Why Objects Move: The Role of Space in Motion Explained

[FallenApple]

So an explanation I heard is that objects move not according to a gravitational force and that the objects move along geodisics within the curved space time caused by the energy the larger object( the thing causing "gravity")

But this doesn't explain why things move without a force. Is it that space itself is moving, bringing everything with it?

Kinda like me moving a picture frame, and everything in the picture changes location relative to where they were before(but not reletive to the frame itself), where the frame is like space, and the things inside it are like objects.

 

[A.T.]

But this doesn't explain why things move without a force.

Things move without a force in Newtonian mechanics already. No reason is given, it's just what we observe. The difference to GR is shown here:

 

[alw34]

Newton's laws of motion are summarized here:
http://csep10.phys.utk.edu/astr161/lect/history/Newton3laws.html

In Einstein's general relativity, which describes gravity, gravity is not considered a force. On the other hand, for example, charged particles are attracted or repelled by a mechanism considered to be a 'force', electromagnetism. Either mechanism, gravity or electromagnetism, may accelerate objects and cause motion.

"Free fall" of a test particle in general relativity [GR] means being on a geodesic. But massive objects, such as the Earth and sun rotating about each other, do follow exact geodesics. Objects subject to other forces, such as that of jet engines on a plane, may obviously change trajectories from geodesic motion.

Is it that space itself is moving, bringing everything with it?

What you may be getting at here is that space and time are BOTH curved [distorted] in GR. So the Earth 'falls' in a curved trajectory around the sun, and to a lesser extent, vice versa, due to curvatures in space and especially time.

Exactly WHY all mass has gravitation is unknown. It's an observed effect for which Einstein described, and predicted some new, effects, but not causes.

 

[FallenApple]

Newton's laws of motion are summarized here:
http://csep10.phys.utk.edu/astr161/lect/history/Newton3laws.html

In Einstein's general relativity, which describes gravity, gravity is not considered a force. On the other hand, for example, charged particles are attracted or repelled by a mechanism considered to be a 'force', electromagnetism. Either mechanism, gravity or electromagnetism, may accelerate objects and cause motion.

"Free fall" of a test particle in general relativity [GR] means being on a geodesic. But massive objects, such as the Earth and sun rotating about each other, do follow exact geodesics. Objects subject to other forces, such as that of jet engines on a plane, may obviously change trajectories from geodesic motion.
What you may be getting at here is that space and time are BOTH curved [distorted] in GR. So the Earth 'falls' in a curved trajectory around the sun, and to a lesser extent, vice versa, due to curvatures in space and especially time.

Exactly WHY all mass has gravitation is unknown. It's an observed effect for which Einstein described, and predicted some new, effects, but not causes.

So is it like a generalized version of Newton's law of intertia? Since gravity is not a force, then the object that moves in a curved spacetime isn't really accelerating relative to it's own frame of reference. Then relative to its own frame of reference, it moves in a straight line at constant velocity?
So mass is just something that distorts spacetime. So then there are only 3 fundamental forces of the universe?

 

[FallenApple]

Things move without a force in Newtonian mechanics already. No reason is given, it's just what we observe. The difference to GR is shown here:

So according to the video, the motion is just the law of inertia under a curved space time. Does that mean the appearent acceleration is only observed from an external frame of reference? That in its own frame of reference, it's not accelerating at all, just moving straight. Like Newton's first law.

 

[FallenApple]

Also, there is the phenomenon of acceleration under curved spacetime as observed by someone outside of the frame of reference of the accelerating object.

I tried to picture it as a number line with evenly spaced tics. 1, 2, 3, 4, 5 for example. Where the tics represent meters( or any other unit of space)

If near one, there is a high gravitational source. then the the space near the source would be more warped. 1,2, 3, 4, 5.

So as a object moves from 5 to 1, it seems to be accelrating, only because its passing the earlier tics more often per unit time.( assuming the time is not cruched up in the same proportion as the space). Or if the time is warped more than the space, then the passage from 5 to 1, even it they are evenly space, will still give raise to the appearance of acceleration.

And under uncurved spacetime, an object starting at 5 will move to 1 with constant velocity since no warping occurs in either space nor time. i.e 1, 2, 3, 4, 5 with equaliy spaced tics between them in space and time.Is this right way to conceptualize the acceleration?

 

[A.T.]

Does that mean the appearent acceleration is only observed from an external frame of reference?

The observed coordinate acceleration (dv/dt) of a falling object, is due to the non-inertiality of the surface frame of reference, which has a proper acceleration upwards (as an acclerometer resting on the surface will show).

That in its own frame of reference, it's not accelerating at all, just moving straight.

In its own frame of reference, everything is at rest, not moving at all.

But in any local inertial frame the falling apple is moving straight. The apple has zero proper acceleration (as an accelerometer attached to it would show).

 

[alw34]

then the object that moves in a curved spacetime isn't really accelerating relative to it's own frame of reference.

Here are a few shortcuts, 'tricks', to remember a few basics of relativity, thanks to experts here, like Dr.Greg, A.T.,bcrowell, Peter Donis and others. You can search 'relativity' and their names here for many details;there may also be FAQ's of interest.

[1] It took Einstein ten years to formulate GR. And he did not know all the math himself; he had help. So it's complicated and takes time to understand, especially the finer points. No one has yet been able to combine GR with the three 'forces' [of the Standard Model of particle physics]; GR is unique. A key aspect of GR is a special geometrical 'curvature'.

[2] Acceleration. To answer your question I quoted in this post, do you feel "acceleration" when you are in free fall? That is, does an accelerometer measure acceleration? No. In contrast, imagine sitting at your computer right now, do you feel a force on your backside? THAT's acceleration in relativity! Just like when you fall down on ice and hit the ground; the 'acceleration' is when you stop and say 'ouch'. That's a different view from Newton's. In GR, you are accelerating when you are not following a 'geodesic' [that's an idealization].

[3] Gravity is a geometrical framework involving very special descriptions of space and time 'distortion', that is, special types of curvature. Consider everyday flat graph paper with a square grid pattern and a path of some object, a 'worldine'...a path through space and time, say 'x' versus 't', a plot of d=vt if you like .

[a] A flat graph paper with square grids frame is inertial motion in SR. The object moves in a straight line.
[These are the "Minkowski' flat coordinates of 'spacetime' of SR; Even Einstein did not at first realize how important it was; Herman Minkowski, a I think Einstein's former math professor pointed it out and Einstein wisely adopted it.]

If you accelerate in SR, the grid squares on the flat graph now appear distorted. That is, a non inertial [accelerating] observer will draw a curved grid on flat graph paper.

[This is why the speed of light in SR looks different from 'c' to an accelerating observer: To the accelerating observer the light appears to be crossing non square, different size grids!.

[c] With gravity, the graph paper reference frame itself is curved in a special way, NOT like at the end of AT's posted illustration. [I'm not sure what the cylinder and cone are supposed to illustrate there...that is not gravity.] This special curvature of GR manifests in such a way that the graph paper cannot be flattened out, say on a table, without further distorting it...visualize a partially crumpled graph paper for example. Gravitational curvature is that special kind of 'distortion', not a rolled up version of flat graph paper into either a cylindrical or a conical shape.

So is it like a generalized version of Newton's law of intertia?

From my notes of an earlier discussion:
Dalespam: One of the great theoretical accomplishments of GR is to unify inertia and gravity. Prior to Einstein it was recognized that the passive gravitational mass was equal to inertial mass, but it was not known why. Afterwards, it became clear that they must be equal since gravitation is inertia in curved spacetime

 

[PeroK]

But this doesn't explain why things move without a force. Is it that space itself is moving, bringing everything with it?
.

It helps to know more about classical, Newtonian physics as well. Newton's laws only apply in inertial reference frames. The centrifugal and Coriolis forces are not real forces, yet they make things move.

Imagine you and your friend are in a spinning circular room, like something at a fairground, with your backs pressed against the wall. A door opens behind your friend and he flies out. But there was no force on him. In fact, it was the absence of a force that made him fly out!