Mach’s Principle, Action at a Distance and Cosmology

ABSTRACT

Hoyle and Narlikar (HN) in the 1960’s [1]-[3] developed a theory of gravitation which was completely Machian and used both retarded and advanced waves to communicate gravitational influence between particles. The advanced waves, which travel backward in time, are difficult to visualize and although they are mathematically allowed by relativistic wave equations, they never really caught on. The HN theory reduced to Einstein’s theory of gravity in the smooth fluid approximation and a transformation into the rest frame of the fluid. Hawking [4] in 1965 pointed out a possible flaw in the theory. This involved integrating out into the distant future to account for all the advanced waves which might influence the mass of a particle here and now. Hawking used infinity as his upper time limit and showed the integral was divergent. We point out that since the universe is known to be expanding, and accelerating, the upper limit in the advanced wave time integral should not be infinite but is bounded by the Cosmic Event Horizon. This event horizon*H*_{e} represents a barrier between future events that can
be observed and those which cannot. We show that the advanced wave integral is
finite when *H*_{e}/*C*, is used as the upper limit of the
advanced wave integral. Hawking’s objection is no longer valid and the HN
theory becomes a working theory once again.

Hoyle and Narlikar (HN) in the 1960’s [1]-[3] developed a theory of gravitation which was completely Machian and used both retarded and advanced waves to communicate gravitational influence between particles. The advanced waves, which travel backward in time, are difficult to visualize and although they are mathematically allowed by relativistic wave equations, they never really caught on. The HN theory reduced to Einstein’s theory of gravity in the smooth fluid approximation and a transformation into the rest frame of the fluid. Hawking [4] in 1965 pointed out a possible flaw in the theory. This involved integrating out into the distant future to account for all the advanced waves which might influence the mass of a particle here and now. Hawking used infinity as his upper time limit and showed the integral was divergent. We point out that since the universe is known to be expanding, and accelerating, the upper limit in the advanced wave time integral should not be infinite but is bounded by the Cosmic Event Horizon. This event horizon

KEYWORDS

Mach’s Principle, Action at a Distance, Advanced Waves, Hoyle-Narlikar Theory, Accelerating Universe, Event Horizon

Mach’s Principle, Action at a Distance, Advanced Waves, Hoyle-Narlikar Theory, Accelerating Universe, Event Horizon

Cite this paper

Fearn, H. (2015) Mach’s Principle, Action at a Distance and Cosmology.*Journal of Modern Physics*, **6**, 260-272. doi: 10.4236/jmp.2015.63031.

Fearn, H. (2015) Mach’s Principle, Action at a Distance and Cosmology.

References

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http://dx.doi.org/10.1098/rspa.1964.0227

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Hoyle, F. and Narlikar, J.V. (1966) Proceedings of the Royal Society of London A, 294, 138.

http://dx.doi.org/10.1098/rspa.1966.0199

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http://dx.doi.org/10.1098/rspa.1965.0146

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http://dx.doi.org/10.1103/RevModPhys.58.647

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[30] Fearn, H., Zachar, A., Woodward, J.F. and Wanser, K. (2014) AIAA Joint Propulsion Conference, Technical Session: Nuclear and Future Flight Propulsion, Theory of a Mach Effect Thruster.

http://arc.aiaa.org/doi/abs/10.2514/6.2014-3821

[1] Hoyle, F. and Narlikar, J.V. (1964) Proceedings of the Royal Society of London A, 282, 191.

http://dx.doi.org/10.1098/rspa.1964.0227

[2] Hoyle, F. and Narlikar, J.V. (1964) Proceedings of the Royal Society of London A, 282, 184.

Hoyle, F. and Narlikar, J.V. (1966) Proceedings of the Royal Society of London A, 294, 138.

http://dx.doi.org/10.1098/rspa.1966.0199

[3] Hoyle, F. and Narlikar, J.V. (1974) Action at a Distance in Physics and Cosmology. W. H. Freeman and Company, San Francisco.

[4] Hawking, S.W. (1965) Proceedings of the Royal Society of London A, 286, 313.

http://dx.doi.org/10.1098/rspa.1965.0146

[5] Einstein, A. (1912) Vierteljahrsschrift fur Gerichtliche Medizin und Offentliches Sanitatswesen, 44, 37-40. (Translated in English and Reprinted in the Collected Papers of Albert Einstein, (CPAE), 4, 126)

[6] Lynden-Bell, D., Bicak, J. and Katz, J. arXiv:gr-qc/9812033.

[7] Einstein, A. (1955) The Meaning of Relativity. Princeton.

[8] Tetrode, H. (1922) Zeitschrift für Physik, 10, 317.

http://dx.doi.org/10.1007/BF01332574

[9] Fokker, A.D. (1929) Zeitschrift für Physik, 58, 386.

http://dx.doi.org/10.1007/BF01340389

[10] Dirac, P.A.M. (1938) Proceedings of the Royal Society of London A, 167, 148.

http://dx.doi.org/10.1098/rspa.1938.0124

[11] Wheeler, J.A. and Feynman, R.P. (1945) Reviews of Modern Physics, 17, 157-181.

http://dx.doi.org/10.1103/RevModPhys.17.157

[12] Lewis, G.N. (1926) Proceedings of the National Academy of Sciences, 12, 22-29.

http://dx.doi.org/10.1073/pnas.12.1.22

[13] Mehra, J. (1994) The Beat of a Different Drum: The Life and Science of Richard Feynman. Clarendon Press, Oxford, 96.

[14] Partridge, R.B. (1973) Nature, 244, 263-265.

http://dx.doi.org/10.1038/244263a0

[15] Cramer, J.G. (2014) Private Email Communication.

[16] Woodward, J.F. (1996) Foundations of Physics Letters, 9, 1-23.

[17] Ellis, G.F.R. and Rothman, T. (1993) American Journal of Physics, 61, 883-893.

http://dx.doi.org/10.1119/1.17400

[18] Weinberg, S. (1972) Gravitation and Cosmology Principles and the Applications of the General Theory of Relativity. John Wiley and Sons, New York, 472.

[19] Rindler, W. (1965) Monthly Notices of the Royal Astronomical Society, 116, 662-677.

http://dx.doi.org/10.1093/mnras/116.6.662

[20] Lineweaver, C.H. and Davis, T.M. (2005) Scientific American, 292, 36-45.

[21] van Oirschot, P., Kwan, J. and Lewis, G.F. (2010) Monthly Notices of the Royal Astronomical Society, 404, 1633-1638.

[22] Kumar, S., (2012) Monthly Notices of the Royal Astronomical Society, 422, 2532-2538.

Giostri, R., et al. (2012) arXiv:1203.3213 [astro-ph.CO].

[23] Peebles, P.J.E. (1993) Principles of Physical Cosmology (Princeton Series in Physics). Princeton University Press, Princeton, 394-397.

[24] Lucchin, F. and Matarrese, S. (1985) Physical Review D, 32, 1316-1322.

http://dx.doi.org/10.1103/PhysRevD.32.1316

[25] Hogarth, J.E. (1962) Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 267, 365-383.

http://dx.doi.org/10.1098/rspa.1962.0105

[26] Riess, A.G., et al. (2004) The Astrophysical Journal, 607, 665-687.

Riess, A.G., et al. (2009) The Astrophysical Journal, 699, 539-563.

[27] Cramer, J.G. (1986) Reviews of Modern Physics, 58, 647-687.

http://dx.doi.org/10.1103/RevModPhys.58.647

[28] Kastner, R.E. (2013) The Transactional Interpretation of Quantum Mechanics. Cambridge University Press, Cambridge.

[29] Woodward, J.F. (2012) Making Starships and Stargates. Springer Press, Berlin.

[30] Fearn, H., Zachar, A., Woodward, J.F. and Wanser, K. (2014) AIAA Joint Propulsion Conference, Technical Session: Nuclear and Future Flight Propulsion, Theory of a Mach Effect Thruster.

http://arc.aiaa.org/doi/abs/10.2514/6.2014-3821