Object with no velocity is placed in a gravitational field

[cml149]

My question is, if an object with no velocity is placed in a gravitational field, what causes it to accelerate?
In Newton's theory of gravity, it was just accepted that if there is a force on an object, it accelerates. However, in general relativity, acceleration is now due to an object's motion through curved space. An object always travels in a straight light in the sense that if it is moving, it takes the shortest distance between two consecutive points in space. If space is curved then this distance is changed. An object moving in a straight line in a curved space would then seem to be, relative to an observer in flat space, moving in a curved path or, changing speed. So I can see why an object that is already moving with respect to another massive object would appear to change velocity...the curvature of space changes the way an object moves through space. But if the object is not already moving why would we see acceleration? I can see why curved space would change motion but not why it would cause it. There doesn't seem to be any reason for an object to "fall" or be impelled towards another massive object. Textbooks have illustrations of our planets "rolling downhill" the curved space surrounding the Sun. But of course this analogy doesn't really explain anything because the only reason objects roll down anything in the first place is because of gravity. So in effect we're saying gravity causes things to accelerate because of gravity.
I've only had a brief introduction to general relativity in my modern physics class so perhaps I'm taking things too literally.

 

[cepheid]

Hi,

I think part of the problem might be that you need to replace the word "space" with "spacetime" in much of what is above. It is spacetime that is curved. An object that does not appear to be moving to us is still moving through spacetime (albeit entirely in the "time" direction). Its path through spacetime is known as its worldline. If spacetime is curved, it may be natural for its worldline be in such a way that it "falls" toward some massive object.

Yes, I think you are taking the rubber sheet analogy too literally. The point of it was that in the presence of a large mass, spacetime is curved. If an object is in the "depression", it will be natural for it to move on a curved path, because that's the way space is shaped there. That's all. The analogy is not tautological, as you suggest.

 

[rcgldr]

still moving through spacetime (albeit entirely in the "time" direction).

but the time aspect doesn't explain relative motion between objects, only a means to describe a rate of motion. Somehow the concept of gravity not being a force just doesn't seem right. I don't see why gravity, which is related to mass, should be treated significantly different than electrical force, which is related to charge.

 

[A.T.]

But if the object is not already moving why would we see acceleration? I can see why curved space would change motion but not why it would cause it.

As cepheid said: everything is advancing in space-time all the time, even if at rest space.

Textbooks have illustrations of our planets "rolling downhill" the curved space surrounding the Sun. But of course this analogy doesn't really explain anything because the only reason objects roll down anything in the first place is because of gravity. So in effect we're saying gravity causes things to accelerate because of gravity.

Very well observed. This analogy is flawed because it omits the time dimension of curved space-time. You will find better visualizations linked here:
https://www.physicsforums.com/showpost.php?p=2244927&postcount=21

I don't see why gravity, which is related to mass, should be treated significantly different than electrical force, which is related to charge.

Gravitation accelerates everything equally, including light which has no mass. The electric force does not. Therefore you can treat gravitational force as an inertial force. The gravitational force model simply doesn't explain orbit precession and the correct amount of light bending. And the concept of a force doesn't work for massless objects at all.

GR doesn't disallow you to see gravity as a force, it just redefines which frame is accelerated and which is inertial in a gravitational field. And so gravity becomes a inertial force present in accelerated frames only.

 

[rcgldr]

Gravitation accelerates everything equally, including light which has no mass.

A beam of light aimed directly at or away from a massive object is not accelerated. Light curves around massive objects, and this could be due to gravity, or it could be coincident with gravity, and due to some unknown property of matter. A light beam is only accelerated in a direction perpendicular to it's current path, regardless of the direction of the beam of light with respect to the radial path to a massive object. The reaction of a beam of light within a gravitational field is significantly different than the reaction of any object with non-zero rest mass.

 

[Al68]

but the time aspect doesn't explain relative motion between objects, only a means to describe a rate of motion. Somehow the concept of gravity not being a force just doesn't seem right. I don't see why gravity, which is related to mass, should be treated significantly different than electrical force, which is related to charge.

The "force" of gravity can be treated as a force. And it's identical to the fictional "force" that causes objects to "accelerate" in the accelerated frame of a spaceship, for example. There is nothing wrong with considering an accelerated frame as "stationary" and attributing the acceleration of all other masses to "forces".

But unlike the electrical force, gravitational force, and fictional forces in general, accelerate all objects equally, regardless of their mass, electrical charge, etc.

 

[Jonathan Scott]

A beam of light aimed directly at or away from a massive object is not accelerated. Light curves around massive objects, and this could be due to gravity, or it could be coincident with gravity, and due to some unknown property of matter. A light beam is only accelerated in a direction perpendicular to it's current path, regardless of the direction of the beam of light with respect to the radial path to a massive object. The reaction of a beam of light within a gravitational field is significantly different than the reaction of any object with non-zero rest mass.

The last sentence is wrong: there is no distinction between the motion of a body traveling at close to c and the motion of a light beam. In both cases, the relative rate of change of momentum of something traveling at speed v (in isotropic coordinates) near a massive body is (1+v²/c²) times the Newtonian result, so the effective force is twice the Newtonian force when v is close to or equal to c.

There is however an additional complication of coordinate systems. In the sort of coordinate system that can describe a whole orbit, space is slightly curved and the coordinate speed of light varies with the distance from the source. In the most common coordinate systems used for this purpose, the coordinate value of c decreases the closer you get to the source, by a fraction which varies twice as fast as the Newtonian potential.

The total energy E of something traveling in any direction in free-fall in a static field is constant (in Newtonian terms, this is because the potential energy is converted to or from kinetic energy). The momentum is Ev/c² so for something falling or rising at around c (without changing direction), the magnitude of the momentum is E/c and the change is entirely due to the opposite change in c, so the local speed is constant and the coordinate speed is changing in the opposite direction to the momentum!

(I've taken some short cuts with the notation above; it would be safer to use some other symbol for the coordinate speed of light to avoid confusion with the standard value of c).

 

[Fredrik]

My question is, if an object with no velocity is placed in a gravitational field, what causes it to accelerate?

If you're going to say that an object is accelerating, you first have to define what it means to be not accelerating. Yes, you have to define it. I think you might find post #6 in this thread useful.

 

[cml149]

So, if a massive object is placed in the gravitational field of a second massive object then, because of the curvature of spacetime time will pass more slowly for that object according to an observer in flat spacetime. How would this change the relative position of the two objects? If I were to stand still, then in my reference frame I am moving entirely through time and not through space. How would changing my motion through time make me move through space?

Something I don't understand about the general theory that perhaps is why I am confused;
Einstein said if we are accelerating there is no way to tell if we are actually moving or, if we are stationary and just feeling the acceleration due to a gravitational field. In the second case in order to be stationary in a gravitational field there would need to be a force in the direction opposite to that of gravity in order that these forces cancel. So, if you were stationary in a gravitational field you would not feel any acceleration because the forces cancel..that's why you are stationary to begin with. So if I'm in my windowless elevator and feel acceleration I can be sure that I am definitely not stationary in a gravitational field, and the warping of time in my frame is due entirely to my motion, per special relativity.

 

[cepheid]

Something I don't understand about the general theory that perhaps is why I am confused;
Einstein said if we are accelerating there is no way to tell if we are actually moving or, if we are stationary and just feeling the acceleration due to a gravitational field. In the second case in order to be stationary in a gravitational field there would need to be a force in the direction opposite to that of gravity in order that these forces cancel. So, if you were stationary in a gravitational field you would not feel any acceleration because the forces cancel..that's why you are stationary to begin with. So if I'm in my windowless elevator and feel acceleration I can be sure that I am definitely not stationary in a gravitational field, and the warping of time in my frame is due entirely to my motion, per special relativity.

I'm not totally sure I understand your argument. I think that the equivalence principle says that the effects of gravity are indistinguishable from the effects of constant acceleration.

If I'm in my windowless elevator and it suddenly starts accelerating upward, I'll feel heavier. How do I know that gravity didn't suddenly just get stronger? If I'm in my windowless elevator and it suddenly starts accelerating downward, I'll feel lighter. How do I know that gravity didn't just get weaker?

 

[cml149]

additionally, if, in the case of gravity we say that a force or, the mechanism that makes things accelerate, is the warping of spacetime, why would the other fundamental forces not be explained in terms of space and time? It seems like general relativity gave us an explanation for what a force is but for some reason it's not applied to the electromagnetic, strong, and weak forces.

 

[cml149]

cepheid,
of course, you could not determine between acceleration due to gravity and acceleration by some other cause. But it seems the force of Einstein's argument comes from the fact that there is no way to distinguish between acceleration and being stationary in a gravitational field. Because special relativity effects only things in motion, if it is possible to say that you are not moving by saying that you are actually stationary in a gravitational field, then there would no longer be relativistic effects like time dilation. Assuming nature isn't ambiguous like this Einstein postulated that a gravitational field warps spacetime. Now if you are stationary in a gravitational field you would still feel the effects of special relativity without having to be moving. Now, when you're in a windowless elevator, feeling acceleration you have a choice of saying whether or not you're moving. All reference frames are equivalent if you assume that gravity warps spacetime.

So (if what I said above was true, maybe its not), Einstein's argument depends on the fact that we feel acceleration when we are stationary in a gravitational field. But, what confuses me, is that if you are stationary in a gravitational field, say because another force is holding you there, then you certainly do not feel any acceleration, even though gravity is "pulling" on you.

 

[cepheid]

Alright, fine. I'll address the "being stationary" part as well. If I'm in my windowless elevator -- no, scratch that -- windowless box that is just sitting there on the ground, and I feel like I weigh 130 lbs, the reason is because the floor is pushing upward on me with that force. If I didn't know anything about gravity, wouldn't it puzzle me that I wasn't weightless and floating around? In the absence of any other information, I might be led to conclude that my box was in fact accelerating upwards at 9.81 m/s².

 

[cml149]

So I guess what I'm stuck on is more elementary physics. You say that when youre sitting on the ground you "feel" your weight of 130 pounds. But, this weight that you "feel" could alternatively be a result of your box accelerating upwards at g m/s². I understand that.
So, embarrassingly, why do we "feel" our weight when we are stationary on the ground? We "feel" the effects of a force by the acceleration it gives us. So, I think we only really "feel" gravity when some part of us is moving against it or, when we're not stationary. If we were truly stationary and not accelerating because the force of gravity is perfectly balanced by our feet or backs, what exactly is it that we're feeling? I mean we feel our muscles straining against our weight but suppose we were paralyzed and didn't have those sensations. Then the only way we would "feel" or sense gravity is if we saw we were accelerating. But when we are sitting stationary on the ground there certainly isn't any acceleration to measure. My point is that there does seem to be a difference between being stationary in a gravitational field and just accelerating(Im sure there isn't a difference I just don't see it).

thanks for your patience.

 

[cepheid]

Yes, apparent weight and actual weight are not the same thing. On Earth, you always have weight, because you are always being pulled towards the centre of the Earth by its gravitational force. However, you don't always feel it (most of the time, though, you do).

So, embarrassingly, why do we "feel" our weight when we are stationary on the ground? We "feel" the effects of a force by the acceleration it gives us.

No, and this is what is tripping you up. We don't necessarily "feel" the effects of a force because it accelerates us. I feel my weight right now, sitting in my chair, even though I am NOT accelerating. The reason is because my chair pushes back up on me. That is what I am feeling.

Conversely, if I put you in a windowless box and throw that box out of a plane (so that you are in free fall), you will feel nothing. You will feel "weightless." Earth's gravity will not be apparent to you, in spite of the fact that this time you ARE accelerating.

So, I think we only really "feel" gravity when some part of us is moving against it or, when we're not stationary. If we were truly stationary and not accelerating because the force of gravity is perfectly balanced by our feet or backs, what exactly is it that we're feeling?

Again, not true. I have provided you with the perfect counterexample. I am stationary, yet I feel my weight. You, falling out of a plane, are not stationary, and yet you don't feel your weight.

 

[cml149]

Why does our body feel the force of a chair on us but not the force from gravity when we are free falling? The only difference seems to be the contact of two objects when we are sitting and the effects of it on our nerves. Would someone paralyzed feel the same sitting in a chair as they would free falling?

 

[cepheid]

Yeah, I think you answered that question. What you 'feel' has to do with more than just physics and is perhaps not the most reliable indicator of whether there is a force acting on you or not. When you are in free fall, what, exactly, is there for you to feel? Nothing.

Even if a guy were paralyzed or had his nerves deadened, I think there might still be a discernible difference between falling and not falling. I mean, in the latter case, your internal organs and everything inside of you is under some minute stress*, because they are all being pulled towards the floor, and the more rigid parts they are attached to are counteracting or resisting that pull, preventing them from actually going anywhere! In the case of free fall, nothing is under any stress because nothing is resisting. Gravity wants to accelerate you (all of you, in your entirety), and nothing is stopping it. If parts of you aren't feeling stresses due to a pulling, then why would you feel anything?

I think we might be verging a bit off topic here, into a discussion of why one "feels" heavy, which does not have anything directly to do with the physics.

*EDIT: Which is not to say that this stress is abnormal. Our bodies obviously evolved taking it for granted that this pulling would be present. It is weightlessness that is the abnormal condition, from a human body standpoint.

 

[cml149]

ok, so, if you had two objects, one accelerating in free space and one stationary in a gravitational field, is there any experiment you could do to distinguish the two situations? The equivalence principle says there isn't. Using the term we are trying to avoid the equivalence principle says the two situations "feel" the same, they are indistinguishable.

But what types of experiment would we do? If we were to measure the acceleration of each there of course would be a difference. The object held stationary in the gravitational field has zero acceleration.

 

[cepheid]

Well, you could throw some rocks around. Note that they don't seem to obey Newton's laws. That they accelerate downwards...etc. The results of the experiment would be the same in both situations. Maybe you could weigh things with a spring scale or some other apparatus. I'm sure you could think of other things.

 

[cml149]

Ok, that makes it clear then. Thanks for spending so much time on this. So, back to my original question, what makes a stationary object accelerate if it is placed in a curved spacetime. You originally said that because of the warping of time, specifically, it would be possible for an object with zero velocity to accelerate. But, if I stand still, then in my reference frame I am moving entirely through time and not at all through space. How would changing my motion through time(like having it be slower in a gravitational field) have any effect on my motion through space?

 

[cepheid]

You originally said that because of the warping of time, specifically

No, I didn't. All I said was that spacetime was curved, and that therefore an object's natural state of motion might be to move along a curved path through spacetime. I believe that the curve through spacetime along which an object moves (between two points in spacetime) is the shortest possible path between those two points, and it is known as a geodesic. In the absence of mass-energy, this geodesic (or shortest possible path) will be a straight line that is entirely in the time direction. In the presence of mass-energy, which leads to a curved spacetime geometry, the geodesic might be some curve that represents motion through both space and time. I am speaking only in vague terms, because I don't know enough about General Relativity to comment further. Therefore, I will leave this thread in others' capable hands.

 

[cml149]

ok, I don't think I'll be able to understand in anymore detail than that. thanks for your help

 

[A.T.]

But, if I stand still, then in my reference frame I am moving entirely through time and not at all through space. How would changing my motion through time(like having it be slower in a gravitational field) have any effect on my motion through space

It is called geodesic deviation. And since it is a geometric concept, you can understand it best from pictures:
http://www.physics.ucla.edu/demoweb...alence_and_general_relativity/curved_time.gif
You see there how a free falling object is initially at rest in space (moves parallel to the time dimension) and starts moving along the vertical space dimension, despite advancing on a straight line trough space-time.

 

[Fredrik]

So, back to my original question, what makes a stationary object accelerate if it is placed in a curved spacetime.

Did you miss post #8 in this thread? It won't accelerate. Not in an objective sense anyway.

 

[cml149]

Frederik,
so we define nonaccelerated motion or, inertial motion as motion along a geodesic where a geodesic defines the shortest distance between two points in spacetime. And then accelerated motion is that which does not move along a geodesic or, deviates from it. So when an object with zero velocity is placed in a gravitational field and begins to move along a geodesic curve it is not, according to our new definition, accelerating since it has not deviated from a geodesic. Is this correct?

 

[Fredrik]

Frederik,
so we define nonaccelerated motion or, inertial motion as motion along a geodesic where a geodesic defines the shortest distance between two points in spacetime. And then accelerated motion is that which does not move along a geodesic or, deviates from it. So when an object with zero velocity is placed in a gravitational field and begins to move along a geodesic curve it is not, according to our new definition, accelerating since it has not deviated from a geodesic. Is this correct?

Yes, you got it right.

There's only thing that I would say differentely: In SR and GR, a geodesic isn't the shortest curve from one point to another. It's the curve with the longest proper time. (Any geodesic on a Riemannian manifold minimizes distance, but there are three kinds of geodesics on a Lorenzian manifold, and the kind we're interested in maximizes proper time instead). Most of the time its actually better to think of a geodesic as a "straight" line instead, i.e. a curve that at every point "continues in the same direction as its tangent vector". The formal (i.e. mathematical) version of that last statement is the best definition of "geodesic", because it works for all types of geodesics on both Riemannian and Lorentzian manifolds.

 

[A.T.]

So when an object with zero velocity is placed in a gravitational field and begins to move along a geodesic curve

Just to make it clear: the object with zero velocity in space is always advancing in space-time, so it doesn't start to advance in space-time. It just starts to advance along a geodesic curve in space-time, when released. It doesn't necessarily move on a geodesic curve in space however.

To avoid confusion i try to use the terms "move in space" and "advance in space-time"

 

[cml149]

A.T.,
if my stationary object, "doesn't necessarily move on a geodesic curve in space", why would it start moving towards the second massive object?
If everything is moving through spacetime at a rate equal to c, then, if something is placed in a gravitational field where it's advancement through time is slowed, then it is necessary for its motion through space to speed up in order that it still travels through spacetime at speed c. Is this why something would start moving through space even if it was originally stationary?

 

[A.T.]

A.T.,
if my stationary object, "doesn't necessarily move on a geodesic curve in space", why would it start moving towards the second massive object?

See post #23

If everything is moving through spacetime at a rate equal to c, then, if something is placed in a gravitational field where it's advancement through time is slowed, then it is necessary for its motion through space to speed up in order that it still travels through spacetime at speed c. Is this why something would start moving through space even if it was originally stationary?

No, but you are right about always advancing at c in space-time - only the direction changes. So in order to start moving in space, your direction in space-time in regards to the dimensions has to change. There are different way to explain why it changes. One is given in post #23 and further visualized in pages linked here:
https://www.physicsforums.com/showpost.php?p=2244927&postcount=21

A second way to see it is: Space-time becomes more dense towards the mass, so there is a density gradient. If you advance trough something with a density gradient you will be diverted towards the denser region. Just like light rays moving trough a medium of varying optical density. So your advance in space-time, initially only along the time dimension, is diverted towards the denser region, your direction in space-time changes and you start moving trough space.

The connection to gravitational time dilation you try to make above, is the following: In the denser region the advance trough space-time (and therefore also trough time) is slower than in a less dense region. This is even true for two stationary clocks and is different from the time dilatation due to movement in space, where the direction in space-time changes.

This are basically two ways to see curvature:
1) Advance trough space-time is constant at c, but distances between coordinates vary.
2) Distances between coordinates are constant, but density varies slowing down the advance trough space-time.

 

[Austin0]

A.T.,
if my stationary object, "doesn't necessarily move on a geodesic curve in space", why would it start moving towards the second massive object?
If everything is moving through spacetime at a rate equal to c, then, if something is placed in a gravitational field where it's advancement through time is slowed, then it is necessary for its motion through space to speed up in order that it still travels through spacetime at speed c. Is this why something would start moving through space even if it was originally stationary?

Hi I think the root of the conceptual difficulty may be simply the stationary object.
I had the same kind of difficulty thinking about a projectile quickly accelerated straight up and then falling back directly to the same point. It was vary hard to see this path as a single continuous inertial straight line until I switched perspective to an inertial frame centered on the Earth traveling a geodesic around the sun. Suddenly it was easy to see the path as a continuous curve , an inertial vector.
There is also the fact that stationary in the sense you seem to be thinking would mean totally without momentum. angular or inertial. Which idea in a universe with momentum conservation and SR seems problematic at best. A motionless object mybe like an absolute rest frame , an ideal gas or a spinless electron. Hard to find.
This all may not be strictly valid within GR' idea of frame but I found it useful or at least comforting.