What Gives a Motionless Meteorite Shard Momentum in the Curvature of the Sun?

[Chaste]

In GR, we know that it is the curvature in 4-d space-time that directs the movement of objects. It basically shows them WHERE to move.

My question is, assuming there are no planets or others masses that can cause any more distortion to the existing curvature created by the Sun. Just the Sun itself, considering placing a motionless(velocity = 0) meteorite shard in the curvature of the Sun.

It does move towards the Sun. But what gives it the momentum that it doesn't have initially?

 

[D H]

The Sun does. The Sun and the meteorite move toward each other.

 

[ZikZak]

You have to remember that it's curvature of spacetime, not space. Even a stationary particle has a trajectory through spacetime. If spacetime is curved, that trajectory will curve, i.e. deviate from a motion in the purely "t" direction.

 

[Chaste]

You have to remember that it's curvature of spacetime, not space. Even a stationary particle has a trajectory through spacetime. If spacetime is curved, that trajectory will curve, i.e. deviate from a motion in the purely "t" direction.

i did say 4-d space-time. Then, for a particle with momentum, it will not deviate from its "t" direction?

 

[MeJennifer]

The matter here is to understand the difference between a kinematic and dynamic view of space.

For instance if two objects come together only due to spacetime curvature could we say there is any momentum involved? Sure there is momentum from a kinematic view but from a dynamic view we have to conclude (at least in GR) that there is no such thing as momentum since there is no way to define the concept of momentum in a coordinate independent way.

 

[Naty1]

i did say 4-d space-time. Then, for a particle with momentum, it will not deviate from its "t" direction?

yes it will deviate a tiny bit from time...as it has velocity in space it's movement in time slows a tiny bit as its momentum increases.

 

[Naty1]

If spacetime is curved, that trajectory will curve, i.e. deviate from a motion in the purely "t" direction.

Spacetime does not have to be curved to divert from "t": any spatial motion diverts motion from the time dimension...

 

[Naty1]

In GR, we know that it is the curvature in 4-d space-time that directs the movement of objects. It basically shows them WHERE to move.

yes, but so does flat spacetime tell mass WHERE to move...straight w/o acceleration.

 

[ZikZak]

Spacetime does not have to be curved to divert from "t": any spatial motion diverts motion from the time dimension...

I was discussing the specific example of a stationary body.

 

[tiny-tim]

Hi Chaste!

But what gives it the momentum that it doesn't have initially?

It is free-falling. It is an inertial observer

So far as it is concerned, it feels no force and no acceleration (and it has no momentum).

It may wonder why the Sun is moving … but then so would any other inertial observer!

 

[81+]

D H, you said:

The Sun does. The Sun and the meteorite move toward each other.

But exactly what causes them to start moving toward each other from a rest position?
(1) Only the relative mass of the two objects?
(2) Only the curvature of spacetime?
(3) A combination of (1) and (2)?

Frank

 

[ZikZak]

But exactly what causes them to start moving toward each other from a rest position?
(1) Only the relative mass of the two objects?
(2) Only the curvature of spacetime?
(3) A combination of (1) and (2)?

Stress-energy (including mass) tells spacetime how to curve.
Curvature of spacetime tells particles how to move.

 

[81+]

Curvature of spacetime tells particles how to move.

ZikZak, I have never understood HOW spacetime "tells" particles how to move. Could you please enlighten me on this? Thanks.

Frank

 

[Fra]

philosophical reflection

ZikZak, I have never understood HOW spacetime "tells" particles how to move. Could you please enlighten me on this? Thanks.

Frank

I think this a bit of a philosophical question right? Or perhaps conceptual.

My favourite envisioning is that no one per see "tells" anyone where to go. Instead if the particle doesn't know, it basically does a random walk, and doing so, for each infinitesimal step the randow walker takes there is feedback, an his "internal map" is updated. This way a sufficiently small step size of the random walker, the randomly followed path is simply the most probable path, which from the geometric point of view is also called a geodesic. I think the easiest idea is that least action principle formulation, which I personally think of as a kind of maximum probability transition.

So IMO, the random walker tends to move in the direction he THINKS is most constructive. Which in turn depends on the observers own motion and mass. But on each infinitesimal movement he receives more information (lets say about the "field") and the random walkers updates his THINKING - again in the direction he thinks is most constructive! (constructive thinking).

This may sound crazy, but I find this way of thinking about this good if you plan ahead. Because once maybe you think you get the idea of classical GR, and acquites some intuition about it, then how the heck does that mix with QM? With THINKING and "receive infromation" I am envisioning the concept of an observers(randomwalker, or particles) INFORMATION about it's environment (a la QM) and the information updates are of course measurements, or interactions (a la QM).

I find that the alternative ways of thinking, with ballons or rubber stuff, while partially successful in classical physics, is really not very helpful at the next level.

Just my opinon though.

/Fredrik

 

[Chaste]

yes, but so does flat spacetime tell mass WHERE to move...straight w/o acceleration.

So how do we use General Relativity account for acceleration in curved space-time? If a particle has acceleration, does it not cause it to have a resultant FORCE? F=ma...

anyway, how particles to move in space-time can be thought as this. From the Big bang Theory, we know that all particles have momentum. so whenever you put them in space-time, they follow wherever space-time tells them to. Space-time is like tracks. Where you put a moving train on... it directs the train where to move.

Or another idea is from some author, Space-time is like a stream, carrying everything that on it, flowing ever onwards. So space-time moves and it carries the particles along with it.
But in this case, no work is done by the particle, because it's just translated(mathematical geometry transformation) in space.

 

[tiny-tim]

field theory

ZikZak, I have never understood HOW spacetime "tells" particles how to move. Could you please enlighten me on this?

Hi Frank!

It's pretty much like how a bumpy field on a hillside "tells" a ball how to move …

the ball, at each point, calculates the gradient vector of the field (the direction of steepest descent), and follows it!

 

[Chaste]

Hi Frank!

It's pretty much like how a bumpy field on a hillside "tells" a ball how to move …

the ball, at each point, calculates the gradient vector of the field (the direction of steepest descent), and follows it!

Isn't that like using gravity to experience gravity?

 

[tiny-tim]

Isn't that like using gravity to experience gravity?

ah … but the ball doesn't feel the bumps, it looks at them …

so it's using eyesight to calculate gravity! ​

 

[MeJennifer]

ZikZak, I have never understood HOW spacetime "tells" particles how to move. Could you please enlighten me on this? Thanks.

Frank

Spacetime does not tell particles how to move. The particles don't move, distances are simply dynamic in curved spacetimes. A distance of 1 meter might after some time become a distance of 50 cm or 2 meters, but neither ends needed to move or accelerate to accomplish this.

You should distinguish kinematic movement from the dynamics of distance in curved spacetimes.

For instance an object in space heading straight towards the center of the Earth's mass could have a zero kinematic movement or proper acceleration with respect to the earth, the decrease in distance between both objects could be completely due to the curvature of spacetime. However an object in orbit around the Earth must have both components. But even in this case, eventually, but very slowly, both objects will come meet.

Another example is the expansion of the universe. Objects are not moving or accelerating away but instead the curvature of spacetime causes an increase in distances between objects. This increase in distances can be faster than the speed of light.

One way to think about it is to consider two points on a flat mirror. Think about the future of those points as two staight lines perpendicular to the surface of the mirror. Now you can readily see that in the case of a flat mirror the future distances between those points remain fixed. However now consider a mirror that is convex or concave, the future distances between the two points will vary in the future. Nothing really moves but the future distances between the points simply change due to the fact that the mirror is not flat.

 

[Dale]

Hi Chaste,

This is best understood in geometrical terms. Do you understand (in SR) how the worldline of an inertially moving object is a straight line? If two inertially moving objects are at rest wrt each other then their worldlines are two parallel lines. In a flat space the distance between two parallel lines is constant and they never intersect.

Now, consider geometry on a sphere. On a sphere a "straight" line is a great circle. Longitude lines are examples of great circles. If you consider two nearby longitude lines at the equator they are parallel, and yet at the poles they intersect and the distance between the two lines is not constant.

So, on a sphere two lines can be parallel at one point and intersect at another point despite the fact that both lines are straight at all points. Translating back to physics, in a curved spacetime two observers can be at rest wrt each other at one point and their paths can intersect despite the fact that neither accelerates at any point (they are each inertial at all points).

 

[Chaste]

Hi Chaste,

This is best understood in geometrical terms. Do you understand (in SR) how the worldline of an inertially moving object is a straight line? If two inertially moving objects are at rest wrt each other then their worldlines are two parallel lines. In a flat space the distance between two parallel lines is constant and they never intersect.

Now, consider geometry on a sphere. On a sphere a "straight" line is a great circle. Longitude lines are examples of great circles. If you consider two nearby longitude lines at the equator they are parallel, and yet at the poles they intersect and the distance between the two lines is not constant.

So, on a sphere two lines can be parallel at one point and intersect at another point despite the fact that both lines are straight at all points. Translating back to physics, in a curved spacetime two observers can be at rest wrt each other at one point and their paths can intersect despite the fact that neither accelerates at any point (they are each inertial at all points).

what you are saying is... two objects moving along "parellel" lines in a positive curved surface will eventually meet each other. but translating to reality, does the a mass and the sun move together such that they meet? or is it the particle moving towards the sun?

and there still is acceleration right? like towards, a particle going towards a massive object will undergo acceleration. Like how things drop on Earth at 9.8m/s2

 

[Dale]

does the a mass and the sun move together such that they meet? or is it the particle moving towards the sun?

There is no absolute (coordinate independent) meaning to this question. You can construct a coordinate system in which either is true.

and there still is acceleration right?

There is no proper acceleration, but you certainly can construct coordinate systems where there is coordinate acceleration.

 

[Naty1]

View from GR
Another way of picturing what happens is the old rubber sheet and bowling ball analogy. If you place a "test ball" on the rubber sheet, it will "fall" naturally towards the bowling ball due to the curvature of space time.

If John Wheeler says "mass tells spacetime how to cuve; spacetime tells mass how to move"
thats a good enough analogy/simplification for my purposes.

Classical Newtonian View

The other way to look at where the momentum comes from are classical Newtonian considerations...F = Ma=Mg and F = GMm/r^2. The attractive gravitational force results in acceleration: Gravitational potential energy decreases as objects come together and is replaced by kinetic energy of motion...which results in momentum.

 

[Chaste]

There is no absolute (coordinate independent) meaning to this question. You can construct a coordinate system in which either is true.

There is no proper acceleration, but you certainly can construct coordinate systems where there is coordinate acceleration.

what is proper acceleration? is not an apple falling from a tree accelerating to the ground at g?

 

[Dale]

Proper acceleration is the acceleration measured by an accelerometer. It is the only kind of coordinate-independent acceleration. When people say "acceleration is absolute" or "acceleration is not relative" they actually are referring to proper acceleration.

An apple is only accelerating to the ground in the rest frame of the ground, in the rest frame of the apple the ground is accelerating up. However, in both frames the proper acceleration of the apple is 0 and the proper acceleration of the ground is g (in the up direction).

 

[Chaste]

Proper acceleration is the acceleration measured by an accelerometer. It is the only kind of coordinate-independent acceleration. When people say "acceleration is absolute" or "acceleration is not relative" they actually are referring to proper acceleration.

An apple is only accelerating to the ground in the rest frame of the ground, in the rest frame of the apple the ground is accelerating up. However, in both frames the proper acceleration of the apple is 0 and the proper acceleration of the ground is g (in the up direction).

haha.. i never understood why is g upwards... relative to all objects that fall to ground, we see g as downwards right? wrt to ground frame, g is upwards?

 

[tiny-tim]

g is for "ground"!

wrt to ground frame, g is upwards?

Hi Chaste!

Depends whether you use an inertial frame or a non-inertial frame.

The ground frame is non-inertial, and so there is a "fictitious" or "inertial" force (inertial means depends on mass but not on any form of charge) which we call gravity, and that g-force is downward.

In GR, we use inertial frames, which have no fictitious or inertial forces … relative to an inertial frame (ie, a free-falling frame), the ground's acceleration is upward.

hmm … when I'm standing on the ground, my acceleration upwards presumably comes from a force on me from the ground … but where does that force come from? … there's nothing on the other side of the Earth pushing … no turtle … is there? ​

 

[A.T.]

It's pretty much like how a bumpy field on a hillside "tells" a ball how to move …
the ball, at each point, calculates the gradient vector of the field (the direction of steepest descent), and follows it!

Isn't that like using gravity to experience gravity?

Yes Chaste, it is explaining gravity with gravity. What is "steepest descent" supposed to mean anyway. It would imply that there is an downwards direction in space-time.

My advice: forget the rolling ball. Think of a toy car going straight forward on a curved surface. Or even better: scotch tape that is sticked onto a curved surface without being torn or folded at its edges. The paths described by the car and the tape are geodesics like the paths in space time of free fallers, or objects without proper acceleration. Simple but good analogy:
http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html

 

[Chaste]

Hi Chaste!

Depends whether you use an inertial frame or a non-inertial frame.

The ground frame is non-inertial, and so there is a "fictitious" or "inertial" force (inertial means depends on mass but not on any form of charge) which we call gravity, and that g-force is downward.

In GR, we use inertial frames, which have no fictitious or inertial forces … relative to an inertial frame (ie, a free-falling frame), the ground's acceleration is upward.

hmm … when I'm standing on the ground, my acceleration upwards presumably comes from a force on me from the ground … but where does that force come from? … there's nothing on the other side of the Earth pushing … no turtle … is there? ​

our inertial frame we see the Earth accelerating upwards... that's just like einstein described in equivalence principle... a lab accelerating upwards... they are the same.
I see.
A.T: I get your analogy. Last time, I used 'tracks' as an analogy explaining to others. where roller coaster(with given momentum) just follow the tracks and doesn't deviate from it unless an external force affects it.

 

[Dale]

our inertial frame we see the Earth accelerating upwards... that's just like einstein described in equivalence principle... a lab accelerating upwards... they are the same.
I see.

It looks like you figured it out! You can also tell which direction the proper acceleration is by considering a simple spring accelerometer (mass between two springs on opposite sides). If you orient it horizontally and accelerate it to the right the spring on the right is in tension, so the acceleration is in the direction of the spring in tension. If you orient it vertically and put it on the ground then the spring on the top is in tension so the acceleration is up.