Action & Reaction: Equal Opposites

[Naveen3456]

Action and reaction are equal and opposite.
So, when mass (matter) acts on space and bends it, why doesn’t space react to this action in any detectable way?

 

[mfb]

Action and reaction are equal and opposite.

Between objects, in Newtonian physics.
Space is not an object, and General Relativity is not Newtonian physics. Why do you expect this concept here?

Matter bends space, space influences the motion of matter.

 

[Dale]

Action and reaction are equal and opposite.
So, when mass (matter) acts on space and bends it, why doesn’t space react to this action in any detectable way?

In the context of Newton's 3rd law "action" and "reaction" are forces. When spacetime bends I am not aware of any sense in which there is a force acting on spacetime.

 

[Naveen3456]

In the context of Newton's 3rd law "action" and "reaction" are forces. When spacetime bends I am not aware of any sense in which there is a force acting on spacetime.

Then, what is the underlying mechanism for this 'bending' to happen?

In other words, If mass reacts with space-time and it does not do so through some kind of 'force', then 'how' does mass do this (lead to this bending of space and time).

Plz be patient. I have thought long-long on this and have come to the thought that there must be some kind of 'physical connection' between mass and space-time that could be detected.

Though, some of my friends say that such things can be explained only by mathematics. I don't vouch for this idea as mathematics only describes some kind of underlying 'physical mechanism'.

 

[DiracPool]

Plz be patient. I have thought long-long on this and have come to the thought that there must be some kind of 'physical connection' between mass and space-time that could be detected.

There is, its called the space-time curvature that is gravity. Einstein's field equations, from my interpretation, do not imply causation so much as they imply a "relation" or correlation. This is in the spirit of Einstein's universe, which is said to be "background independent," versus Netwton's universe, which is said to be "background dependent." In a background dependent universe, objects are actors in a play which is carried out in on a stage which is an unchanging space-time background. In Einstein's universe, space-time evolves along with the characters in the play. These are "relational" properties of space-time and mass...

If mass reacts with space-time and it does not do so through some kind of 'force', then 'how' does mass do this (lead to this bending of space and time).

not "reactionary."

This link explains in more detail.

http://www.einstein-online.info/spotlights/background_independence/?set_language=en

 

[WannabeNewton]

Newtonian gravity can also be made background independent; Newtonian gravity can be reformulated in a generally covariant way so that it too is a manifestation of space-time curvature and so that the space-time geometry is dynamical. The differences between general relativity and Newtonian gravity, once cast in a geometric form, are more specific.

General relativity does not explain why mass-energy induces space-time curvature; it simply tells us how. There is a difference.

 

[BruceW]

In other words, If mass reacts with space-time and it does not do so through some kind of 'force', then 'how' does mass do this (lead to this bending of space and time).

Plz be patient. I have thought long-long on this and have come to the thought that there must be some kind of 'physical connection' between mass and space-time that could be detected.

Force is a classical concept. In quantum theory, there are no 'classical forces', there are only 'interactions'. If you are happy with this idea of 'interactions', then there is hope for a quantum theory of gravity one day, which would mean that general relativity could be thought of as resulting from a large number of quantum-mechanical interactions.

 

[Naveen3456]

In the context of Newton's 3rd law "action" and "reaction" are forces. When spacetime bends I am not aware of any sense in which there is a force acting on spacetime.

Matter interacts with space-time?

What do these 'interactions' involve if not 'force' and other such classical concepts? Is such an agency yet to be discovered or simply it's undiscoverable?

Let's talk about space in a nucleus. Is this space also bent? With so much concentration of matter in a nucleus (and so much of space warping) how could it's constituents move at all?

 

[Naveen3456]

Between objects, in Newtonian physics.
Space is not an object, and General Relativity is not Newtonian physics. Why do you expect this concept here?

Matter bends space, space influences the motion of matter.

I expect this concept here because it is known now that quantum fluctuations of space lead to production of material particles. So why not suppose material properties for space?

 

[Naveen3456]

General relativity does not explain why mass-energy induces space-time curvature; it simply tells us how. There is a difference.

GR tells us about how much mass would produce how much 'bending' and things like that but it does not tell about 'how' this phenomenon takes place i.e. the mechanism of this phenomenon is not explained. The 'why' question is even more difficult.

Let me give a very foolish example ( but it would convey what I want to say).

Suppose, there is a planet in a region of the universe where there is no space (it's outright wrong I know, but still bear with me.) Now, this planet is slowly moved towards a region that has space. Suppose it is 2 light years away from the boundary of this region that has space.

Will this planet bend space from such a distance?

Now, it's moved closer by 1 light year, will the space bend?

Will the effect of this planet travel faster than light and bend the space at once or will it take 1 full year before the effect of this planet (mass) reaches the region of space and bend it?

YOU ARE FREE TO LAUGH AT ME

 

[Dale]

Then, what is the underlying mechanism for this 'bending' to happen?

The underlying mechanism is described by the Einstein field equations (EFE):
https://en.wikipedia.org/wiki/Einstein_field_equations

Matter and fields have a stress-energy tensor, and this tensor is proportional to the curvature tensor.

Though, some of my friends say that such things can be explained only by mathematics. I don't vouch for this idea as mathematics only describes some kind of underlying 'physical mechanism'.

In this case, I agree with both you and your friends. The mathematics indeed are only a description of the physical mechanism, not the physical mechanism itself, but so is any other set of words or human symbols that I could put together. I could give different aspects of the mechanism names, but those names are not the mechanism only a description. I could make analogies between the mechanism and other things, but those analogies are not the mechanism either. It turns out that the math is the most accurate and least biased description of the physical mechanism that we have available.

What do these 'interactions' involve if not 'force' and other such classical concepts?

Why would there be a force involved? Spacetime doesn't have a mass and it doesn't have an acceleration, so why should there be any force involved? Your assumption seems strange to me.

Is such an agency yet to be discovered or simply it's undiscoverable?

Let's talk about space in a nucleus. Is this space also bent? With so much concentration of matter in a nucleus (and so much of space warping) how could it's constituents move at all?

It is quite possible that a working theory of quantum gravity will answer these two questions. Currently we do not have such a theory, but when we do it will also be mathematical in nature. I.e. it will explain the EFE as an approximation to the mathematical equations of a more complete theory.

 

[BruceW]

Let me give a very foolish example ( but it would convey what I want to say).

Suppose, there is a planet in a region of the universe where there is no space (it's outright wrong I know, but still bear with me.) Now, this planet is slowly moved towards a region that has space. Suppose it is 2 light years away from the boundary of this region that has space.

Will this planet bend space from such a distance?

Now, it's moved closer by 1 light year, will the space bend?

Will the effect of this planet travel faster than light and bend the space at once or will it take 1 full year before the effect of this planet (mass) reaches the region of space and bend it?

space is everywhere. But yes, the effect of the planet on bending space can only travel at a maximum speed of c. https://www.physicsforums.com/showthread.php?t=699522

Also, going back to why there is no force... I think once you learn a bit more about general relativity, you will start to see what it is all about. I'll try to give a first explanation. OK, so in General relativity, we allow spacetime to be curved. And Einstein's clever insight is that the force of gravity can't be distinguished from a curvature of spacetime. Therefore, we assume that gravity is not a force, but that it comes about due to a curvature of spacetime. Now, if we have a test mass (say a person) with zero forces acting on him, then from Netwon's laws, we would say he moves in a straight line. But because we are now allowing curved spacetime, there is no such thing as a straight line anymore. We have to generalize to the concept of geodesics. So he moves along a geodesic. This takes into account the curvature of spacetime. And the curvature of spacetime depends on mass and energy in a fairly straightforward way, which reduces to the 'old' concept of gravity in the limit of slow speeds and small curvature.

 

[Naveen3456]

space is everywhere. But yes, the effect of the planet on bending space can only travel at a maximum speed of c. https://www.physicsforums.com/showthread.php?t=699522

Also, going back to why there is no force... I think once you learn a bit more about general relativity, you will start to see what it is all about. I'll try to give a first explanation. OK, so in General relativity, we allow spacetime to be curved. And Einstein's clever insight is that the force of gravity can't be distinguished from a curvature of spacetime. Therefore, we assume that gravity is not a force, but that it comes about due to a curvature of spacetime. Now, if we have a test mass (say a person) with zero forces acting on him, then from Netwon's laws, we would say he moves in a straight line. But because we are now allowing curved spacetime, there is no such thing as a straight line anymore. We have to generalize to the concept of geodesics. So he moves along a geodesic. This takes into account the curvature of spacetime. And the curvature of spacetime depends on mass and energy in a fairly straightforward way, which reduces to the 'old' concept of gravity in the limit of slow speeds and small curvature.

From the foolish example that I gave, it seems to my mind that there is 'something' that emanates or oozes out of mass, which then warps space. this is just a vague thought.

Anyhow, a question has come to my mind.

Suppose, there is a planet which has curved space around it. A ball is placed in this space ( I push it from a roof).

Why does it move towards the planet in the very first place when there is no force acting on the ball by way of gravitation.

If someone says that the gravity of the planet attracts the ball towards itself, the scenario is perfectly understandable. But as per relativity, when gravity is just the curving of space, what makes the ball fall downward. if you say, I gave it a force by pushing it, why does its speed increase all the way down and not remain proportional to the push that I gave to the ball?

Thanks in advance.

 

[The_Duck]

Suppose, there is a planet which has curved space around it. A ball is placed in this space ( I push it from a roof).

Why does it move towards the planet in the very first place when there is no force acting on the ball by way of gravitation.

If someone says that the gravity of the planet attracts the ball towards itself, the scenario is perfectly understandable. But as per relativity, when gravity is just the curving of space, what makes the ball fall downward.

Suppose two people start from different points on the equator of the Earth and walk straight north. Eventually, they will collide at the north pole. Why did they collide, when they were always walking straight and they started out on parallel paths?

The same sort of thing is going on with gravity in general relavity. The curvature of spacetime means that objects following straight paths through spacetime actually end up being attracted to each other. There is no force of gravity in GR. The ball just moves in the straightest possible path through spacetime. The straightest possible path happens to intersect the surface of the planet.

 

[Nugatory]

If someone says that the gravity of the planet attracts the ball towards itself, the scenario is perfectly understandable. But as per relativity, when gravity is just the curving of space, what makes the ball fall downward. if you say, I gave it a force by pushing it, why does its speed increase all the way down and not remain proportional to the push that I gave to the ball?

As long as all the same forces are acting on you and the ball(which means you have to be free-falling along with the ball), the speed of the ball relative to you will remain constant and proportional to the push you gave the ball. Don't be confused by the way that the surface of the Earth is accelerating towards you and the ball.

 

[BruceW]

From the foolish example that I gave, it seems to my mind that there is 'something' that emanates or oozes out of mass, which then warps space. this is just a vague thought.

uh, not quite. general relativity is a local phenomena, in a similar way to how electromagnetism is a local phenomena. In electromagnetism, if we know the charge distribution at a point, then the equations of electromagnetism tell us something about the electric field at that point. And the electric field far from that point is not immediately affected. A similar thing happens in general relativity, but instead of an electric field, we have the metric tensor (which contains information about curvature of space, e.t.c.) itself which mediates gravitational phenomena. So it is the properties of space itself that is 'oozing out'.

Suppose, there is a planet which has curved space around it. A ball is placed in this space ( I push it from a roof).

Why does it move towards the planet in the very first place when there is no force acting on the ball by way of gravitation.

If someone says that the gravity of the planet attracts the ball towards itself, the scenario is perfectly understandable. But as per relativity, when gravity is just the curving of space, what makes the ball fall downward. if you say, I gave it a force by pushing it, why does its speed increase all the way down and not remain proportional to the push that I gave to the ball?

Not sure what you mean here. You seem to imply that a ball falling in curved space would not pick up speed. But surely the ball would pick up speed.

edit: now I think I see what you mean. you mean that since the ball is falling in the generalization of a straight line (a geodesic), then why is it's velocity changing? It is as Nugatory says, it is because you (on the roof) have forces acting on you, and you have some arbitrary path through space. So from your perspective, objects moving along a geodesic could have any kind of motion. (remember that motion is relative).

 

[Naveen3456]

Not sure what you mean here. You seem to imply that a ball falling in curved space would not pick up speed. But surely the ball would pick up speed.

Plz explain why are you so sure about the ball picking speed when no force is present that would increase the speed of the ball. Of course I gave force to the ball by pushing it, but it was a small push of hand ( a small force) which cannot result in the high speed with which the ball hits the ground after falling from the roof.

 

[BruceW]

Newton's first law does not work, since we are using general relativity, and there is a planet, so there is no 'inertial reference frame'. So even though the concept of a geodesic is similar in some ways to a straight line, it is not similar in other ways. The main thing to keep in mind is that "a test object with no forces acting on it moves along a geodesic". This is how it is similar to Newton's "a test object with no forces acting on it moves along a straight line". It may not be similar in other ways.

 

[DrGreg]

Plz explain why are you so sure about the ball picking speed when no force is present that would increase the speed of the ball. Of course I gave force to the ball by pushing it, but it was a small push of hand ( a small force) which cannot result in the high speed with which the ball hits the ground after falling from the roof.

The difference between Einstein's theory and Newton's is that where Newton says the ball is accelerated downwards towards the ground, Einstein says the ground is accelerated upwards towards the ball! So there is no force acting on the ball, causing it to accelerate down. There is a force acting on the ground causing it to accelerate up. The curvature of spacetime (note: spacetime, not space) is necessary to explain how the surface of the Earth can be accelerating outward yet it isn't expanding.

 

[A.T.]

Suppose, there is a planet which has curved space around it.

Curved spacetime not just space.

A ball is placed in this space ( I push it from a roof).Why does it move towards the planet in the very first place when there is no force acting on the ball by way of gravitation.

This is explained here for an apple falling from rest:

https://www.youtube.com/watch?v=DdC0QN6f3G4

 

[BruceW]

yeah, it should be spacetime, not space. I am also guilty of using the word 'space' when I mean 'spacetime' hehe. Partly because I've been reading a lot about cosmological models, where time is effectively treated in the Newtonian way. But terminology is important! Or it will all start to get very confusing very quickly.

 

[Dale]

From the foolish example that I gave, it seems to my mind that there is 'something' that emanates or oozes out of mass, which then warps space. this is just a vague thought.

The EFE are local equations, so there is no need for anything to ooze out. Each bit of stress-energy just bends spacetime in its local vicinity.

Why does it move towards the planet in the very first place when there is no force acting on the ball by way of gravitation.

Remember that it is spacetime which is curved, not just space. A ball "at rest" is still moving through time. In an earth-fixed coordinate system a geodesic which is initially purely in the time direction will gradually curve into the space direction.

EDIT: I see that both of these points have already been made above. At least the message is consistent.

 

[Naveen3456]

Einstein says the ground is accelerated upwards towards the ball! So there is no force acting on the ball, causing it to accelerate down. There is a force acting on the ground causing it to accelerate up. .

Can you take pains to explain these lines, without any mathematics, of course?

 

[Naveen3456]

As long as all the same forces are acting on you and the ball(which means you have to be free-falling along with the ball), the speed of the ball relative to you will remain constant and proportional to the push you gave the ball. Don't be confused by the way that the surface of the Earth is accelerating towards you and the ball.

To my small mind/brain, it is still not at all clear as to why the speed of the ball should increase on falling from the roof when there is nothing called as 'gravitational force?

 

[Nugatory]

To my small mind/brain, it is still not at all clear as to why the speed of the ball should increase on falling from the roof when there is nothing called as 'gravitational force?

The speed of the ball doesn't increase. The surface of the Earth is moving towards the ball at an ever-increasing speed (until they collide).

 

[Naveen3456]

The speed of the ball doesn't increase. The surface of the Earth is moving towards the ball at an ever-increasing speed (until they collide).

What 'force' compels the Earth to do so? Plz keep in mind you are not dealing with a 'physics' person.

 

[BruceW]

pressure keeps the Earth from falling in on itself.

 

[WannabeNewton]

The geodesic equation says that the 4-acceleration $a^{b} = u^{a}\nabla_{a}u^{b} = 0$ for a freely falling particle with 4-velocity $u^{a}$ such as a ball dropped in the Earth's interior uniform gravitational field; this is absolute in the sense that it is independent of any reference frame. This does not imply that $\frac{\mathrm{d} u^{\mu}}{\mathrm{d} \tau} = 0$ identically in an absolute sense; this depends entirely on the chosen frame. A frame fixed to the Earth with $\hat{z}$ being the vertical direction will have $\frac{\mathrm{d} u^{\mu}}{\mathrm{d} t}\approx \frac{\mathrm{d} u^{\mu}}{\mathrm{d} \tau} = -g\delta^{\mu}_{z}$ whereas a frame freely falling with the ball will have $\frac{\mathrm{d} u^{\mu}}{\mathrm{d} \tau} = 0$. The quantity $\frac{\mathrm{d} u^{\mu}}{\mathrm{d} \tau}$ is the coordinate acceleration of the ball; a person standing on the ground of the Earth will see the ball have a non-vanishing coordinate acceleration. The only thing that all observers will agree on is that the ball has vanishing proper acceleration i.e. 4-acceleration. But as far as coordinate acceleration goes, no one frame is any more correct/valid than another (the ground frame fixed to the Earth is just as correct/valid as the one freely falling with the ball).

 

[Bill_K]

This does not imply that $\frac{\mathrm{d} u^{\mu}}{\mathrm{d} \tau} = 0$ identically in an absolute sense; this depends entirely on the chosen frame.

That's because you're writing the ordinary derivative d/dτ which is coordinate dependent, instead of the absolute derivative D/Dτ which is not. See the definition on my blog.

Also note that the expression u^a∇_au^b makes no sense mathematically, since ∇_a is a four-dimensional gradient operator, defined to act on functions of four variables, whereas u^b is a function of only one variable, defined only on the world line of the particle.

 

[Nugatory]

What 'force' compels the Earth to do so? Plz keep in mind you are not dealing with a 'physics' person.

Left to its own devices, every grain of dirt would like to follow the same constant-velocity free-fall trajectory of the dropped ball. But it can't - because there's this great big ball of rock in the way shoving it off its natural trajectory. Go back to post #14 and #20 of this thread again... they will make more sense this time around, or at least help you ask a question that gets you to the next level.

 

[WannabeNewton]

That's because you're writing the ordinary derivative d/dτ which is coordinate dependent, instead of the absolute derivative D/Dτ which is not. See the definition on my blog.

Yes but the absolute derivative just tells us that the proper acceleration vanishes identically; my point is that whether or not the coordinate acceleration vanishes depends on the coordinates chosen. The statement "the velocity of the object doesn't change" is not absolute if one is to interpret the statement as referring to the coordinate acceleration $\frac{du^{\mu}}{d\tau}$ as opposed to the absolute acceleration. A person standing on the ground of the Earth has all the right to say that the ball is accelerating downwards towards him if acceleration refers to coordinate acceleration; only in the coordinates obtained from a frame freely falling with the ball will the vanishing absolute acceleration agree with the vanishing coordinate acceleration. I have read your blog before by the way, and it is a brilliant blog (I also liked your blog on Fermi-Walker transport). Cheers!

EDIT: Just to clarify, I agree completely with Nugatory that the dust grains stuck on the ground and people standing on the ground have a non-vanishing absolute acceleration whereas the ball has a vanishing absolute acceleration but in what absolute sense are the dust grains stuck on the ground and people standing on the ground accelerating "upwards towards" the ball?

 

[A.T.]

To my small mind/brain, it is still not at all clear as to why the speed of the ball should increase on falling from the roof when there is nothing called as 'gravitational force?

Did you watch the video in post #20? It explains exactly that, without math.

 

[pervect]

General relativity is not based on Newton's laws (such as the law of action and reaction you cite numerous times) Insisting that it is or should be just isn't going to get you very far.

Space-time curvature is a more general concept than a "force", thus while forces can be explained in terms of particular sorts of space-time curvature (i.e. via Newton Cartan theory), space-time curvature cannot, in its full generality, be fully described only by forces. Basically, space itself is "curved" according to GR, so for instance the sum of the angles of a triangle will in general be different from 180 degrees. "Forces" cannot change the sum of the angles of a triangle - space time geometry can.

The first step to actually learning GR would probably be to learn how to do Newtonian physics without forces, using Lagrangian methods - via the principle of least action.

 

[BruceW]

yeah, and using non-cartesian reference frames, with a metric that is not just the identity (for example spherical polar coordinate system). The idea of fictitious forces is (in my opinion) probably the closest concept to general relativity, without actually being general relativity.

 

[DrGreg]

Einstein says the ground is accelerated upwards towards the ball! So there is no force acting on the ball, causing it to accelerate down. There is a force acting on the ground causing it to accelerate up.

Can you take pains to explain these lines, without any mathematics, of course?

Maybe the following diagram will help, along with the explanations that others have already given.

A spacetime diagram is just a fancy name for a distance-versus-time graph. When there's no gravity, freely-moving objects are represented by straight lines drawn on a flat sheet of paper (diagram A).

When there's gravity, freely-moving objects are represented by lines drawn as straight as possible on a curved surface (diagram C). In this diagram, the surface of the Earth is represented by the thicker blue line that has an arrow labelled "t" pointing along it. This line is a curved line. The two red lines represent two balls dropped one after the other from a roof. These lines are as straight as possible in the curved surface.

For more details see the post where this diagram came from.

 

[Naty1]

Nuveen:

Partly because I've been reading a lot about cosmological models, where time is effectively treated in the Newtonian way.

No, in the generally accepted FLRW [or FRW] cosmological model, space and time are NOT Newtonian. Their behavior is described via relativity.

 

[BruceW]

eh? It was me who said that, not Nuveen. And time is treated differently to space in the FLRW metric, in a very Newtonian way. Space is still curved. But time is like a separate parameter, for example in spherical universe, the size increases as some function of time. (reminds me lot of the Newtonian way of thinking). Of course, spacetime is still spacetime, but because of the assumptions on what makes up the universe, it seems like a 'Newtonian model' in a certain sense.

edit: to be clear, I am not literally saying that the FLRW metric uses Newtonian physics. I just mean that in several ways, it is similar to a Newtonian model.

 

[soothsayer]

To my small mind/brain, it is still not at all clear as to why the speed of the ball should increase on falling from the roof when there is nothing called as 'gravitational force?

There is a difference, in relativity, between coordinate acceleration, and proper acceleration.

Coordinate acceleration is the Newtonian concept of acceleration. It is the acceleration of an object as viewed from an observer, so, the falling of the ball from the roof towards the surface of the Earth, you see that as an acceleration, classically attributed to gravity.

Proper acceleration is the physical acceleration measured by an object. Imagine sitting in a car an accelerating, you feel a force pushing you against your seat--your inertia keeping you in place. It is an acceleration that you can measure within your reference frame. Note that while accelerating to the Earth, the ball has NO proper acceleration: it feels no force, it is simply in free fall, so while it appears to be going through coordinate acceleration, according to you who are standing on the roof, it is actually YOU who are experiencing proper acceleration. How? Think about your weight. You feel weighted down because the roof you are standing on is opposing your free fall through spacetime. In fact, you are not weighted because of gravity, you are weighted because you are opposing gravity.

So, in this example, the ball is undergoing coordinate acceleration relative to you. This is not caused by a force, but rather, by the ball following the geodesics of spacetime. Because it is following those geodesics, it has no proper acceleration. You are actually the one that is accelerating away from the ball, in a proper sense, due to force from the roof allowing you to oppose the geodesics of spacetime.

 

[BruceW]

I like that explanation. copy, and paste into blog. hehe, nah I wouldn't. It is a nice way to explain it though.

 

[Naty1]

And time is treated differently to space in the FLRW metric, in a very Newtonian way. Space is still curved. But time is like a separate parameter, for example in spherical universe, the size increases as some function of time. (reminds me lot of the Newtonian way of thinking). Of course, spacetime is still spacetime, but because of the assumptions on what makes up the universe, it seems like a 'Newtonian model' in a certain sense.

I have no idea what that means... but better a subject for a separate discussion if you see fit. Newtonian time is a parameter for sure, relativity treats time with sign opposite to that of space... Time is relative in relativity, absolute in Newtonian. I can agree it's like Newtonian locally where your wristwatch ticks with unchanging precision.

 

[soothsayer]

I have no idea what that means... but better a subject for a separate discussion if you see fit. Newtonian time is a parameter for sure, relativity treats time with sign opposite to that of space... Time is relative in relativity, absolute in Newtonian. I can agree it's like Newtonian locally where your wristwatch ticks with unchanging precision.

I think BruceW is basically right. The FLRW metric basically just looks at the spatial component, which contains a scale factor dependent on a time parameter. It is otherwise independent of time, because it doesn't really care about the relativity of time between different observers, does it? But yeah, better discussion for another place, especially seeing as the OP is still confused.

 

[Naty1]

I like that explanation. copy, and paste into blog. hehe, nah I wouldn't.

Don't be proud...when you a find a good explanation, use it and attribute it to the source.

 

[Naty1]

It is otherwise independent of time, because it doesn't really care about the relativity of time between different observers, does it?

Of course it does care ..it is CRITICAL..."At rest wrsp to the CMBR" is what sets those observers time equal...Otherwise, distant observers, at different relative velocities, all have different elapsed times.

 

[Naveen3456]

There is a difference, in relativity, between coordinate acceleration, and proper acceleration.

Coordinate acceleration is the Newtonian concept of acceleration. It is the acceleration of an object as viewed from an observer, so, the falling of the ball from the roof towards the surface of the Earth, you see that as an acceleration, classically attributed to gravity.

Proper acceleration is the physical acceleration measured by an object. Imagine sitting in a car an accelerating, you feel a force pushing you against your seat--your inertia keeping you in place. It is an acceleration that you can measure within your reference frame. Note that while accelerating to the Earth, the ball has NO proper acceleration: it feels no force, it is simply in free fall, so while it appears to be going through coordinate acceleration, according to you who are standing on the roof, it is actually YOU who are experiencing proper acceleration. How? Think about your weight. You feel weighted down because the roof you are standing on is opposing your free fall through spacetime. In fact, you are not weighted because of gravity, you are weighted because you are opposing gravity.

So, in this example, the ball is undergoing coordinate acceleration relative to you. This is not caused by a force, but rather, by the ball following the geodesics of spacetime. Because it is following those geodesics, it has no proper acceleration. You are actually the one that is accelerating away from the ball, in a proper sense, due to force from the roof allowing you to oppose the geodesics of spacetime.

Since you people are the 'physics persons' here, proof of burden lies on you. So, I will be persistent in my efforts at understanding this concept. if not, I will just submit to what you say.

My next question is that it is okay that I have been stopped by the roof, so cannot follow the geodesic. The ball is free to do so, so I see it moving with respect to me. but why does it accelerate? why doesn't it just continue in uniform motion?

Suppose in empty space I and a ball are both moving side by side in uniform motion (i.e. ball is at rest with respect to me). I suddenly stop, will I see the ball accelerating from me or just moving away from me at the same speed(uniform motion).

Now you can say you are talking about linear motion and the space is not curved here. I say what's the proof that the portion of space in which I and the ball are moving in a uniform motion is not a small part of a vast curve that is unnoticeable/unfeelable to both me and the ball. Just like we consider the surface of the Earth to be flat when moving in uniform motion over it.

 

[A.T.]

The ball is free to do so, so I see it moving with respect to me. but why does it accelerate? why doesn't it just continue in uniform motion?

The ball starts moving in space, because its geodesic world-line deviates from the initially purely temporal path in distorted spacetime. See video at 0:48

https://www.youtube.com/watch?v=DdC0QN6f3G4

Suppose in empty space I and a ball are both moving side by side in uniform motion (i.e. ball is at rest with respect to me). I suddenly stop, will I see the ball accelerating from me or just moving away from me at the same speed(uniform motion).

During the process of stopping you will see the ball accelerate. Just as you see it accelerate when standing on the roof. But in both cases it is you who undergoes proper acceleration. The ball just undergoes coordinate acceleration in your frame of reference.

In the video above the green apple represents you standing on the roof, or changing your velocity in space. The red apple represents a free falling ball.

 

[BruceW]

I think A.T. answered pretty well. But also, about this bit:

Now you can say you are talking about linear motion and the space is not curved here. I say what's the proof that the portion of space in which I and the ball are moving in a uniform motion is not a small part of a vast curve that is unnoticeable/unfeelable to both me and the ball. Just like we consider the surface of the Earth to be flat when moving in uniform motion over it.

Yes, that is possible. In this case, the curve is only very slight, so there will only be a very slight effect which is due to the curve. Also, it is good to ask questions. Maybe it would be more time-efficient to learn some general relativity first though. (not trying to be condescending, I still am learning general relativity, and I've only learned some of the basics).

 

[soothsayer]

My next question is that it is okay that I have been stopped by the roof, so cannot follow the geodesic. The ball is free to do so, so I see it moving with respect to me. but why does it accelerate? why doesn't it just continue in uniform motion?

You need to be able to look at the mathematics of general relativity in order to understand why spacetime curvature causes acceleration, but I'll try to explain it qualitatively.

Imagine sitting on a curved, 3D surface, the top of a hill perhaps. You know that the motion of a ball across that 3D surface is influenced by the curvature, but something must actually give that ball a push to get it to accelerate, and move across the surface following geodesics. You're wondering where that push comes from.

In a spacetime metric, we have three spatial components: x, y, z, or r, θ, ∅, etc. depending on how you wish to express your coordinat system. We also have a TIME component. Now, when we start taking derivatives of this 3+1 dimensional metric, as we must in order to solve the metric's geodesics equations, we will be taking second derivatives of these spatial variables with respect to our time variable. Now, hopefully you can tell me what it is called when you take a second time derivative of a position? That is EXACTLY what acceleration is.

You're right, if we simply curved 3D space, we wouldn't expect any acceleration along geodesics, but since we are curving 3 dimensions of space and one of time, we get time derivatives of spatial variables which give us velocity and acceleration. Not acceleration due to any force, but due to the fact that following a 4 dimensional geodesic demands it. This is in perfect keeping with the Newton's laws, because objects travel in straight lines, and a curved, accelerated path is what actually constitutes a straight line in curved 3+1 space.

Suppose in empty space I and a ball are both moving side by side in uniform motion (i.e. ball is at rest with respect to me). I suddenly stop, will I see the ball accelerating from me or just moving away from me at the same speed(uniform motion).

If by empty space you mean there is no gravity acting on you and the ball, then the ball would move away from you at a constant velocity, except for the interval where you are decelerating to a stop: during that time the ball will appear to be accelerating relative to you (again: not proper acceleration, coordinate acceleration. You are the one who will experience the proper acceleration, because there must be a force causing you to stop.)

Now you can say you are talking about linear motion and the space is not curved here. I say what's the proof that the portion of space in which I and the ball are moving in a uniform motion is not a small part of a vast curve that is unnoticeable/unfeelable to both me and the ball. Just like we consider the surface of the Earth to be flat when moving in uniform motion over it.

You're asking how we can really tell whether a region of spacetime is curved or not? In free fall, you can't determine whether you are accelerating, or just moving at constant velocity, since there are no inertial forces on you. There are, however, many tests you could do to determine if you are in a gravitational field: consider that the gravitational field is not constant: it has a gradient and changes at every point. If you had some test particles, you could identify the gravitational field lines. If you had sensitive enough equipment, you could determine the difference in gravitational force acting on your head and your feet (also known as tidal forces--these become very strong around massive bodies. This force gradient is what heats the interior of Jupiter's moons.)

Remember that Einstein's equivalence principle only applies locally in a gravitational field, not globally.

Hopefully this will put your doubts to rest, but if you're still skeptical, don't be afraid to ask away. You'll never learn anything in Physics by simply taking what you're taught at face value; I learned that too late in my college career. I would like to echo Bruce in suggesting that you make sure you are equipped with the physics/math knowledge to understand the answer to your question first. A lot of times in advanced physics, it is hard to water down an explanation without diluting the truth.

 

[soothsayer]

Don't be proud...when you a find a good explanation, use it and attribute it to the source.

Feel free to do so, Bruce

 

[Naty1]

but why does it accelerate? why doesn't it just continue in uniform motion?

There are few answers to 'why' in physics...In this case it IS uniform motion from a GR perspective. YOU have to think new basics in GR, just like you do in quantum mechanics. Stuff is not so simple and straightforward as is commonly perceived.

In this case, you have to think differently than the Newtonian perspective you express. That's just one view. In GR inertial motion, that is uniform motion, follows geodesics, that is, paths in which the free falling mass feels no forces in the frame of reference of the mass particle. "feels no forces" is like Newtonian physics, where inertial motion also is one without applied external forces.

YOU would be accelerating right now in the frame of Earth's surface except the chair you sit in is pushing up against you. Remove the chair, you feel no force as you fall...just like a cannon ball after it is fired...THAT moves along a curve, accelerates towards earth, while maintaining a steady velocity horizontally. Gravity is an pseudo force analogous to centripetal force; What you feel is the restraint against the pseudo force.

It was Einstein's ability to take on new perspectives that enabled him to develop SR and GR. So give it a try!

 

[WannabeNewton]

Naveen, in GR the object isn't accelerating if it is in free fall. The key point is that a freely falling particle is locally inertial; that is, locally it travels on what we normally think of as straight lines. Globally, the trajectory will deviate from straight line motion due to curvature. There is no physics here: in curved geometries the notion of not accelerating is traveling on curves which are as straight as possible i.e. curves which locally can be made to look like the usual straight lines; these curves are called geodesics. The physics comes in when we state that freely falling particles travel on these geodesics.