A Proposed Experiment to Test Einstein's Special Relativity and an Mternative

Transcription

1 Physics Essays volume 5, number 4, 1992 A Proposed Experiment to Test Einstein's Special Relativity and an Mternative Young-Sea Huang Abstract An experiment to test Einstein's special relativir [Einstein, The Meaning of Relativity, 5th ed (Princeton UniversiOJ Press, 1956); H.A. Lorentz, A. Einstein, H. Minkowski, H. Weft, The Principle of Relativity, edited by HA. Lorentz (Oever, NE, 1923)] without involving ambiguities of the space-time concept and other theoretical bones of contention is proposed. It is an experiment well within present tedmoloy#. We also introduce an alternative theory of relativir [Phys. Essays 4, 68 (1991); 194; 532; 5, 159 (1992)], which is different from Einstein's special relativi(y, particularly on the foundational level, that is, the concept of space-time as well as the meaning of the relati~'tic transformation, and in its implications modifying classical force laws, for example, the electromagnetic force law. So far, no available experimental evidence can convincingly differentiate between Einstein's special relativi~ and the alternative theory. The proposed experimental test, however, will differentiate between these two theories of relativir Key words: special relativity, a new theory of relativity, paradoxes in special relativity, experimental tests of special relativity 1. INTRODUCTION Ever since Einstein's theory of relativity was published, (1,2) his spacetime concept has been a subject of controversies, even though many experiments have been claimed to corroborate that theory. Some of these controversies are (1) clock paradox and the problem of simultaneity,/3-13) (2) the length contraction paradox, (14-16) (3) the paradox of the rightangled lever, (17-23) and (4) the incompatibility between Einstein's theory of relativity and quantum theory at the foundational level, t24-29) Among these controversies the clock paradox has created one of the most perplexing and longest-standing arguments in twentieth-century physics. There are many different solutions given to the clock paradox. However, many physicists express in private their displeasure with solutions given to the clock paradox. (3~ As a consequence, the controversies of the clock paradox are still carried on up to the present. (8,11-13) The different versions of resolutions to the clock paradox are found to be contradictory to each other. (32) The clock paradox strikes at the very foundation of Einstein's special relativity. For such a long period of time, to have so many contradictory resolutions given to the clock paradox actually enforces speculation that there may indeed be an inconsistency in Einstein's special relativity - as maintained by Dingle. (6~ This persistency of paradox inevitably provokes concerns on the experimental evidence claiming to have confirmed Einstein's concept of space and time. Those experimental proofs may be either untrue or wrongly interpreted. Controversies will be endless unless Einstein's concept of space and time is finally clarified in his special relativity. However, the meaning of time in Einstein's special relativity, based on light propagation and the constant velocity of light, is a tautological consequence of the definition. ~33) It seems that Einstein's concept of space-time cannot be defined without controversies. It is then impossible to resolve those paradoxes, or to refute Einstein's special relativity, just by theoretical (or logical) arguments without controversies. Therefore, we think that the best way to test Einstein's special relativity is to perform experiments without any ambiguities in space and time coordinates, as well as other theoretical issues of contention involved. We herein propose a clean experiment to test Einstein's special relativity. In addition, the proposed experiment can be performed with existing modem experimental equipment from high-energy physics. To the best of this author's knowledge, no such experiment has been done./34-36~ Since the alternative theory of relativity is mostly unknown to the physical community, and it is easier to discuss the proposed experiment with both Einstein's special relativity and the alternative theory together rather than separately, we first introduce it, and then compare it with Einstein's special relativity - theoretically and experimentally. The paper is organized as follows. In Sec. 2 we introduce the alternative theory of relativity and emphasize that it is free from those paradoxes in Einstein's special relativity and is compatible with quantum theory. We also compare the alternative theory of relativity with Einstein's special relativity in the aspect of experimental tests. In Sec. 3 we analyze experiments that can differentiate between the alter- 451

2 A Proposed Experiment to Test Einstein's Relativity and an Alternative native theory of relativity and Einstein's special relativity. Then we propose a clean experiment to unambiguously test these two theories of relativity. 2. COMPARISONS BETWEEN EINSTEIN'S SPECIAL RELATIVITY AND THE ALTERNATIVE THEORY OF RELATIVITY An alternative theory of relativity was formulated based on three assumptions, besides the principle of relativity: (1) the constancy of the speed of light, (2) the transverse Doppler shift, and (3) the existence of a rest frame (for any motion of a material particle with respect to a reference frame, at any time instant there exists a reference frame in which this particle is at res. ~37) From the first and second assumptions the differential Lorentz transformation is deduced. The relativistic equations of motion are invariant under the differential Lorentz transformation. In addition, the formulas for the relativistic addition of velocities and the relativistic energy-momentum forms, which are the same as those in Einstein's special relativity, are obtained. Therefore, experiments such as the Michelson-Morley experiment, ~) the transverse (relativistic) Doppler shift, (39-41) and the velocity-dependence of relativistic mass (42,43) cannot distinguish the alternative theory of relativity from Einstein's special relativity. Einstein's special relativity entails the global torentz transformation (GET) as the relativistic transformation. The GLT is a transformation of both space-time coordinates and energy-momentum, which is then incompatible with Heisenberg's uncertainty principle in quantum theory. (z4) One may argue that quantum theory is incomplete in describing physical systems as insisted by Einstein. (44) However, laboratory tests indicate that Einstein may be incorrect and that the probability nature of quantum theory has to be accepted. (45) In contrast, this alternative theory entails the differential torentz transformation (DLT) as the relativistic transformation - an instantaneous transformation of the infinitesimal displacement vector only or, equivalently, of the energy-momentum only. (24) The DLT transforms physical quantities, not space and time coordinates, to make the laws of nature invariant. Therefore, the alternative theory of relativity is compatible with quantum theory's limit on determining conjugate variables. When the alternative theory of relativity is applied to modify classical force laws, for example, the electromagnetic force law and Newton's gravitational force law, these force laws become uniquely modified by a scalar factor 1 - (v/c) 2.(46,47) The accelerations of particles by an external force field are always in the same direction of that force field. However, according to Einstein's special relativity, the modification factor depends on the relative orientation between directions of velocity and force field. Consequently, the accelerations of particles in a given external field are, in general, not along the force direction. In addition, Einstein's modification of classical force laws together with the length contraction by the GET induce the so-called right-angled lever paradox. The alternative theory of relativity has no such problem. Furthermore, so far, there is no experimental evidence for the length contraction as predicted by Einstein's special relativity. The time concept adopted by the alternative theory of relativity is still the same as the Newtonian concept of universal time. Two events simultaneously happening in one reference frame have to happen simultaneously in every other reference frame. Therefore, there are no conceptual problems of simultaneity or the clock paradox in the alternative theory, which Einstein's special relativity has. Furthermore, Kantor theoretically analyzes the GLT in Einstein's special relativity and claims that simultaneity should be invariant rather than relative in Einstein's special relativity.(9) In addition, the relativity of simultaneity has not been tested experimentally. (31) We are aware that there are experiments claiming to have confirmed Einstein's space-time concept, for example, Hafele and Keating's experiments (48) and experiments measuring the meson's lifetime. (49-5x) The Hafele and Keating clocks-around-the-world experiment is questioned by opponents either from experimental or theoretical points of view. "The data are presented only graphically in such a gross form that they cannot be examined critically. ''(ira "The authors do not use all the results and apply a statistical analysis, details of which are not given, to those they do use. ''(52) The theoretical formulation of the experiment is based on the time interval in general relativity, and it no longer deals only with Einstein's special relativity. (1~ Furthermore, Comille recently claims that he correctly reinterprets the Hafele and Keating experiment for the first time, and the acceleration has to be taken into account to resolve the clock paradox. 2) However, experiments on measuring the meson's lifetime claim to be unaffected by both transversal accelerations (up to ~-, 1 18 g, where g = 9.8 m/s 2~49) and longitudinal accelerations (up to ~ 5 x 1 15 g).(54) Theoretical calculations also claim to agree with these experiments that the decay rate (and so for the clock behavior) of mesons is independent of their acceleration. {s5) If acceleration does not affect the meson's lifetime, then the time dilation is a pure kinematic effect. Consequently, this turns out to support Dingle's claim that there is an inconsistency in Einstein's special relativity. How does an absolute physical effect of time dilation emerge out of the relative velocities of clocks, the behavior of which shall be reciprocal to each other according to the kinematic interpretation of the Lorentz transformation? Sachs finds a way out of this inconsistency by claiming that the spacetime coordinates in Einstein's special relativity are just parameters that make laws of nature covariant, and that the Lorentz transformation relation between time parameters is not a physical cause-effect relation3 s) There is no physical asymmetric aging of the twin (clock) paradox. Another version, which is equivalent to Sach's version, is as follows: the clock B in the frame B, viewed in the frame A, goes slower than the clock A in the frame & the clock A in the frame A, viewed in the frame B, goes slower than the clock B in the frame B (56'57) Hence the time dilation in Einstein's special relativity is not physically real. However, Sachs's version of Einstein's special relativity has invoked many objections from proponents of Einstein's special relativity that are not entirely coherent, some of them even contradictory. (58) ~rthermore, Pmkhovnick claims to entirely resolve the clock paradox by involving the relativity of simultaneity - clocks that are synchronous in one frame appear systematically nonsynchmnous in another frame with relative uniform rectilinear motion, and vice versa. (n) By the relativity of simultaneity, a transfer of time at the turning point of the traveling clock in an out-and-return journey is introduced to resolve the clock paradox. He also says that "any acceleration effects associated with such transfer must be considered quite separately and are irrelevant in any special-relativity analysis or in any consideration of the self-consistency of special relativity." There are so many different resolutions given to the clock paradox; none of these resolutions are completely convincing. We think that the clock paradox cannot be resolved without controversies via just theoretical (or logical) arguments, unless Einstein's concept of space-time is clarified. On the experimental aspect, experiments measuring relativistic time dilatation for muons moving in a circular orbit by Bailey et al. seem very convincing. (49-51) However, Sachs argues against that appearance by stating that "the actual number of particles that are left (in the muon's frame) is strictly a function of the internal forces that cause its decay and should not depend on the state of motion of some observer who happens to be 452

3 Young-Sea Huang looking at the process. ''(58) Mso, Waldmn complains that Bailey et al. do not explain their graphs of results fully in the text. (59) He points out that the lifetime of muons is about.77 ~LtS (Its = 1-6 s) according to the lower part of Fig. 2 in Bailey et al.'s paper. {51) (Waldmn may have made a mistake in that he refers to Fig. 2 in the paper in Nature (49) instead of Fig. 2 in the paper in Nuovo Cimento. 151>) Examining the lower part of Fig. 2 in the paper in Nuovo Cimento, {5D directly from the decay of the intensity of circulating muonic bunch, we estimate that the lifetime of muons is about 1.8 Its. If we take into account the additional loss of muons due to the instability in the storage ring in the beginning, the lifetime of muons might be about 2.2 Its, the lifetime of muons at rest/~~ There is no time dilation at all. Furthermore, examining Fig. 2 in Ref. 49 (or Fig. 18 in Ref. 5), we find that the muonic bunch circulates slightly less than 27 turns during the time interval from the time 6 Its to the time 1 Its. That is, the muonic bunch circulates ~, 27 turns in a time interval 4 Its. Hence the period of circular motion of the muonic bunch is estimated as ns, not 147 ns as estimated by Bailey et al. (ns = 1-9 s). From the circular motion = v/c = 2~r/Tc, (1) where v is the speed of muons, r the radius of circular motion, T the period of circular motion, and c the speed of light, we obtain [3 = O Here, we use the mean radius r = 7. m, according to Bailey et al.'s experiment. This corresponds to a Lorentz factor "~ = [ 1 - (v/c) 2 ] -1/2 = 7.678, which is substantially less than (4), as they claimed. Even ff we allow the maximum radius of the circular motion to be r = 7.6 m [aperture inside the storage ring: 12 cm (horizontally) x 8 cm (vertically)], we obtain ~ = and T = The Lorentz factor is still much less than (4), as they claimed. In that case, zfwe accept that there is time dilation in accord with Einstein's special relativity, then the lifetime of muons should be equal to Its, which is still substantially smaller than (26) Its, as claimed. This is a very serious inconsistency in an experiment claiming to have confirmed the Einstein time dilation factor with such high precision - a fractional error of at 95% confidence. The lifetime of muons found directly from either the measured period or the decay of the intensity of the circulating muonic bunch is inconsistent with that found by fitting the observed decay electron time spectrum with many parameters as done by Bailey el al. Therefore, the experimental evidence for the relativistic time dilation is not completely convincing. So far, no experimental evidence can convincingly differentiate between Einstein's special relativity and the alternative theory of relativity. 3. PROPOSAL FOR EPERIMENTS TO TEST CONTENTIOUS THEORIES OF RELATIVITY According to Einstein's special relativity, the equation of motion of a particle with mass m and charge q moving in a uniform magnetic field B is(6 ]) d(ymv)/dt =q(v x B). For the simple case of uniform circular motion we have r = (mvlqb) [ 1 - (v/c) 2] -1/2 (3) In contrast, according to the alternative theory of relativity, the equation of (2).-a g c5 d c5 xo d Ln c; "l... l""l... l'~"l '''' xx)c< t~q>,~,, I,,,, I,~,,I,,,,I,,,,.5 I Figure 1. Theoretical data of v/c vs magnetic field for muons in uniform circular motion. The radius of circular motion is 7. m. The symbols x motion is (46) d(mv)/dt =q(v x B)[1 - (v/c)2]. (4) For the simple case of uniform circular motion we have r = (mv/qb)[1 - (v/c)2] -1. (5) From Eqs. 1 and 3, by Einstein's special relativity, we obtain the predictions of v/c versus magnetic field and period versus magnetic field shown in Figs. 1 and 2, respectively. (The x symbol refers to the theoretical data predicted by Einstein's special relativity.) Here, we use the mass of muon m = x 1 28 kg, the charge q = x 1-19 C, and the speed of light c = x 1 8 m/s, (62/ as well as r = 7. m, which is the mean radius of the storage ring at CERN as mentioned in Bailey et al.'s experiments. (5~ Similarly, from Eqs. 1 and 5 by the alternative theory of relativity, we obtain the predictions as shown with the o symbol in the same figures, Figs. 1 and 2. The period of circulating muons is ns at magnetic field 1.47 T predicted by Einstein's special relativity, whereas ns by the alternative theory of relativity. If the uncertainty of the radius of circular motion is allowed to be 1 cm, the deviation of the period is only by ~-, ns for both theories. However, the measured period in Bailey et al.'s experiments should be ~-, ns, which is almost just at the middle between the predictions of Einstein's special relativity and the alternative theory of relativity. The experiments of Bailey et al. do not seem precise enough to confirm (or refute) these two theories of relativity. More systematic experimental tests for these two theories of relativity are necessary. Comparing Einstein's special relativity and the alternative theory of rel- 453

4 A Proposed Experiment to Test Einstein's Relativity and an Alternative ', t~ '' I... I""I""I"" '' ED CN C~ C~ i--',, ~ W- o l,,,,l,,,,l,t,tl,,,,,i.5 t t in,' g g C3 xo..-i o x x x x x o,,,i,,,,i,,,, l,t,,l,,,,i, t t Figure 2. Theoretical data of period vs magnetic field for muons in uniform circular motion. The radius of circular motion is 7. m. The symbols Figure 4. Theoretical data of period vs magnetic field for protons in uniform circular motion. The radius of circular motion is 7. m. The symbols x i il' il I- I I ' III. I I i I i i I I I I r I I i i xx I/3 t'n c~ ''''1... I... i'''' b t33 c~ O3 c~ oo~176 O o Q t'n c5 O LQ O d m ",,,i,,,,[,,,lllttjilik,l,l i C3!.5 1 [ O.L Figure 3. Theoretical data of v/c vs magnetic field for protons in uniform circular motion. The radius of circular motion is 7. m. The symbols Figure 5. Theoretical data of v/c vs magnetic field for protons in uniform circular motion at lower speed. The radius of circular motion is 7. m. The symbols +, and o refer to data predicted by Newton's theory, Einstein's special relativity, and the alternative 454

5 Young-Sea Huang Oo n~ o P. LO o "U '''1''''1''''1'''' protons in the uniform circular motion. Then, by directly measuring the magnetic field inside the storage ring, as well as the period and the mean radius of the circulating protons' bunch, we can test the predictions of these two theories as shown in Figs. 3 and 4. The proposed experiment involves no theoretical bones of contention other than Einstein's special relativity and the alternative theory of relativity. For such experimental tests there are no ambiguities in the meanings of time measurement of the period and space measurement of the mean radius of circular motion in the laboratory frame. In addition, there are advantages to using protons instead of muons in such experimental tests: (1) It is easier to obtain a variety of particle velocities (by a synchrotron accelerator) for protons than for muons, because protons are easier to prepare in experiments and because protons do not decay. (2) Because protons are more massive, the radiation effect due to acceleration is even more negligible for protons than for muons. LO I[ Ill t i i I i i i i I i i ii flail ~l i~ o.25.5 o.o75.t Figure 6. Theoretical data of period vs magnetic field for protons in uniform circular motion at lower speed. The radius of circular motion is 7. m. The symbols +, x, and o refer to data predicted by Newton's theory, Einstein's special relativity, and the alternative ativity, we recognize that experiments with more massive particles, for example, protons, in circular motion inside the storage ring can distinguish more easily the difference between these two theories. The predictions from these two theories, using the mass of proton m x 1-27 kg, the charge q = C,(62) and the mean radius of circular motion r = 7. m, are shown in Figs. 3 and 4. We find that there is ~ 17 ns difference in the period predicted between these two theories at magnetic field 1.47 T. Present technology can surely tell this difference. We also check these two theories with Newton's theory. The predictions from these three theories are shown in Figs. 5 and 6. (The + symbol refers to the predictions by Newton's theory.) We find that these three theories converge to each other when the speed of protons is below about.1 c. We suggest an experiment to utilize a circular storage ring to constrain 4. CONCLUSIONS Modem experiments in high-energy physics are based on the Lorentzcovariant electromagnetic force law to calculate energy and momentum of relativistic particles. However, the Lorentz-covariant electromagnetic force law has not been systematically tested for particles in the relativistic region. (34-36) It is necessary to test directly whether or not the Lorentzcovariant electromagnetic force law is indeed true for relativistic particles. Otherwise, it is still possible that experiments in high-energy physics are based on the Lorentz force law, which may only be approximately true or may even be incorrect. Consequently, it is likely that theories in high-energy physics are based on the experimental evidence, which may not be true. In that case the proposed experiment is certainly worth a try. The proposed experiment is based on direct measures and involves no ambiguities of space-time coordinates as well as no complications of other theoretical issues of contention. In addition, the proposed experiment can be performed with high accuracy within present technology. If the results of the proposed experiment turn out to precisely verify the prediction of Einstein's special relativity, it will provide the most convincing experimental evidence for Einstein's special relativity within the context of that theory itself. Acknowledgment This author gratefully thanks Dr. C.M.L. Leonard for assistance in the preparation of the paper. This author benefitted from his stimulating questions and intellectual discussion. This author sincerely thanks Dr. T.E. Phipps, Jr., for his encouragement and endorsement. Received 2 December

6 A Proposed Experiment to Test Einstein's Relativity and an Alternative R~sum~ On propose ici une exp&ience pour prouver la relativit~ restreinte d'einstein /The Meaning of Relativity, 5th ed.. (Princeton University Press, 1956); HM. Lorentz, A. Einstein, H. minkowski, H. Weft, The Principle of Relativity, edited by HA. Lorentz (Dover, N~, 1923)] sans impliquer des ambiguit~s du concept espace4emps et autres sujets de dd~saccord. C'est une exp&ience bien dam le domaine de la tedmologie d'ajourd'hui. Nous introduisons aussi une thdgrie alternative de la relativit~ [Phys. Essays 4, 68 (1991); 194; 5, 159 (1992)], qui est diff&ente de la relativit~ restreinte d'einstein, particulibrement au niveau de fondation, comme le concept d'espace-temps, ainsi que le signification de la transformation relativiste, et en ses implications de modification des lois classiques de force, notamment, la lois de force ~lectromagndtique. Jusqu'it maintenant, aucune prouve e~mentale disponible peut diff&encier d'une mani#e convainfante entre la relativitd restreinte d'einstein et la theorie alternative. Toutefois, la preuve exppa'mentale propos~e va diffprencier entre ces deux th&ries de relativity. References 1. A. Einstein, The Meaning of Relativily, 5th ed. (Princeton University Press, Princeton, 1956). 2. H.A. Lorentz, A. Einstein, H. Minkowski and H. Weyl, The Princ~Ole of Relativity, edited by H.A. Lorentz (Dover, NY, 1923). 3. P. Langevin, Scientia IO, 31 (1911). 4. G. Builder, Am J. Phys. 27, 656 (1959). 5. Y.P. Terletskii, Paradz~es in the Theory of Relativi{y (Plenum, 1968). 6. H. Dingle, Nature 216, 119 (1967); idem, Science at the Crossroads (Martin Brain & O'Keeffe, London, 1972). 7. L. Essen, The Special Theory of Relal~'vily: A Critical Analysis (Clarendon, Oxford, 1971). 8. M. Sachs, Phys. Today 24, 23 (sept., 1971); Int. J. Theor. Phys. 1, 321 (1974); Found. Phys. 15, 977 (1985); Found. Phys. 19, 1525 (1989). 9. W. Kantor, Czech. J. Phys. B 22, 129 (1972). 1. Idem, Found. Phys. 4, 15 (1974). 11. S.J. Prokhovnik, Found. Phys. 19, 541 (1989). 12. P. Comille, Phys. Lett. A 131, 156 (1988). 13. W.A. Rodrigues, Jr. and M.A.F. Rosa, Found. Phys. 19, 75 (1989). 14. P. Ehrenfest, Phys. Z. 1, 918 (199). 15. T.E. Phipps, Jr., Heretical Verities: Mathematical Themes in Physical Descrtption (Classie Non-fiction Library, Urbana, IL, 1986), p G.P. Sastry, Am. J. Phys. 55, 943 (1987). 17. M. van Lane, Phys. Z. 12, 18 (1911). 18. R.C. Tolman, Relativi& Thermodynamics, and Cosmology (Clarendon, Oxford, 1934), p L. Karlov, Lett. Nuovo Cimento 3, 37 (197). 2. K.A. Johns, Lett. Nuovo Cimento 4, 351 (197). 21. V.S. Shenoy and T.S. Shankara, Spec. Sei. Tech. 3, 379 (198). 22. S.J. Prokhovnik and K.P. Kov~cs, Found. Phys. 15, 167 (1985). 23. D.G. Jensen, Am. J. Phys. 57, 553 (1989). 24. Young-Sea Huang, Phys. Essays 5, 159 (1992). 25. E. Schriktinger, Br. J. Philos. Sei. 4, 328 (1953/54). 26. M. Sachs, Hadronic J. 5, 1781 (1982); /dem, Quantum Mechanics from General Relativity (D. Reidel, nordrecht, 1986). 27. M. Bahai, Int. J. Theor. Phys. 23, 143 (1984). 28. N. Maxwell, Philos. Sei. 52, 23 (1985); Philos. Sci. 55, 64 (1988). 29. A.O. Bamt, Found. Phys. 18, 95 (1988). 3. A.D. Allen, Phys. Today 31, no (~eb. 1978). 31. J.G. Vargas, Found. Phys. 11, 235 (1981). 32. I. McCausland, Electron. Wireless World 89, 63 (Oct., 1983); ~/em, The Relativily Question (Department of Electrical Engineering, University of Toronto, Toronto, Canada, 1988). 33. D.T. MacRoberts, Spec. Sci. Tech. 3, 365 (198). 34. O. Newman, G.W. Ford, & Rich, and E. Sweetman, Phys. Rev. Lett. 4, 1355 (1978). 35. n.w. iacarthur, Phys. Rev. A 33, 1 (1986). 36. R.A. Waldron, Spec. Sci. Tech. 12, 127 (1989). 37. Young-Sea Huang, Phys. Essays 4, 68 (1991). 38. A.A. iichdson and E.H. Morley, Am. J. Sei. 34, 333 (1887). 39. H.E. Ives and G.R. Stilwell, J. Opt. Soc. Am. 28, 215 (1938). 4. D. Hasselkamp, E. Mondry, and A. Sehannann, Z. Phys. A 289, 151 (1979). 41. M. Kaivola, O. Poulsen, E. RiMs, and S.A. Lee, Phys. Rev. Lett. 54, 255 (1985). 42. n.j. Grove and J.C. Fox, Phys. Rev. 9, 378 (1953). 43. V.P. Zrelov, A.A. Tiapkin, and P.S. Farag6, Soy. Phys. JETP 7, 384 (1958). 44. R. Moore, Niels Bohr, 2nd ed. (The MIT Press, Cambridge, MA, 1985), Chap A. Shimony, Sei. Am. 258, 46 (Jan., 1988). 46. Young-Sea Huang, Phys. Essays 4, 194 (1991). 47. Ibid, p J.C. Hafele and R.F. Keating, Science 177, 166 (1972). 49. J. Bailey, K. Borer, F. Combley, H. Dmmm, F. Krienen, F. Lange, E. Picas,so, W. von Riiden, F.J.M. Farley, J.H. Field, W. Flegel, and P.M. Hattersley, Nature 268, 31 (1977). 456

7 Young-Sea Huang 5. J. Bailey, K. Borer, F. Combley, H. Drumm, C. Eck, FJ.M. Farley, J.H. Field, W. Flegel, P.M. Hattersley, F. Krienen, F. Lange, G. Leb~, E. McMillan, G. Petrucci, E. Picasso, O. Rdnolfsson, W. yon Rtiden, R.W. Williams and S. Wojcicki, Nucl. Phys. B 15, 1 (1979). 51. J. Bailey, W. Bartl, G. von Bochmann, R.C.A. Brown, F.J.M. Farley, M. Giesch, H. JSstlein, S. van der Meer, E. Picasso and R.W. Williams, Nuovo Cimento A 9, 369 (1972). 52. L. Essen, Wireless World 84, 44 (Oct., 1978). 53. W.A.S. Murray, Electron. Wireless World 92, 28 (Dec., 1986). 54. C.E. Roos, J. Marraffino, S. Reucroft, J. Waters, M.S. Webster, E.G.H. Williams, A. Manz, R. Settles and G. Wolf, Nature 286, 244 (198). 55. A.M. Eisele, Helve. Phys. Acta. 6, 124 (1987). 56. H. Stopes-Roe, Listener 86, 724 (1971). 57. M.A. Jaswon, Listener 86, 724 (1971). 58. Various, Phys. Today 25, 9 (Jan., 1972). 59. R.A. Waldron, Spec. Sei. Tech. 3, 385, 47 (198). 6. M.P. Balandin, V.M. Grebenyuk, V.G. Zinov, A.3. Konin, and A.N. Ponomarev, Sov. Phys. JEPT 4, 811 (1974). 61. J.D. Jackson, Classical Electrodynamics (John Wiley & Sons, NY, 1975), Chap. 11, D. Halliday and R. Resnick, Fundamentals of Physics, 3rd ed. (John Wiley & Sons, NY, 1988), Appendix B. Young-Sea Huang Department of Physics Soochow University Shih-Lin, Taipei Taiwan 457