The Meaning of Living in 3 Dimensions?

[ronandkryn]

What is the meaning of Living in a World having 3 Dimensions?

As to the guy on the street, how is he affected by being tied to 3 dimensions? Can we make a simplified button list in language that a non scientist can understand?

 

[espen180]

From "spacetime" on Wikipedia:

You can read more http://en.wikipedia.org/wiki/Spacetime#Privileged_character_of_3.2B1_spacetime" on why a different number of spatial/temporal dimentions would cause some strange things to happen.

 

[yuiop]

Wow! That was a stroke of luck that we are there!

 

[bcrowell]

Thanks for pointing us to that, espen180. Very interesting. However, I don't find this particular type of argument from the anthropic principle to be very convincing at all. It's one thing to imagine slightly tweaking a continuous variable such as the fine structure constant. But when we talk about making some radical change, like going to a different number of dimensions, there is no rational way of deciding which other aspects of our own laws of physics ought to be preserved, or which aspects of our own universe's phenomena ought to be preserved (atoms? the periodic table? solar systems? galaxies?). You end up with a "just so" story that explains why ours is the best of all possible worlds. Even in the relatively modest type of anthropic-principle reasoning where all you do is fiddle with continuous parameters, there is a fallacy of only adjusting one parameter without allowing others to vary. If you allow multiple parameters to vary, you may be able to get universes just as congenial to life as ours. E.g., http://arxiv.org/abs/hep-ph/0604027

 

[espen180]

I think what most people do when they consider universes of different dimensionality is to use generealized tensor field equations. For example the assumption that
$$\epsilon_0\nabla_{\mu}E^{\mu}=\rho$$
is still valid for μ=1,2,3,4,...