Question

My question is little bit philosophical. I would like to explain my ideas with a 2 dimensional universe model.

If we had lived in 2 dimensional universe like a plane, What could we observe when seeing a 3d object?

For example: If a square pyramid that is inside full of material comes to the plane universe in right angle, what could the people who live in 2d universe observe? Firstly, we could see small square and slowly it would enlarge and then it would dissappear suddenly. If the scientists who live in the 2d universe observed such event , All scientists could get shocked and they could check their physics formulas because energy is not conversed in that event. They had believed that Energy is conserved and nobody could create energy from nothing and finally they could understand that total observed universe energy can be much more what they calculated with their formulas.

My questions:

What could we see a 4d pyramid comes to our 3d universe? is it correct that Firstly we would see small cube and it would enlarge and then suddenly disappears?

Dark matter and Dark energy is related with such ideas? http://map.gsfc.nasa.gov/universe/uni_matter.html

I know we do not observe such strange events till now but maybe scientists can get some results during micro experiments. Is there any such experimental results at least in micro universe (atomic level experiments in quantum mechanics)?

Sorry for your time if it was asked before.

Answer 1

This idea is explored at great length in the novella "Flatland", which is a classic of pedagogical mathematics. It was published in the late 19th century, and the themes reappear in H.G. Welles "The Time Machine", and in Einstein's relativity. The four-dimensional pyramid will, if it crossed our 3-dimensional universe, as a cube growing from a point, then suddenly vanishing.

With modern computers, it is very easy to simulate four dimensional objects in various 3d projections (then in 2d projection to the screen). These simulations are useful for building up the intuition for higher dimensional spaces.

But as physics, it is impossible to miss a fourth dimension: we would observe objects escaping our plane! This would reveal itself as missing energy in high energy collisions, assuming that it takes a large amount of energy to leave our three-dimensional plane, because we are bound to a surface. These types of ideas became current in variations of Randall Sundrum and Arkani-Hamed,Dvali,Dimopoulos models in the last decade. These are infinite extra dimensions scenarios, and they predict that gravity at long distances will fall off as a different power. This is generally impossible to reconcile with cosmology.

The large-extra-dimension ideas are ruled out with scientific certainty by the observations consistent with a high Planck scale. This includes tiny neutrino masses, lack of proton decay, absence of strong CP violation, absence of electroweak corrections like magnetic moments or non-renormalizable W and Z interactions, absence of direct lepton-quark coupling, and a few other things I can't remember. These issues are discussed here: Can black holes be created on a miniature scale? .