Relativity: Space & Time on a Tempurpedic Mattress?

[Miket123]

In relativity spacetime is usually visualized by placing something on a stretchable fabric of some sort. The object placed on the fabric will bend the fabric, just as a planet or star would in real space. Time can be manipulated when something extremely massive like a black hole is in space. But I was thinking, and please tell me if this could work with relativity, so think of spacetime as a tempurpedic mattress. If I understand relativity correctly usually spacetime would be represented with just a mattress with nothing on it, and when you place an object on it it bends "spacetime". But is it possible that spacetime is actually the tempurpedic mattress with a sheet over it, with the mattress representing space and the sheet representing time or the other way around. If this were possible wouldn't you then be able to manipulate time without changing space which would mean you would not need a very massive object. I am not sure if this is just a stupid question, its just a thought and please let me know what you think.

 

[A.T.]

with the mattress representing space and the sheet representing time or the other way around.

The sheet with a dent represents space (2 dimensions of it). Time is not there at all. You cannot visualize curved 3 dimensions (2 space + time) by embedding them in a 3D diagram. But you can embed curved 2 dimensions:
2 space : the sheet with a dent
1 space + time : http://www.adamtoons.de/physics/gravitation.swf