--- title: "On the Physical Problem of Spatial Dimensions: An Alternative Procedure to Stability Arguments • CBPF Index" description: "CBPF INDEX is the system that tracks the scientific and technological output of CBPF. It lists the articles, books, technical reports and other publications of the whole CBPF community." canonical_url: "https://index.cbpf.br/en/publicacoes/6ad2a767639f62b11adbb7fd" locale: en meta: "og:description": "CBPF INDEX is the system that tracks the scientific and technological output of CBPF. It lists the articles, books, technical reports and other publications of the whole CBPF community." "og:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_~T24gdGhlIFBoeXNpY2FsIFByb2JsZW0gb2YgU3BhdGlhbCBEaW1lbnNpb25zOiBBbiBBbHRlcm5hdGl2ZSBQcm9jZWR1cmUgdG8gU3RhYmlsaXR5IEFyZ3VtZW50cw%2Ctipo_Physics%2BNote%2Ccor_~I2E4MmMwMA%2Cautores_~Ri4gQ2FydXNvOyBSLiBNLiBYLiBBcmF1am8%2Cdetalhe_1986%2Csecao_Publications%2Cp_Ii9lbi9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmI3ZmQi%2Cs_UjqfViYl1PQwwgxO.png" "og:image:height": "600" "og:image:type": image/png "og:image:width": "1200" "og:title": "On the Physical Problem of Spatial Dimensions: An Alternative Procedure to Stability Arguments • CBPF Index" "twitter:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_~T24gdGhlIFBoeXNpY2FsIFByb2JsZW0gb2YgU3BhdGlhbCBEaW1lbnNpb25zOiBBbiBBbHRlcm5hdGl2ZSBQcm9jZWR1cmUgdG8gU3RhYmlsaXR5IEFyZ3VtZW50cw%2Ctipo_Physics%2BNote%2Ccor_~I2E4MmMwMA%2Cautores_~Ri4gQ2FydXNvOyBSLiBNLiBYLiBBcmF1am8%2Cdetalhe_1986%2Csecao_Publications%2Cp_Ii9lbi9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmI3ZmQi%2Cs_UjqfViYl1PQwwgxO.png" --- > Index of every page on this site: [llms.txt](https://index.cbpf.br/llms.txt) **Physics Note****Published** # **On the Physical Problem of Spatial Dimensions: An Alternative Procedure to Stability Arguments** **F. Caruso; R. M. X. Araujo** 1986 [**Download PDF **1 MB](https://index.cbpf.br/files/publicacao/6ad2a767639f62b11adbb7fd/pdf) [**Contact owner**](mailto:apub@cbpf.br?subject=On%20the%20Physical%20Problem%20of%20Spatial%20Dimensions%3A%20An%20Alternative%20Procedure%20to%20Stability%20Arguments) ## **Publication details**
Authors
F. Caruso; R. M. X. Araujo
Type
Physics Note
Status
Published
Publication date
1986
Description
Why is space three-dimensional? The first answer, entirely based on Physics, to this question, was given by Ehrenfest in 1971, who showed that the n-dimensional solar system can be stable only for n= 3. Following this approach, Tangherlini showed, in 1963, from quantum mechanics, that this is the case also for Hydrogen atoms. In the present work, we critically review the epistemological consequences of the use of the stability postulate to derive spatial dimensionality. An alternative procedure to get at it, in which the stability postulate (and the implicit singularities in three-dimensional physics) are not an essential part of the arguments, is proposed. We are then led to discuss the n-dimensional quantum theory as expressed in Plank's law, de Broglie relation and Heisenberg uncertainty relation. From these results we discuss a possible experiment, based on thermal neutron diffraction by crystals, to directly measure the dimensionality of space. Also, from the black body-theory, as applied to the Sun, it is shown that the existence of life on Earth is possible only if space, in the neighborhood of the Sun, has been three-dimensional in a cosmic time scale. Finally, the distinguished rôle of Maxwell' s electromagnetic theory in the determination of space dimensionality is stressed. "Metric" versus "topological" arguments are compared and shown to apply respectively to "matter" and "fields".
Year
1986
Number
CBPF-NF-054/86
Linked to a thesis
No
Linked to a grant
No
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