Why 3 spatial dimensions?

[Martin]

So far no kind of string theory-under-construction or any approach to Quantum Gravity has offered an explanation for why there are visibly 3 spatial dimensions.

 

If a theory has, say, 11 dimensions it will not explain why 7 remain rolled up out of sight and just 3 + 1 come out in plain view.

 

Other Quantum Gravity approaches do not need extra (rolled up) dimensions but instead they work all right with just 3 + 1, or any number

indiscriminately.

They dont explain why it happens to be 3 + 1.

 

So this is a problem that some smart people have been working on in QG. If we had a really good quantum theory of spacetime, they say, then it would explain not only gravity but also why the world has 3 spatial dimensions.

 

This thread is to collect links to mathematical physics papers which tackle this problem. If you have run across a journal article bearing on this problem of "why three spatial dimensions and not some other number?"

please put a link.

 

I have seen some, so I'll try to find the links.

[Martin]

this is one by a Cambridge guy Hendryk Pfeiffer

http://arxiv.org/abs/gr-qc/0404088

Quantum general relativity and the classification of smooth manifolds

 

---quote---

...It turns out that differential topology distinguishes the space-time dimension d=3+1 from any other lower or higher dimension...

---end quote---

[fuhrerkeebs]

I've always thought it's because life is possible in any number of dimensions less than 3...and the more dimensions there are the more chaotic behavior becomes...so 3 physical dimensions seems to be the optimal choice for a universe to sustain life. And if you take the existence of the multiverse as an axiom, you can say we are here to question why we live in 3 dimensions because we live in 3 dimensions. It's more of an "I'm lucky to have been in this world" type of thing...that's my opinion atleast...

[Martin]

I've always thought it's because life is possible in any number of dimensions less than 3...and the more dimensions there are the more chaotic behavior becomes...so 3 physical dimensions seems to be the optimal choice for a universe to sustain life. And if you take the existence of the multiverse as an axiom, you can say we are here to question why we live in 3 dimensions because we live in 3 dimensions. It's more of an "I'm lucky to have been in this world" type of thing...that's my opinion atleast...

 

hello Keebs,

I have had those kind of thoughts too

it is sometimes called a version of the "anthropic principle"

but the trouble is it is not predictive in such a way as to make it falsifiable the way a normal scientific theory has to be

 

a normal scientific theory bets its life constantly on its predictions. If in some future experiment you get results different from what it predicted then the theory is shot down

 

the "anthropic principle" model just says Whatever. whatever turn out from any experiment it must be right because we are here and the world has to be right for us to be here. So it can accommodate any outcome of any experiemnt without batting an eye. this means that it predicts nothing So it is bogus---anything that depends on invoking the A.P. is not part of empirical science. (it can still be good religion or philosophy or poetry, just not science)

 

this is why people have been making a gigantic stink over the past year's behavior of Leonard Susskind. the harder-headed string people seem opposed to taking the easy way out and invoking A.P which is seen as a diminishment or a defeat.

 

Fortunately Smolin recently came out with "Scientific Alternatives to the Anthropic Principle" which does some of the good Multiverse things but makes predictions which enable it to be falsified if some future observation turns up such and such size neutron star and so on.

 

I'd say dont give up on the possibility that a quantum theory of space and time (which is what Quantum Gravity is) will explain its dimensionality as so many other aspects of nature have been explained.

 

Cant say why I feel so confident about this, just do.

 

Come to think of it, it might even be possible to get d = 3+1 out of Smolin's evolutionary Multi. In which case it would already come with predictions to check experimentally.