If space is flat then what is directly under the planets?

[n0sferatu]

I'm reading Parallel Worlds by Michio Kaku and I keep wondering if space is flat, then what would happen if you kept moving directly downward under our solar system (or directly down from any other planet)? What would you see and where would space end or simply curve back around. Thanks!

 

[kleinwolf]

I don't really understand what do you mean with "under" the planet...

 

[Pengwuino]

I think you are talking about the space-time continuum and not the 3d spatial universe. The universe is 3d... spacetime is considered 2d but 1 dimension is space, 1 is time.

 

[Chronos]

Hi n0sferatu! Welcome to PF, where all questions cosmological have been asked, but few answered beyond a reasonable doubt [cosmology is a harsh mistress.] Reaching any putative 'edge' of the universe is not possible. It is receding at the speed of light, so you can't get there from here - or from any other place in the universe. Here is a good place to start - not to mention seeing your tax dollars at work.
http://map.gsfc.nasa.gov/m_uni/uni_101bb2.html

 

[kleinwolf]

I mean under (in physical world, not hierarchical structures) is usually referring to a grav. field, which should be, with your context, given by an outer star or something massive beside the planet you speak about...in the solar system, mercury is under the earth, realtively to the solar system "bottom"/attractive source : the sun.

 

[n0sferatu]

Ok, I think space and space-time is what I'm getting confused. If the orbit of all the planets in our solar system around pluto are at about the same angle, what would happen if we sent a spacecraft 90 degrees from where we usually send it? Like in http://www.enterprisemission.com/_articles/05-14-2004_Interplanetary_Part_1/Solar%20System.jpg, if you picture the orbits of the planet as a flat disc, what is below this disc? More planets, stars, galaxies, etc., right? If space-time is 2D, are there multiple layers of it above and below each other? I'm just having a hard time grasping how the universe is 3D, but space-time is considered 2D? Thanks.

 

[kleinwolf]

Erm, in my view of space-time, it is 4-dimensional (3 spatial direction + time direction). Most of the "time", time is just taken as a kind of parameter you fix...then you get a normal 3d space. I don't know if other people are able to see it as a normal dimension, but within a hyperbolic space ?? (Einstein is sometimes believed to have had that faculty...no proof of course...like everything your brain could percieve or treat..at least i suppose at my stand of knowledge). So it's right, the planets of solar. sys are alomost all lying in the ecliptic plane, but the furthest of them I think to remember, have slighlty inclinated orbits. I don't know if this plane comes from normal attraction between planets for exaplanation of it's presence (the total potential energy should be minimized in the planar conifguration, or something like that ?? i give without any reference..).. I think that often, comets are not coming in the ecliptic, prob. because they come from much further away...

 

[RogerAshford]

Space-time is NOT 2-D, It is 4-D (or, if you include the little curly dimensions beloved of string theorists, 10- or 11-D). Space-time diagrams are usually 2-D (because they are printed on 2-D paper), but only because 2 of the spatial dimensions are suppressed (=ignored).

 

[Labguy]

Flat space does not mean that it is flat like a table top or piece of paper. We can look in all directions and see galaxies out to billions of light years. Flat space is simply a matter of geometry, where the corner angles of a triangle would add to 180 degrees. In the two possible curved shape universes as shown in the link provided by Chronos, a triangles corner angles would not sum to be 180 degrees.

 

[kleinwolf]

By the way, do you know if it is possible to get a quantity which can in certain case obtained only by describing a surface extrinsically : z=f(x,y), instead of intrinsically : metric g(x,y) (does not need the embedding space with z)...or the opposite way. The same question tackled me about hyperbolical Minkowskian space : how is it possible to make a negative metric coefficient, with an extrinsic description of the space-time, because the diagonal metric coefficient are defined as gn=<xn|xn> which can be only negative is the scalar product in the embedding space is itself not positive definite, hence non-euclidean...

Second question : let give a curve (1-dimensional variety). If it is described intrinsically, how do you know you have followed a knotted path or not. Indeed, if the extrinsic description of the curve is given, it is clear that, embedding a curve in a 2D space does not allow knots (because you have to cross the curve itself, which is but allowed in 3 (and upper dimensions)