Wave Mechanics and C-equivalence

Satyanad Kichenassamy (LMR)

REVIEW 4 major objections 4 minor 27 references

Wave Mechanics and C-equivalence

T0 review · 4 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The matter wave introduced in the 1924 Thesis is not a wave on a pre-existing space but a physical proper system defining its own units of length and time, expressible in the C-equivalence framework.

desk verdict A historically careful but programmatic essay that explicitly postulates its central physical claim; worth reading for de Broglie scholarship, but not a derivation. read the letter →

arxiv 2507.07069 v1 pith:YRYFVA3A submitted 2025-07-08 physics.hist-ph

Satyanad Kichenassamy (LMR) This is my paper · ORCID

classification physics.hist-ph PACS 02.40.-k03.30.+p03.75.-b04.20.Cv04.80.-y32.80.-t

keywords phasewaveC-equivalencepropersystemmattermechanicsspace-timeunitsmanifoldofobserversfoundationsquantum

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to establish that the phase wave of the 1924 Thesis is not a disturbance running through a pre-existing spacetime. Rather, the wave is the expression of an extended physical object—a system of real oscillators—that defines its own local units of length and time, with special relativity holding locally inside that system. It argues that the C-equivalence framework, in which observers communicate by light rays and each possesses a local pseudo-inertial system with its own units, is the natural language for this picture and can be extended from gravitation to microphysics. The conclusion is a postulate: an atom, electron, or molecule, even at rest in the laboratory, carries its own space-time units, which need not coincide with the lab's standard units. If true, this gives wave mechanics the missing mathematical formulation its creator sought and forces a revision of the usual notion of a manifold as a common point-space.

What carries the argument

The carrying mechanism is the phase of the wave treated as a physical scalar. An expression like $\exp(i\omega t)$ in the proper system of the object becomes $\exp(i\omega\gamma(t' - vx'/c^2))$ in another inertial frame, so the wave is not defined on a background space but is the appearance, to an outside observer, of the object's internal phase. The second piece is the C-equivalence framework, a protocol in which observers who communicate only by light rays establish partial correspondences between their own event manifolds; each observer is assigned a local pseudo-inertial system with its own units, defined by physical operations rather than by a pre-existing coordinate space. The argument uses these two together to invert the usual logical order: the wave determines a local spacetime instead of being placed in one.

What would settle it

A decisive test would be to measure emission frequencies of atoms at the same instantaneous velocity but different acceleration histories—for example, atoms in laser cooling sampled at different phases of their rapid deceleration bursts. The postulate predicts small differences traceable to the proper system's changing units; an accurate null result would falsify it. A different, purely mathematical falsifier would be a demonstration that the C-equivalence protocol cannot assign a definite unit system to a single atom at rest without reference to the laboratory.

Watch

Extended reading notes

Core claim

The central claim, stated as a postulate in the conclusion, is that the proper system of a microscopic object—an atom, electron, or molecule, possibly interacting with a field—is a physical object defining its own units of space and time, and that these units are not necessarily those of the laboratory's standard inertial system even when the object is at rest. Reading the 1924 Thesis closely, the paper argues that to postulate the phase wave is already to assert this: the wave is generated by a distributed system of synchronized oscillators at rest relative to one another, and its phase is a relativistic scalar, so in another inertial frame the same physical phase appears as a wave. For non-uniform motion the carried-along system is not the momentarily comoving inertial frame, so each observer and each stage of its evolution needs a different local spacetime. The paper maintains that the C-equivalence framework supplies the needed structure: partial correspondences between observers' event-manifolds, established by light-ray communication, with each observer's system carrying its own units. It concludes that the usual manifold of point events must be replaced by a manifold of observers.

Load-bearing premise

The whole interpretation rests on the postulate, not derived in the paper, that a microscopic system at rest in the laboratory nevertheless possesses a 'proper system' with its own units of space and time; if that postulate cannot be given a coherent quantitative formulation, the central claim has no testable content.

Editorial extensions

If this is right

If the postulate is right, no microscopic system is correctly described as embedded in a pre-existing spacetime; each system's own units are primary, and the laboratory space-time is one observer's chart among many.
The usual manifold axioms would have to be modified: instead of one topological point-space covered by charts, one would need a 'manifold of observers' whose charts are the event-spaces of individual observers, with transition maps only where observers can effectively coordinate.
The proper time of a non-uniformly accelerated system can be recovered from laboratory measurements of its acceleration through four-dimensional frame formulas, giving a new operational definition of proper time for such systems.
Accelerated systems such as atoms undergoing laser cooling or molecules capturing electrons should show small modifications of their emission frequencies during non-uniform acceleration phases, making the postulate experimentally accessible.
The distinction between the manifold of events and the manifold of observers becomes unavoidable; it collapses to the usual picture only under the unprovable assumption that a single point-space underlies all observers.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The paper leaves implicit that this picture has consequences for clock comparisons: if each atom carries its own units, then comparisons of atomic clocks at different locations or acceleration histories are always protocol-mediated, and a global time coordinate is at best an emergent approximation.
A testable extension is to search specifically for acceleration-history-dependent frequency shifts at fixed instantaneous velocity—for instance, comparing emission during the rapid deceleration bursts of laser cooling with emission during uniform motion at the same speed; the paper suggests the situations but does not design the measurement.
The argument suggests a mathematical research program: a differential geometry of observer-dependent charts that does not presuppose a common underlying point set, going beyond the standard embedding picture that the paper criticizes.
A sympathetic reading implies that the observer-dependence of the wave function emphasized in the later writings is not merely epistemic but geometric: different observers genuinely possess different local unit systems, so the same physical situation is described through different proper spacetimes.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

This is a historical-philosophical essay, and it should be read as one. The author reads de Broglie's thesis closely and brings out a real tension: de Broglie's phase wave seems to require a proper system attached to the particle, with its own local inertial frame, rather than a wave propagating on a pre-existing spacetime. Connecting that to C-equivalence—an older framework for comparing observers without a common background manifold—is a genuinely interesting move, and the historical citations are attentive. The critique of the usual manifold axiom as presupposing a single point-space accessible to all observers is philosophically pointed and worth taking seriously.

The paper is also honest. It explicitly says it "postules" that the proper system of an atom or electron is an extended physical object defining its own units (Section 5), and it uses "suggérons" for the experimental ideas. There is no deceptive dressing-up of a conjecture as a theorem.

The soft spots are exactly where the reader's report lands. The step from "the phase is Lorentz-invariant" to "there is an extended physical system with its own units" is not justified; Lorentz invariance of a phase only selects a preferred frame, it does not conjure an extended oscillator distribution. The Pound-Rebka example does not discriminate: standard GR already explains the frequency shift via the metric and proper time along the atom's worldline, without giving the atom its own units. The suggested experiments are qualitative, with no quantitative predictions that could fail. And footnote 6 openly says the essential elements are already in the author's earlier work, so the standalone novelty is limited.

All that said, these issues are proportionate to the paper's genre. It is not pretending to be a technical derivation; it is a proposal for a different interpretive framework. The lack of a mathematical construction of the proper systems is a real gap, but the paper at least frames the question clearly.

Who is this for? A philosopher or historian of physics working on de Broglie, on observer-dependent spacetime, or on the foundations of relativity. It deserves a serious referee in that context—the referee should focus on whether the postulate can be made precise and whether it yields any testable difference from standard quantum mechanics plus general relativity. For a primary physics journal, it is not a fit. I would not cite it in my own work, but I might bring it to a reading group for the historical angle.

Referee Report

4 major / 4 minor

Summary. The paper argues, through a close reading of Louis de Broglie's 1924 thesis, that the phase wave of a 'morceau d'énergie' is not a wave propagating on a pre-existing spacetime, but rather itself defines a 'système propre' (proper system) with its own units of space and time. This proper system is interpreted as a pseudo-inertial system in the framework of Kichenassamy's C-equivalence. The paper further claims that this reinterpretation undermines the standard manifold notion of spacetime and applies the idea to several physical situations: optical resonance in mercury vapor, electron-molecule collisions, Doppler cooling, and the accelerated electron. The conclusion explicitly postulates that the proper system of an atom, electron, or molecule, even at rest in the laboratory, defines its own units, which need not coincide with those of laboratory inertial instruments.

Significance. The paper offers a useful historical-philosophical reconstruction of de Broglie's view that the phase wave has physical reality and that the proper system of a microscopic object is an extended physical system. It also draws attention to the little-known C-equivalence framework and to early experimental work on spatial extension in optical resonance. The proposal is thought-provoking: if correct, it would invert the logical relation between wave and spacetime and challenge the usual manifold axiomatics. However, the central physical claim is presented as a postulate rather than a derivation, and no quantitative predictions are given that would distinguish the proposal from standard quantum mechanics plus general relativity. The paper's value is therefore primarily interpretive and programmatic, not demonstrative.

major comments (4)

[Abstract and §5] The abstract states 'Nous établissons' (we establish) that the de Broglie wave determines a proper system, but §5 concludes that the compatibility of wave mechanics and C-equivalence 'conduit à postuler' (leads to postulating) that the proper system of an atom, electron, or molecule defines its own units. These two formulations are in tension: a postulate is not an established result. Since the central conclusion rests on this postulate, the paper should either provide a derivation from the cited de Broglie passages and physical principles, or explicitly reframe the contribution as a proposal for an interpretation rather than an establishment. This is a load-bearing issue because the paper's abstract and conclusion make different epistemological claims.
[§2, first point] The step from Lorentz invariance of the phase to the existence of an extended physical system of oscillators is a reification that is not justified. The paper notes that a phase such as exp(iωt) transforms to exp(iωγ(t′−vx′/c²)) and concludes from this that the proper system is 'un objet physique, étendu' and 'un système distribué d'oscillateurs réels'. Lorentz invariance of a phase only shows that the phase is a scalar under coordinate transformations; it does not by itself entail that the system described by the phase is an extended object with its own units of space and time. A concrete mathematical model of the proposed extended oscillator system, with a specification of how its spatial extension and characteristic frequencies are to be defined, is needed before this inference can be evaluated.
[§2 (Pound-Rebka) and §4] The empirical arguments are qualitative and do not discriminate between the proposed framework and standard quantum mechanics plus general relativity. The Pound-Rebka argument in §2, that an atom at rest in a gravitational field has modified emission frequencies and therefore different proper units, is already fully accounted for in GR by the metric and proper time along the atom's worldline, without assigning intrinsic units to the atom itself. Similarly, the examples in §4 are hedged: the optical resonance discussion calls for repeating experiments ('il serait souhaitable de répéter ces expériences'), and the Doppler-cooling suggestion says only that 'il n'est pas exclu' that transverse irradiation could reveal a frequency modification. No quantitative prediction is provided that could falsify the C-equivalence interpretation while remaining consistent with standard theory. Without such a prediction, the paper's central claim remains an interpretive postulate rather than an established physical result.
[§3 and §5] The paper relies heavily on the C-equivalence framework introduced in earlier works by the author, but it does not provide the mathematical structure needed to extend C-equivalence to microphysics. In particular, the 'système propre' of an atom or electron is asserted to be a physical object with its own units, but the paper does not specify how these units are defined, how the extension of the proper system is computed, or how different proper systems are coordinated beyond a reference to earlier publications. Since C-equivalence itself is not fully restated here, the reader cannot verify the central claim without consulting a separate body of literature. The paper should at least state the axioms or operational definitions of C-equivalence that are being extended, or clearly mark this dependence as a limitation.

minor comments (4)

[Title and body] The title in the running head contains an anomalous space: 'C-ÉQUIV ALENCE' should read 'C-ÉQUIVALENCE'.
[§3] The phrase 'l’image analytique de l’onde place monochromatique' appears to contain a typographical error; it should likely be 'l’onde plane monochromatique' (plane monochromatic wave).
[§4] In 'It n’est cependant pas exclu', the English word 'It' intrudes into the French text and should be 'Il'.
[References] The reference to Frémont [14] is given as a book title without a year or publisher details, which differs from the formatting of other references and makes the citation difficult to verify.

Circularity Check

3 steps flagged · score 8.0 of 10

The central claim is embedded in the author's own definition of C-equivalence and supported by a self-citation chain, so the 'derivation' reduces to a postulate restating the framework.

self definitional [Section 1, p. 100 (Introduction)]
"l'onde de phase d'un « morceau d'énergie » est pour lui une réalité physique définissant son système propre, que nous interprétons comme un pseudo-système d'inertie au sens de la C-équivalence [2, 3]. Autrement dit, c'est pour nous l'objet physique qui définit son espace et son temps."

The interpretive move 'interprétons comme un pseudo-système d'inertie au sens de la C-équivalence' is immediately glossed as 'Autrement dit, c'est ... l'objet physique qui définit son espace et son temps.' Thus the paper's central conclusion—that the proper system is a physical object defining its own units—is packed into the initial identification with C-equivalence. Section 5 then repeats this as a 'postulat' rather than deriving it from independent quantum-mechanical or experimental facts, so the claimed establishment reduces to a definitional labeling of de Broglie's proper system with the author's own framework.
self citation load bearing [Section 5, p. 109 (Conclusion)]
"La C-équivalence semble être la seule théorie qui n'assimile pas le mouvement à un déplacement géométrique dans un espace indépendant de l'observateur, et qui permette de tirer des conséquences physiques et mathématiques de cette distinction."

This uniqueness claim is the load-bearing justification for choosing C-equivalence. It is not derived in the paper; the only support offered is the author's own prior work (refs [2,3,16,17]), and reference [3] itself concedes that the full examination underlying C-equivalence 'n'a pas entièrement été publié.' The 'only theory' assertion therefore imports a self-issued uniqueness verdict rather than an external theorem, and it is used to dismiss the standard manifold treatment without an independent argument.

1 more flagged steps

self citation load bearing [Section 4, p. 108 (Application à quelques situations concrètes)]
"Enfin, l'analyse de l'électron accéléré [16] a montré que le bilan d'énergie était modifié par le changement d'unités du système propre."

The alleged empirical support for the C-equivalence picture is itself a citation to the author's earlier paper [16]; the claimed effect ('changement d'unités du système propre') is exactly the conclusion at issue. Since no quantitative prediction, independent reproduction, or external measurement is given, this step uses the conclusion as its own evidence via a self-citation chain.

full rationale

The paper does not test a quantitative prediction against independent data; its empirical sections explicitly call for repeating experiments ('Il serait souhaitable de répéter ces expériences') and phrase possible observations as non-exclusive possibilities ('il n'est pas exclu'). The central claim is openly introduced as a postulate in the conclusion. This alone is an overclaim relative to the abstract's 'nous établissons,' but postulation is not circularity. The circularity lies in the chain by which the postulate is presented as supported: the initial identification of de Broglie's proper system with a C-equivalence pseudo-system already contains the 'object defining its own space and time' conclusion; the uniqueness of C-equivalence among theories is asserted on the basis of the author's own unpublished and self-cited framework; and the only 'analysis' invoked for accelerated electrons is a self-citation whose content is the very unit-change conclusion. External anchors are absent: no machine-checked formalization, no independent numerical prediction, no falsifiable quantitative consequence. Therefore, the paper's derivation chain reduces to its own definitions and self-citations, warranting a high circularity score despite the paper's candor in labeling the result a postulate.

Assumptions & free parameters 0 free parameters · 4 assumptions · 1 invented entities

The paper introduces no fitted numerical parameters, but it relies on several postulates: the physical reality of the 'proper system', the inadequacy of point-based manifolds for observers, and the validity of the author's C-equivalence framework. These are load-bearing and not independently established.

assumptions (4)

ad hoc to paper Le système propre d'un 'morceau d'énergie', même microscopique, est un objet physique étendu qui définit ses propres unités de temps et d'espace.
Postulated as 'premier point' in Section 2 and in the Conclusion (Section 5); it is the load-bearing physical assertion of the paper.
domain assumption Il faut distinguer variété des événements et variété des observateurs; chaque observateur dispose de sa propre variété d'événements.
Stated as 'second point' in Section 2 and elaborated in Section 3; used to justify replacing the usual manifold of points.
ad hoc to paper La C-équivalence, développée par l'auteur, fournit le cadre correct pour décrire ces systèmes propres.
The paper's argument is entirely conducted within the author's own C-equivalence framework (refs [2],[3]); no independent derivation or external validation is provided.
domain assumption L'axiome (i) de la définition usuelle des variétés (espace de Hausdorff) est 'proprement invérifiable' et doit être modifié.
Section 3; this epistemological claim is used to motivate the proposed 'variété des observateurs'.

invented entities (1)

Système propre (proper system) of an atom, electron, or molecule as an extended physical object with its own units of space and time.
purpose: To ground the reinterpretation of de Broglie's matter wave and to extend C-equivalence to microphysics.
The paper suggests experiments (e.g., modified emission frequencies during acceleration) but gives no quantitative predictions or measurement protocols that would provide independent evidence.

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Cite this review

Pith. "Pith review of Wave Mechanics and C-equivalence." pith.science (2026). https://pith.science/paper/YRYFVA3A

@misc{pith2026250707069,
  author       = {Pith},
  title        = {Pith review of: Wave Mechanics and C-equivalence},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YRYFVA3A}},
  note         = {Machine review of arXiv:2507.07069}
}

read the original abstract

We establish that de Broglie's wave, as it is introduced in his Thesis, is not a wave on a given space, but on the contrary itself determines a system in which Special Relativity is locally valid. This local system is a physical object, that defines its own units of length and time. C-equivalence provides a natural framework both for its mathematical description and its physical interpretation.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

27 extracted references · 27 canonical work pages

[1]

Introduction Si les prédictions de la Mécanique ondulatoire ont reçu les c onﬁrmations que l’on sait, la vision de Louis de Broglie n’a jamais reçu la formulation mathématique cohérente qu’il n’avait cessé d’appeler de se s vœux. On montre, par une lecture attentive de passages de sa Thèse [1] , que l’onde de phase d’un « morceau d’énergie » est pour lui ...

work page 1946
[2]

Chacun se souvient de l’image ([1], Ch

Le système propre dans la Thèse de Louis de Broglie La Thèse de Broglie montre qu’il n’est pas nécessaire de fair e inter- venir un sujet conscient pour envisager un observateur loca l. Chacun se souvient de l’image ([1], Ch. I, §I, p. 23 sqq.) d’un « plateau circulaire horizontal de très grand rayon » : « à ce plateau, sont suspendus des systèmes identiq...

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[3]

L’obser v ateur et sa v ariété des événements On pourrait penser que l’introduction d’un calcul d’opérat eurs dispen- serait d’examiner les notions d’espace et de temps attachée s à un obser- vateur. Ainsi, von Neumann aﬃrmait en 1933, alors même que la notion moderne de variété n’avait pas été complètement élaborée [8 ], que les ma- thématiques qu’il con...

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[4]

simultanés

Application à quelques situations concrètes Un aspect du problème – l’extension spatiale du système prop re –, semble avoir été identiﬁé dès 1957. En eﬀet, Lennuier avait m ontré dans sa thèse, sur le cas de la vapeur de mercure, que la résonance opt ique pouvait Mécanique ondulatoire et C-équivalence 9 être provoquée par une lumière de fréquence légèreme...

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[5]

Conclusion Le rapprochement de la Mécanique ondulatoire et de la C-équi valence conduit à postuler que le système propre d’un atome, d’un éle ctron ou d’une molécule, éventuellement en interaction avec un champ, est un objet physique, déﬁnissant ses propres unités d’espace et de temp s qui, même lorsqu’il est au repos dans le laboratoire, ne sont pas néce...

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Louis de Broglie, Recherches sur la Théorie des Quanta : Réédition du texte de 19 24, Masson, Paris, 1963

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Kichenassamy, Compléments à l’interpreétation phys ique de la Relativité générale : Applica- tions

S. Kichenassamy, Compléments à l’interpreétation phys ique de la Relativité générale : Applica- tions. Annales de l’Inst. H. Poincaré, Section A (N. S.) , 1 (2), 129–145, (1964). Voir également C. R. Acad. Sci. Paris , 258, 470–473, (1964)

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[8]

On trouvera les principaux a rguments dans les articles cités note

La C-équivalence est l’aboutissement d’un examen serré de toutes les théories antérieures, qui n’a pas entièrement été publié. On trouvera les principaux a rguments dans les articles cités note

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[9]

et dans les travaux suivants : (i) Annales de l’Inst. H. Poincaré, Section A (N. S.) , 4 (2), 139–158, (1966) ; (ii) « La Relativité Générale », Relativité et quanta : les grandes théories de la Physique moderne, Masson, Paris, 1968, chapitre II, pages 27–58 ; (iii) « Rema rks...

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De même pour l’esp ace

Cette assertion ne va pas de soi : Pour Nietzsche : « Le temp s en soi est une absurdité, il n’a de temps que pour un être doué de sensation. De même pour l’esp ace. » (Zeit an sich ist ein Unsinn : nur für ein empﬁndenden [p. 110] Wesen gibt es Zeit. E benso Raum. Das Philoso...

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Kichenassamy à Paris dans les années 1960-70, malheureusement inédits

Ce point a été développé très clairement dans les cours de S. Kichenassamy à Paris dans les années 1960-70, malheureusement inédits. On trouvera un ap erçu dans [3, (ii) et (iii)] et dans Annales de la Fond. L. de Broglie , 5 (3), 1980, 191–202. Les éléments essentiels de notr...

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[13]

J. L. Anderson, Revista Mexicana de Fisica, III (3), 176–184, (1957), E. Wigner, Rev. Mod. Phys. 29, 255–268, (1957). On trouvera une synthèse des principaux a rguments dans [3, (iii)]

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Whitney, « Diﬀe- rentiable manifolds », Ann

On fait généralement remonter la notion moderne de varié té diﬀérentielle à H. Whitney, « Diﬀe- rentiable manifolds », Ann. Math., 37 (3), 645-680, (1936). Il montre qu’une version simpliﬁée de 12 Mécanique ondulatoire et C-équivalence la notion de variété selon Cartan équivau...

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Leçons sur la géométrie des espaces de Riemann , Gauthier-Villars, Paris, 2 e édition, revue et augmentée, 1946 (nouveau tirage : 1951), p. 57. Encore aujou rd’hui, les variétés ne sont traitées dans Bourbaki que dans un fascicule de résultats : N. Bourbak i, Variétés diﬀérent...

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, 40, (1923), 325-412 ; 41, (1923), 1-25 ; 42, (1923), 17-88

Cartan, Élie, Annales Scientiﬁques de l’E.N.S. , 40, (1923), 325-412 ; 41, (1923), 1-25 ; 42, (1923), 17-88. Faut-il rappeler qu’Élie Cartan était l’un d es membres du jury de thèse de Louis de Broglie ?

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[17]

Kichenassamy, S., « Interaction entre matière et rayon nement au voisinage de la résonance optique », Journal de Physique et Le Radium , 12, 863–867, (1951)

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Kichenassamy, C

S. Kichenassamy, C. R. Acad. Sci. Paris , 234, 1035-1036 et 1530–1532, (1952)

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Blamont, Jean Brossel , J

Marie-Anne Guiochon, Jacques E. Blamont, Jean Brossel , J. Phys. Radium , 18, 99–108 (1957)

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François Frémont, Young-type Interferences with Electrons , Springer, 2014

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Claude Cohen-Tannoudji, Rev. Mod. Phys. , 70 (3), 707–719, (1998)

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Kichenassamy, C

S. Kichenassamy, C. R. Acad. Sci. Paris , B262, 1591–1593, (1966)

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S. Kichenassamy, C. R. Acad. Sci., Paris , 260, 3865–3868, (1965)

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von Neumann, Mathematische Grundlagen der Quantenmechanik , Springer, 1932

J. von Neumann, Mathematische Grundlagen der Quantenmechanik , Springer, 1932. Nous citons la traduction d’A. Proca (Alcan, Paris, 1946. Réimpr. : Gaba y, Sceaux, 1988). [p. 111]

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Louis de Broglie, Physique et microphysique , Albin Michel, Paris, 1947

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« The Principle of Equivalence performed the essential oﬃce of midwife at the birth of general relativity, [...] I suggest that the midwife be now buried wi th appropriate honors and the facts of absolute space-time faced. » J. L. Synge, Relativity : The General Theory , North...

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Laboratoire de Mathématiques, Université de Reims Champagne -Ardenne, Moulin de la Housse, B.P

Shoshichi Kobayashi et Katsumi Nomizu, Foundations of Diﬀerential Geometry, I , Wiley- Interscience, New York, 1963. Laboratoire de Mathématiques, Université de Reims Champagne -Ardenne, Moulin de la Housse, B.P. 1039, F-51687 Reims Cedex 2, France. Email address : satyanad.ki...

1963

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

Introduction Si les prédictions de la Mécanique ondulatoire ont reçu les c onﬁrmations que l’on sait, la vision de Louis de Broglie n’a jamais reçu la formulation mathématique cohérente qu’il n’avait cessé d’appeler de se s vœux. On montre, par une lecture attentive de passages de sa Thèse [1] , que l’onde de phase d’un « morceau d’énergie » est pour lui ...

work page 1946

[2] [2]

Chacun se souvient de l’image ([1], Ch

Le système propre dans la Thèse de Louis de Broglie La Thèse de Broglie montre qu’il n’est pas nécessaire de fair e inter- venir un sujet conscient pour envisager un observateur loca l. Chacun se souvient de l’image ([1], Ch. I, §I, p. 23 sqq.) d’un « plateau circulaire horizontal de très grand rayon » : « à ce plateau, sont suspendus des systèmes identiq...

work page

[3] [3]

L’obser v ateur et sa v ariété des événements On pourrait penser que l’introduction d’un calcul d’opérat eurs dispen- serait d’examiner les notions d’espace et de temps attachée s à un obser- vateur. Ainsi, von Neumann aﬃrmait en 1933, alors même que la notion moderne de variété n’avait pas été complètement élaborée [8 ], que les ma- thématiques qu’il con...

work page 1933

[4] [4]

simultanés

Application à quelques situations concrètes Un aspect du problème – l’extension spatiale du système prop re –, semble avoir été identiﬁé dès 1957. En eﬀet, Lennuier avait m ontré dans sa thèse, sur le cas de la vapeur de mercure, que la résonance opt ique pouvait Mécanique ondulatoire et C-équivalence 9 être provoquée par une lumière de fréquence légèreme...

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[5] [5]

Conclusion Le rapprochement de la Mécanique ondulatoire et de la C-équi valence conduit à postuler que le système propre d’un atome, d’un éle ctron ou d’une molécule, éventuellement en interaction avec un champ, est un objet physique, déﬁnissant ses propres unités d’espace et de temp s qui, même lorsqu’il est au repos dans le laboratoire, ne sont pas néce...

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[6] [6]

Louis de Broglie, Recherches sur la Théorie des Quanta : Réédition du texte de 19 24, Masson, Paris, 1963

work page 1963

[7] [7]

Kichenassamy, Compléments à l’interpreétation phys ique de la Relativité générale : Applica- tions

S. Kichenassamy, Compléments à l’interpreétation phys ique de la Relativité générale : Applica- tions. Annales de l’Inst. H. Poincaré, Section A (N. S.) , 1 (2), 129–145, (1964). Voir également C. R. Acad. Sci. Paris , 258, 470–473, (1964)

work page 1964

[8] [8]

On trouvera les principaux a rguments dans les articles cités note

La C-équivalence est l’aboutissement d’un examen serré de toutes les théories antérieures, qui n’a pas entièrement été publié. On trouvera les principaux a rguments dans les articles cités note

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