Gauge dependence and self-force from Galilean to Einsteinian free fall, compact stars falling into black holes, Hawking radiation and the Pisa tower at the general relativity centennial. (English) Zbl 1351.83012
Summary: Obviously, in Galilean physics, the universality of free fall implies an inertial frame, which in turns implies that the mass \(m\) of the falling body is omitted (because it is a test mass; put otherwise, the center of mass of the system coincides with the center of the main, and fixed, mass \(M\); or else, we consider only a homogeneous gravitational field). Conversely, an additional (in the opposite or same direction) acceleration proportional to \(m/M\) would rise either for an observer at the center of mass of the system, or for an observer at a fixed distance from the center of mass of \(M\). These elementary, but overlooked, considerations fully respect the equivalence principle (EP) and the (local) identity of an inertial or a gravitational pull for an observer in the Einstein cabin. They value as fore-runners of the self-force and gauge dependency in general relativity. Because of its importance in teaching and in the history of physics, coupled to the introductory role to Einstein’s EP, the approximate nature of Galilei’s law of free fall is explored herein. When stepping into general relativity, we report how the geodesic free fall into a black hole was the subject of an intense debate again centered on coordinate choice. Later, we describe how the infalling mass and the emitted gravitational radiation affect the free fall motion of a body. The general relativistic self-force might be dealt with to perfectly fit into a geodesic conception of motion. Then, embracing quantum mechanics, real black holes are not classical static objects any longer. Free fall has to handle the Hawking radiation, and leads us to new perspectives on the varying mass of the evaporating black hole and on the varying energy of the falling mass. Along the paper, we also estimate our findings for ordinary masses being dropped from a Galilean or Einsteinian Pisa-like tower with respect to the current state of the art drawn from precise measurements in ground and space laboratories, and to the constraints posed by quantum measurements. Appendix A describes how education physics and high impact factor journals discuss the free fall. Finally, case studies conducted on undergraduate students and teachers are reviewed.
MSC:
| 83C10 | Equations of motion in general relativity and gravitational theory |
| 83-02 | Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory |
| 83-03 | History of relativity and gravitational theory |
| 01A60 | History of mathematics in the 20th century |
| 83C57 | Black holes |
Keywords:
free fall; Galileo Galilei; black holes; self-force; entropy; Hawking radiation; equivalence principle; universality of free fall; inertial frameReferences:
| [1] | 1. K. L. Nordtvedt Jr., Gravitation theory: Empirical status from solar system experiments, Science178 (1972) 1157. genRefLink(16, ’S0219887816300142BIB001’, ’10.1126 |
| [2] | 2. http://nssdc.gsfc.nasa.gov/planetary/lunar/apollo_15_feather_drop.html. |
| [3] | 3. D. MacIsaac, Galileo’s ”falling bodies” experiment ”re-created” at Pisa, Phys. Teach.48 (2012) 350, see also D. MacIsaac, Galileo Redux: Dropping objects of unequal mass (the guinea and the feather) just to be cool, Phys. Teach.53 (2015) 60. |
| [4] | 4. http://www.symmetrymagazine.org/breaking/2009/10/17/galileos-falling-bodies-experiment-re-created-at-pisa. |
| [5] | 5. S. Detweiler and E. Poisson, Low multipole contributions to the gravitational self-force, Phys. Rev. D69 (2004) 084019, arXiv:gr-qc/0312010 [arXiv] . genRefLink(16, ’S0219887816300142BIB005’, ’10.1103 |
| [6] | 6. L. M. Diaz-Rivera, E. Messaritaki, B. F. Whiting and S. Detweiler, Scalar field self-force effects on orbits about a Schwarzschild black hole, Phys. Rev. D70 (2004) 124018, arXiv:gr-qc/0410011 [arXiv] . genRefLink(16, ’S0219887816300142BIB006’, ’10.1103 |
| [7] | 7. S. Detweiler, Perspective on gravitational self-force analyses, Class. Quantum Grav.22 (2005) S681, arXiv:gr-qc/0501004 [arXiv] . genRefLink(16, ’S0219887816300142BIB007’, ’10.1088 |
| [8] | 8. S. Detweiler, Consequence of the gravitational self-force for circular orbits of the Schwarzschild geometry, Phys. Rev. D77 (2008) 124026, arXiv:0804.3529 [arXiv] [gr-qc]. genRefLink(16, ’S0219887816300142BIB008’, ’10.1103 |
| [9] | 9. S. Detweiler, Elementary development of the gravitational self-force, in Mass and Motion in General Relativity, eds. L. Blanchet, A. Spallicci and B. Whiting, Fundamental Theories of Physics, Vol. 162 (Springer, Berlin, 2011), p. 271, arXiv:0908.4363 [arXiv] [gr-qc]. · Zbl 1213.83037 |
| [10] | 10. A. Spallicci, Free fall and self-force: an historical perspective, in Mass and Motion in General Relativity, eds. L. Blanchet, A. Spallicci and B. Whiting, Fundamental Theories of Physics, Vol. 162 (Springer, Berlin, 2011), p. 561, arXiv:1005.0611 [arXiv] [physics.hist-ph]. · Zbl 1213.83013 |
| [11] | 11. A. D. A. M. Spallicci and P. Ritter, A fully relativistic radial fall, Int. J. Geom. Meth. Mod. Phys.11 (2014) 1450090, arXiv:1407.5391 [arXiv] [gr-qc]. [Abstract] genRefLink(128, ’S0219887816300142BIB011’, ’000346972500013’); · Zbl 1327.83056 |
| [12] | 12. P. Ritter, S. Aoudia, A. D. A. M. Spallicci and S. Cordier, Indirect (source-free) integration method. II. Self-force consistent radial fall, Int. J. Geom. Meth. Mod. Phys.13 (2016) 1650019, arXiv:1511.04277 [arXiv] [gr-qc]. [Abstract] genRefLink(128, ’S0219887816300142BIB012’, ’000369690800014’); · Zbl 1332.83025 |
| [13] | 13. Y. Mino, M. Sasaki and T. Tanaka, Gravitational radiation reaction to a particle motion, Phys. Rev. D55 (1997) 3457, arXiv:gr-qc/9606018 [arXiv] . genRefLink(16, ’S0219887816300142BIB013’, ’10.1103 |
| [14] | 14. T. C. Quinn and R. M. Wald, An axiomatic approach to electromagnetic and gravitational radiation reaction of particles in curved spacetime, Phys. Rev. D56 (1997) 3381, arXiv:gr-qc/9610053 [arXiv] . genRefLink(16, ’S0219887816300142BIB014’, ’10.1103 |
| [15] | 15. S. Detweiler and B. F. Whiting, Self-force via a Green’s function decomposition, Phys. Rev. D67 (2003) 024025, arXiv:gr-qc/0202086 [arXiv] . genRefLink(16, ’S0219887816300142BIB015’, ’10.1103 |
| [16] | 16. A. D. A. M. Spallicci, P. Ritter and S. Aoudia, Self-force driven motion in curved spacetime, Int. J. Geom. Meth. Mod. Phys.11 (2014) 1450072, arXiv:1405.4155 [arXiv] [gr-qc]. [Abstract] genRefLink(128, ’S0219887816300142BIB016’, ’000341784600008’); · Zbl 1304.83010 |
| [17] | 17. https://www.elisascience.org. · JFM 43.0156.03 |
| [18] | 18. D. Harlow, Jerusalem lectures on black holes and quantum information, Rev. Mod. Phys.88 (2016) 15002, arXiv:1409.1231 [arXiv] [hep-th]. genRefLink(16, ’S0219887816300142BIB018’, ’10.1103 |
| [19] | 19. M. H. P. M. van Putten, On the nature of black hole information from unitarity, arXiv:1506.08075 [gr-qc], Korea Institut for Advanced Study (KIAS) – Center for Future High Energy Physics (CFHEP) Workshop and 5th KIAS Workshop on Particle Physics and Cosmology Meeting, 9-13 November 2015 Seoul, http://indico.kias.re.kr/indico/event/3/speakers. |
| [20] | 20. R. Taibu, D. Rudge and D. Schuster, Phys. Rev. ST: Phys. Educ. Res.11 (2015) 010117. genRefLink(16, ’S0219887816300142BIB020’, ’10.1103 |
| [21] | 21. A. M. Nobili, D. M. Lucchesi, M. T. Crosta, M. Shao, S. G. Turyshev, R. Peron, G. Catastini, A. Anselmi and G. Zavattini, On the universality of free fall, the equivalence principle, and the gravitational redshift, Am. J. Phys.81 (2013) 527. genRefLink(16, ’S0219887816300142BIB021’, ’10.1119 |
| [22] | 22. A. Peters, K. Y. Chung and S. Chu, Measurement of gravitational acceleration by dropping atoms, Nature400 (1999) 849. genRefLink(16, ’S0219887816300142BIB022’, ’10.1038 |
| [23] | 23. P. Touboul, G. Métris, V. Lebat and A. Robert, The MICROSCOPE experiment, ready for the in-orbit test of the equivalence principle, Class. Quantum Grav.29 (2012) 184010. genRefLink(16, ’S0219887816300142BIB023’, ’10.1088 |
| [24] | 24. B. Altschul, Q. G. Bailey, L. Blanchet, K. Bongs, P. Bouyer, L. Cacciapuoti, S. Capozziello, N. Gaaloul, D. Giulini, J. Hartwig, L. Iess, P. Jetzer, A. Landragin, E. Rasel, S. Reynaud, S. Schiller, C. Schubert, F. Sorrentino, U. Sterr, J. D. Tasson, G. M. Tino, P. Tuckey and P. Wolf, Quantum tests of the Einstein equivalence principle with the STE-QUEST space mission, Adv. Space Res.55 (2015) 501, arXiv:1404.4307 [arXiv] [gr-qc]. genRefLink(16, ’S0219887816300142BIB024’, ’10.1016 |
| [25] | 25. http://thatsmaths.com/2014/11/27/falling-bodies-2-philae/. |
| [26] | 26. T. W. B. Kibble, Classical Mechanics, 3rd edn. (Longman Scientific & Technical, Burnt Mill, Harlow, 1985). |
| [27] | 27. C. Rovelli, Aristotle’s physics: A physicist’s look, J. Am. Philos. Ass.1 (2015) 23, arXiv:1312.4057 [arXiv] [physics.hist-ph]. genRefLink(16, ’S0219887816300142BIB027’, ’10.1017 |
| [28] | 28. F. C. Santos, V. Soares and A. C. Tort, A note on the conservation of mechanical energy and the Galilean principle of relativity, Eur. J. Phys.31 (2010) 827. genRefLink(16, ’S0219887816300142BIB028’, ’10.1088 |
| [29] | 29. J. Michell, On the means of discovering the distance, magnitude, &c. of the fixed stars, in consequence of the diminution of the velocity of their light, in case such a diminution should be found to take place in any of them, and such other data should be procured from observations, as would be farther necessary for that purpose. By the Rev. John Michell, B.D.F.R.S. in a letter to Henry Cavendish, Esq. F.R.S. and A.S., Philos. Trans. R. Soc. Lond.74 (1784) 35. genRefLink(16, ’S0219887816300142BIB029’, ’10.1098 |
| [30] | 30. P.-S. Laplace, Exposition du Système du Monde, Vol. 2 (Imprimerie du Cercle-Social, Paris, 1796), The System of the World (Richard Phillips, London, 1809). · JFM 18.0166.01 |
| [31] | 31. P.-S. La Place, Beweis des satzes, daß die anzihende kraft bey einem weltkörper so groß seyn könne, daß das licht davon nicht ausströmen kann, Allg. Geograph. Ephem.4 (1799) 1. Proof of the theorem that the attractive power of a heavenly body can be so large that light cannot leak out from it, arXiv:gr-qc/0304087 (2003). |
| [32] | 32. K. Schwarzschild, Über das gravitationsfeld eines massenpunktes nach der Einsteinschen theorie, Sitzungsber. Preuß. Akad. Wissenschaften Berlin Phys. Math. Kl. (1916) 189. On the gravitational field of a mass point according to Einstein’s theory, arXiv:physics/9905030 [physics.hist-ph]. |
| [33] | 33. J. Droste, Het zwaartekrachtsveld van een of meer lichamen volgens de theorie van Einstein, Doctorate thesis (Dir. H. A. Lorentz) Rijksuniversiteit van Leiden (1916). · JFM 46.1330.03 |
| [34] | 34. J. Droste, Het veld van een enkel centrum in Einstein’s theorie der zwaartekracht, en de beweging van een stoffelijk punt in dat veld, Kon. Ak. Wetensch. Amsterdam25 (1916) 163. The field of a single centre in Einstein’s theory of gravitation, and the motion of a particle in that field, Proc. Acad. Sc. Amsterdam19 (1917) 197. |
| [35] | 35. J. A. Wheeler, Our universe: The known and the unknown, address before the American Association for the Advancement of Science, 29 December 1967, New York. |
| [36] | 36. J. A. Wheeler, Our universe: The known and the unknown, Am. Scholar37 (1968) 248. genRefLink(128, ’S0219887816300142BIB036’, ’A1968ZL88100003’); |
| [37] | 37. J. A. Wheeler, Our universe: The known and the unknown, Am. Scientist56 (1968) 1. genRefLink(128, ’S0219887816300142BIB037’, ’A1968A699100001’); |
| [38] | 38. J. Eisenstaedt, Trajectoires et impasses de la solution de Schwarzschild, Arch. Hist. Exact Sci.37 (1987) 275. genRefLink(128, ’S0219887816300142BIB038’, ’A1987L309600001’); · Zbl 0632.01017 |
| [39] | 39. G. Cavalleri and G. Spinelli, Motion of particles entering the Schwarzschild field, Lett. Nuovo Cimento6 (1973) 5. genRefLink(16, ’S0219887816300142BIB039’, ’10.1007 |
| [40] | 40. G. Cavalleri and G. Spinelli, Note on motion in the Schwarzschild field, Phys. Rev. D15 (1977) 3065. genRefLink(16, ’S0219887816300142BIB040’, ’10.1103 |
| [41] | 41. G. Cavalleri and G. Spinelli, Motion of particles entering the Schwarzschild field, Lett. Nuovo Cimento22 (1978) 113. genRefLink(16, ’S0219887816300142BIB041’, ’10.1007 |
| [42] | 42. G. Spinelli, Gravitational repulsion in the Schwarzschild field, in 5th Marcel Grossmann Meeting, eds. D. Blair, M. Buckingham and R. Ruffini (World Scientific, Singapore, 1989), p. 373. |
| [43] | 43. R. U. Sexl, Theories of gravitation, Ann. Phys.15 (1967) 269. |
| [44] | 44. W. E. Thirring, An alternative approach to the theory of gravitation, Ann. Phys.16 (1961) 96. genRefLink(16, ’S0219887816300142BIB044’, ’10.1016 |
| [45] | 45. J. Jaffe and I. I. Shapiro, Lightlike behavior of particles in a Schwarzschild field, Phys. Rev. D6 (1972) 405. genRefLink(16, ’S0219887816300142BIB045’, ’10.1103 |
| [46] | 46. J. Jaffe and I. I. Shapiro, Comment on the definition of particle velocity in a Schwarzschild field, Phys. Rev. D8 (1973) 4642. genRefLink(16, ’S0219887816300142BIB046’, ’10.1103 |
| [47] | 47. D. Hilbert, Die grundlagen der physik. Zweite mitteilung, Nachr. Ges. Wis. Göttingen Math. Phys. Kl. (1917) 53. · JFM 46.1298.01 |
| [48] | 48. D. Hilbert, Die grundlagen der physik, Math. Ann. (1924) 1. genRefLink(16, ’S0219887816300142BIB048’, ’10.1007 |
| [49] | 49. L. Page, Gravitational deflection of high-speed particles, Nature104 (1920) 692. genRefLink(16, ’S0219887816300142BIB049’, ’10.1038 |
| [50] | 50. A. S. Eddington, Gravitational deflection of high-speed particles, Nature105 (1920) 37. genRefLink(16, ’S0219887816300142BIB050’, ’10.1038 |
| [51] | 51. M. von Laue, Die Relativitätstheorie. Die Allgemeine Relativitätstheorie, Vol. 2 (Vieweg und Sohn, Braunschweig, 1921). |
| [52] | 52. H. Bauer, Mathematische Einführung in die Gravitationstheorie Einsteins: Nebst einer Exakten Darstellung ihrer Wichtigsten Ergebnisse (F. Deuticke, Leipzig und Wien, 1922). |
| [53] | 53. C. de Jans, Sur le mouvement d’une particule matérielle dans un champ de gravitation à symétrie sphérique, Mem. Acad. R. Belgique Cl. Sci.7 (1923) 1. |
| [54] | 54. C. de Jans, Sur la stabilité du mouvement d’une particule massique dans le champ de Schwarzschild, Mem. Acad. R. Belgique Cl. Sci.7 (1924) 1. · JFM 50.0597.03 |
| [55] | 55. C. de Jans, Complément au mémoire sur le mouvement d’une particule matérielle, Mem. Acad. R. Belgique Cl. Sci.7 (1924) 96. |
| [56] | 56. G. C. McVittie, General Relativity and Cosmology (Chapman and Hall, London, 1956). |
| [57] | 57. C. Møller, The Theory of Relativity (Oxford University Press, Oxford, 1960). · Zbl 0047.20602 |
| [58] | 58. H. Treder, Die Relativität de Trägheit (Akademie Verlag, Berlin, 1972). |
| [59] | 59. H. Treder and K. Fritze, Die fallbeschleunigung in der Schwarzschild-metrik, Astron. Nachr.296 (1975) 109. genRefLink(16, ’S0219887816300142BIB059’, ’10.1002 |
| [60] | 60. M. Carmeli, Behavior of fast particles in the Schwarzschild field, Lett. Nuovo Cimento3 (1972) 379. genRefLink(16, ’S0219887816300142BIB060’, ’10.1007 |
| [61] | 61. M. Carmeli, Classical Fields: General Relativity and Gauge Theory (Wiley, New York, 1982). |
| [62] | 62. L. Y. Arifov, General static solution of the Einstein equations for a spherical source (in Russian). Probl. Teor. Gravit.i Èlem. Chastits.11 (1980) 96. |
| [63] | 63. L. Y. Arifov, Izv. Vyssh. Uchebn. Zaved. Fiz.4 (1981) 61. Phenomenon of gravitational repulsion in the general theory of relativity, Russian Phys. J.24 (1981) 346. |
| [64] | 64. C. H. McGruder III, Gravitational repulsion in the Schwarzschild field, Phys. Rev. D25 (1982) 3191. genRefLink(16, ’S0219887816300142BIB064’, ’10.1103 |
| [65] | 65. E. A. Partridge, Galileo’s experiment from the leaning tower, Science52 (1920) 272. genRefLink(16, ’S0219887816300142BIB065’, ’10.1126 |
| [66] | 66. M. von Laue, La Théorie de la Relativité. La Relativité Générale et la Théorie de la Gravitation d’Einstein, 2nd edn., Vol. 2 (Gauthier-Villars et Cie, Paris, 1926). |
| [67] | 67. P. Drumaux, Sur la force gravifique, Ann. Soc. Sci. Brux.56 (1936) 5. · JFM 62.1480.04 |
| [68] | 68. E. von Rabe, Zur singularität der Schwarzschilden losüng für r=2m, Astron. Nachr.275 (1947) 251. genRefLink(16, ’S0219887816300142BIB068’, ’10.1002 |
| [69] | 69. E. Whittaker, A History of the Theories of Aether and Electricity: From the Age of Descartes to the Close of the Nineteenth Century, Longman, Greens and Co., London; Hodges, Figgis & Co. Ltd., Dublin, 1910). · JFM 41.0072.01 |
| [70] | 70. K. N. Srinivasa Rao, The motion of a falling particle in a Schwarzschild field, Ann. Inst. H. Poincaré A5 (1966) 227. genRefLink(128, ’S0219887816300142BIB070’, ’A19668993500003’); · Zbl 0151.43404 |
| [71] | 71. Ya. B. Zel’dovich and I. D. Novikov, Relyativistskaya Astrofyzika (Izdatel’svo Nauka, Moskva, 1967). Relativistic Astrophysics (University Chicago Press, Chicago, 1971). |
| [72] | 72. F. L. Markley, Motion in the Schwarzschild field, Am. J. Phys.41 (1973) 45. genRefLink(16, ’S0219887816300142BIB072’, ’10.1119 |
| [73] | 73. A. Loinger and T. Marsico, On Hilbert’s gravitational repulsion (a historical note), arXiv:0904.1578 [physics.gen-ph]. |
| [74] | 74. M. Kutschera and W. Zajiczek, Shapiro effect for relativistic particles – testing general relativity in a new window, Acta Phys. Pol. B41 (2010) 1273, arXiv:0906.5088 [arXiv] [astro-ph.EP]. |
| [75] | 75. S. I. Blinnikov, L. B. Okun’ and M. I. Vysotskiĭ, Relativity and c/\sqrt{3}, in Festschrift Dedicated to the 60th Birthday of Holger Bech Nielsen, eds. N. Mankoč Borštnik, C. D. Froggatt and D. Lukman (2001), p. 115, arXiv:hep-ph/0212221 [arXiv] . |
| [76] | 76. S. I. Blinnikov, L. B. Okun’ and M. I. Vysotskiĭ, Usp. Fiz. Nauk46 (2003) 1131; Critical velocities c/3 and c/2 in the general theory of relativity, Phys. Usp.46 (2003) 1099, arXiv:gr-qc/0310020. |
| [77] | 77. F. J. Zerilli, Gravitational field of a particle falling in a Schwarzschild geometry analyzed in tensor harmonics, Phys. Rev. D2 (1970) 2141, Errata, in Black holes, eds. C. DeWitt and B. DeWitt (Gordon and Breach Science Publisher, New York, 1973). · Zbl 1227.83025 |
| [78] | 78. P. A. M. Dirac, The classical theory of radiating electrons, Proc. R. Soc. London A167 (1938) 148. genRefLink(16, ’S0219887816300142BIB078’, ’10.1098 · Zbl 0023.42702 |
| [79] | 79. E. Poisson, Constructing the self-force, in Mass and Motion in General Relativity, eds. L. Blanchet, A. Spallicci and B. Whiting, Fundamental Theories of Physics, Vol. 162 (Springer, Berlin, 2011), p. 309, arXiv:0909.2994 [arXiv] [gr-qc]. · Zbl 1213.83042 |
| [80] | 80. E. Poisson, A. Pound and I. Vega, The motion of point particles in curved spacetime, Living Rev. Relativ.14 (2011), [http://www.livingreviews.org/lrr-2011-7] . genRefLink(16, ’S0219887816300142BIB080’, ’10.12942 · Zbl 1316.83024 |
| [81] | 81. S. E. Gralla and R. M. Wald, A rigorous derivation of gravitational self-force, Class. Quantum Grav.25 (2008) 205009, Corrigendum 28 (2011) 159501, arXiv:0806.3293 [gr-qc]. · Zbl 1152.83405 |
| [82] | 82. S. E. Gralla and R. M. Wald, Derivation of gravitational self-force, in Mass and Motion in General Relativity, eds. L. Blanchet, A. Spallicci and B. Whiting, Fundamental Theories of Physics, Vol. 162 (Springer, Berlin, 2011), p. 263, arXiv:0907.0414 [arXiv] [gr-qc]. · Zbl 1225.83011 |
| [83] | 83. A. D. A. M. Spallicci and S. Aoudia, Perturbation method in the assessment of radiation reaction in the capture of stars by black holes, Class. Quantum Grav.21 (2004) S563, arXiv:gr-qc/0309039 [arXiv] . genRefLink(16, ’S0219887816300142BIB083’, ’10.1088 |
| [84] | 84. L. Barack and A. Ori, Mode sum regularization approach for the self-force in black hole spacetime, Phys. Rev. D61 (2000) 061502(R), arXiv:gr-qc/0107056 [arXiv] . genRefLink(16, ’S0219887816300142BIB084’, ’10.1103 |
| [85] | 85. L. Barack and A. Ori, Gravitational self-force and gauge transformations, Phys. Rev. D64 (2001) 124003, arXiv:gr-qc/9912010 [arXiv] . genRefLink(16, ’S0219887816300142BIB085’, ’10.1103 |
| [86] | 86. J. D. Beckenstein, Black holes and entropy, Phys. Rev. D7 (1973) 2333. genRefLink(16, ’S0219887816300142BIB086’, ’10.1103 |
| [87] | 87. S. W. Hawking, Particle creation by black holes, Comm. Math. Phys.43 (1975) 199. genRefLink(16, ’S0219887816300142BIB087’, ’10.1007 |
| [88] | 88. C. E. Shannon, A mathematical theory of communication, Bell Syst. Tech. J.27 (1948) 379. genRefLink(16, ’S0219887816300142BIB088’, ’10.1002 |
| [89] | 89. G. ’t Hooft, Dimensional reduction in quantum gravity, (1993), arXiv:gr-qc/9310026. |
| [90] | 90. L. Susskind, The world as hologram, J. Math. Phys.36 (1995) 6377, arXiv:hep-th/9409089 [arXiv] . genRefLink(16, ’S0219887816300142BIB090’, ’10.1063 |
| [91] | 91. M. H. P. M. van Putten, A holographic bound on the total number of computations in the visible universe, Int. J. Mod. Phys. D.24 (2015) 1550024, arXiv:1302.3470 [arXiv] [gr-qc]. [Abstract] genRefLink(128, ’S0219887816300142BIB091’, ’000350113100007’); · Zbl 1310.81044 |
| [92] | 92. B. Carter, Axisymmetric black hole has only two degrees of freedom, Phys. Rev. Lett.26 (1971) 331. genRefLink(16, ’S0219887816300142BIB092’, ’10.1103 |
| [93] | 93. S. W. Hawking, Black holes in general relativity, Comm. Math. Phys.25 (1972) 152. genRefLink(16, ’S0219887816300142BIB093’, ’10.1007 |
| [94] | 94. S. W. Hawking, Information loss in black holes, Phys. Rev. D72 (2005) 084013, arXiv:hep-th/0507171 [arXiv] . genRefLink(16, ’S0219887816300142BIB094’, ’10.1103 |
| [95] | 95. S. W. Hawking, Black hole explosions?, Nature248 (1974) 30. genRefLink(16, ’S0219887816300142BIB095’, ’10.1038 |
| [96] | 96. M. H. P. M. van Putten, Entropic force in black hole binaries and its Newtonian limits, Phys. Rev. D85 (2012) 064046, arXiv:1107.1764 [arXiv] [hep-th]. genRefLink(16, ’S0219887816300142BIB096’, ’10.1103 |
| [97] | 97. J. D. Bekenstein and V. F. Mukhanov, Spectroscopy of the quantum black hole, Phys. Lett. B360 (1995) 7, arXiv:gr-qc/9505012 [arXiv] . genRefLink(16, ’S0219887816300142BIB097’, ’10.1016 |
| [98] | 98. N. Margolus and L. B. Levitin, The maximum speed of dynamical evolution, Physica D120 (1988) 188, arXiv:quant-ph/9710043 [arXiv] . genRefLink(16, ’S0219887816300142BIB098’, ’10.1016 |
| [99] | 99. R. M. Wald, General Relativity (University of Chicago Press, Chicago, 1984). genRefLink(16, ’S0219887816300142BIB099’, ’10.7208 |
| [100] | 100. S. A. Fulling, Energy-momentum tensor near an evaporating black hole, Phys. Rev. D13 (1976) 2720. genRefLink(16, ’S0219887816300142BIB100’, ’10.1103 |
| [101] | 101. P. C. W. Davies, Scalar production in Schwarzschild and rindler metrics, J. Phys. A8 (1975) 609. genRefLink(16, ’S0219887816300142BIB101’, ’10.1088 |
| [102] | 102. P. C. W. Davies, S. A. Fulling and W. G. Unruh, The gravity field of a particle. ii, Phys. Rev. D13 (1976) 2720. genRefLink(16, ’S0219887816300142BIB102’, ’10.1103 |
| [103] | 103. W. G. Unruh, Notes on black-hole evaporation, Phys. Rev. D14 (1976) 870. genRefLink(16, ’S0219887816300142BIB103’, ’10.1103 |
| [104] | 104. J. Steinhauer, Observation of self-amplifying Hawking radiation in an analog black hole laser, Nature Phys.10 (2014) 864, arXiv:1409.6550 [arXiv] [cond-mat.quant-gas]. genRefLink(16, ’S0219887816300142BIB104’, ’10.1038 |
| [105] | 105. J. Steinhauer, Observation of quantum Hawking radiation and its entanglement in an analogue black hole, Nature Phys., Published online 15 August 2016. |
| [106] | 106. Le Canard Enchaîné, February 24, March 3, March 10, March 17 (1999). |
| [107] | 107. C. Allègre, Un Peu de Science pour Tout le Monde (Fayard, Paris, 2003). |
| [108] | 108. Y. Lehavi and I. Galili, The status of Galileo’s law of free-fall and its implications for physics education, Am. J. Phys.77 (2009) 417. genRefLink(16, ’S0219887816300142BIB108’, ’10.1119 |
| [109] | 109. L. R. de la Vega, Gravity acceleration is a function of mass, Phys. Teach.16 (1978) 291. genRefLink(16, ’S0219887816300142BIB109’, ’10.1119 |
| [110] | 110. Y. Lehavi and I. Galili, Do all bodies fall equally? On the importance of stating the area of validity in physics education, in Physics Curriculum Design, Development and Validation, ed. N. P. C. P. Constantinou (GIREP Groupe International de Recherche sur l’Enseignement de la Physique, 2008), [http://lsg.ucy.ac.cy/girep2008] . |
| [111] | 111. I. Galili, Thought experiments: Determining their meaning, Sc. Educ.18 (2009) 1. genRefLink(16, ’S0219887816300142BIB111’, ’10.1007 |
| [112] | 112. E. Iacopini, In pursuit of the fifth force, Nature328 (1987) 578. genRefLink(16, ’S0219887816300142BIB112’, ’10.1038 |
| [113] | 113. P. Ball, Tall tales, Nature, Published online 17 June 2005. |
| [114] | 114. J. E. Faller, Precision measurement of the gravitational acceleration, Science158 (1967) 60. genRefLink(16, ’S0219887816300142BIB114’, ’10.1126 |
| [115] | 115. I. A. Halloun and D. Hestenes, Common sense concepts about motion, Am. J. Phys.53 (1985) 1056. genRefLink(16, ’S0219887816300142BIB115’, ’10.1119 |
| [116] | 116. I. Wereley, Galileo’s argument on free fall, Phys. Teach.26 (1988) 394. genRefLink(16, ’S0219887816300142BIB116’, ’10.1119 |
| [117] | 117. J. H. Hardcastle, Prof. Turner and Aristotle, Nature82 (1914) 584. genRefLink(16, ’S0219887816300142BIB117’, ’10.1038 |
| [118] | 118. A. Franklin, Galileo and the leaning tower: an Aristotelian interpretation, Phys. Educ.14 (1979) 60. genRefLink(16, ’S0219887816300142BIB118’, ’10.1088 |
| [119] | 119. C. G. Adler and B. L. Coulter, Galileo and the tower of Pisa experiment, Am. J. Phys.46 (1978) 199. genRefLink(16, ’S0219887816300142BIB119’, ’10.1119 |
| [120] | 120. I. E. Drabkin and S. Drake, On Motion and On Mechanics (University of Winsconsin Press, Madison, 1960); English version of the works by G. Galilei, Della Scienza Mecanica e delle Utilità che si Traggono da gl’Istromenti di quella. Opera Cavata da Manoscritti dell’Eccellentissimo Matematico Galileo Galilei (Luca Danesi, Ravenna, 1634), De motu, and Le Mecaniche (G. Barbera, Firenze, 1890-1909); see also Les Mechaniques de Galilée, Mathematicien et Ingenieur du Duc de Florence (H. Guénon, Paris, 1634), and Questions physico-mathematiques et les Mechaniques du Siur Galilée Tres Excellent Mathematicien, & et Ingenieur du Duc de Florence (H. Guénon, Paris, 1635). |
| [121] | 121. S. Drake, Two New Sciences (University of Winsconsin Press, Madison, 1974); English version of the works by G. Galilei, Discorsi e Dimostrazioni Matematiche Intorno à due Nuove Scienze Attinenti alla Mecanica e ai Moti Locali (Lodewijk Elzevir, Leiden, 1638). |
| [122] | 122. A.-M. Pendrill, P. Ekström, L. Hansson, P. Mars, L. Ouattara and U. Ryan, The equivalence principle comes to schoolfalling objects and other middle school investigations, Phys. Educ.49 (2014) 425. genRefLink(16, ’S0219887816300142BIB122’, ’10.1088 |
| [123] | 123. A. J. Mallmann, J. L. Hock and K. M. Ogden, Surprising facts about gravitational forces, Phys. Teach.42 (1994) 492. genRefLink(16, ’S0219887816300142BIB123’, ’10.1119 |
| [124] | 124. J. Dellavalle, Search in science – an approach for nonscience students, Phys. Teach.12 (1974) 30. genRefLink(16, ’S0219887816300142BIB124’, ’10.1119 |
| [125] | 125. H. Bondi, Relativity theory and gravitation, Eur. J. Phys.7 (1986) 106. genRefLink(16, ’S0219887816300142BIB125’, ’10.1088 |
| [126] | 126. J. Gallant and J. Carlson, Long-distance free fall, Phys. Teach.37 (1999) 166. genRefLink(16, ’S0219887816300142BIB126’, ’10.1119 |
| [127] | 127. J. Gallant, Errata in long-distance free fall, Phys. Teach.37 (1999) 261. genRefLink(16, ’S0219887816300142BIB127’, ’10.1119 |
| [128] | 128. A. P. French, Comments on long-distance free fall, Phys. Teach.37 (1999) 261. genRefLink(16, ’S0219887816300142BIB128’, ’10.1119 |
| [129] | 129. A. J. Mallinckrodt, Comments on long-distance free fall, Phys. Teach.37 (1999) 261. genRefLink(16, ’S0219887816300142BIB129’, ’10.1119 |
| [130] | 130. Editor, Comments on long-distance free fall, Phys. Teach.37 (1999) 262. |
| [131] | 131. L. Borghi, A. De Ambrosis, N. Lamberti and P. Mascheretti, A teaching learning sequence on free fall motion, Phys. Educ.40 (2005) 266. genRefLink(16, ’S0219887816300142BIB131’, ’10.1088 |
| [132] | 132. P. Hewitt, Inertia and acceleration, Phys. Teach.43 (2005) 332. genRefLink(16, ’S0219887816300142BIB132’, ’10.1119 |
| [133] | 133. H. I. Brown, Do physicists need myths?, Am. J. Phys.74 (2006) 382. genRefLink(16, ’S0219887816300142BIB133’, ’10.1119 |
| [134] | 134. S. K. Foong, From Moon-fall to motions under inverse square-law, Am. J. Phys.40 (2008) 579. · Zbl 1291.70040 |
| [135] | 135. R. S. Christensen, R. Teiwes, S. V. Petersen, U. I. Uggerhøj and B. Jacoby, Laboratory test of the Galilean universality of the free fall, Phys. Educ.49 (2014) 201. genRefLink(16, ’S0219887816300142BIB135’, ’10.1088 |
| [136] | 136. H. Khrapko, Dependence of acceleration on speed in the general relativistic Galileo experiment, Eur. J. Phys.36 (2015) 038001. genRefLink(16, ’S0219887816300142BIB136’, ’10.1088 |
| [137] | 137. L. T. Pockman, Newtonian mechanics and the equivalence of gravitational and inertial mass, Am. J. Phys.19 (1951) 305. genRefLink(16, ’S0219887816300142BIB137’, ’10.1119 |
| [138] | 138. G. Burniston Brown, Gravitational and inertial mass, Am. J. Phys.28 (1960) 475. genRefLink(16, ’S0219887816300142BIB138’, ’10.1119 |
| [139] | 139. G. Burniston Brown, Newton, language and mass, Phys. Educ.11 (1976) 373. genRefLink(16, ’S0219887816300142BIB139’, ’10.1088 |
| [140] | 140. M. Eggdall, Teaching relativity to the layperson, Phys. Teach.47 (2009) 522. genRefLink(16, ’S0219887816300142BIB140’, ’10.1119 |
| [141] | 141. A. Bandyopadhyay and A. Kumar, Probing students ideas of the principle of equivalence, Eur. J. Phys.32 (2011) 139. genRefLink(16, ’S0219887816300142BIB141’, ’10.1088 |
| [142] | 142. R. B. Lindsay, Galileo Galilei, 1564-1642, and the motion of falling bodies, Am. J. Phys.10 (1942) 285, Errata, Am. J. Phys.11 (1943) 40. |
| [143] | 143. J. Cunningham and R. Karplus, Free fall demonstration experiment, Am. J. Phys.656 (1962) 30. |
| [144] | 144. G. Feinberg, Fall of bodies near the Earth, Am. J. Phys.33 (1965) 501. genRefLink(16, ’S0219887816300142BIB144’, ’10.1119 |
| [145] | 145. R. J. Seeger, Galileo, yesterday and today, Am. J. Phys.33 (1965) 680. genRefLink(16, ’S0219887816300142BIB145’, ’10.1119 |
| [146] | 146. V. V. Raman, The leaning tower of Pisa experiment, Phys. Teach.10 (1972) 196. genRefLink(16, ’S0219887816300142BIB146’, ’10.1119 |
| [147] | 147. B. M. Casper, Galileo and the fall of Aristotle: A case of historical injustice?, Am. J. Phys.45 (1977) 325. genRefLink(16, ’S0219887816300142BIB147’, ’10.1119 |
| [148] | 148. B. Gee, Gravitation as Newton first saw it, Phys. Educ.12 (1977) 347. genRefLink(16, ’S0219887816300142BIB148’, ’10.1088 |
| [149] | 149. J. L. Redding, Aristotle’s theory of falling bodies, Am. J. Phys.46 (1978) 689. genRefLink(16, ’S0219887816300142BIB149’, ’10.1119 |
| [150] | 150. A. Franklin, Principle of inertia in the Middle Ages, Am. J. Phys.44 (1976) 529. genRefLink(16, ’S0219887816300142BIB150’, ’10.1119 |
| [151] | 151. C. G. Adler and B. L. Coulter, Quasi-history revisited, Phys. Educ.14 (1979) 398. genRefLink(16, ’S0219887816300142BIB151’, ’10.1088 |
| [152] | 152. A. B. Champagne, L. E. Klopfer and J. H. Anderson, Factors influencing the learning of classical mechanics, Am. J. Phys.48 (1980) 1074. genRefLink(16, ’S0219887816300142BIB152’, ’10.1119 |
| [153] | 153. D. K. Nachtingall, What is wrong with physics teachers’ education?, Eur. J. Phys.11 (1990) 1. genRefLink(16, ’S0219887816300142BIB153’, ’10.1088 |
| [154] | 154. R. J. Whitaker, Aristotle is not dead: Student understanding of trajectory motion, Am. J. Phys.51 (1983) 352. genRefLink(16, ’S0219887816300142BIB154’, ’10.1119 |
| [155] | 155. J. Lythcott, ”Aristotelian” was given as an answer, but what was the question?, Am. J. Phys.53 (1984) 428. genRefLink(16, ’S0219887816300142BIB155’, ’10.1119 |
| [156] | 156. L. H. Ryder, From Newton to Einstein, Phys. Educ.22 (1987) 342. genRefLink(16, ’S0219887816300142BIB156’, ’10.1088 |
| [157] | 157. W. Klein and P. Mittelstaedt, A simple demonstration of the principle of equivalence, Am. J. Phys.65 (1997) 316. genRefLink(16, ’S0219887816300142BIB157’, ’10.1119 |
| [158] | 158. E. Disy and J. Garner, Hypothetical pre-classical equations of motion, Phys. Teach.37 (1999) 42. genRefLink(16, ’S0219887816300142BIB158’, ’10.1119 |
| [159] | 159. L. Hsu, Testing Newton’s laws before projectile motion, Phys. Teach.39 (2001) 206. genRefLink(16, ’S0219887816300142BIB159’, ’10.1119 |
| [160] | 160. M. Trainer, About the origins of the general theory of relativity: Einstein’s search for the truth, Eur. J. Phys.26 (2005) S91. genRefLink(16, ’S0219887816300142BIB160’, ’10.1088 |
| [161] | 161. A. Art, Experiments in free fall, Phys. Educ.41 (2006) 380. genRefLink(16, ’S0219887816300142BIB161’, ’10.1088 |
| [162] | 162. A. Corona, J. Slisko and G. Planinsic, Freely rising bottle of water also demonstrates weightlessness, Phys. Educ.41 (2006) 208. genRefLink(16, ’S0219887816300142BIB162’, ’10.1088 |
| [163] | 163. O. Pantano and S. Talas, Physics thematic paths: laboratorial activities and historical scientific instruments, Phys. Educ.45 (2010) 140. genRefLink(16, ’S0219887816300142BIB163’, ’10.1088 |
| [164] | 164. J. R. Persson and J. E. Hagen, Videos determine the Moon’s g, Phys. Educ.46 (2011) 12. genRefLink(16, ’S0219887816300142BIB164’, ’10.1088 |
| [165] | 165. F. Vera and R. Rivera, A piece of paper falling faster than free fall, Eur. J. Phys.32 (2011) 1245. genRefLink(16, ’S0219887816300142BIB165’, ’10.1088 |
| [166] | 166. B. Kožnjak, Was Aristotle an exponent of antiscientific mumbo-jumbo?, Phys. Educ.47 (2012) 545. genRefLink(16, ’S0219887816300142BIB166’, ’10.1088 |
| [167] | 167. S. AbdElazem and W. Al-Basheer, Measuring the acceleration due to gravity using an IR transceiver, Phys. Educ.36 (2015) 045017. |
| [168] | 168. W. Jack, Galileo and the application of mathematics to physics, Nature21 (1879) 40. genRefLink(16, ’S0219887816300142BIB168’, ’10.1038 |
| [169] | 169. G. H. Bryan, Science in the days of the inquisition, Nature69 (1904) 505. genRefLink(16, ’S0219887816300142BIB169’, ’10.1038 |
| [170] | 170. P. Duhem, Societies and academies, Nature78 (1908) 45. genRefLink(16, ’S0219887816300142BIB170’, ’10.1038 |
| [171] | 171. G. Greenhill, Prof. Turner and Aristotle, Nature92 (1914) 584. genRefLink(16, ’S0219887816300142BIB171’, ’10.1038 |
| [172] | 172. W. Ramsay, Aristotle’s physics, Nature92 (1914) 606. genRefLink(16, ’S0219887816300142BIB172’, ’10.1038 |
| [173] | 173. R. T. Gunther, Galileo and the leaning tower of Pisa, Nature136 (1935) 6. genRefLink(16, ’S0219887816300142BIB173’, ’10.1038 |
| [174] | 174. A. S. Eve, Galileo and scientific history. the leaning tower and other stories, Nature137 (1936) 8. genRefLink(16, ’S0219887816300142BIB174’, ’10.1038 |
| [175] | 175. L. Cooper, Galileo and scientific history, Nature137 (1936) 488. genRefLink(16, ’S0219887816300142BIB175’, ’10.1038 |
| [176] | 176. E. N. da C. Andrade, Science in the seventeen century, Nature142 (1938) 19. genRefLink(16, ’S0219887816300142BIB176’, ’10.1038 |
| [177] | 177. M. D., Book review, Nature144 (1939) 899. |
| [178] | 178. Editor, Aristotle’s views on falling bodies, Nature158 (1946) 906. |
| [179] | 179. J. Rosen, Galileo Galilei (1564-1642), Nature201 (1964) 653. genRefLink(16, ’S0219887816300142BIB179’, ’10.1038 |
| [180] | 180. J. R. Ravetz, Origin of modern science, Nature258 (1975) 306. |
| [181] | 181. W. Gratzer, A litany of folly, Nature372 (1986) 781. genRefLink(16, ’S0219887816300142BIB181’, ’10.1038 |
| [182] | 182. G. Æ. Oravas, A window on scientific progress, Nature404 (2000) 17. genRefLink(16, ’S0219887816300142BIB182’, ’10.1038 |
| [183] | 183. J.-M. Lévy-Leblond, Science’s fiction, Nature413 (2001) 573. genRefLink(16, ’S0219887816300142BIB183’, ’10.1038 |
| [184] | 184. C. L. Doolittle, Scientific research, Science15 (1902) 841. genRefLink(16, ’S0219887816300142BIB184’, ’10.1126 |
| [185] | 185. R. H. Thurston, Scientific research – the art of revelation and of prophecy, Science16 (1902) 401. genRefLink(16, ’S0219887816300142BIB185’, ’10.1126 |
| [186] | 186. F. W. Clarke, The atomic theory, Science18 (1903) 513. genRefLink(16, ’S0219887816300142BIB186’, ’10.1126 |
| [187] | 187. F. E. Nipher, The man of science and his duties, Science33 (1911) 950. genRefLink(16, ’S0219887816300142BIB187’, ’10.1126 |
| [188] | 188. E. V. Huntington, The fundamental equations of mechanics, Science43 (1916) 312. genRefLink(16, ’S0219887816300142BIB188’, ’10.1126 |
| [189] | 189. G. F. Hull, Some aspects in war and peace, Science51 (1920) 221. genRefLink(16, ’S0219887816300142BIB189’, ’10.1126 |
| [190] | 190. F. Cajori, Aristotle and Galilei on falling bodies, Science51 (1920) 615. genRefLink(16, ’S0219887816300142BIB190’, ’10.1126 |
| [191] | 191. F. Cajori, Galileo’s experiments from the tower of Pisa, Science52 (1920) 409. genRefLink(16, ’S0219887816300142BIB191’, ’10.1126 |
| [192] | 192. D. W. Horn, Romancing in science, Science53 (1921) 44. genRefLink(16, ’S0219887816300142BIB192’, ’10.1126 |
| [193] | 193. F. Cajori, Reply to Professor Horn, Science53 (1921) 139. genRefLink(16, ’S0219887816300142BIB193’, ’10.1126 |
| [194] | 194. D. W. Horn, A correction, Science53 (1921) 139. genRefLink(16, ’S0219887816300142BIB194’, ’10.1126 |
| [195] | 195. A. G. Webster, Galileo and wood, Science53 (1921) 212. genRefLink(16, ’S0219887816300142BIB195’, ’10.1126 |
| [196] | 196. R. Cole, The modern hospital and medical progreass, Science64 (1926) 123. genRefLink(16, ’S0219887816300142BIB196’, ’10.1126 |
| [197] | 197. J. Zeleny, The place of physics in the modern world, Science58 (1928) 629. genRefLink(16, ’S0219887816300142BIB197’, ’10.1126 |
| [198] | 198. H. H. Turner, The scientific restrospect, Science69 (1929) 281. genRefLink(16, ’S0219887816300142BIB198’, ’10.1126 |
| [199] | 199. E. D. Lawrence, Science and technology, Science86 (1937) 295. genRefLink(16, ’S0219887816300142BIB199’, ’10.1126 |
| [200] | 200. D. J. de Solla Price, The science of mechanics in the middle ages, Science130 (1959) 1568. |
| [201] | 201. N. R. Hanson, Galileo’s discoveries in dynamics, Science147 (1965) 471. genRefLink(16, ’S0219887816300142BIB201’, ’10.1126 |
| [202] | 202. J. T. Edsall, Personal recollections, Science196 (1977) 769. genRefLink(16, ’S0219887816300142BIB202’, ’10.1126 |
| [203] | 203. C. Holden, Proving Einstein right (or wrong), Science251 (1991) 870. genRefLink(16, ’S0219887816300142BIB203’, ’10.1126 |
| [204] | 204. A. Watson, Gravity’s gravity vindicates Einstein, Science286 (1999) 1065. genRefLink(16, ’S0219887816300142BIB204’, ’10.1126 |
| [205] | 205. R. J. Raphael, Bringing Galileo to life, Science331 (2011) 535. genRefLink(16, ’S0219887816300142BIB205’, ’10.1126 |
| [206] | 206. C. M. Will, Theory and Experiment in Gravitational Physics (Cambridge University Press, Cambridge, 1993). genRefLink(16, ’S0219887816300142BIB206’, ’10.1017 · Zbl 0785.53068 |
| [207] | 207. C. M. Will, The confrontation between general relativity and experiment, Living Rev. Relativ.17 (2014) 4. genRefLink(16, ’S0219887816300142BIB207’, ’10.12942 |
| [208] | 208. J. L. Synge, Relativity: The General Theory (North-Holland Publishing Co., Amsterdam, 1960). · Zbl 0090.18504 |
| [209] | 209. P. Fayet, Equivalence principle tests, equivalence theorems and new long-range forces, C. R. Acad. Sci. Paris, IV2 (2001) 1257, arXiv:hep-ph/0111282 [arXiv] . genRefLink(128, ’S0219887816300142BIB209’, ’000172843600003’); |
| [210] | 210. T. Damour, Theoretical aspects of the equivalence principle, Class. Quantum Grav.29 (2012) 184001, arXiv:1202.6311 [arXiv] [gr-qc]. genRefLink(16, ’S0219887816300142BIB210’, ’10.1088 |
| [211] | 211. E. Di Casola, S. Liberati and S. Sonego, Nonequivalence of equivalence principles, Am. J. Phys.83 (2015) 39, arXiv:1310.7426 [arXiv] [gr-qc]. genRefLink(16, ’S0219887816300142BIB211’, ’10.1119 |
| [212] | 212. H. C. Ohanian, What is the principle of equivalence, Am. J. Phys.45 (1977) 903. genRefLink(16, ’S0219887816300142BIB212’, ’10.1119 |
| [213] | 213. H. C. Ohanian, Reply to Professor Waldstadt ”principle of equivalence”, Am. J. Phys.47 (1979) 1006. genRefLink(16, ’S0219887816300142BIB213’, ’10.1119 |
| [214] | 214. A. Walstad, The equivalence principle, Am. J. Phys.47 (1979) 565. genRefLink(16, ’S0219887816300142BIB214’, ’10.1119 |
| [215] | 215. G. Preti, Schwarzschild radius before general relativity: Why does Michell-Laplace argument provide the correct answer?, Found. Phys.39 (2009) 1046. genRefLink(16, ’S0219887816300142BIB215’, ’10.1007 |
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