January 16, 2010

  • Question 210 - Struggling with question on Geocentrism Part 3

    Ok, thanks although I'm not sure what you mean by "Schwarzchild radius at Saturn".  A Schwarzchild radius is a radius at which a object is compressed to where it becomes a black Hole.

    Thanks,

    Chesley

    R. Sungenis: Yes, but it is also the point at which the centrifugal and Coriolis forces reach their limit in a rotating mass. if the rotating mass is the universe, the limit is around the orbit of Saturn. Here is the excerpt on that topic in my book Galileo Was Wrong:

     

    Bondi’s Geocentrism

     Like the rest of the physicists to whom we ascribe the word “geocentrism” in this chapter, Sir Hermann Bondi (d. 2005) would not refer to himself as a geocentrist. He, nevertheless, would be one of the first to admit that modern physics ably defends geocentric cosmology. This becomes abundantly clear in a 1994 paper Bondi wrote titled: “Angular Momentum of Cylindrical Systems in General Relativity.”[1]

          

    Bondi discovered two important facts from General Relativity that can be employed to defend geocentrism. First, Bondi derived and quantified what has been traditionally known as angular momentum, discovering in the process that the universe’s cylindrical symmetry prohibits gravitational waves from carrying angular momentum. This finding resolves a critique of geocentrism which posited that, to conserve angular momentum, the universe would slow down if a mass is raised on Earth and accelerate if the same mass were lowered. Bondi showed that, according to General Relativity, this is not the case, and thus the criticism is neutralized. Related to the above, Bondi also discovered that, according to General Relativity, all the mass beyond the Schwarzschild radius (where the tangential speed of the universe exceeds c) can be ignored, since it will contribute nothing more to the frame dragging and centrifugal forces already present. He writes:

     

    The main point to note is that whereas in the newtonian, non-rotation of the reference system at infinity is taken for granted, in the relativistic treatment such rotation is permitted but irrelevant to the measure of angular momentum, which is an intrinsic characteristic of the material system….What is the nature of this limit? For such a cylinder the required angular velocity makes the tangential velocity at r = r2 equal to the speed of light….Both the space drag on the core and A [angular momentum] will be unaffected by such outside layers….The conservation of A occurs even if gravitational waves are emitted by the cylinder. This is perhaps not surprising, since the cylindrical symmetry of the waves precludes their carrying angular momentum…. Therefore the intrinsic nature of the angular momentum of the inner becomes patent as it is wholly unaffected by anything that goes on outside. Thus there is no transfer of angular momentum between outer and inner.[2]

     

    Bondi arrived at the above derivation a little earlier in his paper:

     

    It is a remarkable fact, discussed later, and of some relevance to Machian considerations, that this unique conserved measure of angular momentum appropriate to the symmetry imposed is independent of any superposed state of rotation.[3]

     

    The same conclusion was stated in a different way in Bondi’s abstract: “It emerges that angular momentum and space drag behave very differently as thicker and thicker spinning cylinders are studied.”[4] Hence, from the perspective of General Relativity, Bondi makes geocentrism completely feasible. That is, if the argument against geocentrism that appeals to the conservation of angular momentum is valid, it would violate the strong principle of Relativity. To rescue Relativity theory from this failure, Bondi, by means of his meticulous tensor analysis, has simultaneously refuted the objection as it has traditionally been directed against geocentrism. The angular velocities used by Bondi are completely compatible with geocentric mechanics, since his analysis specifically validates cosmologies which have rotations at tangential velocities far greater than the speed of light.

     

    [1] Royal Society Proceedings, Series A - Mathematical and Physical Sciences, vol. 446, no. 1926, July 8, 1994, pp. 57-66.

     

    [2] “Angular Momentum of Cylindrical Systems in General Relativity Royal Society Proceedings,” Series A - Mathematical and Physical Sciences, vol. 446, no. 1926, July 8, 1994, pp. 63-64.

     

    [3] Ibid., p. 61. My thanks to Martin Selbrede for bringing Bondi’s paper to my attention, and his help in analyzing it.

     

    [4] Ibid., p. 57.