [1927, as is clear, La., from the reference to Davisson]. As document I11 a manuscript entitled “Philosophical foundations of the quantum theory” is reproduced. It consists of 8 numbered pages written in pencil in Klein’s handwriting with a few corrections by Bohr. It is not dated. As document IV a manuscript entitled “Fundamental problems of the quantum theory” is reproduced. It consists of 8 numbered pages written in ink in Bohr’s handwriting, all dated 13 September 1927. The material is on microfilm Bohr MSS no. 11. As will be apparent from the facsimile reproduction, this manuscript was evidently written in great haste. Hence many words are hardly legible and spelling and punctation are rather careless. In the transcript we have attempted to give as faithful a reproduction as possible, indicating uncertainties by square brackets and question marks. However, some trivial slips of the pen have been corrected. Some of the formulae are hardly legible, but most of the symbols seem to correspond to those used in the printed versions of the Como Lecture.
PART I: THE EMERGENCE OF THE COMPLEMENTARITY ARGUMENT
I 10-7-1926 [1927] Enhver Oplysning om Atomer udtrykt i klassiske Begreber Alle klassiske Begreber defineret ved Rum Tids Billeder Derfor Begyndelse ti1 Quantum[theori ?] en stykkevis Brug af Rum Tids Billeder knyttet formelt sammen med Relationer indeholdende Plancks Konstant. og paa Konservation af Energi og Bevagelsesmangde. Forbindelsen af vasentlig diskontinuert og statistisk Art. Bestrabelsen paa at knytte de statistiske Love op ti1 Egenskaberne af Billeder forte saaledes ti1 at de fremtraadte som Almindelig[gorelse] af den klassiske Theory og specielt konvergerer ti1 denne Theoris Forlangender i den Granse [hvor] man i statistisk Anvendelse kan se bort fra det diskontinuerte Element. forte ti1 Erkendelsen af en vidtgaaende Korrespondens mellem Quanteteorien og den klassiske Theory og ti1 det Program at udvikle en [konsistent ?] Kvantitativ Beskrivelse [ved] at s0ge analoge Trak hos den klassiske Theori. Det viste sig dog umuligt med Rum Tids billeder at give denne quantitativt Udtryk. [Ja ?] Theory udviste en Dualitet hvis man saa paa Superpositionsprincippet paa den ene Side og Bevarelsen af Energi og Bevagelsesmasngde paa den anden. Komplementare Sider af Erfaringen der ikke lader sig forene i et Rum Tidsbillede baseret paa de klassiske Theorier. +
I1 10-7-1926 [1927].
Ja som tilmed synes at stride saa starkt mod den klassiske Rum Tidsbeskrivelse at det var w a r t at [se] hvorledes den [kunde] forenes dermed. LysBolger kraver Tid for deres Definition, +
1* L=nA [?I n = &
Partikler maa andre deres Hastighed hurtigt. Lyskvantum kan ikke gmes tilstraekkelig lille Ez = I X = h [?I
-
A E . T- A I * L h .
* [We surmise that these equations are intended to indicate that the extension of the wave group is large compared to the wavelength.]
MS, p. 2
PART I: THE EMERGENCE OF THE COMPLEMENTARITY ARGUMENT
Forandring ved Berlgeteorien for Materien. De Broglie. Einstein Bekrzftigelse af Davidson. Ogsaa beskrive en Particle ved Superposition af Berlger. Samme Relation som [for] Lyskvanter. (Relativiteten vasentlig)
MS,P. PI
Mulighed for Rum og Tid Beskrivelse nerjeste knyttet op ti1 “Conservation theorems”. Maaling af Energi eller Impuls med given Nerjagtighed medfarer Tab af Phaserelationer, der medferrer Umulighed af Interferens ved Superposition. Vanskelighed ved Rum og Tid uadskilleligt fra Vanskelighed ved Benyttelse af klassiske Begreber defineret i Rum og Tid. Henvist ti1 statistisk Brug af klassiske Begreber. ferrst forsergt ved at passe Rum Tid Billeder sammen med Bevaring af Energy og Impuls. Korrespondens d.v.s. Forbindelse af de statistiske Love med Billedernes Trak. Muligt i betydeligt Omfang. men ferrte ti1 Formodning om Statistik af Energy. Tydeligt komplementser Side hos Erfaringen “naar den beskrives med klassiske Begreber”. Einstein. Umuligt at udtrykke i Rum Tidsbilleder [hentet ?] fra klassisk Teori. Tydeligt at Modifikation af Tids Rum Beskrivelsen nadvendiggjorde Modifikation af “Erhaltung”
Interpoiation in Klein’s handwriting
Crossed out
Added in Klein’s handwriting
Moderne Udvikling giver Midlerne i Haende. Midlerne symbolske. og Behandling vasentlig statistisk. Heisenberg Undersergelse af Statistikens Sammenhzng med Betingelser for Maalinger. Giver et vasentligt Bidrag ti1 Forstaaelse af Teoriens Modsigelsesfrihed og samtidig ti1 den reffeAnvendelse. Nerje Forbindelse med Rum-Tidsproblemet . Interessant at analysere dette sidste Vekselspil og samtidig [Forholdene for Rum Tidsbeskrivelsen.
?I
Uadskilligheden af Modsigelsesfrihed og Principperne for Teoriens Anvendelse. Problemet om Anskuelighed
P A R T I: T H E E M E R G E N C E O F T H E C O M P L E M E N T A R I T Y A R G U M E N T
TRANSLATION I 10-7-1926 [1927] All information about atoms expressed in classical concepts
All classical concepts defined through space-time pictures Therefore beginning of quantum [theory ?] piecewise use of space-time pictures formally connected by relations containing Planck’s constant. and on conservation of energy and momentum. The connection of essentially discontinuous and statistical kind. The endeavours at connecting the statistical laws with the properties of pictures thus implied that they appeared as generalization of the classical theory, and in particular converge to the demands of this theory in the limit [where] in statistical applications one may disregard the discontinuous element. led to the recognition of a far-reaching correspondence between the quantum theory and the classical theory and to the programme of developing a [consistent ?] quantitative description [by] looking for analogous features in the classical theory. However, it proved impossible to express this quantitatively by space-time pictures. [Indeed ?I, the theory exhibited a duality when one considered on the one hand the superposition principle and on the other hand the conservation of energy and momentum. Complementary aspects of experience that cannot be united into a space-time picture based on the classical theories. --t I1 10-7-1926 [1927]. And which indeed seem to be in such a strong conflict with the classical space-time description that it was difficult to [see], how it [could be] reconciled with it. Light waves require time for their definition, +
L=nA[?]
1 *
n=-
&
* [We surmise that these equations are intended to indicate that the extension of the wave group is large compared to the wavelength.]
MS, p. 2
PART I : THE EMERGENCE OF THE COMPLEMENTARITY ARGUMENT
Particles must change their velocity rapidly. Light quantum cannot be made sufficiently small E T = I X = h[?] A E . T- A I . L
- h.
Change with wave theory of matter. De Broglie. Einstein Confirmation by Davidson. Also describe a particle by superposition of waves. Same relation as [for] light quanta. (Relativity essential)
MS, P. PI
Possibility for space-time description closely connected with conservation theorems. Measurement of energy or momentum with given accuracy implies loss of phase relations, which implies impossibility of interference by superposition. Difficulty with space and time inseparable from difficulty by application of classical concepts defined in space and time. Compelled to statistical use of classical concepts. first attempted by connecting, space-time pictures with conservation of energy and momentum. Correspondence, i.e. connection of the statistical laws with features of the pictures. Possible to a considerable extent. but led to the hypothesis of statistics of energy. Clearly complementary aspect of experience “when it is described by classical concepts”. Einstein. Impossible to express in space-time pictures [taken over ?] from classical theory. Clear that modification of time-space description necessitated modification of conservation
Interpolation in Klein’s handwriting Crossed out
Added in Klein’s handwriting
Modern development provides the means. The means symbolic. and treatment fundamentally statistical. Heisenberg investigation of the relationship between the statistics and the conditions for measurements. Gives an essential contribution to the understanding of the consistency of the theory and at the same time to its proper application. Close relation to the space-time problem. Interesting to analyse the latter interplay and at the same time the [conditions for ?] the space-time description. Inseparability of consistency and the principles for the application of the theory. The problem of visualizability.
See Introduction to Part I, sect. 3.
P A R T I: T H E E M E R G E N C E O F T H E C O M P L E M E N T A R I T Y A R G U M E N T
“COMO LECTURE 11” The folder “Como Lecture 11”, 1927, contains a large number of drafts and notes, comprising 181 sheets, a few of which have notes on the reverse, making a total of 195 written pages. Most of them are handwritten, in pencil or ink, in Klein’s, Bohr’s, Mrs Margrethe Bohr’s and an unidentified hand. There are a few typed pages and carbon copies. The languages are English, Danish and German. Many sheets are dated, carrying dates between 2 July 1927 and 13 September 1927 (except for 2 pages, dated 1926, apparently by mistake). The main titles are: “Atomteori og Berlgemekanik” (“Atomic Theory and Wave Mechanics”), “Philosophical Foundations of the Quantum Theory”, ‘‘Fundamental Problems of the Quantum Theory”, “Uber die Wellentheorie des Lichts und der Materie” (“On the Wave Theory of Light and Matter”), and “Zur Frage des begrifflichen Aufbaus der Quantentheorie” (“On the Question of the Conceptual Structure of the Quantum Theory”). We have here (as document 11) reproduced 3 pages in Danish written in ink in Bohr’s handwriting with an amendment in pencil in Klein’s handwriting at the end. The first two pages are numbered and are dated 10 July 1926 [1927, as is clear, La., from the reference to Davisson]. As document I11 a manuscript entitled “Philosophical foundations of the quantum theory” is reproduced. It consists of 8 numbered pages written in pencil in Klein’s handwriting with a few corrections by Bohr. It is not dated. As document IV a manuscript entitled “Fundamental problems of the quantum theory” is reproduced. It consists of 8 numbered pages written in ink in Bohr’s handwriting, all dated 13 September 1927. The material is on microfilm Bohr MSS no. 11. As will be apparent from the facsimile reproduction, this manuscript was evidently written in great haste. Hence many words are hardly legible and spelling and punctation are rather careless. In the transcript we have attempted to give as faithful a reproduction as possible, indicating uncertainties by square brackets and question marks. However, some trivial slips of the pen have been corrected. Some of the formulae are hardly legible, but most of the symbols seem to correspond to those used in the printed versions of the Como Lecture.
PART I: THE EMERGENCE OF THE COMPLEMENTARITY ARGUMENT
I 10-7-1926 [1927] Enhver Oplysning om Atomer udtrykt i klassiske Begreber Alle klassiske Begreber defineret ved Rum Tids Billeder Derfor Begyndelse ti1 Quantum[theori ?] en stykkevis Brug af Rum Tids Billeder knyttet formelt sammen med Relationer indeholdende Plancks Konstant. og paa Konservation af Energi og Bevagelsesmangde. Forbindelsen af vasentlig diskontinuert og statistisk Art. Bestrabelsen paa at knytte de statistiske Love op ti1 Egenskaberne af Billeder forte saaledes ti1 at de fremtraadte som Almindelig[gorelse] af den klassiske Theory og specielt konvergerer ti1 denne Theoris Forlangender i den Granse [hvor] man i statistisk Anvendelse kan se bort fra det diskontinuerte Element. forte ti1 Erkendelsen af en vidtgaaende Korrespondens mellem Quanteteorien og den klassiske Theory og ti1 det Program at udvikle en [konsistent ?] Kvantitativ Beskrivelse [ved] at s0ge analoge Trak hos den klassiske Theori. Det viste sig dog umuligt med Rum Tids billeder at give denne quantitativt Udtryk. [Ja ?] Theory udviste en Dualitet hvis man saa paa Superpositionsprincippet paa den ene Side og Bevarelsen af Energi og Bevagelsesmasngde paa den anden. Komplementare Sider af Erfaringen der ikke lader sig forene i et Rum Tidsbillede baseret paa de klassiske Theorier. +
I1 10-7-1926 [1927].
Ja som tilmed synes at stride saa starkt mod den klassiske Rum Tidsbeskrivelse at det var w a r t at [se] hvorledes den [kunde] forenes dermed. LysBolger kraver Tid for deres Definition, +
1* L=nA [?I n = &
Partikler maa andre deres Hastighed hurtigt. Lyskvantum kan ikke gmes tilstraekkelig lille Ez = I X = h [?I
-
A E . T- A I * L h .
* [We surmise that these equations are intended to indicate that the extension of the wave group is large compared to the wavelength.]
MS, p. 2
PART I: THE EMERGENCE OF THE COMPLEMENTARITY ARGUMENT
Forandring ved Berlgeteorien for Materien. De Broglie. Einstein Bekrzftigelse af Davidson. Ogsaa beskrive en Particle ved Superposition af Berlger. Samme Relation som [for] Lyskvanter. (Relativiteten vasentlig)
MS,P. PI
Mulighed for Rum og Tid Beskrivelse nerjeste knyttet op ti1 “Conservation theorems”. Maaling af Energi eller Impuls med given Nerjagtighed medfarer Tab af Phaserelationer, der medferrer Umulighed af Interferens ved Superposition. Vanskelighed ved Rum og Tid uadskilleligt fra Vanskelighed ved Benyttelse af klassiske Begreber defineret i Rum og Tid. Henvist ti1 statistisk Brug af klassiske Begreber. ferrst forsergt ved at passe Rum Tid Billeder sammen med Bevaring af Energy og Impuls. Korrespondens d.v.s. Forbindelse af de statistiske Love med Billedernes Trak. Muligt i betydeligt Omfang. men ferrte ti1 Formodning om Statistik af Energy. Tydeligt komplementser Side hos Erfaringen “naar den beskrives med klassiske Begreber”. Einstein. Umuligt at udtrykke i Rum Tidsbilleder [hentet ?] fra klassisk Teori. Tydeligt at Modifikation af Tids Rum Beskrivelsen nadvendiggjorde Modifikation af “Erhaltung”
Interpoiation in Klein’s handwriting
Crossed out
Added in Klein’s handwriting
Moderne Udvikling giver Midlerne i Haende. Midlerne symbolske. og Behandling vasentlig statistisk. Heisenberg Undersergelse af Statistikens Sammenhzng med Betingelser for Maalinger. Giver et vasentligt Bidrag ti1 Forstaaelse af Teoriens Modsigelsesfrihed og samtidig ti1 den reffeAnvendelse. Nerje Forbindelse med Rum-Tidsproblemet . Interessant at analysere dette sidste Vekselspil og samtidig [Forholdene for Rum Tidsbeskrivelsen.
?I
Uadskilligheden af Modsigelsesfrihed og Principperne for Teoriens Anvendelse. Problemet om Anskuelighed
P A R T I: T H E E M E R G E N C E O F T H E C O M P L E M E N T A R I T Y A R G U M E N T
TRANSLATION I 10-7-1926 [1927] All information about atoms expressed in classical concepts
All classical concepts defined through space-time pictures Therefore beginning of quantum [theory ?] piecewise use of space-time pictures formally connected by relations containing Planck’s constant. and on conservation of energy and momentum. The connection of essentially discontinuous and statistical kind. The endeavours at connecting the statistical laws with the properties of pictures thus implied that they appeared as generalization of the classical theory, and in particular converge to the demands of this theory in the limit [where] in statistical applications one may disregard the discontinuous element. led to the recognition of a far-reaching correspondence between the quantum theory and the classical theory and to the programme of developing a [consistent ?] quantitative description [by] looking for analogous features in the classical theory. However, it proved impossible to express this quantitatively by space-time pictures. [Indeed ?I, the theory exhibited a duality when one considered on the one hand the superposition principle and on the other hand the conservation of energy and momentum. Complementary aspects of experience that cannot be united into a space-time picture based on the classical theories. --t I1 10-7-1926 [1927]. And which indeed seem to be in such a strong conflict with the classical space-time description that it was difficult to [see], how it [could be] reconciled with it. Light waves require time for their definition, +
L=nA[?]
1 *
n=-
&
* [We surmise that these equations are intended to indicate that the extension of the wave group is large compared to the wavelength.]
MS, p. 2
PART I : THE EMERGENCE OF THE COMPLEMENTARITY ARGUMENT
Particles must change their velocity rapidly. Light quantum cannot be made sufficiently small E T = I X = h[?] A E . T- A I . L
- h.
Change with wave theory of matter. De Broglie. Einstein Confirmation by Davidson. Also describe a particle by superposition of waves. Same relation as [for] light quanta. (Relativity essential)
MS, P. PI
Possibility for space-time description closely connected with conservation theorems. Measurement of energy or momentum with given accuracy implies loss of phase relations, which implies impossibility of interference by superposition. Difficulty with space and time inseparable from difficulty by application of classical concepts defined in space and time. Compelled to statistical use of classical concepts. first attempted by connecting, space-time pictures with conservation of energy and momentum. Correspondence, i.e. connection of the statistical laws with features of the pictures. Possible to a considerable extent. but led to the hypothesis of statistics of energy. Clearly complementary aspect of experience “when it is described by classical concepts”. Einstein. Impossible to express in space-time pictures [taken over ?] from classical theory. Clear that modification of time-space description necessitated modification of conservation
Interpolation in Klein’s handwriting Crossed out
Added in Klein’s handwriting
Modern development provides the means. The means symbolic. and treatment fundamentally statistical. Heisenberg investigation of the relationship between the statistics and the conditions for measurements. Gives an essential contribution to the understanding of the consistency of the theory and at the same time to its proper application. Close relation to the space-time problem. Interesting to analyse the latter interplay and at the same time the [conditions for ?] the space-time description. Inseparability of consistency and the principles for the application of the theory. The problem of visualizability.