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

  1. May 19, 2010 #1
    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.
     
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  3. May 19, 2010 #2

    Nabeshin

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    Re: Gravity

    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.
     
  4. May 19, 2010 #3
    Re: Gravity

    innewtionan its easy to understand cos theres a force.
    so it is only friction in GR because theres 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 doesnt 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
     
    Last edited: May 19, 2010
  5. May 19, 2010 #4

    tiny-tim

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    Welcome to PF!

    Hi latter ! Welcome to PF! :smile:
    No, the geodesic is a curve in space and time

    as Nabeshin :smile: 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. :wink:
     
  6. May 19, 2010 #5
    Re: Gravity

    hi and thanks

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

    yes ok

    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 travelling in time make a difference ?
    why doesnt it go back down the curve it came up?

    and just out of intrest 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.
     
    Last edited: May 19, 2010
  7. May 19, 2010 #6
    Re: Gravity

    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.
     
  8. May 19, 2010 #7
    Re: Gravity

    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
     
  9. May 20, 2010 #8

    tiny-tim

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    Hi latter! :smile:
    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. :wink:

    (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. :smile:
     
  10. May 20, 2010 #9
    Re: Gravity

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

    No.
     
    Last edited: May 20, 2010
  11. May 20, 2010 #10
    Re: Gravity

    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.
     
  12. May 20, 2010 #11
    Re: Gravity

    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.
     
  13. May 20, 2010 #12
    Re: Gravity

    well forgive me if i dont 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.


    if someone fully answered this you would really see my point.
    or in simple terms if anything stops in a gravity field , gravity couldnt start to move it again because it has no force to do so.

    you have picked me out about time,fine but i dont seen how time can move something.so what is your point about time.

    also i,m intrested in the way it looks if the earth moves while its up there,but again whats 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 doesnt it stop)?
    it seems to me you are saying regardless of whether the ball stops. Because it really is on a straight line it doesnt 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.
     
    Last edited: May 20, 2010
  14. May 20, 2010 #13
  15. May 20, 2010 #14

    Ich

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    Re: Gravity

    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.
     
  16. May 20, 2010 #15
    Re: Gravity

    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 dont have a force in Einsteins GRAVITY,
    so in your talk i ask what has caused the floor to move towards the ball.but i dont 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 doesnt 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 doesnt 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.
     
    Last edited: May 20, 2010
  17. May 20, 2010 #16

    Ich

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    Re: Gravity

    That's not what I'm saying.
    I say the floor is accelerating, not the ball.
    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.
    That sea of magma on which the continental crust is swimming. Quite a force.
    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.
     
  18. May 20, 2010 #17
    Re: Gravity

    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 concider 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.
     
  19. May 20, 2010 #18
    Re: Gravity

    One single mass is already enough to make spacetime curved.

    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.
     
    Last edited: May 20, 2010
  20. May 20, 2010 #19
    Re: Gravity

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

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

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

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

    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.
     
  21. May 20, 2010 #20
    Re: Gravity

    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 havent 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 stoped at the top ,but neverthless we will move on along the line and try and cover up the fact. poor sod wont notice.
    i take it thats 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 dont 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 dont 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.
     
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