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Equivalence or equal?

  1. Jan 24, 2006 #1
    Hi. New to this forum. Great place.
    A long time ago when I first read about equivalence in relation to gravity I thought it seems too much like a coincidence. I thought if it smells like a duck, looks like a duck, and quacks like a duck, chances are its a duck.
    I mean what if gravity is indeed the effect of inertial acceleration and not just equivalent to it? What if earth, and all matter is actually expanding at some equal accelerated rate. We don't notice the expansion since we are also expanding so the scale stays the same. We do however feel the outward expansion of the earth as gravity as our bodies are accelerated outwards when standing on the surface of the earth.
    For example when an apple falls from a tree, it doesn't really fall. It just sits in free space and the surface of the earth rushes upwards and hits it. Being on the frame of reference of the surface of the earth we see the apple as falling.
    We don't feel anything during "free fall" because nothing is happening. We are just sitting in one spot in space and the surface of the earth is rushing towards us.
    Anyhow just and idea from a non-physicist. Never knew who I could tell this idea until I found this forum. I'm sure there are many flaws in the idea.
  2. jcsd
  3. Jan 24, 2006 #2


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    I think that's what "equivalent" already means, they really are the same thing. My understanding is that any time you have some effects which are modeled as being due to a gravitational field in one coordinate system, you can pick another coordinate system where the same effects are modeled as being due solely to acceleration, and the two descriptions are equally valid. But I don't have too much knowledge of general relativity, maybe someone else can confirm this.
  4. Jan 25, 2006 #3
    tbitz - the idea that everything is blowing up so the earth and other bodies are catching up to the objects has been put forth several times - but a bit of thinking should convince you that things can't work that way - try to explain how an object can stay in orbit - i.e., if a satellite is above NY at one moment - it cannot get to another part of the globe and be the same distance above the surface unless it moves in a curved path - so if the earth were merely rising to meet the satellite at an accelerating rate - the satellite is not going to appear as being in an orbit that circumscribes the earth

    That being said - there are other theories of gravity based upon some sort of accelerating dynamic - one that has found favor with relativity dissidents is the inflow theory - the notion being that space is falling into matter - the greater the density of the mass the greater the inflow rate - this theory cannot be so easily dismissed - it has some merit in that it relates the time dilatation that is consequent to motion in special relativity to the amount of time dilation that is measured between clocks at different gravitational potentials - so a clock at the earth's surface runs slower than a clock at an altitude of 1000 meters by exactly the same factor as would be measured if space were falling inwardly and the spatial velocity were increasing as you got closer to the earth in proportion to a factor which corresponds to the escape velocity.

    There are also dynamic theories that relate the magnitude of the gravitational constant to the rate of expansion of the universe - these are based upon a spherical model of the universe that is expanding in accordance with Hubble's law - when a sphere dilates at a constant radial rate the volume increases geometrically (as the cube of the radius) ..in other words the volume is accelerating - and the magnitude of that acceleration corresponds to G (which incidentally has units of volumetric acceleration per unit mass).

    All this is probably more than you wanted to know in any case.
  5. Jan 25, 2006 #4
    If the "inflow" speed of space at any radius r in this case is supposed to be the coordinate speed, as measured by an observer at infinity, this seems inconsistent with GR. Coordinate speed increases at first (almost following the rate of the escape velocity) but decreases again beyond a radius slightly over the Schwarzschild radius. At the Schwarzschild radius, coordinate speed is zero. So this "inflow" speed must be related to something else, I suppose?
  6. Jan 25, 2006 #5
    hi Mortimer - should probably not be describing a theory that I am only slightly familiar with - there are a lot of posts on the net - I neither endorse nor reject the idea - it is of interest because those who do have a strong mathematical background have proposed certain tests to determine whether GR or inflow best describes reality. Einstein in GR considers space as static - so too in SR - but the universe as a whole is actually a giant dynamic - expansion and internal motion are part of the whole - - the inflow theory captures a different physical picture that leads to the same equations according to its advocates
  7. Jan 25, 2006 #6


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    The equivalence principle is important -- in some sense, any way of looking at the situation is equally valid.

    IOW, it doesn't matter if you look at it as if the surface of the Earth is "stationary" and you're falling down to it, or if you look at it as you are "stationary" and the Earth is rising to meet you. (Or many other, seemingly silly ways to look at it, some with the Earth expanding, some contracting, some distorting into funny shapes...)

    But what you are really feeling here are the electromagnetic forces that prevent your feet and the ground from getting too close.
    Last edited: Jan 25, 2006
  8. Jan 26, 2006 #7
    Hurkyl - I think what the author of the thread is talking about is a theory that the earth itself is actually expanding at 32 ft/sec^2 and the Sun would be expanding at a different rate as would all masses - they would be expanding at an accelerating rate that comports with the g field experienced at the surface of the mass
  9. Jan 26, 2006 #8
    Yeah, the orbit thing doesn't fit well with the theory.

    It does explain why objects of any mass fall at the same rate very well. I always thought this didn't seem right using conventional theory of gravity.


  10. Jan 26, 2006 #9


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    Question for Hurkyl or other GR experts--would it be possible to come up with a crazy coordinate system for the entire neighborhood of the earth where this would actually be true, so the G-force experienced by both me and some guy on the opposite side of the earth would be explained in terms of the surface of the earth accelerating us in opposite directions in this coordinate system? Or is it only possible to come up with local coordinate systems where the G-force you experience is a consequence of the earth underneath your feet accelerating you upwards?
  11. Jan 27, 2006 #10
    According to GR, the acceleration that you feel on the surface of the Earth is a result of being pushed off the geodesic (straight) path that you would be following in free fall (I think the correct term is that your velocity vector is no longer "parallel transported" along the geodesic). It is the electromagnetic forces that are pushing in this case. In free fall, your 4D velocity is unaccelerated and follows a straight path. On the surface of the Earth, your 4D velocity is continuously changing, i.e., your direction in 4D continuously changes. Compare e.g. the acceleration that you feel while sitting on a spinning disc (which is the 3D analogy). So that indicates that your local 4D coordinate system is "spinning", not expanding.
    Last edited: Jan 28, 2006
  12. Jan 27, 2006 #11
    According to GR, a clock at the bottom of a tall building ticks more slowly than an identical clock on the top floor. This has been strongly supported by empirical data. If gravity were the result of acceleration, the opposite would be seen.
  13. Jan 29, 2006 #12
    Welcome and greatings!

  14. Feb 7, 2006 #13
    Well, I’ve often read that Einstein’s notion was that the ground accelerates upward to meet the apple, and this is implied by his description of the equivalence principle. That doesn’t require a preferred frame, nor does it require the Earth to expand. Just think that the apple stays in one spot in space that falls to the ground. Then the ground accelerates through space, locally just like a rocket accelerating through flat spacetime at 1 Earth gravity felt by its crew. About the equivalence principle, Einstein said that the rocket’s acceleration and the acceleration we feel on the ground are the exact same thing, not just equal. In general relativity, the coordinate system in which the apple stays in one spot in space that falls to the ground is called free-fall coordinates (google for it).
  15. Feb 7, 2006 #14
    Only one problem, Tony. If the earth is expanding at an some rate, why is it that matter at different heights above the earth appear to 'fall' toward the surface at DIFFERENT rates?:uhh:
    Apparently its not a duck afterall.:rolleyes:

    Last edited: Feb 7, 2006
  16. Feb 8, 2006 #15
    I'm not suggesting there is a prefered frame of reference. Just trying to explain what is actually happening.

    The current explaination (as I understand it) is that the mass of earth causes gravitational field which curves space thus making objects fall towards earth.

    I'm just thinking of another explaination.

    As mentioned earlier, the theory doesn't explain how satellites can orbit the earth. Until orbits can be explained with this expansion theory, it isn't really of much use. I've thought long an hard to try an make it orbits fit in this expansion theory, but just can't make it work.


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