spacetime - Can we actually prove with 100% certainty that there are more than 3 dimensions plus time $(t,x,y,z)$?

Can we actually prove with 100% accuracy that there are more than 3 dimensions plus time?

In the news there are always articles like "there are probably 7, 11 or more dimensions", "time is actually not a 4th dimension" etc.

My question is:

Could we be 100% sure that there are more than 3 dimensions and what field of physics except some theoretical or hypothetical branches of physics and mathematics take that in count that there are more than 3 dimensions plus time?

I know the example of a 2D "creature" being unable to see 3D creature (maybe only the interference when the 3d object collide with the 2d world. But I can argue that there are no 2d or 1d beings like in that episode of Star Trek. So, this proof is only an illusion and all we see is 3d and not 1d or 2d. the light itself is bending in space-time depending how the object looks.

I think that 1d or 2d objects can not exist in 3d world at all and it's just an illusion we created, the same way as we speak about 4th,7th etc. dimensions and probably it's all 3d (or chose the name as you wish).

Is this guy correct that 3 dimensions and time is all we need?http://mathematicalmulticore.wordpress.com/2010/04/23/four-dimensions-a-simple-proof/

Could it be that we are creating other dimensions only because we don't understand our Universe good enough?

I mean, don't get me wrong, but the whole 7,11,21,1000-dimensions seems to me like a marketing, something too provincial (as Feynman would say), something like... religion ;D.

Answer

We could easily prove that more than four dimensions exist simply by observing a fifth dimension, but proving that only four dimensions exist is much harder and probably impossible. This is an example of the general case that proving something doesn't exist is usually impossible outside the halls of Mathematics.

I wouldn't stake my life on no proof being possible. It's conceivable that someone might come up with a potentially observable feature of the universe that couldn't exist if there were more than four dimensions. However any such argument would almost certainly require assumptions that could be challenged by the multidimensionalists.

The blog post you link doesn't prove anything. It argues that the observable universe is compatible with there being four dimensions, so extra dimensions aren't necessary, but it gives no proof that extra dimensions can't exist.

Some footnotes:

As far as I know there are no real (as opposed to mathematical) objects with 1 or 2 spatial dimensions. Everything has three spatial dimensions.

Time isn't the fourth dimension, or at least not for us physicists because we usually make time the first dimension i.e. we write spacetime coordinates as $(t, x, y, z, ... )$.