In Ensteins theroy of gravity.when a cannon ball is fired up,it

[latter]

in Ensteins theroy of gravity.
when a cannon ball is fired up,it slows to a stop due to friction.at the moment it stops going upwhy does it go back towards the earth.
because there is no force acting on it.there are no force particles or fields there are just paths created by masses.but these paths are not forces pulling something towards a mass.so why does the cannon ball abon "stopping" from going up go back down.

 

[Nabeshin]

The cannon ball does not stop due to friction.

You should really first understand the Newtonian picture of how this works before you start to try and go to general relativity... Gravity is pulling the cannonball back down, so even without friction it will stop and then come back down.

In GR, as you note GR is not a force, merely curvature of spacetime, so the cannonball is simply following a geodesic in four dimensions. For a cannonball moving sufficiently slowly, it goes away from the central mass (earth) for a short time, and then curves back and returns. In terms of geometry there isn't really any succinct way to explain it without resorting to rubber sheet analogies and the like.

 

[latter]

innewtionan its easy to understand cos there's a force.
so it is only friction in GR because there's no force.
you seem to be saying the cannon ball goes up and curve,s at the top .i feel there is a moment where a force is required at the top.becaue it must come to a stop.at the top and a force is required to move it.
also you are saying that the cannon ball comes back down not on the same path it went up it moved slighly left or right.

at the peak of the curve i see the ball stopping .it run out of energy for upwards moition.but it doesn't have a little more to tip it over the top.
its just stuck there at the peak perfectly balanced.needing a force to move it again.but there is no force.
so why does it fall

 

[tiny-tim]

Welcome to PF!

Hi latter ! Welcome to PF!

you seem to be saying the cannon ball goes up and curve,s at the top …

No, the geodesic is a curve in space and time …

as Nabeshin says, the cannonball is simply following a geodesic …

it is not going up in one dimension, and then coming back down, it is curving up in two dimensions (height and time), levelling out (travelling purely in time), and then curving back down again.

 

[latter]

hi and thanks

Originally Posted by latter
you seem to be saying the cannon ball goes up and curve,s at the top …

No, the geodesic is a curve in space and time …

i was unaware i wasnt including time i thought i was?

it is not going up in one dimension, and then coming back down, it is curving up in two dimensions (height and time)

yes ok

levelling out (travelling purely in time)

dont get this
and this is where my hole point of what i,m saying lies.i see it as running out of energy and stopping at the very peak of the curve .Why should it have just enough energy to tip it just past the peak allowing it to go back down.
why should it traveling in time make a difference ?
why doesn't it go back down the curve it came up?

and just out of interest do you agree that if it did stop(which you seem to be saying it doesnt).it would just stay there because there is no force in gravity to move it?

tiny-tim wrote
levelling out (travelling purely in time)

this also suggests to me that in time the ball will indeed level out.
and it is at this moment that it levels (if it does indeed level out)out that i am saying there is now no impetus for it to unlevel again.for there is no force to move it.

 

[Al68]

innewtionan its easy to understand cos there's a force.
so it is only friction in GR because there's no force.
you seem to be saying the cannon ball goes up and curve,s at the top .i feel there is a moment where a force is required at the top.becaue it must come to a stop.at the top and a force is required to move it.
also you are saying that the cannon ball comes back down not on the same path it went up it moved slighly left or right.

at the peak of the curve i see the ball stopping .it run out of energy for upwards moition.but it doesn't have a little more to tip it over the top.
its just stuck there at the peak perfectly balanced.needing a force to move it again.but there is no force.
so why does it fall

In GR, the ball only appears to change velocity due to using an accelerating reference frame (earth's surface). The same effect is seen in Newtonian physics if we used an accelerating spaceship in deep space as reference and threw the ball in the direction of the ship's acceleration. The ball will slow to a stop, then "fall" back.

In other words, in GR, Earth's surface (not the ball) is accelerating upward the whole time.

 

[PaulS1950]

The ball, if traveling straight up (from our perspective) will go up, decellerating, until it reaches the maximum altitude and then follows the lines (pull) of space - time back toward the point that you threw it from.
Although this is not exact it is a way to explain what is happening:
The space - time is constantly moving toward the Earth (or any other object of mass) so when the ball can no longer fight the "current" it follows it back to earth.

Paul, the 60 year old student

 

[tiny-tim]

Hi latter!

i was unaware i wasnt including time i thought i was?

You're not including time … this is clear from your question …

why doesn't it go back down the curve it came up?

… if you were including time, you would accept that the curve followed must have time increasing …

in other words, using the usual 2D graph for height and time, the curve can go up or down, but cannot go left … it must always go up-right level-right or down-right.

(so it cannot "go back down the curve it came up")

… i see it as running out of energy and stopping at the very peak of the curve .Why should it have just enough energy to tip it just past the peak allowing it to go back down.
why should it traveling in time make a difference ?

Energy has nothing to do with it (neither has impetus) … it is following a straight line between two points.

That straight line looks curved on the usual 2D graph, but it's still straight.

Nothing needs a reason for keeping to a straight line … once it's on it, it stays there … when it levels out on the 2D graph, and then starts curving down, that's because it's really going straight, and no explanation is needed.

 

[Passionflower]

In GR, as you note GR is not a force, merely curvature of spacetime, so the cannonball is simply following a geodesic in four dimensions.

A cannonball shot up and coming down is not following a geodesic. This first part of the path, the shooting, is accelerated movement.

as Nabeshin says, the cannonball is simply following a geodesic …

No.

 

[1bobwhite]

latter,

Lets expand the envelope of the observation of the cannonball just a bit.

Lets say you threw the cannonball vertically with such a velocity that it could go 1000 miles high before it comes to its peak and momentarily "stops".

Since it has no ability of its own to further accelerate, it will immediately start to slow down as it is released from your hand. (gravity). We will not consider any friction for this illustration.
But you don't notice any slowing down from your viewpoint. However a certain amount of time has elapsed from the moment of release to its "stopped" point.

From the instant of release, your position on the ground is changing continuously so that after a few moments your view of the cannonball will no longer be vertical. After more time, your position will be further from the vertical because you are standing upon the rotating platform of the earth. Your view of the cannonball will be that the cannonball is curving away because you viewpoint has now moved far to the side. Now the cannonball reaches its apex and starts its decent. The same amount of time elapses for its return to the ground. By the time it hits the ground, you are now far to the side, and the flight path of the cannonball appeared to you as long arch.
Not counting any of the other movements that are involved, if you launched the cannonball high enough, your rotation around the Earth could bring you back to where the cannonballs' return would drop it on your head. OUCH! Don't do that.

Satellites (cannonballs) are launched so that when they "return" to earth, the Earth has already moved out of the way and the path of return is now an orbit around the earth.

I don't believe it is possible to determine a "straight" path for anything that has a time element, when the observer is in motion.

I hope this helps a little.
Bob.

 

[IcedEcliptic]

At the risk of appearing rude, the OP needs to learn the basics of Newtonian mechanics, and spend a little time with SR to get a feel for the notion of spacetime. I think there is lacking in geometry here. I do not mean to insult, but perhaps scrubbing this and starting with first principles would result in a better educational outcome.

 

[latter]

Hi latter!


You're not including time … this is clear from your question …


… if you were including time, you would accept that the curve followed must have time increasing …

in other words, using the usual 2D graph for height and time, the curve can go up or down, but cannot go left … it must always go up-right level-right or down-right.

(so it cannot "go back down the curve it came up")


Energy has nothing to do with it (neither has impetus) … it is following a straight line between two points.

That straight line looks curved on the usual 2D graph, but it's still straight.

Nothing needs a reason for keeping to a straight line … once it's on it, it stays there … when it levels out on the 2D graph, and then starts curving down, that's because it's really going straight, and no explanation is needed.

well forgive me if i don't understand but so far my point is not really been seen.
what has time got to do with it.my point is when the ball reaches the top of the curve or straight line and stops why does it come back down.thAT it has stopped at the top is the critical point .i am saying.

latter wrote
and just out of interest do you agree that if it did stop(which you seem to be saying it doesnt).it would just stay there because there is no force in gravity to move it?

if someone fully answered this you would really see my point.
or in simple terms if anything stops in a gravity field , gravity couldn't start to move it again because it has no force to do so.

you have picked me out about time,fine but i don't seen how time can move something.so what is your point about time.

also i,m interested in the way it looks if the Earth moves while its up there,but again what's that got to do with my point

tiny-tim wrote
That straight line looks curved on the usual 2D graph, but it's still straight

so the ball runs out of upwards motion (does it stop or doesn't it stop)?
it seems to me you are saying regardless of whether the ball stops. Because it really is on a straight line it doesn't matter,it carrys on.what is speical about a straight line that means that if something stops on it , it can restart because it is on a straight line.

 

[espen180]

Explanation of curved spacetime:
http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html

Demonstration of geodesic motion in spacetime:
http://www.adamtoons.de/physics/relativity.swf

By setting the initial velocity to 0 and gravtiy to 1, you can see how the ball will behave in space and time after it reaches the top of its flight. Notice that the ball accelerates in space and decellerates in time.

 

[Ich]

well forgive me if i don't understand but so far my point is not really been seen.

In GR, it's not the ball that is accelerating. The floor is accelerating towards the ball, the ball does nothing but stay where it is. No force on the ball, but on the floor.

 

[latter]

Ich
you are talking about if the ball is falling.but saying that its not the ball falling its the floor rising.so what
the point is is whether the ball stops at the top of its motion upwards.and i mean "stop"
stop meaning you would need a force to move it.
in Newtonian physics you would call on the graviton.as soon as the ball stops the little gravitons could pull it.
but we don't have a force in Einsteins GRAVITY,
so in your talk i ask what has caused the floor to move towards the ball.but i don't seen the point of thinking like that because its the same either way round

espen180
i can not yet work out whether that is helping .
is it showing whether the ball stops at the top or not.
and how it would restart.it doesn't look like it to me

if something is in motion when it enters space curves there is no problem because you have motion.but if something doesn't have motion (and it is in space curve )it can not remove on a space curve "this is my point".
and this is why i ask has the ball stopped.at the top.

because if it did then things that stopped in a gravity field could no longer be moved by gravity.and would stay there until they were moved by some other force.

 

[Ich]

you are talking about if the ball is falling.but saying that its not the ball falling its the floor rising.so what

That's not what I'm saying.
I say the floor is accelerating, not the ball.

the point is is whether the ball stops at the top of its motion upwards.and i mean "stop"

You throw it upwards, and it's moving away. You accelerate with the floor, and when you reach the same speed as the ball, it's no longer moving away. Accelerating further, and you catch up with it.
The ball simply moves inertially.

so in your talk i ask what has caused the floor to move towards the ball.

That sea of magma on which the continental crust is swimming. Quite a force.

but i don't seen the point of thinking like that because its the same either way round

Of course is the result the same. Otherwise GR would fail the simples experimental tests.
The description is different. No force acting on the ball. And that was your question, IIRC.

 

[espen180]

espen180
i can not yet work out whether that is helping .
is it showing whether the ball stops at the top or not.
and how it would restart.it doesn't look like it to me

if something is in motion when it enters space curves there is no problem because you have motion.but if something doesn't have motion (and it is in space curve )it can not remove on a space curve "this is my point".
and this is why i ask has the ball stopped.at the top.

because if it did then things that stopped in a gravity field could no longer be moved by gravity.and would stay there until they were moved by some other force.

Aha! There is the problem. You do not yet understand how masses move in space-time.

In GR, all masses always move at the speed of light through space-time. The velocity of the mass is a vector with one temporal and three spatial components which behave such that the length of the velocity vector is constantly the speed of light. This is easy to see by looking at the equations for the lorentz transformations.

If there are no other masses present, space-time is flat. This means that unless a force acts on the ball, the direction of the velocity vector doesn't change. This in turn implies that the ball travels in a straight line through space.

Now consider curved space. For a mathematical treatment of curved coordinates go here: http://en.wikipedia.org/wiki/Curvilinear_coordinates . If we draw a straight line through a curved space, the components of the tangent vector of the straight line change as you progress along it. This means that although the line is straight, it's components are changing. This is the case also in GR. The ball is moving in a straight line throguh curved 4-dimensional space-time. Therefore, eventhough the line stays flat and the ball has constant speed c, the spatial components of the velocity vector change with time.

Thus, when the ball is at the top of the curve, it has zero spatial components, and a temporal component equal c. Nevertheless, when we progress along the straight line, the velocity vector changes direction according to the spacetime coordinates. The spatial components become nonzero, and the ball falls.

I hope this made this concept easier to visualize. I also appologize should anything I just said be inaccurate.

 

[Passionflower]

If there are no other masses present, space-time is flat. This means that unless a force acts on the ball, the direction of the velocity vector doesn't change. This in turn implies that the ball travels in a straight line through space.

One single mass is already enough to make spacetime curved.

Now consider curved space. For a mathematical treatment of curved coordinates go here: http://en.wikipedia.org/wiki/Curvilinear_coordinates . If we draw a straight line through a curved space, the components of the tangent vector of the straight line change as you progress along it. This means that although the line is straight, it's components are changing. This is the case also in GR. The ball is moving in a straight line throguh curved 4-dimensional space-time. Therefore, eventhough the line stays flat and the ball has constant speed c, the spatial components of the velocity vector change with time.

This explanation is bound to give people a big misunderstanding.

An object without proper acceleration moves on a geodesic but a geodesic is not necessarily a straight line. For instance on a sphere, which is a curved surface, the geodesics are curves.

 

[starthaus]

In GR, all masses always move at the speed of light through space-time. The velocity of the mass is a vector with one temporal and three spatial components which behave such that the length of the velocity vector is constantly the speed of light.

This statement is highly misleading. The correct statement is that the norm of the four-vector proper velocity:

$$\vec{U}=(dx/d\tau,dy/d\tau,dz/d\tau,cdt/d\tau)$$ is $$c$$.

This is easy to see by looking at the equations for the lorentz transformations.

Actually, it is more complicated than that, it is a consequence of the fact that:

$$|U|=\sqrt{(cdt/d\tau)^2-\Sigma(dx/d\tau)^2}=c$$

If there are no other masses present, space-time is flat. This means that unless a force acts on the ball, the direction of the velocity vector doesn't change. This in turn implies that the ball travels in a straight line through space.
This is the case also in GR. The ball is moving in a straight line throguh curved 4-dimensional space-time.

No, the ball is moving along a geodesic.In the presence of gravitational masses, the geodesics are not straight lines. Passionflower already corrected you on this.

 

[latter]

its strange but because you said this

Aha! There is the problem

i believe you.
i have to say believe because as yet i can not understand that atall.but for some reason i believe you see what i was getting at.
i will not ask for more explanations ,i,m goner try and work on what you,ve said ,and that could take weeks, months, years.thanks

i think this is what i need to understand

Thus, when the ball is at the top of the curve, it has zero spatial components, and a temporal component equal c. Nevertheless, when we progress along the straight line, the velocity vector changes direction according to the spacetime coordinates. The spatial components become nonzero, and the ball falls

i take it this is what i need to understand to answer my question.because this is what happens to the ball at the top.
just reading it quickly. You haven't just progressed along a line here

Nevertheless, when we progress along the straight line, the velocity vector changes direction according to the spacetime coordinates

its the

Nevertheless

word that worries me ,it just looks like a jump,
it just sounds like your thinking "the ball has stopped at the top ,but neverthless we will move on along the line and try and cover up the fact. poor sod won't notice.
i take it that's not what your doing ,but it just sounded a bit like it.


"Ich wrote
You throw it upwards, and it's moving away. You accelerate with the floor, and when you reach the same speed as the ball, it's no longer moving away. Accelerating further, and you catch up with it.
The ball simply moves inertially."


but this is if the Earth is accelerateing up like the old lift thing .if i was in a big lift and throw the ball upwards it would go up and if the lift accelerated quickly just after to match the ball ,the ball would be accelerateing but seem still again.i don't see the point of this in relation to whati was asking.

so in your talk i ask what has caused the floor to move towards the ball.
"Ich wrote
That sea of magma on which the continental crust is swimming. Quite a force."

i am sorry i don't get this either .because here i could simplely ask what is causing the magma to do this .so on and so on and eventaully you would have to quote a force .
my point was Einstiens gravity has no force.

 

[IcedEcliptic]

its strange but because you said this

i believe you.
i have to say believe because as yet i can not understand that atall.but for some reason i believe you see what i was getting at.
i will not ask for more explanations ,i,m goner try and work on what you,ve said ,and that could take weeks, months, years.thanks

i think this is what i need to understand

i take it this is what i need to understand to answer my question.because this is what happens to the ball at the top.
just reading it quickly. You haven't just progressed along a line here

its the word that worries me ,it just looks like a jump,
it just sounds like your thinking "the ball has stopped at the top ,but neverthless we will move on along the line and try and cover up the fact. poor sod won't notice.
i take it that's not what your doing ,but it just sounded a bit like it.


Ich
You throw it upwards, and it's moving away. You accelerate with the floor, and when you reach the same speed as the ball, it's no longer moving away. Accelerating further, and you catch up with it.
The ball simply moves inertially.
but this is if the Earth is accelerateing up like the old lift thing .if i was in a big lift and throw the ball upwards it would go up and if the lift accelerated quickly just after to match the ball ,the ball would be accelerateing but seem still again.i don't see the point of this in relation to whati was asking.

so in your talk i ask what has caused the floor to move towards the ball.

That sea of magma on which the continental crust is swimming. Quite a force.
i am sorry i don't get this either .because here i could simplely ask what is causing the magma to do this .so on and so on and eventaully you would have to quote a force .
my point was Einstiens gravity has no force.

I can't tell if you're conceding the point to Ich which you SHOULD, or if you're talking in circles... you need to quote properly.

You are right that gravity is spacetime curvature, and not a force in GR, but your previous statements don't make that clear.

 

[latter]

yea sorry i haven't learned to quote in the edit mode yet
no i,m not conceding to Ich atall.
infact i thought he was taking the micky by making it complicated to see what i knew.
i don't get how what he is saying relates to my question
Ich reminds me of a lift going upwards and if it ket pace with the ball the ball would seem stationary,but when the ball runs at of momentum the lift will have to either keep pace and slow down or the ball will hit the floor. this is to do with the Equivalence principle.perhaps but i don't see its point to my question yet.

balls may be moving along geodesics
but this is not my point my point. Its if the ball stopped how can it restart again.there are no gravitons to move it .AND geodesic lines are not a force
and there is no universal up and down to a geodesic line meaning something that's stopped doesn't start running down geodesic line as though there's a universal down.
so i am simply asking can something stop in a gravity field and how does it restart again.
in the case of the ball does it actaully stop at the top.this is what i had thought. Then how does it remove to go down.IF IT HAD STOPPED.that is

 

[IcedEcliptic]

yea sorry i haven't learned to quote in the edit mode yet
no i,m not conceding to Ich atall.
infact i thought he was taking the micky by making it complicated to see what i knew.
i don't get how what he is saying relates to my question.

balls may be moving along geodesics
but this is not my point my point. Its if the ball stopped how can it restart again.there are no gravitons to move it .AND geodesic lines are not a force
and there is no universal up and down to a geodesic line meaning something that's stopped doesn't start running down geodesic line as though there's a universal down.
so i am simply asking can something stop in a gravity field and how des it restart again.

OK, well let us put aside Gravitons, which are hypothetical and would be part of a QFT (Quantum Field Theory) not GR. The ball is opposed by the force of the ground, but if that and all friction were removed it would fall through the Earth and oscillate, up and down...! If you place a ball on a hill, and halfway down I stop it with my foot, when I move my foot the ball continues to fall, because of the slope of the hill.

To reintroduce Gravitons, they either represent something that does not fit with GR, or they could be the quanta of spacetime curvature. Does that help at all?

 

[Passionflower]

yea sorry i haven't learned to quote in the edit mode yet
no i,m not conceding to Ich atall.
infact i thought he was taking the micky by making it complicated to see what i knew.
i don't get how what he is saying relates to my question.

balls may be moving along geodesics
but this is not my point my point. Its if the ball stopped how can it restart again.there are no gravitons to move it .AND geodesic lines are not a force
and there is no universal up and down to a geodesic line meaning something that's stopped doesn't start running down geodesic line as though there's a universal down.
so i am simply asking can something stop in a gravity field and how des it restart again.

The "stopping" and "re-starting" of the ball is caused by a combination of two factors:

A: The cannonball and the Earth inertially moving away from each other (caused by the initial firing of the cannon).
B: The cannonball and the Earth inertially accelerating (thus without proper acceleration) towards each other (caused by the curvature of spacetime)

So, at the stopping point, B just has overcome A and now B takes over.

 

[latter]

Passionflower wrote

The "stopping" and "re-starting" of the ball is caused by a combination of two factors:

A: The cannonball and the Earth inertially moving away from each other (caused by the initial firing of the cannon).
B: The cannonball and the Earth inertially accelerating (thus without proper acceleration) towards each other (caused by the curvature of spacetime)

So, at the stopping point, B just has overcome A and now B takes over.

but B not happen at the same time as a
so when does B happen in time ?
hang on let me try and think this threw.

A hapens when i throw the ball and as the ball is nearly stopping at the top the Earth is slowing its movement away
so that as the ball stops the Earth has stopped moving away.
is this right so far?
are you now saying that the Earth now moves back in and this movement of the Earth back in causes the ball to go over the top.(or to restart its self)
is this right?
i hope so because i really like this.
and the Earth moves back in because of what?sorry just can't quite see this point I am sure i should but cant.
but thanks as long as i know why the Earth moves back in and i have understood the rest.
i can sit back and light a fat cigar.


IcedEcliptic wrote
If you place a ball on a hill, and halfway down I stop it with my foot, when I move my foot the ball continues to fall, because of the slope of the hill.
if you don't have gravitons in this then it seems to me you are having the idea of universal down.

why would it go down there is no force to move it.the geodesic lines are not a force so why would it go down .
to me you are having a notion of a universal down as if all things that have stopped fall down if the stopper is removed in a gravity field.

 

[Passionflower]

A and B happen at the same time. While the Earth and the cannonball move inertially away from each other due to the initial proper acceleration when the cannonball was fired, the Earth and the cannonball also accelerate inertially towards each other due to the curvature of spacetime. The acceleration B "catches up" with A when the ball turns around.

 

[yuiop]

A cannonball shot up and coming down is not following a geodesic. This first part of the path, the shooting, is accelerated movement.
...

As you say, the shooting is not inertial movement. However, after the cannonball has left the cannon, its movement is inertial (if there is no atmosphere). Both its path up and back down is following a geodesic. I am not saying you are wrong, just adding to what you are saying and hopefully clarifying.

 

[latter]

o god no
i don't get it.of course I am not saying your wrong.
but how can this happen
unless the curvature is tiny and the Earth is moving in a tiny arc perhaps?

The acceleration B "catches up" with A when the ball turns around.
but A and B are the Earth and ball there are not 2 sets of Earth's and balls
so do you mean the momentum of B somehow pulls the ball over the top.im sure that cannot be it because there's no force convade from the Earth to the ball
i,m sure your right but for now i can't quite see it

just looking at this point.
when B "catches up" with A this is the moment that it would make the ball go over the top?
but WHAT force/mechanism is acting between Earth and ball to do this. ie: like hidden strings it almost seems i no its not but you get the idea i mean.

getting back to this
"While the Earth and the cannonball move inertially away from each other due to the initial proper acceleration when the cannonball was fired,"
ok
"the Earth and the cannonball also accelerate inertially towards each other due to the curvature of spacetime"
but surely because the Earth has to go round a curve at least for a short peroid the Earth is moving away frome the ball?

i also don't see how the ball is moving towards the earth.I can see how perhaps the Earth has curved round and is moving towards the ball .SO perhaps one can say the ball is moving towards the earth.

But as the ball gets to the top. The Earth now does what spring back round the curve it went on and this causes the ball to go over?
but i still don't see the mechanism between Earth and ball.ie there's no hidden strings pulling the ball over.

 

[1bobwhite]

Latter,

In both GR and SR, it is the relationship of the observer and the object being observed that accounts for the perceived positional changes.

If you were positioned upon the cannonball, you would observe the cannon and the Earth retreating away from you, stopping, and then accelerating toward you until you collided.

Because the cannonball and you are in ballistic freefall, you would not perceive yourself decelerating, stopping, and accelerating again. Observed from the cannon, the cannonball does the moving.

Observed from the side, both the cannonball and the cannon move away from each other in an arc with no observed speed changes.

Since the cannonball is actually in a curved trajectory, it will only appear to "stop" when the observers view is in such a position that the cannonballs flight is in a straight line. Then when it is at the top of the arc, it appears to momentarily "stop".

Being on a rotating sphere, even if the cannon was fired on such a trajectory that it would return to the muzzle of the barrel, its observed flight path would appear to be the same as the previous scenarios, all based on the observers position of view.

The math describes the relationship of the relative positional changes between the observer and the observed based upon their relative speeds and masses and the time frame reference used. The notions of light speed and gravity are also based on the math to describe these observations.

 

[yuiop]

... so why does the cannon ball apon "stopping" from going up go back down.

The cannon ball never truly stops in any absolute sense. In relativity, being at rest and moving is just... ummm... relative. Imagine the cannon ball is fired in flat space so that it moves with constant velocity, according to some observer that remains at rest with the cannon. Imagine another observer in an accelerating rocket chasing after the cannon ball. To the rocket observer the cannon ball appears to slow dow, momentarily come to rest (as the rocket speed matches the cannon ball speed) and then go backwards (as the rocket speed exceeds the speed of the cannon ball). Even though the ball appears to stop briefly in the accelerating rocket frame (equivalent to point of view of an observer on the Earth's surface) it is clear that it never stops in the inertial cannon frame (after the firing event).