Spacetime curvature and the force pulling an object down the curvature

1. Sep 10, 2011

Trevormbarker

Spacetime curvature and the force pulling an object "down" the curvature

ok , I have a question about the current model of gravity.
If mass bends spacetime I understand that it accounts for things like how long light takes to travel through its geodesics but "why" does this curvature make objects fall towards the centre, I am having troubles wording my question, pretty much in a vaccum an object (near no other large masses) will not roll down a ramp so why does the curvature of the spacetime arround a massive object pull things inwards, i dont see how just the curvature of the spacetime arround it is enough to do this

2. Sep 10, 2011

Staff: Mentor

Re: Spacetime curvature and the force pulling an object "down" the curvature

Here's an analogy on a curved two-dimensional surface:

Consider two airplanes flying northward from the equator, one along the 10°E longitude line, and the other along the 20°E longitude line. At the equator they are flying parallel to each other. As they proceed further north, without any action by the pilots except to maintain a constant heading, they steadily approach other, and will collide with each other at the North Pole if they arrive there at the same time.

3. Sep 10, 2011

Trevormbarker

Re: Spacetime curvature and the force pulling an object "down" the curvature

sorry if im not just getting this, i understand that though they are parrallel at one point and keep a constant heading the do meet up and if at the same time crash, but the jets are propelling themselves, whats propelling the apple that hit newtons head? I dont see how just the presence of the geodesic makes the object go through it
thanks for the quick response though!

4. Sep 10, 2011

DrGreg

5. Sep 10, 2011

Trevormbarker

Re: Spacetime curvature and the force pulling an object "down" the curvature

Thanks alot. that link was extremely helpfull. And as for the first reply thanks for the help aswell, after reading the web page i realised how great your metaphor was

6. Sep 11, 2011

khemist

Re: Spacetime curvature and the force pulling an object "down" the curvature

Just thinking out loud, this is why our position graph (1d motion) is shaped the way it is?

7. Sep 11, 2011

pervect

Staff Emeritus
Re: Spacetime curvature and the force pulling an object "down" the curvature

The geodesics are not just spatial, they are "space time" geodesics.

You always progress through time at 1 second per second, even if you're not "moving".

8. Sep 11, 2011

bahamagreen

Re: Spacetime curvature and the force pulling an object "down" the curvature

The analogies always seem to have some flaw.

The rubber sheet of "space" dimpled with heavy balls implies that the balls are pressing against and deforming the sheet because of some force... perpendicular to the normal plane of the sheet... as if there is an additional requirement for there to be gravity pulling the balls into the sheet. So gravity within the space sheet is "explained" or modeled by requiring an additional assumption of something suspiciously like gravity from outside the sheet.

The "parallel" airplane flights along the latitudes breaks the stipulation that the flights are parallel straight lines; in fact they are contant radius curves clearly going from the equator to the pole. True straight lines would be tangent to the Earth's surface and if parallel at the beginning would remain equidistant throughout.

Even if the path of motion through the curved space is accepted as describing the appearance of gravitational interaction, what about an object that is not moving along the curve? What instigates it's motion if moving along the curve is "forceless"?

Are there any analogies that do not ask one to forgive the violations of geometry or confound the measurements in one frame of dimensions with another?

There is so much effort and thought spent on making sure that novice relativity thinkers do not confound measures from different inertial reference frames, not confuse definitions and measurements of distance, time, and simultaneity, and in general not bring the classical and perceptual bias into their analysis of relativity phenomenon.

Yet, when offering the usual analogies, it is just these assumptions and misapprehensions that are required in order for the mechanism of the analogy to serve its demonstration.

Again; has anyone ever created or run across any physical analogies for relativistic phenomenon that truly do not ask us to contort and violate dimensional levels - showing "N"D as a ("N"-1)D model - without breaking the geometric properties of the "N"-1 dimension?

Or is there a proof that using the next lower dimension to model the higher will always result in these inconsistencies?

9. Sep 16, 2011

A.T.

Re: Spacetime curvature and the force pulling an object "down" the curvature

That is a bad one indeed. And unfortunately the most popular one.

But that is the point of this analogy: The lines of longitude start out parallel at the equator, they are straight within the 2D surface, and yet they cross.

The universal advance trough spacetime is simply postulated by the model, and always applies to all objects. There are no objects that don't advance trough spacetime in this model.

The problem is that even flat 4D spacetime is hard to visualize. Curved 4D even more so. You have to reduce it to curved 2D, so you can embed it in Eucleadian 3D.

So far the best analogy I know is the one posted already:
http://www.relativitet.se/spacetime1.html

You can extend it to include to interior of the planet: