Answers in search of a question: ‘proofs’ of the tri-dimensionality of space

Callender, Craig

doi:10.1016/j.shpsb.2004.09.002

Cited by 36 publications

(16 citation statements)

References 18 publications

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“…The need for understanding this aspect of our universe can be tracked to the ancient Greece [24]. In modern times, this problem was first studied by Kant in 1746 [25] and later, among others, by Ehrenfest in 1917 [26], Barrow in 1983 [24], Brandenberger and Vafa in 1989 [6] and Tegmark in 1997 [27] (see also [19,[28][29][30]). …”

Section: Introductionmentioning

confidence: 99%

A Possible Cosmological Application of Some Thermodynamic Properties of the Black Body Radiation in n-Dimensional Euclidean Spaces

González-Ayala

Pérez-Oregon

Cordero

et al. 2015

Entropy

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In this work, we present the generalization of some thermodynamic properties of the black body radiation (BBR) towards an n-dimensional Euclidean space. For this case, the Planck function and the Stefan-Boltzmann law have already been given by Landsberg and de Vos and some adjustments by Menon and Agrawal. However, since then, not much more has been done on this subject, and we believe there are some relevant aspects yet to explore. In addition to the results previously found, we calculate the thermodynamic potentials, the efficiency of the Carnot engine, the law for adiabatic processes and the heat capacity at constant volume. There is a region at which an interesting behavior of the thermodynamic potentials arises: maxima and minima appear for the n-dimensional BBR system at very high temperatures and low dimensionality, suggesting a possible application to cosmology. Finally, we propose that an optimality criterion in a thermodynamic framework could be related to the 3-dimensional nature of the universe.

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Section: Introductionmentioning

confidence: 99%

A Possible Cosmological Application of Some Thermodynamic Properties of the Black Body Radiation in n-Dimensional Euclidean Spaces

González-Ayala

Pérez-Oregon

Cordero

et al. 2015

Entropy

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“…The 3-dimensional Coulomb force can be generalized to n-dimensional Euclidean space, by means of Gauss' law using the generalized area  A n1 as derived in [3].…”

Section: Novel Virial Theorem Analysismentioning

confidence: 99%

“…Callender in his penetrating review and critique [3] concludes that n-space arguments based on orbital stability of either planets or atomic orbital electrons fall short of the mark in asserting that space must be three-dimensional. He asserts that the often repeated claim that stable orbits are possible in only three dimensions is not even remotely established.…”

Section: Introductionmentioning

confidence: 99%

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Why observable space is solely three dimensional

Rabinowitz¹

2014

astp

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Quantum (and classical) binding energy considerations in n-dimensional space indicate that atoms (and planets) can only exist in three-dimensional space. This is why observable space is solely 3-dimensional. Both a novel Virial theorem analysis, and detailed classical and quantum energy calculations for 3-space circular and elliptical orbits indicate that they have no orbital binding energy in greater than 3-space. The same energy equation also excludes the possibility of atom-like bodies in strictly 1 and 2-dimensions. A prediction is made that in the search for deviations from  r 2 of the gravitational force at sub-millimeter distances such a deviation must occur at < ~  10 10 m (or <   10 12 m considering muoniom), since atoms would disintegrate if the curled up dimensions of string theory were larger than this. Callender asserts that the often-repeated claim in previous work that stable orbits are possible in only three dimensions is not even remotely established. The binding energy analysis herein avoids the pitfalls that Callender points out, as it circumvents stability issues. An uncanny quantum surprise is present in very high dimensions.

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“…But there are some features that we discuss below that, to our knowledge, have not been drawn out in detail in the literatureincluding, for instance, the status of the initial value formulation and the non-existence of 4 See, for instance, Brunetti et al (2012), Rejzner (2016), and Feintzeig (2016c,b). 5 To our knowledge, the projects that come closest to this strategy are those that evaluate arguments that spacetime must have a certain dimensionality (Callender, 2005); or those that consider the details of constructive quantum field theory, which often considers lower-dimensional models (Ruetsche, 2011;Hancox-Li, 2017). 6 See, for instance, Glimm and Jaffe (1987); for a discussion of quantum gravity in particular, see Carlip (2003).…”

Section: Introductionmentioning

confidence: 99%

Would two dimensions be world enough for spacetime?

Fletcher

Manchak

Schneider

et al. 2018

Studies in History and Philosophy of Science Part B: Studies in

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We consider various curious features of general relativity, and relativistic field theory, in two spacetime dimensions. In particular, we discuss: the vanishing of the Einstein tensor; the failure of an initial-value formulation for vacuum spacetimes; the status of singularity theorems; the non-existence of a Newtonian limit; the status of the cosmological constant; and the character of matter fields, including perfect fluids and electromagnetic fields. We conclude with a discussion of what constrains our understanding of physics in different dimensions. (James Owen Weatherall) 1 For background on geometrized Newtonian gravitation, see Trautman (1965) and (especially) Malament (2012, Ch. 4). For projects that aim to use this theory to provide new insight into general relativty, see, for instance,

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Answers in search of a question: ‘proofs’ of the tri-dimensionality of space

Cited by 36 publications

References 18 publications

A Possible Cosmological Application of Some Thermodynamic Properties of the Black Body Radiation in n-Dimensional Euclidean Spaces

A Possible Cosmological Application of Some Thermodynamic Properties of the Black Body Radiation in n-Dimensional Euclidean Spaces

Why observable space is solely three dimensional

Would two dimensions be world enough for spacetime?

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