Why does the bending of space necessitate gravitational effects

[Padraic]

I understand that space is curved inwards by the mass of the planet and I understand how curved space could redirect things towards the planet when they are moving. What is strange to me is the idea that curved space time itself could move me towards the earth. Gravity it seems to me is an actual pull towards the earth, while curved space-time would seem more like a redirection of force rather than a force itself capable of pulling me back down when I jump in the air. If you guys could explain what I'm misunderstanding that would be great.

 

[gatz]

I believe GR states the converse; curvature of spacetime does not necessitate gravitational effects, but rather, gravity curves spacetime. This resulting curvature leads to, as you said, the direction of moving objects to the mass.
The gravitational effects are simply the direct product of gravity, space time would not be curved without there being mass.

 

[Padraic]

That makes much more sense to me but at the same time I hear different things. For instance Wikipedia says this:

"Modern physics describes gravitation using the general theory of relativity by Einstein, in which it is a consequence of the curvature of spacetime governing the motion of inertial objects."

And Brian Green has both stated that the moon is held in orbit by the curvature of space time and that it is held in place by the power of gravity so that would seem to imply that he's saying they are the same thing.

 

[gatz]

What is key to understanding GR is that in Newtonian mechanics, a force initiates acceleration; in the case of a gravitational field in Newtonian mechanics, all points a have a force vector. However, in Einsteinian mechanics, gravitation curves spacetime in a way such that motion occurs without an applied force. Meaning that for a free-falling body, it is as natural to fall towards the mass as it is to move forward in time.

 

[Trevormbarker]

curving of space-time! not just space, you are always progressing through the time dimension of space time, hopefully that clarifies this!

 

[Padraic]

What is key to understanding GR is that in Newtonian mechanics, a force initiates acceleration; in the case of a gravitational field in Newtonian mechanics, all points a have a force vector. However, in Einsteinian mechanics, gravitation curves spacetime in a way such that motion occurs without an applied force. Meaning that for a free-falling body, it is as natural to fall towards the mass as it is to move forward in time.

And then me lifting me arm up is me resisting that general current headed down towards the earth?

I understand that. It still seems like there's a piece missing when things just naturally move along something rather than needing a force to move them.

curving of space-time! not just space, you are always progressing through the time dimension of space time, hopefully that clarifies this!

But how does traveling through time produce motion? I know they're linked and that traveling through space slows time (according to Brian Green) but how does traveling through time produce motion through space?

 

[Trevormbarker]

when we travel forwards through time we ARE experiencing some kind of motion. Mass and energy bends space-time not just space. I think what you are asking is similar to this: having a ramp in space and placing a ball on the top, the ball would not roll down the ramp. So you are asking what provides the force to "push" objects down the curved space. but its space-time not just space!

 

[A.T.]

how does traveling through time produce motion through space?

http://www.physics.ucla.edu/demoweb/demomanual/modern_physics/principal_of_equivalence_and_general_relativity/curved_time.gif

From:
http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html

 

[Padraic]

when we travel forwards through time we ARE experiencing some kind of motion. Mass and energy bends space-time not just space. I think what you are asking is similar to this: having a ramp in space and placing a ball on the top, the ball would not roll down the ramp. So you are asking what provides the force to "push" objects down the curved space. but its space-time not just space!

Yes that's exactly what I'm saying, the ramp analogy is perfect. I understand that there is space-time but why would time cause me to move in one direction as opposed to another? Time physically moves us along the curvatures of space? When I lift my arm up in the air I'm resisting where time naturally is sending me? When I resist gravity I'm resisting time's pull in a direction?

http://www.physics.ucla.edu/demoweb/demomanual/modern_physics/principal_of_equivalence_and_general_relativity/curved_time.gif

From:
http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html

That is just so weird.

 

[Tea Jay]

I think you always follow the path of least resistance...so, if you are on the surface of a ball, say the earth, and travel in "A straight line from the north pole to the south pole", you don't remember not going in a straight line...but, you went in as straight a line as far as the compass was concerned.

So, if you are "falling" you follow the path of least resistance, but if space-time is shaped so as to make your path curved towards a source of gravity...your fall towards that gravity might be as direct as your straight line from the north pole to the south pole.

IE: Straight to you, but curved if viewed from the proper perspective.

 

[gatz]

Newton stated that an object would need to be subjected to a force to deviate from its straight-line path whereas Einstein stated that an object would need to be subjected to a force to deviate from a geodesic.
For the example of your arm, your moving it upwards means you have taken the longer route in space time from time1 to time2.

Newton described gravity as a force because it caused objects to deviate from the straight-line path. Einstein described gravity as a condition of spacetime; the tendency of objects to take the shortest path from point a to point b.

 

[Trevormbarker]

Yes that's exactly what I'm saying, the ramp analogy is perfect. I understand that there is space-time but why would time cause me to move in one direction as opposed to another? Time physically moves us along the curvatures of space? When I lift my arm up in the air I'm resisting where time naturally is sending me? When I resist gravity I'm resisting time's pull in a direction?



That is just so weird.

It is wierd, but that's how it works! I can't seem to find it now but i was stuggling with this awhile ago and one of the mentors gave me an awesome link. But anyways yeah that's relitivities theory on it! I think it is important to understand that it is space time that is curved, not space and once you think about this the answer should start to make more sense.

 

[Padraic]

I think you always follow the path of least resistance...so, if you are on the surface of a ball, say the earth, and travel in "A straight line from the north pole to the south pole", you don't remember not going in a straight line...but, you went in as straight a line as far as the compass was concerned.

So, if you are "falling" you follow the path of least resistance, but if space-time is shaped so as to make your path curved towards a source of gravity...your fall towards that gravity might be as direct as your straight line from the north pole to the south pole.

IE: Straight to you, but curved if viewed from the proper perspective.

But if I put a pencil in the air it should stay in the air unless it is moved in which case it would fall along that path of least resistance to the earth. I follow the idea of the path of least resistance but if I'm simply suspended in air I shouldn't fall to the ground until I try to move in a particular direction. So is it really time that is causing me to move along that path of least resistance?

Newton stated that an object would need to be subjected to a force to deviate from its straight-line path whereas Einstein stated that an object would need to be subjected to a force to deviate from a geodesic.
For the example of your arm, your moving it upwards means you have taken the longer route in space time from time1 to time2.

Newton described gravity as a force because it caused objects to deviate from the straight-line path. Einstein described gravity as a condition of spacetime; the tendency of objects to take the shortest path from point a to point b.

Even if it is the longer path why would it get sent back down once it's there? Why shouldn't it just stay there?

 

[Padraic]

It is wierd, but that's how it works! I can't seem to find it now but i was stuggling with this awhile ago and one of the mentors gave me an awesome link. But anyways yeah that's relitivities theory on it! I think it is important to understand that it is space time that is curved, not space and once you think about this the answer should start to make more sense.

I guess. Still weird though.

 

[Padraic]

If there was a point in space where it wasn't curved by anything what direction would time move you.

 

[gatz]

Even if it is the longer path why would it get sent back down once it's there? Why shouldn't it just stay there?

Because just as the the shortest path from time1 to time2 was towards the mass, it will always be the shorter path to go towards the mass. The reason your arm doesn't just stay there is because staying in the same place from time1 to time2 is the longer path in 4-D spacetime.

 

[gatz]

If there was a point in space where it wasn't curved by anything what direction would time move you.

If there was absolutely no curvature, progression in time would still leave you in the same place. In classical mechanics, you would say there is no force acting on you so you would remain at rest.

 

[Padraic]

Well I guess that answers all my questions about gravity. Thanks guys.

 

[A.T.]

But if I put a pencil in the air it should stay in the air unless it is moved

No, because the pencil still moves along the time-dimension. And if space-time is curved it will deviate from that direction, and start moving along the spatial dimensions as well. Here is a rocket (engines are off) instead of a pencil:
http://www.adamtoons.de/physics/relativity.swf
Set initial speed to 0 and gravity to something other that 0 to simulate free fall from intial rest.

If there was a point in space where it wasn't curved by anything what direction would time move you.

If space time is not curved you keep your initial direction in space time, when free falling. If you start out at rest in space, advancing only along the time dimension, you keep doing so.

 

[Padraic]

I've finally got it down in my mind. Cool link btw.