Spacetime curvature and the force pulling an object down the curvature

In summary, the force pulling an object "down" the curvature of spacetime is due to the geodesics of spacetime.
  • #1
Trevormbarker
67
0
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 vacuum 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 don't see how just the curvature of the spacetime arround it is enough to do this
 
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  • #2


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


sorry if I am 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, what's propelling the apple that hit Newtons head? I don't see how just the presence of the geodesic makes the object go through it
thanks for the quick response though!
 
  • #5


DrGreg said:

Thanks alot. that link was extremely helpfull. And as for the first reply thanks for the help aswell, after reading the web page i realized how great your metaphor was
 
  • #6


Just thinking out loud, this is why our position graph (1d motion) is shaped the way it is?
 
  • #7


Trevormbarker said:
sorry if I am 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, what's propelling the apple that hit Newtons head? I don't see how just the presence of the geodesic makes the object go through it
thanks for the quick response though!

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


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


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

bahamagreen said:
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.
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.

bahamagreen said:
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?
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.

bahamagreen said:
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?
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:
http://www.adamtoons.de/physics/gravitation.swf

And you can switch between visualizing curved 2D-space-time, and curved 2D-space-space, depending what you want to explain:
http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html
 
Last edited:

1. What is spacetime curvature and how does it affect objects?

Spacetime curvature is a concept in Einstein's theory of general relativity that describes how the presence of massive objects can cause the fabric of spacetime to bend. This curvature affects the motion of objects by altering the trajectory of their paths and creating a force that pulls objects towards the source of the curvature.

2. How is the force pulling an object down the curvature related to gravity?

The force pulling an object down the curvature is directly related to the force of gravity. In fact, Einstein's theory of general relativity explains gravity as a result of the curvature of spacetime caused by massive objects. The greater the curvature, the stronger the force of gravity.

3. Is the force pulling an object down the curvature the same as the force of gravity on Earth?

Yes, the force pulling an object down the curvature and the force of gravity on Earth are essentially the same thing. However, on Earth, the curvature of spacetime is caused by the mass of the planet, whereas in other situations, the curvature may be caused by the presence of other massive objects.

4. How does the force pulling an object down the curvature change with distance?

The force pulling an object down the curvature decreases as the distance between the object and the source of the curvature increases. This is because the curvature of spacetime decreases with distance, resulting in a weaker force of gravity. This is why objects appear to fall faster when they are closer to the source of the curvature, such as when an object is dropped from a tall building.

5. Can the force pulling an object down the curvature be counteracted or reversed?

Yes, the force pulling an object down the curvature can be counteracted or reversed by an opposing force, such as the force of thrust from a rocket. This is possible because the curvature of spacetime is not a fixed or absolute concept, and it can be altered by the presence of massive objects or energy. However, in most situations, the force of gravity is dominant and cannot be completely eliminated.

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