318:
17:
1136:
In both cases an apparent net torque on an object (when viewed from a certain frame of reference) does not result in any rotation of the object, and in both cases this is explained by correctly accounting, in the relativistic way, for the transformation of all the relevant forces, momenta and the accelerations produced by them. The early history of descriptions of this experiment is reviewed by
Janssen (1995).
1148:(1904). His result is based on the assumption that the torque and momentum due to electrostatic forces are compensated by the torque and momentum due to molecular forces. However, there is no known mechanism for how a Lorentz transformation could produce such molecular forces. In addition, if two point charges are connected by a flexible string, no molecular force could produce a turning moment.
1679:
2279:
Using this relation between relativistic force and acceleration, it can be shown that no rotation occurs in this system. Similar considerations are also to be applied to the right-angle lever and
Trouton–Noble paradox. So the paradoxes are resolved, because the two accelerations (as vectors) point to
1347:
in 1911. They applied the notion of a relativistic mass that was different in the longitudinal direction and the transverse direction so that force and acceleration do not always have the same direction. The role played by the concept of force in relativity is very different from that of
Newtonian
1135:
The detailed relativistic analysis of both the
Trouton–Noble paradox and the right-angle lever paradox requires care to correctly reconcile, for example, the effects seen by observers in different frames of reference, but ultimately all such theoretical descriptions are shown to give the same result.
304:
However, while the negative experimental outcome can easily be explained in the rest frame of the device, the explanation from the viewpoint of a non-co-moving frame (concerning the question, whether the same torque should arise as in the "aether frame" described above, or whether no torque arises at
1962:
296:
On the other hand, the assertion of special relativity that
Maxwell's equations are invariant for all frames of reference moving at constant velocities would predict no torque (a null result). Thus, unless the aether were somehow fixed relative to the Earth, the experiment is a test of which of
741:
43:
which kept alternate plates of the capacitor charged to 3000 volts. The opposite plates of the capacitor as well as the celluloid ball were kept at ground voltage by means of a platinum wire that dipped into a sulfuric acid bath that not only served as a conductive
1786:. Does this lead to a rotation of the rod? No, because Epstein now considered the accelerations caused by the two forces. He used the concept of a relativistic mass that was different in the longitudinal direction and the transverse direction such that
1348:
mechanics. A similar conclusion was reached by
Franklin (2006), using invariant mass that did not change with direction, but using the fact that the direction of relativistic acceleration is different from the direction of relativistic force.
948:
2274:
1773:
2073:
1792:
1163:. According to Laue, an energy current connected with a certain momentum ("Laue current") is produced in moving bodies by elastic stresses. The resulting mechanical torque in the case of the Trouton–Noble experiment amounts to:
1037:
560:
746:
It can be seen that the torque is not zero, which apparently would cause the lever to rotate in the non-co-moving frame. Since no rotation is observed, Lewis and Tolman thus concluded that no torque exists, therefore:
1506:
1122:
826:
1318:
490:
228:
1498:
1236:
1323:
which exactly compensates the electromagnetic torque mentioned above, thus no rotation occurs on both cases. Or in other words: The electromagnetic torque is actually necessary for the uniform motion of a body,
127:
such as the "Trouton–Noble paradox," and the "right-angle lever" or "Lewis–Tolman paradox". Several solutions have been proposed to solve this kind of paradox, all of them in agreement with special relativity.
2637:
2760:
4436:
Ivezić, Tomislav (2005). "Axiomatic
Geometric Formulation of Electromagnetism with Only One Axiom: The Field Equation for the Bivector Field F with an Explanation of the Trouton-Noble Experiment".
2130:
2811:
2327:
1399:
1331:
Since then, many papers appeared which elaborated on Laue's current, providing some modifications or re-interpretations, and included different variants of "hidden" momentum.
39:
that was covered with conductive paint, and which was suspended by a fine phosphor-bronze wire 37 cm long within a grounded tube. The wire was connected to one electrode of a
3005:
Michel
Janssen, "A comparison between Lorentz's ether theory and special relativity in the light of the experiments of Trouton and Noble, Ph.D. thesis (1995). Online:
2729:
1424:
291:
540:
513:
400:
369:
251:
4039:
4332:
Spavieri, G.; Gillies, G. T. (2003). "Fundamental tests of electrodynamic theories: Conceptual investigations of the
Trouton-Noble and hidden momentum effects".
271:
2141:
1957:{\displaystyle m_{\rm {long.}}={m_{0}\gamma ^{3}},\ m_{\rm {tr.}}=m_{0}\gamma ,\quad {\rm {where}}\quad \gamma ={\frac {1}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}}
4642:
1687:
1978:
4311:
Nieves, L.; Rodriguez, M.; Spavieri, G.; Tonni, E. (2001). "An experiment of the
Trouton-Noble type as a test of the differential form of Faraday's law".
959:
841:
736:{\displaystyle \tau =f_{x}\cdot L_{0}-f_{y}\cdot L_{0}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}=L_{0}\left(f_{x}-f_{y}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}\right)}
3508:
Cavalleri, G.; Grøn, Ø.; Spavieri, G.; Spinelli, G. (1978). "Comment on the article "Right-angle lever paradox" by J. C. Nickerson and R. T. McAdory".
4001:
Cavalleri, G.; Salgarelli, G. (1969). "Revision of the relativistic dynamics with variable rest mass and application to relativistic thermodynamics".
4483:
Ivezić, Tomislav (2006). "Four-Dimensional Geometric Quantities versus the Usual Three-Dimensional Quantities: The Resolution of Jackson's Paradox".
73:
4602:
3026:
1674:{\displaystyle f_{x}=f'_{x},\ f_{y}=f'_{y}\cdot {\sqrt {1-{\frac {v^{2}}{c^{2}}}}},\ \tan \alpha =\tan \alpha '{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}
3014:
3010:
2901:
753:
105:
4809:
4856:
1048:
1247:
4773:
4675:
4835:
4804:
4635:
4680:
158:
1169:
4741:
4163:
Cavalleri, G.; Spavieri, G.; Spinelli, G. (1975). "Ropes and pulleys in special relativity (relativistic statics of threads)".
2826:
See "further reading", especially Nickerson/McAdory (1975), Singal (1993), Teukolsky (1996), Jefimenko (1999), Jackson (2004).
412:
4778:
4736:
4711:
3183:
3164:
3141:
3114:
1437:
4851:
4628:
4877:
2082:
52:. A mirror attached to the capacitor was viewed through a telescope and allowed fine changes in orientation to be viewed.
4078:
96:: no motion relative to the aether could be detected. This null result was reproduced, with increasing sensitivity, by
4746:
4726:
3964:
Newburgh, R. G. (1969). "The relativistic problem of the right-angled lever: The correctness of the Laue solution".
3666:
Jackson, J. D. (2004). "Torque or no torque? Simple charged particle motion observed in different inertial frames".
2310:
F. T. Trouton and H. R. Noble, "The mechanical forces acting on a charged electric condenser moving through space,"
4685:
4670:
4237:
Hernández, A.; Rivas, M.; Aguirregabiria, J. M. (1982). "A quantitative analysis of the trouton-noble experiment".
4788:
4665:
89:
3927:
Rohrlich, F. (1966). "True and apparent transformations, classical electrons, and relativistic thermodynamics".
4731:
4695:
1368:
4783:
2289:
4399:
Spavieri, Gianfranco (1990). "Proposal for experiments to detect the missing torque in special relativity".
4362:
Prokhovnik, S. J.; Kovács, K. P. (1985). "The application of special relativity to the right-angled lever".
305:
all) is much more difficult and is called "Trouton–Noble paradox," which can be solved in several ways (see
4908:
4768:
4716:
3038:
4928:
4651:
3696:
3194:
1156:
117:
3034:
3030:
3022:
3018:
3006:
4592:
3299:
Furry, W. H. (1969). "Examples of Momentum Distributions in the Electromagnetic Field and in Matter".
2581:
3270:
Aranoff, S. (1969). "Torques and Angular Momentum on a System at Equilibrium in Special Relativity".
77:
3253:
4923:
4918:
4913:
4903:
4882:
3133:
1373:
1155:(1911), who gave the standard solution for these kind of paradoxes. It was based on the so-called "
137:
81:
69:
1339:
A solution without compensating forces or redefinitions of force and equilibrium was published by
4614:
3601:
Singal, Ashok K. (1993). "On the "explanation" of the null results of Trouton-Noble experiment".
2665:"Electromagnetic phenomena in a system moving with any velocity smaller than that of light"
144:
is held by a fine torsion fiber and is charged. If the aether theory were correct, the change in
113:
3328:
Butler, J. W. (1969). "A Proposed Electromagnetic Momentum-Energy 4-Vector for Charged Bodies".
3202:
Gamba, A. (1967). "Physical Quantities in Different Reference Systems According to Relativity".
4872:
4354:
3248:
3106:
145:
2425:
2387:"Über Versuche zur Auffindung elektrodynamischer Wirkungen der Erdbewegung in großen Höhen II"
2348:"Über Versuche zur Auffindung elektrodynamischer Wirkungen der Erdbewegung in großen Höhen I"
276:
88:
moving through the aether should orient itself perpendicular to the motion. Like the earlier
4089:
Grøn, Ø. (1973). "The asynchronous formulation of relativistic statics and thermodynamics".
3153:
3125:
3098:
3097:
Pauli, Wolfgang (1981) . "Applications to special cases. Trouton's and Noble's experiment".
4549:
4502:
4455:
4408:
4371:
4341:
4320:
4283:
4246:
4209:
4172:
4135:
4098:
4054:
4010:
3973:
3936:
3899:
3853:
3836:
3807:
3760:
3713:
3675:
3646:
3610:
3581:
3550:
3517:
3486:
3453:
3444:
Aranoff, S. (1973). "More on the Right-Angled Lever at Equilibrium in Special Relativity".
3424:
3395:
3366:
3337:
3308:
3279:
3240:
3211:
3058:
2963:
2926:
2879:
2789:
2707:
2677:
2553:
2518:
2507:"Bemerkung zu meinen Versuchen zur Auffindung elektrodynamischer Wirkungen in großen Höhen"
2479:
2442:
2398:
2359:
518:
498:
378:
347:
337:
333:
236:
3631:
2506:
2386:
2347:
8:
4200:
Chamorro, A.; Hernández, A. (1978). "A synchronous formulation of relativistic statics".
3126:
3085:
2269:{\displaystyle {\frac {d{\bf {p}}}{dt}}=m{\frac {d}{dt}}({\bf {v}}\gamma )=m\gamma ^{3}.}
1344:
65:
4553:
4506:
4459:
4412:
4375:
4345:
4324:
4287:
4250:
4213:
4176:
4139:
4102:
4058:
4014:
3977:
3940:
3903:
3857:
3811:
3764:
3717:
3679:
3650:
3614:
3585:
3554:
3521:
3490:
3457:
3428:
3399:
3370:
3341:
3312:
3283:
3244:
3215:
3062:
2967:
2930:
2883:
2793:
2711:
2681:
2557:
2522:
2483:
2446:
2402:
2363:
1404:
1328:, to hinder the body to rotate due to the mechanical torque caused by elastic stresses.
4760:
4565:
4539:
4518:
4492:
4471:
4445:
4424:
4387:
4299:
4262:
4225:
4188:
4151:
4114:
4070:
4026:
3989:
3952:
3915:
3869:
3823:
3797:
3776:
3750:
3729:
3704:
Aguirregabiria, J. M.; Hernandez, A.; Rivas, M. (1982). "A Lewis-Tolman-like paradox".
2979:
2953:
2602:
1768:{\displaystyle {\frac {f_{x}}{f_{y}}}={\frac {\tan \alpha }{1-{\frac {v^{2}}{c^{2}}}}}}
543:
325:
298:
256:
124:
109:
4585:
3865:
3572:
Holstein, Barry R.; Swift, Arthur R. (1982). "Flexible string in special relativity".
406:
must be equal to obtain equilibrium, thus no torque is given by the law of the lever:
317:
4825:
4690:
4428:
4391:
4303:
4266:
4229:
4192:
4155:
4118:
4074:
4030:
3993:
3956:
3919:
3827:
3819:
3772:
3733:
3179:
3160:
3137:
3110:
3099:
2975:
2068:{\displaystyle a_{x}={\frac {f_{x}}{m\gamma ^{3}}},\ a_{y}={\frac {f_{y}}{m\gamma }}}
1972:
is accelerated by these two forces in the longitudinal and transverse direction, are
1340:
40:
4522:
3780:
3725:
2983:
1032:{\displaystyle {\frac {f_{x}}{f_{y}}}={\frac {1}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}}
4569:
4557:
4510:
4475:
4463:
4416:
4379:
4291:
4254:
4217:
4180:
4143:
4106:
4062:
4018:
3981:
3944:
3907:
3873:
3861:
3815:
3768:
3721:
3683:
3654:
3618:
3589:
3558:
3525:
3494:
3461:
3432:
3403:
3374:
3345:
3316:
3287:
3258:
3219:
3066:
2971:
2887:
2849:
2797:
2715:
2594:
2561:
2526:
2487:
2450:
2406:
2367:
943:{\displaystyle f_{x}=f'_{x},\ f_{y}=f'_{y}\cdot {\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}
97:
16:
3741:
Franklin, Jerrold (2006). "The lack of rotation in the Trouton Noble experiment".
2944:
Franklin, Jerrold (2006). "The lack of rotation in the Trouton Noble experiment".
2580:
4606:
2470:
2433:
1145:
3788:
Franklin, Jerrold (2008). "The lack of rotation in a moving right angle lever".
3070:
2745:
Laue, Max von (1911). "Bemerkungen zum Hebelgesetz in der Relativitätstheorie".
1500:. As already shown above, these forces have the form in a non-co-moving frame:
4620:
4561:
4514:
4467:
4274:
Ai, Hsiao-Bai (1993). "The historical misconception in relativistic statics".
2853:
4897:
4830:
4756:
3882:
3507:
2891:
2801:
2719:
2530:
2410:
2371:
835:(1911), this is in contradiction with the relativistic expressions of force,
101:
4310:
116:
and the absence of any absolute rest frame (or aether). The experiment is a
4236:
3703:
2491:
2454:
1152:
832:
152:
causing the plates to align perpendicular to the motion. This is given by:
2622:
Laue, Max von (1911). "Ein Beispiel zur Dynamik der Relativitätstheorie".
2135:
Franklin used the relativistic connection between force and acceleration,
2838:"Non-Newtonian Mechanics :— The Direction of Force and Acceleration"
821:{\displaystyle {\frac {f_{x}}{f_{y}}}={\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}
93:
4544:
4497:
4450:
3755:
3047:"Drawing the line between kinematics and dynamics in special relativity"
3046:
2958:
2917:
Epstein, P. S. (1927). "Conference on the Michelson-Morley experiment".
2606:
1042:
When applied to the law of the lever, the following torque is produced:
4420:
4383:
4295:
4258:
4221:
4184:
4147:
4110:
4066:
4022:
3985:
3948:
3911:
3472:
2664:
1160:
1127:
Which is principally the same problem as in the Trouton–Noble paradox.
297:
these two descriptions is more accurate. Its null result thus confirms
3687:
3465:
3436:
3407:
3378:
3349:
3320:
3291:
3262:
3223:
2565:
4162:
3092:, Berkeley: University of California press, pp. 539–776, 152–153
2598:
2280:
the center of gravity of the system, although the two forces do not.
141:
85:
49:
45:
21:
3890:
Arzeliès, H. (1965). "Sur le problème relativiste du levier coudé".
3658:
3622:
3593:
3563:
3538:
3529:
2867:
2837:
2777:
2695:
1117:{\displaystyle \tau =-L_{0}\cdot f'_{x}\cdot {\frac {v^{2}}{c^{2}}}}
3499:
3474:
3386:
Rohrlich, F. (1970). "Electromagnetic Momentum, Energy, and Mass".
2578:
1313:{\displaystyle \tau =L_{0}\cdot f'_{x}\cdot {\frac {v^{2}}{c^{2}}}}
3802:
3571:
2544:
H. C. Hayden (1994). "High sensitivity Trouton–Noble experiment".
2468:
Carl T. Chase (1927). "The Trouton–Noble Ether Drift Experiment".
3123:
2670:
Proceedings of the Royal Netherlands Academy of Arts and Sciences
108:
in 1994. Such experimental results are now seen, consistent with
32:
2582:"The Principle of Relativity, and Non-Newtonian Mechanics"
4126:
Pahor, S.; Strnad, J. (1974). "Statics in special relativity".
149:
4361:
2638:
An Example Concerning the Dynamics of the Theory of Relativity
2328:
The Forces Acting on a Charged Condenser moving through Space.
1144:
The first solution of the Trouton–Noble paradox was given by
223:{\displaystyle \tau =-E'{\frac {v^{2}}{c^{2}}}\sin 2\alpha '}
148:
due to the Earth's motion through the aether would lead to a
61:
4530:
Ivezić, Tomislav (2006). "Trouton Noble Paradox Revisited".
1231:{\displaystyle \tau =E'{\frac {v^{2}}{c^{2}}}\sin 2\alpha '}
554:
in a non-co-moving system, thus the law of the lever gives:
293:
the angle between the normal of the plate and the velocity.
4000:
3632:"The explanation of the Trouton-Noble experiment revisited"
2761:
Remarks on the Law of the Lever in the Theory of Relativity
28:
4331:
3415:
Sears, Francis W. (1972). "Another Relativistic Paradox".
2426:"A Repetition of the Trouton-Noble Ether Drift Experiment"
4199:
3231:
Butler, J. W. (1968). "On the Trouton-Noble Experiment".
324:
The Trouton–Noble paradox is essentially equivalent to a
3844:
Jefimenko, Oleg D. (1999). "The Trouton-Noble paradox".
3357:
Butler, J. W. (1970). "The Lewis-Tolman Lever Paradox".
2587:
Proceedings of the American Academy of Arts and Sciences
485:{\displaystyle \tau '=L_{0}\left(f'_{x}-f'_{y}\right)=0}
2661:
2624:
Verhandlungen der Deutschen Physikalischen Gesellschaft
1968:
The relativistic expressions in the case, where a mass
1493:{\displaystyle {\tfrac {f'_{x}}{f'_{y}}}=\tan \alpha '}
1442:
2144:
2085:
1981:
1795:
1690:
1509:
1440:
1434:, and equilibrium in its rest frame is achieved when
1407:
1376:
1250:
1172:
1051:
962:
844:
756:
563:
521:
501:
415:
381:
350:
279:
259:
239:
161:
4398:
2812:
On the Theory of the Experiment of Trouton and Noble
1778:
So the resultant force does not directly point from
340:
in 1909. Suppose a right-angle lever with endpoints
35:, was fitted into a smooth spherical celluloid ball
27:, 7.7 cm in diameter, built from multiple layers of
4125:
2663:
2125:{\displaystyle {\frac {a_{x}}{a_{y}}}=\tan \alpha }
3843:
3629:
3473:Nickerson, J. Charles; McAdory, Robert T. (1975).
3152:
2835:
2306:
2304:
2268:
2124:
2067:
1956:
1767:
1673:
1492:
1418:
1393:
1312:
1230:
1116:
1031:
942:
820:
735:
542:the rest length of one lever arm. However, due to
534:
507:
484:
394:
363:
285:
265:
245:
222:
3787:
3740:
3414:
2943:
2778:"Zur Theorie des Versuches von Trouton und Noble"
2255:
2243:
4895:
4529:
4482:
4435:
3600:
123:The Trouton–Noble experiment is also related to
4650:
3963:
2919:Contributions from the Mount Wilson Observatory
2301:
1351:Epstein imagined a massless rod with endpoints
3665:
2916:
2865:
2579:Lewis, Gilbert N.; Tolman, Richard C. (1909),
48:, but also damped oscillations and acted as a
4636:
4273:
3356:
3327:
3230:
3124:Panofsky, Wolfgang; Phillips, Melba (2005) .
2775:
2744:
2693:
2621:
2467:
2423:
3926:
3889:
3385:
3298:
3173:
3083:
2543:
2504:
2384:
2345:
312:
4037:
3443:
3269:
2730:On the Dynamics of the Theory of Relativity
131:
4643:
4629:
68:, and was conducted in 1901–1903 by
4805:Tests of relativistic energy and momentum
4543:
4496:
4449:
3801:
3754:
3562:
3498:
3252:
3201:
3178:(2nd ed.). Dover. pp. 467–468.
2957:
1334:
4088:
3536:
316:
15:
4742:Lorentz-violating neutrino oscillations
4586:Trouton-Noble and The Right-Angle Lever
3539:"Relativistics statics and F. W. Sears"
3150:
3044:
2617:
2615:
60:was an attempt to detect motion of the
4896:
4810:Kaufmann–Bucherer–Neumann experiments
4779:Experimental testing of time dilation
4737:Antimatter tests of Lorentz violation
4712:Modern searches for Lorentz violation
4624:
3096:
2696:"Zur Dynamik der Relativitätstheorie"
2652:Janssen (1995), see "Further reading"
2646:
2612:
4878:Test theories of special relativity
4040:"Equilibrium in special relativity"
3128:Classical electricity and magnetism
76:. It was based on a suggestion by
13:
3090:The theory of relativity of motion
2993:
1903:
1900:
1897:
1894:
1891:
1860:
1857:
1811:
1808:
1805:
1802:
14:
4940:
4836:Michelson–Gale–Pearson experiment
4747:Lorentz-violating electrodynamics
4727:Experiments of Rayleigh and Brace
4578:
112:, to reflect the validity of the
4789:Length contraction confirmations
4686:de Sitter double star experiment
3051:Symposium on Time and Relativity
2900:English Wikisource translation:
2810:English Wikisource translation:
2759:English Wikisource translation:
2728:English Wikisource translation:
2662:Lorentz, Hendrik Antoon (1904),
2636:English Wikisource translation:
2546:Review of Scientific Instruments
2326:F. T. Trouton and H. R. Noble, "
2252:
2246:
2237:
2227:
2195:
2153:
1359:, and a particle with rest mass
1159:" in its general formulation by
344:. In its rest frame, the forces
2937:
2910:
2902:Concerning Relativistic Statics
2859:
2829:
2820:
2769:
2738:
2687:
2655:
1908:
1888:
1151:This was further elaborated by
1139:
136:In the experiment, a suspended
92:, Trouton and Noble obtained a
4857:Refutations of emission theory
4696:Measurements of neutrino speed
4438:Foundations of Physics Letters
4401:Foundations of Physics Letters
3045:Janssen, Michel H. P. (2008),
2572:
2537:
2498:
2461:
2417:
2378:
2339:
2320:
2260:
2222:
2203:
2190:
1401:with the y'-axis. Now a force
1241:and in the right-angle lever:
306:
1:
2868:"Über relativistische Statik"
2295:
2290:History of special relativity
1394:{\displaystyle \tan \alpha '}
273:the energy of the condenser,
4852:Refutations of aether theory
4774:Moessbauer rotor experiments
4676:Moessbauer rotor experiments
4671:Kennedy–Thorndike experiment
3105:. New York: Dover. pp.
1355:, which is mounted at point
1130:
7:
4666:Michelson–Morley experiment
4652:Tests of special relativity
4593:The Trouton Experiment and
3866:10.1088/0305-4470/32/20/308
3790:European Journal of Physics
3743:European Journal of Physics
3706:European Journal of Physics
3697:European Journal of Physics
3668:American Journal of Physics
3639:American Journal of Physics
3630:Teukolsky, Saul A. (1996).
3603:American Journal of Physics
3574:American Journal of Physics
3543:American Journal of Physics
3510:American Journal of Physics
3479:American Journal of Physics
3475:"The Trouton-Noble paradox"
3446:American Journal of Physics
3417:American Journal of Physics
3388:American Journal of Physics
3359:American Journal of Physics
3330:American Journal of Physics
3301:American Journal of Physics
3272:American Journal of Physics
3233:American Journal of Physics
3204:American Journal of Physics
3195:American Journal of Physics
3071:10.1016/j.shpsb.2008.06.004
2946:European Journal of Physics
2836:Tolman, Richard C. (1911),
2283:
1370:). The rod forms the angle
90:Michelson–Morley experiment
10:
4945:
4732:Trouton–Rankine experiment
3820:10.1088/0143-0807/29/6/N01
3773:10.1088/0143-0807/27/5/024
3176:Classical Electromagnetism
2976:10.1088/0143-0807/27/5/024
118:test of special relativity
4865:
4844:
4818:
4797:
4784:Hafele–Keating experiment
4755:
4704:
4658:
4562:10.1007/s10701-007-9116-x
4515:10.1007/s10701-006-9071-y
4468:10.1007/s10702-005-7533-7
3726:10.1088/0143-0807/3/1/008
3155:Classical Electrodynamics
3151:Jackson, John D. (1998).
2854:10.1080/14786440908637142
2747:Physikalische Zeitschrift
2312:Phil. Trans. Royal Soc. A
330:right angle lever paradox
313:Right-angle lever paradox
4883:Standard-Model Extension
4769:Ives–Stilwell experiment
4722:Trouton–Noble experiment
4717:Hughes–Drever experiment
3086:"The Right-Angled Lever"
2892:10.1002/andp.19113411404
2802:10.1002/andp.19123430705
2720:10.1002/andp.19113400808
2531:10.1002/andp.19273891709
2411:10.1002/andp.19263851304
2372:10.1002/andp.19263832403
132:Trouton–Noble experiment
70:Frederick Thomas Trouton
58:Trouton–Noble experiment
3159:(3rd ed.). Wiley.
2866:Epstein, P. S. (1911).
2317:, 165–181 (1903).
301:of special relativity.
286:{\displaystyle \alpha }
114:principle of relativity
4873:One-way speed of light
4532:Foundations of Physics
4485:Foundations of Physics
4364:Foundations of Physics
4355:Foundations of Physics
2842:Philosophical Magazine
2776:Laue, Max von (1912).
2694:Laue, Max von (1911).
2492:10.1103/PhysRev.30.516
2455:10.1103/PhysRev.28.378
2424:Carl T. Chase (1926).
2336:(479): 132-133 (1903).
2270:
2126:
2069:
1958:
1769:
1675:
1494:
1420:
1395:
1335:Force and acceleration
1314:
1232:
1118:
1033:
944:
822:
737:
536:
509:
486:
396:
365:
321:
287:
267:
247:
224:
53:
4681:Resonator experiments
4611:Einstein for Everyone
3174:Franklin, J. (2017).
3084:Tolman, R.C. (1917),
2505:R. Tomaschek (1927).
2385:R. Tomaschek (1926).
2346:R. Tomaschek (1925).
2271:
2127:
2070:
1959:
1770:
1676:
1495:
1421:
1396:
1315:
1233:
1119:
1034:
945:
831:However, as shown by
823:
738:
537:
535:{\displaystyle L_{0}}
510:
508:{\displaystyle \tau }
487:
397:
395:{\displaystyle f_{x}}
366:
364:{\displaystyle f_{y}}
332:, first discussed by
320:
288:
268:
248:
246:{\displaystyle \tau }
225:
19:
4038:Aranoff, S. (1972).
3846:Journal of Physics A
3837:Journal of Physics A
3101:Theory of Relativity
2142:
2083:
1979:
1793:
1688:
1507:
1438:
1405:
1374:
1248:
1170:
1049:
960:
842:
754:
561:
519:
499:
413:
379:
348:
338:Richard Chase Tolman
334:Gilbert Newton Lewis
277:
257:
237:
159:
4909:Physics experiments
4798:Relativistic energy
4554:2007FoPh...37..747I
4507:2006FoPh...36.1511I
4460:2005FoPhL..18..401I
4413:1990FoPhL...3..291S
4376:1985FoPh...15..167P
4346:2003NCimB.118..205S
4325:2001NCimB.116..585N
4288:1993NCimB.108....7A
4251:1982NCimB..72....1H
4214:1977NCimB..41..236C
4177:1975NCimB..25..348C
4140:1974NCimB..20..105P
4103:1973NCimB..17..141G
4059:1972NCimB..10..155A
4015:1969NCimA..62..722C
3978:1969NCimB..61..201N
3941:1966NCimB..45...76R
3904:1965NCim...35..783A
3858:1999JPhA...32.3755J
3812:2008EJPh...29...55F
3765:2006EJPh...27.1251F
3718:1982EJPh....3...30A
3680:2004AmJPh..72.1484J
3651:1996AmJPh..64.1104T
3615:1993AmJPh..61..428S
3586:1982AmJPh..50..887H
3555:1978AmJPh..46..249G
3522:1978AmJPh..46..108C
3491:1975AmJPh..43..615N
3458:1973AmJPh..41.1108A
3429:1972AmJPh..40..771S
3400:1970AmJPh..38.1310R
3371:1970AmJPh..38..360B
3342:1969AmJPh..37.1258B
3313:1969AmJPh..37..621F
3284:1969AmJPh..37..453A
3245:1968AmJPh..36..936B
3216:1967AmJPh..35...83G
3063:2009SHPMP..40...26J
2968:2006EJPh...27.1251F
2931:1928CMWCI.373...43E
2884:1911AnP...341..779E
2794:1912AnP...343..370L
2712:1911AnP...340..524L
2682:1903KNAB....6..809L
2558:1994RScI...65..788H
2523:1927AnP...389..161T
2484:1927PhRv...30..516C
2447:1926PhRv...28..378C
2403:1926AnP...385..509T
2364:1926AnP...383..743T
1567:
1535:
1469:
1456:
1345:Paul Sophus Epstein
1282:
1086:
902:
870:
515:is the torque, and
470:
454:
146:Maxwell's equations
125:thought experiments
66:luminiferous aether
4929:Physical paradoxes
4761:Length contraction
4705:Lorentz invariance
4605:2015-10-17 at the
4421:10.1007/BF00666019
4384:10.1007/BF00735288
4334:Il Nuovo Cimento B
4313:Il Nuovo Cimento B
4296:10.1007/BF02874335
4276:Il Nuovo Cimento B
4259:10.1007/BF02894929
4239:Il Nuovo Cimento B
4222:10.1007/BF02726555
4202:Il Nuovo Cimento B
4185:10.1007/BF02737685
4165:Il Nuovo Cimento B
4148:10.1007/BF02721111
4128:Il Nuovo Cimento B
4111:10.1007/BF02906436
4091:Il Nuovo Cimento B
4067:10.1007/BF02911417
4047:Il Nuovo Cimento B
4023:10.1007/BF02819595
4003:Il Nuovo Cimento A
3986:10.1007/BF02710928
3966:Il Nuovo Cimento B
3949:10.1007/BF02710587
3929:Il Nuovo Cimento B
3912:10.1007/BF02739341
3132:. Dover. pp.
2872:Annalen der Physik
2782:Annalen der Physik
2700:Annalen der Physik
2511:Annalen der Physik
2391:Annalen der Physik
2352:Annalen der Physik
2266:
2122:
2065:
1954:
1765:
1671:
1555:
1523:
1490:
1471:
1457:
1444:
1419:{\displaystyle f'}
1416:
1391:
1310:
1270:
1228:
1114:
1074:
1029:
940:
890:
858:
818:
733:
544:length contraction
532:
505:
482:
458:
442:
392:
361:
326:thought experiment
322:
299:Lorentz invariance
283:
263:
243:
220:
110:special relativity
54:
4891:
4890:
4831:Sagnac experiment
4826:Fizeau experiment
4691:Hammar experiment
4591:Michel Janssen, "
4491:(10): 1511–1534.
3852:(20): 3755–3762.
3688:10.1119/1.1783902
3674:(12): 1484–1487.
3537:Grøn, Ø. (1978).
3466:10.1119/1.1987485
3437:10.1119/1.1986643
3408:10.1119/1.1976082
3394:(11): 1310–1316.
3379:10.1119/1.1976326
3350:10.1119/1.1975297
3336:(12): 1258–1272.
3321:10.1119/1.1975729
3292:10.1119/1.1975612
3263:10.1119/1.1974358
3224:10.1119/1.1973974
3185:978-0-486-81371-4
3166:978-0-471-30932-1
3143:978-0-486-43924-2
3116:978-0-486-64152-2
2566:10.1063/1.1144955
2188:
2167:
2108:
2063:
2029:
2022:
1952:
1951:
1949:
1850:
1763:
1760:
1713:
1669:
1667:
1610:
1603:
1601:
1541:
1470:
1341:Richard C. Tolman
1308:
1209:
1157:inertia of energy
1112:
1027:
1026:
1024:
985:
938:
936:
876:
816:
814:
779:
726:
724:
651:
649:
266:{\displaystyle E}
201:
104:(1926, 1927) and
78:George FitzGerald
41:Wimshurst machine
4936:
4645:
4638:
4631:
4622:
4621:
4573:
4547:
4538:(4–5): 747–760.
4526:
4500:
4479:
4453:
4432:
4395:
4349:
4328:
4307:
4270:
4233:
4196:
4159:
4122:
4085:
4083:
4077:. Archived from
4044:
4034:
3997:
3960:
3923:
3892:Il Nuovo Cimento
3877:
3831:
3805:
3784:
3758:
3749:(5): 1251–1256.
3737:
3691:
3662:
3645:(9): 1104–1109.
3636:
3626:
3597:
3568:
3566:
3533:
3504:
3502:
3469:
3452:(9): 1108–1109.
3440:
3411:
3382:
3353:
3324:
3295:
3266:
3256:
3227:
3189:
3170:
3158:
3147:
3131:
3120:
3104:
3093:
3073:
2988:
2987:
2961:
2952:(5): 1251–1256.
2941:
2935:
2934:
2914:
2908:
2895:
2863:
2857:
2856:
2848:(129): 458–463,
2833:
2827:
2824:
2818:
2805:
2773:
2767:
2754:
2742:
2736:
2723:
2691:
2685:
2684:
2667:
2659:
2653:
2650:
2644:
2631:
2619:
2610:
2609:
2599:10.2307/20022495
2584:
2576:
2570:
2569:
2541:
2535:
2534:
2502:
2496:
2495:
2465:
2459:
2458:
2430:
2421:
2415:
2414:
2382:
2376:
2375:
2343:
2337:
2331:Proc. Royal Soc.
2324:
2318:
2308:
2275:
2273:
2272:
2267:
2259:
2258:
2231:
2230:
2221:
2220:
2199:
2198:
2189:
2187:
2176:
2168:
2166:
2158:
2157:
2156:
2146:
2131:
2129:
2128:
2123:
2109:
2107:
2106:
2097:
2096:
2087:
2074:
2072:
2071:
2066:
2064:
2062:
2054:
2053:
2044:
2039:
2038:
2027:
2023:
2021:
2020:
2019:
2006:
2005:
1996:
1991:
1990:
1963:
1961:
1960:
1955:
1953:
1950:
1948:
1947:
1938:
1937:
1928:
1920:
1916:
1907:
1906:
1881:
1880:
1868:
1867:
1866:
1848:
1844:
1843:
1842:
1833:
1832:
1819:
1818:
1817:
1774:
1772:
1771:
1766:
1764:
1762:
1761:
1759:
1758:
1749:
1748:
1739:
1730:
1719:
1714:
1712:
1711:
1702:
1701:
1692:
1680:
1678:
1677:
1672:
1670:
1668:
1666:
1665:
1656:
1655:
1646:
1638:
1636:
1608:
1604:
1602:
1600:
1599:
1590:
1589:
1580:
1572:
1563:
1551:
1550:
1539:
1531:
1519:
1518:
1499:
1497:
1496:
1491:
1489:
1472:
1465:
1452:
1443:
1425:
1423:
1422:
1417:
1415:
1400:
1398:
1397:
1392:
1390:
1319:
1317:
1316:
1311:
1309:
1307:
1306:
1297:
1296:
1287:
1278:
1266:
1265:
1237:
1235:
1234:
1229:
1227:
1210:
1208:
1207:
1198:
1197:
1188:
1186:
1123:
1121:
1120:
1115:
1113:
1111:
1110:
1101:
1100:
1091:
1082:
1070:
1069:
1038:
1036:
1035:
1030:
1028:
1025:
1023:
1022:
1013:
1012:
1003:
995:
991:
986:
984:
983:
974:
973:
964:
949:
947:
946:
941:
939:
937:
935:
934:
925:
924:
915:
907:
898:
886:
885:
874:
866:
854:
853:
827:
825:
824:
819:
817:
815:
813:
812:
803:
802:
793:
785:
780:
778:
777:
768:
767:
758:
742:
740:
739:
734:
732:
728:
727:
725:
723:
722:
713:
712:
703:
695:
693:
692:
680:
679:
665:
664:
652:
650:
648:
647:
638:
637:
628:
620:
618:
617:
605:
604:
592:
591:
579:
578:
541:
539:
538:
533:
531:
530:
514:
512:
511:
506:
491:
489:
488:
483:
475:
471:
466:
450:
436:
435:
423:
401:
399:
398:
393:
391:
390:
370:
368:
367:
362:
360:
359:
292:
290:
289:
284:
272:
270:
269:
264:
252:
250:
249:
244:
229:
227:
226:
221:
219:
202:
200:
199:
190:
189:
180:
178:
98:Rudolf Tomaschek
80:that a charged
4944:
4943:
4939:
4938:
4937:
4935:
4934:
4933:
4924:1903 in science
4919:1902 in science
4914:1901 in science
4904:Aether theories
4894:
4893:
4892:
4887:
4861:
4840:
4814:
4793:
4759:
4751:
4700:
4654:
4649:
4607:Wayback Machine
4581:
4576:
4545:physics/0606176
4498:physics/0602105
4451:physics/0412167
4081:
4042:
3756:physics/0603110
3659:10.1119/1.18329
3634:
3623:10.1119/1.17236
3594:10.1119/1.13002
3580:(10): 887–889.
3564:10.1119/1.11164
3530:10.1119/1.11106
3254:10.1.1.144.9274
3239:(11): 936–941.
3186:
3167:
3144:
3117:
2996:
2994:Further reading
2991:
2959:physics/0603110
2942:
2938:
2915:
2911:
2878:(14): 779–795.
2864:
2860:
2834:
2830:
2825:
2821:
2774:
2770:
2743:
2739:
2692:
2688:
2660:
2656:
2651:
2647:
2620:
2613:
2593:(25): 709–726,
2577:
2573:
2542:
2538:
2517:(17): 161–162.
2503:
2499:
2471:Physical Review
2466:
2462:
2434:Physical Review
2428:
2422:
2418:
2397:(13): 509–514.
2383:
2379:
2358:(24): 743–756.
2344:
2340:
2325:
2321:
2309:
2302:
2298:
2286:
2236:
2235:
2226:
2225:
2216:
2212:
2194:
2193:
2180:
2175:
2159:
2152:
2151:
2147:
2145:
2143:
2140:
2139:
2102:
2098:
2092:
2088:
2086:
2084:
2081:
2080:
2055:
2049:
2045:
2043:
2034:
2030:
2015:
2011:
2007:
2001:
1997:
1995:
1986:
1982:
1980:
1977:
1976:
1943:
1939:
1933:
1929:
1927:
1915:
1890:
1889:
1876:
1872:
1856:
1855:
1851:
1838:
1834:
1828:
1824:
1823:
1801:
1800:
1796:
1794:
1791:
1790:
1754:
1750:
1744:
1740:
1738:
1731:
1720:
1718:
1707:
1703:
1697:
1693:
1691:
1689:
1686:
1685:
1661:
1657:
1651:
1647:
1645:
1637:
1629:
1595:
1591:
1585:
1581:
1579:
1571:
1559:
1546:
1542:
1527:
1514:
1510:
1508:
1505:
1504:
1482:
1461:
1448:
1441:
1439:
1436:
1435:
1408:
1406:
1403:
1402:
1383:
1375:
1372:
1371:
1337:
1302:
1298:
1292:
1288:
1286:
1274:
1261:
1257:
1249:
1246:
1245:
1220:
1203:
1199:
1193:
1189:
1187:
1179:
1171:
1168:
1167:
1146:Hendrik Lorentz
1142:
1133:
1106:
1102:
1096:
1092:
1090:
1078:
1065:
1061:
1050:
1047:
1046:
1018:
1014:
1008:
1004:
1002:
990:
979:
975:
969:
965:
963:
961:
958:
957:
930:
926:
920:
916:
914:
906:
894:
881:
877:
862:
849:
845:
843:
840:
839:
808:
804:
798:
794:
792:
784:
773:
769:
763:
759:
757:
755:
752:
751:
718:
714:
708:
704:
702:
694:
688:
684:
675:
671:
670:
666:
660:
656:
643:
639:
633:
629:
627:
619:
613:
609:
600:
596:
587:
583:
574:
570:
562:
559:
558:
550:is longer than
526:
522:
520:
517:
516:
500:
497:
496:
462:
446:
441:
437:
431:
427:
416:
414:
411:
410:
386:
382:
380:
377:
376:
355:
351:
349:
346:
345:
315:
278:
275:
274:
258:
255:
254:
253:is the torque,
238:
235:
234:
212:
195:
191:
185:
181:
179:
171:
160:
157:
156:
134:
12:
11:
5:
4942:
4932:
4931:
4926:
4921:
4916:
4911:
4906:
4889:
4888:
4886:
4885:
4880:
4875:
4869:
4867:
4863:
4862:
4860:
4859:
4854:
4848:
4846:
4842:
4841:
4839:
4838:
4833:
4828:
4822:
4820:
4816:
4815:
4813:
4812:
4807:
4801:
4799:
4795:
4794:
4792:
4791:
4786:
4781:
4776:
4771:
4765:
4763:
4753:
4752:
4750:
4749:
4744:
4739:
4734:
4729:
4724:
4719:
4714:
4708:
4706:
4702:
4701:
4699:
4698:
4693:
4688:
4683:
4678:
4673:
4668:
4662:
4660:
4659:Speed/isotropy
4656:
4655:
4648:
4647:
4640:
4633:
4625:
4619:
4618:
4589:
4584:Kevin Brown, "
4580:
4579:External links
4577:
4575:
4574:
4527:
4480:
4444:(5): 401–429.
4433:
4407:(3): 291–302.
4396:
4370:(2): 167–173.
4351:
4350:
4329:
4308:
4271:
4234:
4208:(1): 236–244.
4197:
4171:(1): 348–356.
4160:
4134:(1): 105–112.
4123:
4097:(1): 141–165.
4086:
4084:on 2012-03-28.
4053:(1): 155–171.
4035:
4009:(3): 722–754.
3998:
3972:(2): 201–209.
3961:
3924:
3898:(3): 783–791.
3879:
3878:
3833:
3832:
3796:(6): N55–N58.
3785:
3738:
3693:
3692:
3663:
3627:
3609:(5): 428–433.
3598:
3569:
3549:(3): 249–250.
3534:
3516:(1): 108–109.
3505:
3500:10.1119/1.9761
3485:(7): 615–621.
3470:
3441:
3423:(5): 771–773.
3412:
3383:
3365:(3): 360–368.
3354:
3325:
3307:(6): 621–636.
3296:
3278:(4): 453–454.
3267:
3228:
3191:
3190:
3184:
3171:
3165:
3148:
3142:
3121:
3115:
3094:
3080:
3079:
3075:
3074:
3042:
3002:
3001:
2997:
2995:
2992:
2990:
2989:
2936:
2909:
2907:
2906:
2905:
2904:
2858:
2828:
2819:
2817:
2816:
2815:
2814:
2788:(7): 370–384.
2768:
2766:
2765:
2764:
2763:
2737:
2735:
2734:
2733:
2732:
2706:(8): 524–542.
2686:
2654:
2645:
2643:
2642:
2641:
2640:
2611:
2571:
2552:(4): 788–792.
2536:
2497:
2478:(4): 516–519.
2460:
2441:(2): 378–383.
2416:
2377:
2338:
2319:
2299:
2297:
2294:
2293:
2292:
2285:
2282:
2277:
2276:
2265:
2262:
2257:
2254:
2251:
2248:
2245:
2242:
2239:
2234:
2229:
2224:
2219:
2215:
2211:
2208:
2205:
2202:
2197:
2192:
2186:
2183:
2179:
2174:
2171:
2165:
2162:
2155:
2150:
2121:
2118:
2115:
2112:
2105:
2101:
2095:
2091:
2077:
2076:
2061:
2058:
2052:
2048:
2042:
2037:
2033:
2026:
2018:
2014:
2010:
2004:
2000:
1994:
1989:
1985:
1966:
1965:
1946:
1942:
1936:
1932:
1926:
1923:
1919:
1914:
1911:
1905:
1902:
1899:
1896:
1893:
1887:
1884:
1879:
1875:
1871:
1865:
1862:
1859:
1854:
1847:
1841:
1837:
1831:
1827:
1822:
1816:
1813:
1810:
1807:
1804:
1799:
1757:
1753:
1747:
1743:
1737:
1734:
1729:
1726:
1723:
1717:
1710:
1706:
1700:
1696:
1682:
1681:
1664:
1660:
1654:
1650:
1644:
1641:
1635:
1632:
1628:
1625:
1622:
1619:
1616:
1613:
1607:
1598:
1594:
1588:
1584:
1578:
1575:
1570:
1566:
1562:
1558:
1554:
1549:
1545:
1538:
1534:
1530:
1526:
1522:
1517:
1513:
1488:
1485:
1481:
1478:
1475:
1468:
1464:
1460:
1455:
1451:
1447:
1430:is applied at
1414:
1411:
1389:
1386:
1382:
1379:
1363:is mounted at
1336:
1333:
1321:
1320:
1305:
1301:
1295:
1291:
1285:
1281:
1277:
1273:
1269:
1264:
1260:
1256:
1253:
1239:
1238:
1226:
1223:
1219:
1216:
1213:
1206:
1202:
1196:
1192:
1185:
1182:
1178:
1175:
1141:
1138:
1132:
1129:
1125:
1124:
1109:
1105:
1099:
1095:
1089:
1085:
1081:
1077:
1073:
1068:
1064:
1060:
1057:
1054:
1040:
1039:
1021:
1017:
1011:
1007:
1001:
998:
994:
989:
982:
978:
972:
968:
951:
950:
933:
929:
923:
919:
913:
910:
905:
901:
897:
893:
889:
884:
880:
873:
869:
865:
861:
857:
852:
848:
829:
828:
811:
807:
801:
797:
791:
788:
783:
776:
772:
766:
762:
744:
743:
731:
721:
717:
711:
707:
701:
698:
691:
687:
683:
678:
674:
669:
663:
659:
655:
646:
642:
636:
632:
626:
623:
616:
612:
608:
603:
599:
595:
590:
586:
582:
577:
573:
569:
566:
529:
525:
504:
493:
492:
481:
478:
474:
469:
465:
461:
457:
453:
449:
445:
440:
434:
430:
426:
422:
419:
389:
385:
358:
354:
314:
311:
282:
262:
242:
231:
230:
218:
215:
211:
208:
205:
198:
194:
188:
184:
177:
174:
170:
167:
164:
133:
130:
100:(1925, 1926),
9:
6:
4:
3:
2:
4941:
4930:
4927:
4925:
4922:
4920:
4917:
4915:
4912:
4910:
4907:
4905:
4902:
4901:
4899:
4884:
4881:
4879:
4876:
4874:
4871:
4870:
4868:
4864:
4858:
4855:
4853:
4850:
4849:
4847:
4843:
4837:
4834:
4832:
4829:
4827:
4824:
4823:
4821:
4819:Fizeau/Sagnac
4817:
4811:
4808:
4806:
4803:
4802:
4800:
4796:
4790:
4787:
4785:
4782:
4780:
4777:
4775:
4772:
4770:
4767:
4766:
4764:
4762:
4758:
4757:Time dilation
4754:
4748:
4745:
4743:
4740:
4738:
4735:
4733:
4730:
4728:
4725:
4723:
4720:
4718:
4715:
4713:
4710:
4709:
4707:
4703:
4697:
4694:
4692:
4689:
4687:
4684:
4682:
4679:
4677:
4674:
4672:
4669:
4667:
4664:
4663:
4661:
4657:
4653:
4646:
4641:
4639:
4634:
4632:
4627:
4626:
4623:
4616:
4612:
4608:
4604:
4601:
4600:
4596:
4590:
4588:at MathPages.
4587:
4583:
4582:
4571:
4567:
4563:
4559:
4555:
4551:
4546:
4541:
4537:
4533:
4528:
4524:
4520:
4516:
4512:
4508:
4504:
4499:
4494:
4490:
4486:
4481:
4477:
4473:
4469:
4465:
4461:
4457:
4452:
4447:
4443:
4439:
4434:
4430:
4426:
4422:
4418:
4414:
4410:
4406:
4402:
4397:
4393:
4389:
4385:
4381:
4377:
4373:
4369:
4365:
4360:
4359:
4358:
4357:
4356:
4347:
4343:
4339:
4335:
4330:
4326:
4322:
4318:
4314:
4309:
4305:
4301:
4297:
4293:
4289:
4285:
4281:
4277:
4272:
4268:
4264:
4260:
4256:
4252:
4248:
4244:
4240:
4235:
4231:
4227:
4223:
4219:
4215:
4211:
4207:
4203:
4198:
4194:
4190:
4186:
4182:
4178:
4174:
4170:
4166:
4161:
4157:
4153:
4149:
4145:
4141:
4137:
4133:
4129:
4124:
4120:
4116:
4112:
4108:
4104:
4100:
4096:
4092:
4087:
4080:
4076:
4072:
4068:
4064:
4060:
4056:
4052:
4048:
4041:
4036:
4032:
4028:
4024:
4020:
4016:
4012:
4008:
4004:
3999:
3995:
3991:
3987:
3983:
3979:
3975:
3971:
3967:
3962:
3958:
3954:
3950:
3946:
3942:
3938:
3934:
3930:
3925:
3921:
3917:
3913:
3909:
3905:
3901:
3897:
3893:
3888:
3887:
3886:
3885:
3884:
3883:Nuovo Cimento
3875:
3871:
3867:
3863:
3859:
3855:
3851:
3847:
3842:
3841:
3840:
3839:
3838:
3829:
3825:
3821:
3817:
3813:
3809:
3804:
3799:
3795:
3791:
3786:
3782:
3778:
3774:
3770:
3766:
3762:
3757:
3752:
3748:
3744:
3739:
3735:
3731:
3727:
3723:
3719:
3715:
3711:
3707:
3702:
3701:
3700:
3699:
3698:
3689:
3685:
3681:
3677:
3673:
3669:
3664:
3660:
3656:
3652:
3648:
3644:
3640:
3633:
3628:
3624:
3620:
3616:
3612:
3608:
3604:
3599:
3595:
3591:
3587:
3583:
3579:
3575:
3570:
3565:
3560:
3556:
3552:
3548:
3544:
3540:
3535:
3531:
3527:
3523:
3519:
3515:
3511:
3506:
3501:
3496:
3492:
3488:
3484:
3480:
3476:
3471:
3467:
3463:
3459:
3455:
3451:
3447:
3442:
3438:
3434:
3430:
3426:
3422:
3418:
3413:
3409:
3405:
3401:
3397:
3393:
3389:
3384:
3380:
3376:
3372:
3368:
3364:
3360:
3355:
3351:
3347:
3343:
3339:
3335:
3331:
3326:
3322:
3318:
3314:
3310:
3306:
3302:
3297:
3293:
3289:
3285:
3281:
3277:
3273:
3268:
3264:
3260:
3255:
3250:
3246:
3242:
3238:
3234:
3229:
3225:
3221:
3217:
3213:
3209:
3205:
3200:
3199:
3198:
3197:
3196:
3187:
3181:
3177:
3172:
3168:
3162:
3157:
3156:
3149:
3145:
3139:
3135:
3130:
3129:
3122:
3118:
3112:
3108:
3103:
3102:
3095:
3091:
3087:
3082:
3081:
3077:
3076:
3072:
3068:
3064:
3060:
3056:
3052:
3048:
3043:
3040:
3036:
3032:
3028:
3024:
3020:
3016:
3012:
3008:
3004:
3003:
2999:
2998:
2985:
2981:
2977:
2973:
2969:
2965:
2960:
2955:
2951:
2947:
2940:
2932:
2928:
2924:
2920:
2913:
2903:
2899:
2898:
2897:
2896:
2893:
2889:
2885:
2881:
2877:
2873:
2869:
2862:
2855:
2851:
2847:
2843:
2839:
2832:
2823:
2813:
2809:
2808:
2807:
2806:
2803:
2799:
2795:
2791:
2787:
2783:
2779:
2772:
2762:
2758:
2757:
2756:
2755:
2752:
2748:
2741:
2731:
2727:
2726:
2725:
2724:
2721:
2717:
2713:
2709:
2705:
2701:
2697:
2690:
2683:
2679:
2675:
2671:
2666:
2658:
2649:
2639:
2635:
2634:
2633:
2632:
2629:
2625:
2618:
2616:
2608:
2604:
2600:
2596:
2592:
2588:
2583:
2575:
2567:
2563:
2559:
2555:
2551:
2547:
2540:
2532:
2528:
2524:
2520:
2516:
2512:
2508:
2501:
2493:
2489:
2485:
2481:
2477:
2473:
2472:
2464:
2456:
2452:
2448:
2444:
2440:
2436:
2435:
2427:
2420:
2412:
2408:
2404:
2400:
2396:
2392:
2388:
2381:
2373:
2369:
2365:
2361:
2357:
2353:
2349:
2342:
2335:
2332:
2329:
2323:
2316:
2313:
2307:
2305:
2300:
2291:
2288:
2287:
2281:
2263:
2249:
2240:
2232:
2217:
2213:
2209:
2206:
2200:
2184:
2181:
2177:
2172:
2169:
2163:
2160:
2148:
2138:
2137:
2136:
2133:
2119:
2116:
2113:
2110:
2103:
2099:
2093:
2089:
2059:
2056:
2050:
2046:
2040:
2035:
2031:
2024:
2016:
2012:
2008:
2002:
1998:
1992:
1987:
1983:
1975:
1974:
1973:
1971:
1944:
1940:
1934:
1930:
1924:
1921:
1917:
1912:
1909:
1885:
1882:
1877:
1873:
1869:
1863:
1852:
1845:
1839:
1835:
1829:
1825:
1820:
1814:
1797:
1789:
1788:
1787:
1785:
1781:
1776:
1755:
1751:
1745:
1741:
1735:
1732:
1727:
1724:
1721:
1715:
1708:
1704:
1698:
1694:
1662:
1658:
1652:
1648:
1642:
1639:
1633:
1630:
1626:
1623:
1620:
1617:
1614:
1611:
1605:
1596:
1592:
1586:
1582:
1576:
1573:
1568:
1564:
1560:
1556:
1552:
1547:
1543:
1536:
1532:
1528:
1524:
1520:
1515:
1511:
1503:
1502:
1501:
1486:
1483:
1479:
1476:
1473:
1466:
1462:
1458:
1453:
1449:
1445:
1433:
1429:
1412:
1409:
1387:
1384:
1380:
1377:
1369:
1366:
1362:
1358:
1354:
1349:
1346:
1342:
1332:
1329:
1327:
1303:
1299:
1293:
1289:
1283:
1279:
1275:
1271:
1267:
1262:
1258:
1254:
1251:
1244:
1243:
1242:
1224:
1221:
1217:
1214:
1211:
1204:
1200:
1194:
1190:
1183:
1180:
1176:
1173:
1166:
1165:
1164:
1162:
1158:
1154:
1149:
1147:
1137:
1128:
1107:
1103:
1097:
1093:
1087:
1083:
1079:
1075:
1071:
1066:
1062:
1058:
1055:
1052:
1045:
1044:
1043:
1019:
1015:
1009:
1005:
999:
996:
992:
987:
980:
976:
970:
966:
956:
955:
954:
931:
927:
921:
917:
911:
908:
903:
899:
895:
891:
887:
882:
878:
871:
867:
863:
859:
855:
850:
846:
838:
837:
836:
834:
809:
805:
799:
795:
789:
786:
781:
774:
770:
764:
760:
750:
749:
748:
729:
719:
715:
709:
705:
699:
696:
689:
685:
681:
676:
672:
667:
661:
657:
653:
644:
640:
634:
630:
624:
621:
614:
610:
606:
601:
597:
593:
588:
584:
580:
575:
571:
567:
564:
557:
556:
555:
553:
549:
545:
527:
523:
502:
479:
476:
472:
467:
463:
459:
455:
451:
447:
443:
438:
432:
428:
424:
420:
417:
409:
408:
407:
405:
387:
383:
374:
356:
352:
343:
339:
335:
331:
327:
319:
310:
308:
302:
300:
294:
280:
260:
240:
216:
213:
209:
206:
203:
196:
192:
186:
182:
175:
172:
168:
165:
162:
155:
154:
153:
151:
147:
143:
139:
129:
126:
121:
119:
115:
111:
107:
103:
99:
95:
91:
87:
83:
79:
75:
71:
67:
63:
59:
51:
47:
42:
38:
34:
30:
26:
23:
18:
4845:Alternatives
4721:
4610:
4598:
4594:
4535:
4531:
4488:
4484:
4441:
4437:
4404:
4400:
4367:
4363:
4353:
4352:
4337:
4333:
4316:
4312:
4279:
4275:
4242:
4238:
4205:
4201:
4168:
4164:
4131:
4127:
4094:
4090:
4079:the original
4050:
4046:
4006:
4002:
3969:
3965:
3935:(1): 76–83.
3932:
3928:
3895:
3891:
3881:
3880:
3849:
3845:
3835:
3834:
3793:
3789:
3746:
3742:
3712:(1): 30–33.
3709:
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