Are space-time dimensions a fundamental property of the universe or an emergent result of other physical laws?

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    $\begingroup$ What do you mean by that? Please elaborate. (Also, why is it labelled projectile?) $\endgroup$ – Sanya Oct 5 '16 at 15:25
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    $\begingroup$ Related: physics.stackexchange.com/q/10651/2451 , physics.stackexchange.com/q/110876/2451 and links therein. $\endgroup$ – Qmechanic Oct 5 '16 at 15:32
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    $\begingroup$ there is no right or wrong answer for that question, as the axioms of any theory can be rearranged into an equivalent one in which the axioms (fundamental properties) are exchanged with the theorems (emergent results). In short, what is fundamental or not is a matter of choice) $\endgroup$ – user126422 Oct 5 '16 at 15:46
  • $\begingroup$ Comment to the post (v5): 1. Are you asking within the setting of superstring theory? 2. Are you asking about all spacetime dimensions? 3. Or are you only asking about the large 3+1 spacetime dimensions? $\endgroup$ – Qmechanic Oct 6 '16 at 13:36
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    $\begingroup$ What experiment could possibly be done to resolve this question? Even if we had a universe-maker and it only produced 3+1 manifolds, how would we know that there is no universe-maker-maker which can give us universe-makers which make 4+1 manifolds? $\endgroup$ – CR Drost Jan 31 '17 at 13:26

The number of spacetime dimensions is set, as far as I know, empirically through observation, although there have been studies arguing this exact question. For instance, I recommend you to have a look at the paper Is the (3+1)−d nature of the universe a thermodynamic necessity?.

There are also studies arguing that the actual number of dimensions of our spacetime is greater than $3+1$. I'm referring to string theories, in which consistency conditions specify the number of dimensions. There is an interesting discussion about this (although very mathematical) here. However, string theorists then use the tool of compactifications to return to a $3+1$-dimensional spacetime.

So, regarding your question, I don't think anybody has ever considered whether the existence of spacetime dimensions is a fundamental property or an emergent result, while the nature of the number of them has attracted attention and there exist theories arguing that it is a fundamental property and theories arguing that it is an emergent phenomenon.

However, I recommend you to also read the topics mentioned by @Qmechanic.

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    $\begingroup$ In Loop Quantum Gravity (the less popular of the two main groups of quantum gravity researchers), the number of space-time dimensions is an emergent quantity. In the other (basically String Theory), the number of space-time dimensions is put in by hand, is generally much greater than 4, and is reduced by one of various means. We don't know which version is true. $\endgroup$ – ohwilleke Nov 19 '16 at 3:11

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