Why would it moves in the first place ?

[killium]

It is said that objects in free fall passively follows the geodesics of space-time. If space-time is curved at some random place, due to the presence of a nearby gravitationnal field, the object will continue to follow the straight path of the geodesics, which will appear as a curved trajectory for us. This is the official explanation for how does gravity works and it describes very well HOW objects moves in a gravitationnal field. But to my ears, this is an incomplete explanation. It doesn't explain WHY an hypothetical stationnary object would START to move in the first place. I take it like this: if the train moves and the tracks are curved, the train will turn. But if the train is at rest, it takes more than curved tracks to make it moves....

 

[SpeedFreek]

Because nowhere is space-time completely flat, except in an empty universe.

 

[centsworth_II]

...It doesn't explain WHY an hypothetical stationnary object would START to move in the first place.....

It may be harder to explain how you could find an absolutely stationary object in the universe. The best you could do is find an object that is stationary in relation to some other object, or frame of reference.

It seems that everything has been moving since the Big Bang. In theory, tiny quantum fluctuations at the moment of the Big Bang were magnified into slight irregularities in the distribution of matter and energy. These irregularities led to clumping which led to the formation of galaxies, stars, planets, etc. As matter clumped, irregularities of mass distribution in the clumps led to rotation about centers of mass. Forming clumps affected the motions of other, nearby forming clumps.

So, motion of all matter is a consequence of quantum irregularities at the time of the Big Bang.

 

[killium]

...It doesn't explain WHY an hypothetical stationnary object would START to move in the first place.....

It may be harder to explain how you could find an absolutely stationary object in the universe. The best you could do is find an object that is stationary in relation to some other object, or frame of reference.

yes, that's what i meant, suppose one object is the Earth, and the other is a rock your holding at 5' high. Why does it start moving towards the center of the Earth when you free it ? there must be something more than curved space for that to happen, no ?

 

[kelvinzero]

It is said that objects in free fall passively follows the geodesics of space-time. If space-time is curved at some random place, due to the presence of a nearby gravitationnal field, the object will continue to follow the straight path of the geodesics, which will appear as a curved trajectory for us. This is the official explanation for how does gravity works and it describes very well HOW objects moves in a gravitationnal field. But to my ears, this is an incomplete explanation. It doesn't explain WHY an hypothetical stationnary object would START to move in the first place. I take it like this: if the train moves and the tracks are curved, the train will turn. But if the train is at rest, it takes more than curved tracks to make it moves....

Here is my partially informed guess:

When you say something is 'stationary in space' what you mean is it's position is not changing with respect to time.

Dont consider a particle as moving though space-time. Instead consider that particle as inhabiting a curve through space-time. A totally stationary particle, in the absence of any gravity, still has such a curve. In this case its curve is a perfectly straight line aligned with the time axis. If a particle only inhabited a single point in space-time, that would imply it only existed for one instant.

A totally stationary particle in the presence of a stationary gravity well has a curve that has the same position coordinates as that gravity well for some certain time coordinate 'in the future'.

Also remember that a particle with the same position and direction of motion in space but a different speed has a different direction in space-time, which is why its curve describes a totally different motion.

 

[centsworth_II]

....suppose one object is the Earth, and the other is a rock your holding at 5' high. Why does it start moving towards the center of the Earth when you free it ? there must be something more than curved space for that to happen, no ?

I don't think so. The force (or space-time curve) that moves the rock toward the Earth's center is acting on the rock the entire time you are holding it. You are exerting enough force in the opposite direction to keep the rock from moving. When you release the rock, there is no new force or action on the rock, just the gravitational force that was present all the time. The reason the rock begins to move is that you remove the force that opposed the gravitational force on the rock.

An object near Earth wants to roll down into Earth's gravity well. But a force can be applied to that object to prevent that. This force could come from a rocket motor or from your hand (in the case of the rock). The object still wants to roll into Earth's gravity well and Earth's gravity still is acting on it but the opposing force is overpowering the effect of gravity. When the opposing force is removed, there is no opposition to gravity and nature takes its course.

 

[centsworth_II]

... if the train moves and the tracks are curved, the train will turn. But if the train is at rest, it takes more than curved tracks to make it moves....

Three dimensional representations of a gravitational field show this field as a depression in the flat sheet of space time. In a model where gravitational fields are represented by depressions, your train at rest (stationary) in a gravitational field would be better represented by a train on the slope of a depression representing curved space time. The only way the train could remain unmoving in curved space time would be if a force were applied to it to keep it from moving.

 

[5hot6un]

It moved in the first place becasue it is a hypothetical situation designed to describe how the curvature of space-time affects something moving.

 

[kelvinzero]

I think the rubber sheet analogy is confusing to most people because it implies you need a pull of gravity in the down direction to make it work.

I am pretty sure the rubber sheet analogy is just to describe stretched space. It doesnt matter whether those humps go up or down. That is just a way for us to visualize the idea of one square on a checker board having more area than another.

We do not need a 'cause' for the ball to roll along a curve through space-time. If the ball did not inhabit some sort of curve through space-time (ie only existed at a single point in space time: (x,y,z,t) ) then it would only exist for a single instant of time, which of course is not what we mean by stationary.