Saturday, July 01, 2006

Sample from Galileo Was Wrong, Sent to Stephen M. Barr

Robert Sungenis sent this sample to Dr. Barr to clarify some issues regrading superluminal velocity in geocentric systes. The footnotes have been renumbered starting at (1).

Bondi's Geocentrism
Although like the rest of the physicists to whom we ascribe the word "geocentrism" in this chapter, Sir Hermann Bondi (d. 2005) would not explicitly refer to himself as a geocentrist, nevertheless, he 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 Schwarzchild 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 = r^2 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." 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.

The Lemaître-Tolman-Bondi Model

Another aspect of Bondi's teaching that makes geocentrism feasible is his development, along with Georges Lemaître and Richard Tolman, of the spherically symmetrical expanding universe.[4] Einstein's field equations allow at least two possible universes that were, more or less, diametrically opposed to one another: an isotropic homogeneous universe or an isotropic inhomogeneous universe. The former is the model that eventually developed into the Big Bang theory. As we noted earlier, such a universe will appear the same from every direction, and thus it has no center or distinguishing point. Today this model generally goes by the name of the Lemaître-Robertson-Walker model. But Einstein's field equations also allowed a spherical universe with a center, which was developed by Lemaître, and later Tolman, Bondi and a few others. As we noted in Chapter 3 in the discussion of Stephen Hawking's "modesty," is a spherical univere with a center, and most likely with Earth in that very center Few admit the fact that Lemaître introduced a prior model, which was non-homogeneous and isotropic, and thus it necessarily comprised a center, that is, a distinct place from which the view of the universe would be unique. This is commonly known among physicists today as the Lemaître-Tolman-Bondi model.

Astrophysicist George Ellis, whom we noted previously had advocated that the Earth is in a central location in the universe, affirmed the Tolman-Bondi model in his award-winning 1978 paper. His abstract states:

It is shown that spherically symmetric static general relativistic cosmological space-times can reproduce the same cosmological observations as the currently favored Friedmann-Robertson-Walker universes, if the usual assumptions are made about the local physical laws determining the behavior of matter, provided that the universe is inhomogeneous and our galaxy is situated close to one of its centers.[5]

Ellis adds that only three things can lead us to conclude that the universe we live in is not such a static space-time spherically symmetric universe: "(i) unverifiable a priori assumptions, (ii) detailed physical and astrophysical arguments, or (iii) observation of the time variation of cosmological quantities" and concludes:

...the standard models of a princile of uniformity (the cosmological or Copernican principle). This is assumed for a priori reasons and not tested by observations. However, it is precisely this principle that we wish to call into question. The static inhomogeneous model discussed in this paper shows that the usual unambiguous deduction that the universe is expanding is a consequence of an unverified assumption, namely, the uniformity assumption. This assumption is made because it is believed to be unreasonable that we should be near the center of the Universe. [Ellis adds footnote here citing Steven Weinberg's Gravitation and Cosmology, 1972].[6]

As we noted previously, the inhomogeneous models of the universe were being proposed mainly because there were simply too many problems cropping up in the homogeneous models. Modern cosmology was, as the saying goes, "caught between a rock and a hard place." Accepting the homogeneous models would produce universe that would either explode or implode. If they accepted the inhomogeneous model, they also had to accept the distinct possibility of an Earth-centered universe, which was apt to be rejected on "philosophical grounds." To their consternation, cosmologists were producing very stable inhomogeneous universes, and doing so, ironically, with Einstein's field equations.[7] Yet, as Gerard de Vaucouleurs noted:

With few exceptions, modern theories of cosmology have come to be variations on the homogeneous, isotropic models of general relativity. Other theories are usually referred to as "unorthodox," probably as a warning to students against heresy. When inhomogeneities [read: theories that can lead to an Earth-centered universe] are considered (if at all), they are treated as unimportant fluctuations amenable to first-order variational treatment. [8]


[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] "Angular Momentum of Cylindrical Systems in General Relativity Royal Society Proceedings," p. 61. My thanks to Martin Selbrede for bringing Bondi's paper to my attention, and for his help analyzing it.

[4] Hermann Bondi, "Spherically Symmetrical Models in General Relativity," Monthly Notices of the Royal Astronomical Society, vol. 107, Nos. 5, 6, 1947, pp. 410-425. By "spherically symmetrical" Bondi means that there is a center to the universe. He says as much in his paper: "We shall show that in our spherically symmetrical universe with the standard source at its center..." (ibid., p. 413).

[5] George F. R. Ellis, "Is the Universe Expanding?" General Relativity and Gravitation, vol. 9, no. 2, February, 1978, p. 87.

[6] George F. R. Ellis, "Is the Universe Expanding?" General Relativity and Gravitation, vol. 9, no. 2, February, 1978, p. 87. In a subsequent work, Ellis, et al., state: "The problem is that while isotropy is directly observable, homogeneity (on a cosmological scale) is not. In the standard discussions the assumption of homogeneity is made a priori, either directly, or in some equivalent form (e.g., as the assumption that the Universe is isotropic for all observers), and so is not subjected to observational verification. Accordingly the standard 'proof' of the expansion of the Universe is based on an unverified a priori assumption" (George F. R. Ellis, R. Maartens and S. D. Nel, "The Expansion of the Universe,"Monthly Notices of the Royal Astronomical Society, 184, 1978, p. 440).

[7] Summary analysis by Andrzej Krasinski, Inhomogeneous Cosmological Models, University of Cambridge Press, 1997; George A. Lemaître, The Expanding Universe, 1933 Ann. Soc. Sci Bruxelles A53 51 (French), reprinted in 1997 in General Relativity and Gravitation, 29, 641; Hermann Bondi, "Spherically Symmetrical Models in General Relativity," Monthly Notices of the Royal Astronomical Society, vol. 107, 410B, 1947; Richard Tolman, The Effect of Inhomogeneity on Cosmological Models, 1934 Proceedings of the National Academy of Sciences, 20 169, reprinted in 1997 General Relativity and Gravitation, 29 935; A. Krasinski A and C. Hellaby, “Structure Formation in the Lemaître-Tolman model," Physical Review, D65 023501, 2002; Guy C. Omer, Jr., “A Nonhomogeneous Cosmological Model," The Astrophysical Journal, vol. 109, 1949, pp. 164-176; Ronald Kantowski, "The Coma Cluster as a Spherical Inhomogeneity in Relativistic Dust," The Astrophysical Journal, vol. 155, March 1969; Gerard de Vaucouleurs, Science, "The Case for a Hierarchial Cosmology," vol. 167, No. 3922, Feb. 27, 1970; W. B. Bonnor, "A Non-Uniform Relativistic Cosmological Model," Monthly Notices of the Royal Astronomical Society, 159, 1972, pp. 261-268; Stamatia Mavrides, "Anomalous Hubble Expansion and Inhomogeneous Cosmological Models," Monthly Notices of the Royal Astronomical Society, 177, 1976, pp. 709-716.

[8] Gerard de Vaucouleurs, "The Case for a Hierarchial Cosmology," Science, vol. 167, No. 3922, 1970, p. 1204


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