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What gravity?

  1. Sep 2, 2009 #1
    Assuming a universe with only space and two motionless masses, would the two masses start to move toward each other?
     
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  3. Sep 2, 2009 #2

    Pengwuino

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    Yes, they will, they both create gravitational fields.
     
  4. Sep 2, 2009 #3
    No, because without time, no motion can occur.
     
  5. Sep 2, 2009 #4

    Hootenanny

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    I don't think that the OP meant "space" to mean only the spatial dimensions. I rather think that they meant "nothing but empty space and two masses".
     
  6. Sep 2, 2009 #5
    I see. In that case we have a more tricky question on our hands.

    So firstly i'll assume the particles are "point" particles. Then there exists only 1 "ruler", if you like, in space in which distance can be measured with. That is, the distance between these two particles is the only possible measuring device.

    This to me implies that describing the particle's as moving towards one another is meaningless, because there is no concievable way to infact identify that the distance between the particles is decreasing.

    What analogy can I use to make my picture clear. Immagine that tommorrow, everything in the universe is exactly half the size it was today. That is, I am now half my height, and the ruler I use to measure my height is also half the height of what it was today, and the expectation value of the radius of an electron around the universe is halved. Clearly in this situation, because everything in the universe has halved, there is absolutely no way to tell at all that anything has changed.

    In fact, because in the previous paragraph, the consequences of everything in the universe halving in size, is identical to the theory that nothing in the universe changed at all, we would use occam's razor to say that in fact nothing in the universe changed at all.

    Similarly in your example of a two particle universe. Whether the distance between the particles is decreasing or staying the same, because the only distance unit in your scenario is the distance between the two particles, these scenarios would be equivalent.

    Therefore, it is reasonable to suggest that no motion occurs.
     
  7. Sep 2, 2009 #6

    Born2bwire

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    There would still be means of denoting the motion. First, since the force is dependent upon the separation of the masses, the force will increase as the masses attract each other. So the observers on the either mass will not only experience an extra acceleration, but a changing acceleration which should be measurable. In addition, one could make measurements of the other mass and derive it's motion in the same way that we have deduced the expansion of the universe despite being part of it. In your analogy, the universe is changing in size which is what is happening currently in the real Universe but despite not being able to observe the Universe outside of it (disregarding the physical implications of whether this is a possible supposition) we are still able to take the appropriate measurements to observe this.
     
  8. Sep 2, 2009 #7

    Hootenanny

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    Nonsense. There are several measurements that observers on either mass could make that would show that the masses were not only accelerating, but accelerating at an increasing rate.

    Edit: I seem to be following Born2bwire around today :rolleyes:
     
  9. Sep 2, 2009 #8
    A body in free fall cannot detect that it is in free fall.
    An analogy is that when you stand in an elevator that is free falling, the laws of physics are such that the elevator is approximately an inertial reference frame.
     
  10. Sep 2, 2009 #9

    Born2bwire

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    Yes, but we have the caveat here that the force applied is not constant. If the force was constant, then the acceleration would be constant and one could argue this. But with the change of the force as a function of distance, we cannot make the same argument. If I am in an elevator that is going up, while it is in motion between two floors it just feels like I have consumed one too many Krispy Kremes that morning, but during the moments that elevator starts up and stops at a floor I can detect the changing acceleration.
     
  11. Sep 2, 2009 #10

    Hootenanny

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    Free fall (or more precisely the equivalence principle) only applies when the acceleration is constant, which is not the case here.

    Edit: dammit Born2bwire!
     
  12. Sep 2, 2009 #11
    In fact, the force acting on the free falling elevator is also not constant because as the elevator gets closer to the Earth, the acceleration will increase. There is no way to determine the change in acceleration, because the elevator does not exert a force on your body. This is because your body is subject to the same external acceleration the elevator is subjected to.
     
  13. Sep 2, 2009 #12

    Hootenanny

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    So technically, the equivalence principle doesn't apply here. However, the gravitational field can be approximated as uniform near the earth's surface. The correction is so small that the elevator can be approximated as free-falling. Once once again, the equivalence principle only applies in a uniform field.
     
  14. Sep 2, 2009 #13
    Ok, so you seem to be implying that there is something special about changing acceleration that can be detected.

    Let's consider a person in a spaceship (At the present, the person is hovering in the middle of the spaceship). Assume there is no gravity between the person and the spaceship. Now let the spaceship be attracted by gravity to a planet in space, and thus as the spaceship approaches the planet, the acceleration will also increase.

    Now because the acceleration of the person inside the spaceship will always be the same as the acceleration of the spaceship itself, the velocity of the spaceship will always be the same as the man within the spaceship at any time and therefore there will be no force or interaction between the spaceship and the person within the spaceship. The man will always remain where he is, in the centre of the spaceship.

    This implies that the man cannot detect his changing acceleration based on his physical interaction with the spaceship.

    So by what mechanism can the man detect his changing acceleration?
     
  15. Sep 2, 2009 #14

    Born2bwire

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    Again, take the example of a real elevator. When the elevator starts up and when it slows down, you can physically feel it, the change in acceleration. When it is moving between floors at a more or less constant speed, we are experiencing a constant accleration (due to the net force from gravity and the movement of the elevator propagated through our contact with it on the floor). At this point, everything else is just a question of figuring out how to quantify this measurement, the change of acceleration (called "jerk" I believe) using a device. Whether this device is our own body or some black box is now irrelevant.

    EDIT: If you want an example of a device, a simple one would be a submerged ball in a graduated cylinder. The cylinder would be filled with a fluid that has a gradient density. Let's say various oils of different densities. The oils will form layers of constant densities, the highest at the bottom, the lowest at the top. The acceleration of the float in the liquid will give it a weight and cause it to seek out one of the oil layers. As the acceleration changes, the float's weight changes and it will move to a different oil layer. I guess to make sure that the oils are not affected by the changing accleration we would need to stipulate that they are incompressible.
     
  16. Sep 2, 2009 #15
    Please read my previous post. It explains why your intuitive view is flawed. The "jerk" you feel in an elevator is due to the additional force between the elevator and the human. The "jerk" is not experienced when it is an external force that is causing the changing acceleration. Do read my previous post.
     
  17. Sep 2, 2009 #16

    Hootenanny

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    Any object of non-zero dimensions in a non-uniform gravitational field would experience a tidal force, which is most certainly detectable. In fact these so-called tidal forces appear as components of the Riemann tensor.
     
    Last edited: Sep 2, 2009
  18. Sep 2, 2009 #17

    Born2bwire

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    No, we can always sense an additional force. When the elevator is moving up, there is an additional force and we sense that as an overall increase in our body weight. However, we detect the jerk by the fact that we can sense a time dependent change in our body weight. If I have a mass on a spring, the amount of deflection of the spring is a measurement of the weight of the mass. A jerk would cause this deflection to change over time. It doesn't matter whether this jerk is transmitted at a subset of points on the mass or our body (like the surface of our feet in contact with the elevator floor) or if it is spread out through our body (like due to a gravitational force). The end result is that there will be change in weight which is detectable because if we have weight then there is still a net force acting on us and our bodies, or devices, can detect a change in this force even if we cannot detect the force when constant if we are in free fall.
     
  19. Sep 2, 2009 #18
     
  20. Sep 2, 2009 #19
     
  21. Sep 2, 2009 #20

    Born2bwire

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    Then you simply apply a constant force to an object along the direction of the jerk, the resultant net force would be time dependent.

    Edit: To clarify, you could do something as simple as toss a ball and measure it's path, the jerk would result in a path different from that of a constant force. This would be compounded even more by the fact that the force on the ball after being tossed is spatially dependent and time dependent in this context.
     
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