Physics/Essays/Anonymous/Solar planets as gravitational resonators
Solar planets as gravitational resonators form some law like the s.c. Titzius-Bode law for the planets mass-radius characteristics.
History
[edit | edit source]The theory of the quantum gravitational resonator (QGR) is based on the Maxwell-like gravitational equations and similar in many relation to the theory of quantum electromagnetic resonator (QER), therefore the QGR history is close connected with the QER history.
Gravitational resonators
[edit | edit source]Due to McDonald^{[1]} first who used Maxwell equations to describe gravity was Oliver Heaviside^{[2]} The point is that in the weak gravitational field the standard theory of gravity could be written in the form of Maxwell equations^{[3]}
In the 90-ties Kraus ^{[4]} first introduced the gravitational characteristic impedance of free space, which was detaled later by Kiefer ^{[5]}, and now Raymond Y. Chiao^{[6]} ^{[7]} ^{[8]} ^{[9]} ^{[10]} who is developing the ways of experimental determination of the gravitational waves.
Velocity circulation quantum
[edit | edit source]First the VCQ was proposed in the early 50-th for the quantum superfluids in the general form by R.Feynman ^{[11]}, ^{[12]}:
where could be integer or fractional in the general case.
Further developments this approach was made by Yakymakha (1994) for inversion layers in MOSFETs ^{[13]}.
Gravitational resonator approach to the Solar System
[edit | edit source]General resonator characteristics
[edit | edit source]Geometrical properties of a planet define the following resonance frequency:
where is velocity of light, and is the planet radius. This frequency could be connected with the "minimal mass conseption":
where is the reduced Planck constant. Considering that total planet mass is replaced on the resonator surface:
and therefore the "minimal mass" should be placed on the minimal surface:
Thus, the minimal radius will be:
Velocity circulation quantum approach
[edit | edit source]In the general case the velocity circulation quantum is defined as:
where is integer number. This equation could be rewritten in the "mass form":
For this equation defines the minimal mass as:
Note that this definition is compatible with the gravitational resonato approach presented in the above section.
Solar system gravitational characteristics
[edit | edit source]The full sets of the planetary data are presented in the Table 1.
Object | Radius, m | Mass, kg | Minimal Mass, kg | Minimal Radius, m | |
---|---|---|---|---|---|
Sun | |||||
Jupiter | |||||
Saturn | |||||
Neptun | |||||
Uran | |||||
Earth | |||||
Venus | |||||
Mars | |||||
Mercury |
Note that all planetary data were taken from the textbook ^{[14]}.
See also
[edit | edit source]- Quantum Gravitational Resonator
- Velocity circulation quantum
- Planck scale
- Stoney scale
- Natural scale
- Dirac large numbers
References
[edit | edit source]- ↑ K.T. McDonald, Am. J. Phys. 65, 7 (1997) 591-2.
- ↑ O. Heaviside, Electromagnetic Theory (”The Electrician” Printing and Publishing Co., London, 1894) pp. 455-465.
- ↑ W. K. H. Panofsky and M. Phillips, Classical Electricity and Magnetism (Addison-Wesley, Reading, MA, 1955), p. 168, 166.
- ↑ J. D. Kraus, IEEE Antennas and Propagation. Magazine 33, 21 (1991).
- ↑ C. Kiefer and C. Weber, Annalen der Physik (Leipzig) 14, 253 (2005).
- ↑ Raymond Y. Chiao. "Conceptual tensions between quantum mechanics and general relativity: Are there experimental consequences, e.g., superconducting transducers between electromagnetic and gravitational radiation?" arXiv:gr-qc/0208024v3 (2002). [PDF
- ↑ R.Y. Chiao and W.J. Fitelson. Time and matter in the interaction between gravity and quantum fluids: are there macroscopic quantum transducers between gravitational and electromagnetic waves? In Proceedings of the “Time & Matter Conference” (2002 August 11-17; Venice, Italy), ed. I. Bigi and M. Faessler (Singapore: World Scientific, 2006), p. 85. arXiv: gr-qc/0303089. PDF
- ↑ R.Y. Chiao. Conceptual tensions between quantum mechanics and general relativity: are there experimental consequences? In Science and Ultimate Reality, ed. J.D. Barrow, P.C.W. Davies, and C.L.Harper, Jr. (Cambridge:Cambridge University Press, 2004), p. 254. arXiv:gr-qc/0303100.
- ↑ Raymond Y. Chiao. "New directions for gravitational wave physics via “Millikan oil drops” arXiv:gr-qc/0610146v16 (2009). PDF
- ↑ Stephen Minter, Kirk Wegter-McNelly, and Raymond Chiao. Do Mirrors for Gravitational Waves Exist? arXiv:gr-qc/0903.0661v10 (2009). PDF
- ↑ Putterman S.J. (1974). Superfluid hydrodynamics. North-Holland, Amsterdam
- ↑ Feynman, R. P. (1955). Application of quantum mechanics to liquid helium. Progress in Low Temperature Physics 1: 17–53. ISSN 00796417
- ↑ Cite error: Invalid
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- ↑ Allen C.W.(1973). Astrophysical quantities. 3-d edition. University of London, The Athlone Press