Questioning 3D Model views of effect of large bodies on curving space.

[MiguelCapelo]

Hi everyone. I am not a physicist or scientist but this is a question I have pondered for a while now.

Everytime I see a model of how large bodies (eg Earth and sun) bend the planar representation of space (creating a "cup" or "dip") I always feel that this is not completely representative. Is it just me that thinks a better representation would be if the large bodies were enveloped in a tight fitting stocking thus allowing the "dips" or bends to be up and down as well instead of just left, right and down ?

In my small mind this "stocking" that envelops EVERYTHING might be an attempt at a theory of everything ie the stocking envelopes the galaxy finger print, the gravity fingerprint, the planet fingerprint, the human fingerprint, the molecular finger print, the atomic fingerprint, the neutron/proton/electron fingerprint, the quark fingerprint and finally arriving at one single string doubling in over itself to form the STOCKING of everything. the alpha and omega, if you wish, is the tubular membrane of the stocking formed by the string.

A black hole in space would be a pinch of the 2 membranes of the stocking almost like if we pinch the 2 membranes and pull them out together to form a single "pinch" of the double membrane.

I don't feel I am a genius or special in anyway, just asking people more knowledgeable than myself something that has had me thinking for a long while.

Kind Regards

Miguel Capelo

 

[Mordred]

what you describing is just a simplified image of spacetime curvature, to attempt to draw how it actually would behave would be too complex. The images is just the x,z influences. Your right that gravity would also include the y axis. The visualization is merely a tool to help visualize curvature.

 

[Chalnoth]

Basically, it is fundamentally impossible to properly visualize the curvature of three-dimensional space in three dimensions. So the visualizations they provide are taking a two-dimensional slice, and then projecting that slice into three dimensions so you can see its curvature.

Sort of. I don't think they usually are that accurate in terms of precisely how the curvature is shown. But the general picture they present is usually correct, if you understand that that's what any two-dimensional slice through the massive body looks like in terms of its curvature.

 

[PeterDonis]

Everytime I see a model of how large bodies (eg Earth and sun) bend the planar representation of space (creating a "cup" or "dip") I always feel that this is not completely representative.

You're right, it's not. There are two main reasons why not:

(1) The representation is only of space curvature, not spacetime curvature. It represents the curvature of a spacelike slice of constant time, in a region of spacetime that is static--nothing is changing with time. (Of course this is an idealization, but that's all that this representation can show.)

(2) The representation, as others have pointed out, is only of a two-dimensional spacelike surface; it doesn't include the third spatial dimension. This works because the space being represented is spherically symmetric, so all the information about how the space curves can be represented using a curved two-dimensional surface. A space that isn't perfectly spherically symmetric can't be represented this way.

Is it just me that thinks a better representation would be if the large bodies were enveloped in a tight fitting stocking thus allowing the "dips" or bends to be up and down as well instead of just left, right and down?

Yes. I don't see how such a "stocking" representation would do a better job, because it wouldn't be any better with respect to either of the above issues. As others have pointed out, there's no way to directly visualize the curvature of a four-dimensional spacetime. To really understand it, you need to work out the math involved and understand what the math is representing physically.