Physics NotePublished
On the Physical Problem of Spatial Dimensions: An Alternative Procedure to Stability Arguments
F. Caruso; R. M. X. Araujo
1986
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