Three spatial and one temporal dimension are physically privileged for stable orbits.
the verdict
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the evidence backs this
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Retrieved physics literature and analyses support the claim that three spatial and one temporal dimension are physically privileged, as other dimensionalities fail to support stable orbits or atomic structures.
# Gravity in other than 3 spatial dimensions and stable orbits
Tags: newtonian-gravity, spacetime-dimensions, orbital-motion, stability
- Score: 29
- Views: 17458
- Answers: 5
- Answered: yes
- Asked by: PixelArtDragon (485 rep)
- Asked: 2013-01-13
- Edited: 2018-08-01
- Site: physics
## Question
I have heard from here that stable orbits (ones that require a large amount of force to push it significantly out of it's elliptical path) can only exist in a three spatial dimensions because gravity would operate differently in a two or four dimensional space. Why is this?
## Answers
### Answer by DilithiumMatrix (score: 36 [ACCEPTED])
Specifically what that is referring to is the 'inverse-square law', nature of the gravitational force, i.e. the force of gravity is inversely proportional to the square of the distance:
$F_g \propto \frac{1}{d^2}$.
If you expand this concept to that of general power-law forces (e.g. when you're thinking about the virial theorem), you can write:
$F \propto d^a$,
Stable orbits are only possible for a few, special values of the exponent '$a$'---in particular, and more specifically 'closed1', stable orbits only occur for $a = -2$ (the inverse-square
# On the dimensionality of spacetime
Classical and Quantum Gravity. Published: 1997-04-01. 136 citations.
## Authors
- Max Tegmark (Institute for Advanced Study): h-index 109; 64,699 citations; corresponding author
## Topics
- Cosmology and Gravitation Theories
- Black Holes and Theoretical Physics
- Earth Systems and Cosmic Evolution
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# arXiv:gr-qc/9702052v2 5 Apr 1997
On the dimensionality of spacetime
Max Tegmark Institute for Advanced Study, Olden Lane, Princeton, NJ 08540; max@ias.edu
Some superstring theories have more than one effective low-energy limit, corresponding to classical spacetimes with different dimensionalities. We argue that all but the 3+1dimensional one might correspond to “dead worlds”, devoid of observers, in which case all such ensemble theories would actually predict that we should find ourselves inhabiting a 3+1-dimensional spacetime. With more or less than one time-dimension, the partial differential equations of nature would lack the hyperbolicity property that enables observers to make predictions. In a space with more than three di mensions, there can be no traditional atoms and perhaps no stable structures. A space with less than three
Cosmic coincidence | New Scientist
WHY do we live in a universe with three dimensions of space and one of time? According to a Swedish physicist, it is because physics in space-times with more or less than four dimensions would not permit the existence of observers like us. “Such universes would either be too simple, too unstable or too unpredictable,” says Max Tegmark of the Institute for Advanced Study in Princeton, New Jersey.
The question of the dimensions of space-time has become important principally because of superstring theories, which picture fundamental particles as tiny pieces of “string” vibrating in space-times with up to 26 dimensions. Theorists say that all but four of those dimensions are rolled up in a strange way so that we are not aware of them, though they have never come up with any compelling reason why this should have happened.
But now, having examined the physics of space-times that do not have three space dimensions and one of time, Tegmark says there are serious problems with all of them (Classical and Quantum Gravity, vol 14, p L69).
Obviously, life as we know it could not exist in a universe with less than three space dimensions, Tegmark says. What
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