Abstract
This article expands the development of the concept of reciprocal symmetry (Ref. 1) and points out that it is (by definition) the supersymmetry of nature. First we derive the relation between the supersymmetric, reciprocal spacetime coordinate transformations of Ref. 1 and the standard Lorentz transformations of relativity. Then we demonstrate or prove the assertion in Ref. 1 that the Robertson-Walker and the Schwarzschild metrics map (exactly) reciprocally. Finally, we derive the relativistic cosmic redshift as a function of distance of the source from the observer in the implied pseudo-dynamic Machian observable universe model. This uniquely consistent physical cosmological model is then applied to interpret the redshifts from quasars. In so doing, we find that this new interpretation puts the quasars considerably closer than does the interpretation of the big-bang theory [see Eq. (36)] and seems to remove the brightness or magnitude anomaly for these objects. As discussed in the Appendix, it also explains why the big-bang interpretation (including the inflationary universe model, etc.) gives good results.
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1. SinceR = 2GM/c 2, it might seem that the correction factor forH should be ∼f −2 ≈ 0.057. This is a moot point. In any event, however, the “pseudo-relativistic” corrections sketched out in this paragraph would obviously only apply for the more distant objects. On the other hand, the accepted range of probable values ofH 0 ≈ (40 - 110) km s−1/Mpc, was derived by Sandage and De Vaucouleurs from relatively nearby sources. Therefore, one might object to the small present value of Hubble's constant,H 0 ≈ 25.2 km s−1/Mpc, calculated in Ref. 1, as compared with the generally accepted probable range of values ofH 0, since this small value is used to discuss the magnitude anomaly of the QSOs and since it would imply the need to rescale cosmic distances by a factor of 2 to 4. This is indeed a reasonable concern. However, the response is quite simple: The method that is most commonly used to determine extragalactic distances is based upon theassumed but uncertain luminosity of the choice of a “standard candle,” in which one particular galaxy in a cluster of galaxies is chosen according to some criterion (e.g., it may be the fourth brightest galaxy in the cluster or some such thing) and it is assumed that the corresponding galaxies in other clusters have the same absolute luminosity,L, which is a highly uncertain assumption. The apparent luminosityℓ is related to the absolute luminosityL by the formulaℓ =L/[4πr 2(1 +Z)2] [e.g., see M. Demiański,Relativistic Astrophysics (Pergamon, 1985), p. 269]. But the luminosity distancer is also given by Eq. (28′). Then, combining these two expressions, one obtainsL =πR 2 ℓ[Z(Z + 1)(Z + 2)]2. Therefore, givenR ≡c/H 0, the absolute luminosity is completely determined byZ andℓ in the big-bang theory. But observational astronomy makes use of the bolometric stellar magnitudem rather than the apparent luminosityℓ. These two quantities are related by the expressionm = -2.5logℓ + constant; hence,m - M = 25 - 5logH 0 + 5logcZ + ..., whereH 0 is measured in km s−1/Mpc andM is the absolute magnitude. Therefore, the absolute magnitudeM of the galaxy, i.e., of the “standard candle,” varies very slowly withH 0 (i.e., as logH 0). Then a factor of, say, 2 to 4 in the value of the Hubble constant corresponds to a difference of only 5log2 to 5log4 ≈ 1.5 to 3.0 magnitudes, an uncertainty which is easily less than that in the absolute magnitude of the “standard candle.” Therefore, it is entirely possible that, as this new model suggests, current estimates of the cosmic distance scale (i.e., ofH 0) are wrong by as much as a factor of 2 to 4. Indeed, there is nothing sacred about the estimates of Sandage (viz.,H 0 ≈ 50 km s−1/Mpc) and De Vaucouleurs (viz.,H 0 ≈ 100 km s−1/Mpc), which are manifestly uncertain by a factor of at least 2 and, notwithstanding popular opinion, there is absolutely no credible justification for assuming that these are absolute lower and upper bounds, respectively, on the actual cosmic distance scale.
2. One might ask, “What physical reason would prevent a larger accretion rate, into a larger black hole, from producing ... more luminosity?” As it turns out, the maximum possible energy generation rates estimated for this most exo-energetic of currently conceivable physical mechanisms (i.e., for mass accretion onto black holes) are limited [viz., to the Eddington limit, ∼ 1045 - 1046erg/s; e.g., see the review article by B. Carter, “Black holes; an introductory review,” and the articles by J. E. Gunn, “Feeding the monster: gas discs in elliptical galaxies,” and by R. McCray, “Spherical accretion onto supermassive black holes,” all inActive Galactic Nuclei, C. Hazard and S. Mitton, eds. (Cambridge University Press, 1979)]. As has been noted by various other authors in the past several years, these maximum energy generation rates will not support the apparently unbounded absolute luminosity predictions which are evolving from the big-bang theory distance estimates for some of the more luminous distant QSOs. The very limited sampling of data undertaken in the paper is adequate to demonstrate how the new interpretation limits the luminosities of these same QSOs to values that are accountable in terms of the maximum energy generation rates available from the mechanism of accretion onto supermassive black holes.
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Shannon, D.L. Anomalous brightness of quasars resolved by supersymmetry. Found Phys Lett 2, 437–469 (1989). https://doi.org/10.1007/BF00689813
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DOI: https://doi.org/10.1007/BF00689813