Trouton–Noble experiment

The Trouton–Noble experiment attempted to detect motion of the Earth through the luminiferous aether, and was conducted in 1901–1903 by Frederick Thomas Trouton (who also developed the Trouton's ratio) and H. R. Noble. It was based on a suggestion by George FitzGerald that a charged parallel-plate capacitor moving through the aether should orient itself perpendicular to the motion. (Such thought experiments are also referred to as "Trouton-Noble paradox", "Right-angle lever paradox", or "Lewis-Tolman paradox"). Like the earlier Michelson–Morley experiment, Trouton and Noble obtained a null result: no motion relative to the aether could be detected.

This null result was reproduced, with increasing sensitivity, by Rudolf Tomaschek (1925, 1926), Chase (1926, 1927) and Hayden in 1994. Such experimental results are now seen, consistent with special relativity, to reflect the validity of the principle of relativity and the absence of any absolute rest frame (or aether). See also Tests of special relativity.

Experiment

In the experiment, a suspended parallel-plate capacitor is held by a fine torsion fiber and is charged. If the aether theory were correct, the change in Maxwell's equations due to the Earth's motion through the aether would lead to a torque causing the plates to align perpendicular to the motion. 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 these two descriptions is more accurate. Its null result thus confirms Lorentz invariance of special relativity.

Like any experiment measuring very small forces, the Trouton–Noble experiment is very difficult to control so as to eliminate outside influences. For example, based on standard electromagnetism and relativity, Nieves et al. predict that a very slight deflection could result from the interaction with the Earth's magnetic field and its axial rotation. However, this effect would be far smaller than that originally sought by Trouton and Noble.

Analysis

The detailed relativistic analysis of the null result requires care to correctly reconcile, for example, the effects seen by observers in different frames of reference (see e.g. Max von Laue (1911-12), Paul Sophus Epstein (1911), and the list below), but ultimately all such theoretical descriptions are shown to give the same result. The early history of descriptions of this experiment is reviewed by Janssen (1995).

The Trouton–Noble experiment is essentially equivalent to the so-called "right angle lever paradox" thought experiment, first discussed by Lewis and Tolman in 1909. 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 and momenta.

See also

• History of special relativity

Further reading

• Butler, J. W. (1968). "On the Trouton-Noble Experiment". American Journal of Physics. 36 (11): 936–941. Bibcode:1968AmJPh..36..936B. doi:10.1119/1.1974358.

• Furry, W. H. (1969). "Examples of Momentum Distributions in the Electromagnetic Field and in Matter". American Journal of Physics. 37 (6): 621–636. doi:10.1119/1.1975729.

• Newburgh, R. G. (1969). "The relativistic problem of the right-angled lever: The correctness of the Laue solution". Il Nuovo Cimento B. 61 (2): 201–209. doi:10.1007/BF02710928.

• Butler, J. W. (1970). "The Lewis-Tolman Lever Paradox". American Journal of Physics. 38 (3): 360–368. doi:10.1119/1.1976326.

• Aranoff, S. (1972). "Equilibrium in special relativity" (PDF). Il Nuovo Cimento B. 10 (1): 155–171. Bibcode:1972NCimB..10..155A. doi:10.1007/BF02911417.

• Sears, Francis W. (1972). "Another Relativistic Paradox". American Journal of Physics. 40 (5): 771–773. doi:10.1119/1.1986643.

• Grøn, Ø. (1973). "The asynchronous formulation of relativistic particle mechanics". Il Nuovo Cimento B. 34 (1): 127–140. doi:10.1007/BF02723345.

• Nickerson, J. Charles; McAdory, Robert T. (1975). "The Trouton-Noble paradox". American Journal of Physics. 43 (7): 615–621. doi:10.1119/1.9761.{{cite journal}}: CS1 maint: multiple names: authors list (link)

• 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". American Journal of Physics. 46 (1): 108–109. doi:10.1119/1.11106.{{cite journal}}: CS1 maint: multiple names: authors list (link)

• Holstein, Barry R.; Swift, Arthur R. (1982). "Flexible string in special relativity". American Journal of Physics. 50 (10): 887–889. doi:10.1119/1.13002.{{cite journal}}: CS1 maint: multiple names: authors list (link)

• Singal, Ashok K. (1993). "On the "explanation" of the null results of Trouton-Noble experiment". American Journal of Physics. 61 (5): 428–433. Bibcode:1993AmJPh..61..428S. doi:10.1119/1.17236.

• 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: TOC, pref., intro-I, 1, 2, intro-II, 3, 4, refs.

• Teukolsky, Saul A. (1996). "The explanation of the Trouton-Noble experiment revisited". American Journal of Physics. 64 (9): 1104–1109. Bibcode:1996AmJPh..64.1104T. doi:10.1119/1.18329.

• Jefimenko, Oleg D. (1999). "The Trouton-Noble paradox". Journal of Physics A. 32 (20): 3755–3762. Bibcode:1999JPhA...32.3755J. doi:10.1088/0305-4470/32/20/308.

• Jackson, J. D. (2004). "Torque or no torque? Simple charged particle motion observed in different inertial frames". American Journal of Physics. 72 (12): 1484–1487. doi:10.1119/1.1783902.

• Franklin, Jerrold (2006). "The lack of rotation in the Trouton Noble experiment". European Journal of Physics. 27 (5): 1251–1256. arXiv:physics/0603110. Bibcode:2006EJPh...27.1251F. doi:10.1088/0143-0807/27/5/024.

• Ivezić, Tomislav (2006). "Trouton Noble Paradox Revisited". Foundations of Physics. 37 (4–5): 747–760. arXiv:physics/0606176. Bibcode:2007FoPh...37..747I. doi:10.1007/s10701-007-9116-x.

External links

• Kevin Brown, "Trouton-Noble and The Right-Angle Lever at MathPages.
• Michel Janssen, "The Trouton Experiment and E = mc²," Einstein for Everyone course at UMN (2002).