Abstract
In the last chapter we’ve seen that Kip Thorne’s work on wormholes was widely recognized as having a direct bearing on the problem of rapid spacetime transport. But the requirements he and his collaborators suggested were and remain so daunting that almost no one has paid much attention to them when trying to devise realistic advanced propulsion systems. The single scheme recently proposed that addresses the issues squarely, Jack Sarfatti’s “softening” scheme, is based on physical assumptions that almost certainly are not correct. But his proposal is based on serious physics that can be tested in the laboratory. Should we be fabulously lucky, his proposal may turn out to have merit.
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Notes
- 1.
Nowadays it is fashionable to use either SI units or “natural” units. With natural units one or more of the constants of nature, like Planck’s constant and/or the speed of light in a vacuum, are set equal to one. In the case of SI units, one carries around a lot of factors involving π and small integers, and the values of things scale to human size objects rather than the small constituents of real material structures. With natural units, the magnitude of things as we usually measure them get transformed into unintuitive values owing to the very large or small values of the constants of nature. Gaussian units avoid both of these issues.
- 2.
Purists will point out that division by zero is “undefined.” But for situations like these, when one lets the denominator go to zero, the quotient obviously goes to infinity as the radius goes to zero.
- 3.
Recall that the relationship between the wave properties of the electromagnetic field and photon energy is E = hν, where h is Planck’s constant and ν is the frequency of the wave.
- 4.
The story of these developments has been told many times in many ways. Of the accounts I have read, I like that of Robert Crease and Charles Mann, The Second Creation the best.
- 5.
This length is actually much larger than the sizes of elementary particles by at least several orders of magnitude. It comes from the Compton effect, where X-ray photons are scattered from electrons, the photon wavelengths being increased in the scattering process because the recoiling electrons carry away some of the incident photon energy. The Compton wavelength, in terms of the rest mass m of the electron and Planck’s constant h, is h/mc. Since m is the rest mass, the Compton wavelength is a universal constant.
- 6.
In my reading of the electron modeling literature years ago now, I once ran across a quote attributed to Einstein that went, roughly, “Every Tom, Dick, and Harry thinks he knows what electrons are. They are mistaken.” This seems to be a widely shared view in the electron modeling community.
- 7.
Wesson, P., “Constants and Cosmology: The Nature and Origin of Fundamental Constants in Astrophysics and Particle Physics,” Space Sci. Rev. 1992 59:365–406.
- 8.
Ashtekar, A , “Recent Developments in Quantum Gravity,” Annals. N.Y. Acad. Sci. 1989 571:16–26.
- 9.
Lloyd, a friend of the family [my mother was an astronomer who had met Lloyd at Harvard when she was a grad student there in the 1930s], had given them to me when I was a grad student. Mom had sent me to visit with Lloyd in his attic office in Pupin Hall at Columbia University hoping, I suspect, that Lloyd would counsel me with good sense. At that time Lloyd was a staid senior professor of astronomy and the author of texts on astronomy and cosmology. Little did Mom know that Lloyd was also an electron modeler and quantum gravitier who was delighted to regale me with his work on the problem. In addition to the copies of his papers, published and unpublished, he showed me a hand-written postcard from Abdus Salam complimenting him on his work on gravity and fundamental particles. An absolutely delightful afternoon.
- 10.
- 11.
Note, however, that the essentially exclusive decay mode of the muon is an electron accompanied by a pair of neutrinos mediated by a W boson.
- 12.
As a technical matter, the absolute value of m o is used in the gravitational radius, as that is a positive quantity for both positive and negative mass objects.
References
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Arnowitt R, Deser S, Misner CW (1960b) Interior schwarschild solutions and interpretation of source terms. Phys Rev 120:321–324
Ashtekar A (1989) Recent developments in quantum gravity. Ann N Y Acad Sci 571:16–26
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Excerpt from Ashtekar.
Reprinted from Abhay Ashtekar, “Recent Developments in Quantum Gravity,” Annals of the New York Academy of Sciences, vol. 571, pp. 16–26 (1989) with permission of John Wiley and Sons.
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© 2013 James F. Woodward
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Woodward, J.F. (2013). Where Do We Find Exotic Matter?. In: Making Starships and Stargates. Springer Praxis Books(). Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5623-0_7
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