Trouton–Noble Experiment
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The Trouton–Noble experiment was an attempt to detect motion of the
Earth Earth is the third planet from the Sun and the only astronomical object known to Planetary habitability, harbor life. This is enabled by Earth being an ocean world, the only one in the Solar System sustaining liquid surface water. Almost all ...
through the
luminiferous aether Luminiferous aether or ether (''luminiferous'' meaning 'light-bearing') was the postulated Transmission medium, medium for the propagation of light. It was invoked to explain the ability of the apparently wave-based light to propagate through empt ...
, and was conducted in 1901–1903 by
Frederick Thomas Trouton Frederick Thomas Trouton (; 24 November 1863 – 21 September 1922) was an Irish experimental physicist known for Trouton's rule and his experiments to detect the Earth's rotation through the luminiferous aether. Life and work Trouton was ...
and H. R. Noble. It was based on a suggestion by George FitzGerald that a charged
parallel Parallel may refer to: Mathematics * Parallel (geometry), two lines in the Euclidean plane which never intersect * Parallel (operator), mathematical operation named after the composition of electrical resistance in parallel circuits Science a ...
-plate
capacitor In electrical engineering, a capacitor is a device that stores electrical energy by accumulating electric charges on two closely spaced surfaces that are insulated from each other. The capacitor was originally known as the condenser, a term st ...
moving through the aether should orient itself perpendicular to the motion. Like the earlier
Michelson–Morley experiment The Michelson–Morley experiment was an attempt to measure the motion of the Earth relative to the luminiferous aether, a supposed medium permeating space that was thought to be the carrier of light waves. The experiment was performed between ...
, Trouton and Noble obtained a
null result In science, a null result is a result without the expected content: that is, the proposed result is absent. It is an experimental outcome which does not show an otherwise expected effect. This does not imply a result of zero or nothing, simply a res ...
: no motion relative to the aether could be detected.F. T. Trouton and H. R. Noble, "The mechanical forces acting on a charged electric condenser moving through space," ''Phil. Trans. Royal Soc. A'' 202, 165–181 (1903). This null result was reproduced, with increasing sensitivity, by
Rudolf Tomaschek Rudolf Karl Anton Tomaschek (23 December 1895 in Budweis, Bohemia – 8 February 1966, Breitbrunn am Chiemsee) was a German experimental physicist. His scientific efforts included work on phosphorescence, fluorescence, and ( tidal) gravitatio ...
(1925, 1926),
Chase Chase or CHASE may refer to: Businesses * Chase Bank, a national American financial institution * Chase UK, a British retail bank * Chase Aircraft (1943–1954), a defunct American aircraft manufacturer * Chase Coaches, a defunct bus operator in ...
(1926, 1927) and
Hayden Hayden may refer to: Places Inhabited places in the United States * Hayden, Alabama *Hayden, Arizona *Hayden's Ferry, former name of Tempe, Arizona *Hayden, California, former name of Hayden Hill, California *Hayden, Colorado *Hayden, Idaho *Hayde ...
in 1994. Such experimental results are now seen, consistent with
special relativity In physics, the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between Spacetime, space and time. In Albert Einstein's 1905 paper, Annus Mirabilis papers#Special relativity, "On the Ele ...
, to reflect the validity of the
principle of relativity In physics, the principle of relativity is the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference. For example, in the framework of special relativity, the Maxwell equations ...
and the absence of any absolute rest frame (or aether). The experiment is a test of special relativity. The Trouton–Noble experiment is also related to
thought experiment A thought experiment is an imaginary scenario that is meant to elucidate or test an argument or theory. It is often an experiment that would be hard, impossible, or unethical to actually perform. It can also be an abstract hypothetical that is ...
s 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.


Trouton–Noble experiment

In the experiment, a suspended
parallel Parallel may refer to: Mathematics * Parallel (geometry), two lines in the Euclidean plane which never intersect * Parallel (operator), mathematical operation named after the composition of electrical resistance in parallel circuits Science a ...
-plate
capacitor In electrical engineering, a capacitor is a device that stores electrical energy by accumulating electric charges on two closely spaced surfaces that are insulated from each other. The capacitor was originally known as the condenser, a term st ...
is held by a fine torsion fiber and is charged. If the aether theory were correct, the change in
Maxwell's equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, Electrical network, electr ...
due to the Earth's motion through the aether would lead to a
torque In physics and mechanics, torque is the rotational analogue of linear force. It is also referred to as the moment of force (also abbreviated to moment). The symbol for torque is typically \boldsymbol\tau, the lowercase Greek letter ''tau''. Wh ...
causing the plates to align perpendicular to the motion. This is given by: :\tau=-E'\frac\sin2\alpha' where \tau is the torque, E the energy of the condenser, \alpha the angle between the normal of the plate and the velocity. 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 In a relativistic theory of physics, a Lorentz scalar is a scalar expression whose value is invariant under any Lorentz transformation. A Lorentz scalar may be generated from, e.g., the scalar product of vectors, or by contracting tensors. While ...
of special relativity. 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 all) is much more difficult and is called "Trouton–Noble paradox," which can be solved in several ways (see
Solutions Solution may refer to: * Solution (chemistry), a mixture where one substance is dissolved in another * Solution (equation), in mathematics ** Numerical solution, in numerical analysis, approximate solutions within specified error bounds * Solutio ...
below).


Right-angle lever paradox

The Trouton–Noble paradox is essentially equivalent to a
thought experiment A thought experiment is an imaginary scenario that is meant to elucidate or test an argument or theory. It is often an experiment that would be hard, impossible, or unethical to actually perform. It can also be an abstract hypothetical that is ...
called the ''right angle lever paradox'', first discussed by
Gilbert Newton Lewis Gilbert Newton Lewis (October 23 or October 25, 1875 – March 23, 1946) was an American physical chemist and a dean of the college of chemistry at University of California, Berkeley. Lewis was best known for his discovery of the covalent bon ...
and Richard Chase Tolman in 1909. Suppose a right-angle lever with endpoints ''abc''. In its rest frame, the forces f_y towards ''ba'' and f_x towards ''bc'' must be equal to obtain equilibrium, thus no torque is given by the law of the lever: :\tau'=L_\left(f'_-f'_\right)=0 where \tau is the torque, and L_0 the rest length of one lever arm. However, due to
length contraction Length contraction is the phenomenon that a moving object's length is measured to be shorter than its proper length, which is the length as measured in the object's own rest frame. It is also known as Lorentz contraction or Lorentz–FitzGerald ...
, ''ba'' is longer than ''bc'' in a non-co-moving system, thus the law of the lever gives: :\tau=f_\cdot L_-f_\cdot L_\sqrt=L_\left(f_-f_\sqrt\right) 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: :\frac=\sqrt However, as shown by
Max von Laue Max Theodor Felix von Laue (; 9 October 1879 – 24 April 1960) was a German physicist who received the Nobel Prize in Physics in 1914 "for his discovery of the X-ray diffraction, diffraction of X-rays by crystals". In addition to his scientifi ...
(1911), :*English Wikisource translation: An Example Concerning the Dynamics of the Theory of Relativity this is in contradiction with the relativistic expressions of force, :f_=f'_,\ f_=f'_\cdot\sqrt which gives :\frac=\frac When applied to the law of the lever, the following torque is produced: :\tau=-L_\cdot f'_\cdot\frac Which is principally the same problem as in the Trouton–Noble paradox.


Solutions

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. 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).Janssen (1995), see "Further reading"


Laue current

The first solution of the Trouton–Noble paradox was given by
Hendrik Lorentz Hendrik Antoon Lorentz ( ; ; 18 July 1853 – 4 February 1928) was a Dutch theoretical physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for their discovery and theoretical explanation of the Zeeman effect. He derive ...
(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. This was further elaborated by
Max von Laue Max Theodor Felix von Laue (; 9 October 1879 – 24 April 1960) was a German physicist who received the Nobel Prize in Physics in 1914 "for his discovery of the X-ray diffraction, diffraction of X-rays by crystals". In addition to his scientifi ...
(1911), who gave the standard solution for these kind of paradoxes. It was based on the so-called " inertia of energy" in its general formulation by
Max Planck Max Karl Ernst Ludwig Planck (; ; 23 April 1858 – 4 October 1947) was a German Theoretical physics, theoretical physicist whose discovery of energy quantum, quanta won him the Nobel Prize in Physics in 1918. Planck made many substantial con ...
. 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: :\tau=E'\frac\sin2\alpha' and in the right-angle lever: :\tau=L_\cdot f'_\cdot\frac 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, ''i.e.'', to hinder the body to rotate due to the mechanical torque caused by elastic stresses. Since then, many papers appeared which elaborated on Laue's current, providing some modifications or re-interpretations, and included different variants of "hidden" momentum.


Force and acceleration

A solution without compensating forces or redefinitions of force and equilibrium was published by
Richard C. Tolman Richard Chace Tolman (March 4, 1881 – September 5, 1948) was an American mathematical physicist and physical chemist who made many contributions to statistical mechanics and theoretical cosmology. He was a professor at the California Ins ...
and
Paul Sophus Epstein Paul Sophus Epstein (; March 20, 1883 – February 8, 1966) was a Russian-American mathematical physicist. He was known for his contributions to fluid dynamics and to the development of quantum mechanics. Early life and studies Paul Eps ...
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 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. Epstein imagined a massless rod with endpoints ''OM'', which is mounted at point ''O'', and a particle with rest mass ''m'' is mounted at ''M'' (se

. The rod forms the angle \tan\alpha' with the y'-axis. Now a force f' towards ''O'' is applied at ''M'', and equilibrium in its rest frame is achieved when \tfrac=\tan\alpha'. As already shown above, these forces have the form in a non-co-moving frame: :f_=f'_,\ f_=f'_\cdot\sqrt,\ \tan\alpha=\tan\alpha'\sqrt Thus \frac=\frac. So the resultant force does not directly point from ''O'' to ''M''. 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 :m_=,\ m_=m_0\gamma,\quad \quad \gamma=\frac. The relativistic expressions in the case, where a mass ''m'' is accelerated by these two forces in the longitudinal and transverse direction, are :a_=\frac,\ a_=\frac. Thus \frac=\tan\alpha. Franklin used the relativistic connection between force and acceleration, :\frac=m\frac(\gamma)=m\gamma^3 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 the center of gravity of the system, although the two forces do not.


See also

*
History of special relativity The history of special relativity consists of many theoretical results and empirical findings obtained by Albert A. Michelson, Hendrik Lorentz, Henri Poincaré and others. It culminated in the theory of special relativity proposed by Albert Ein ...


References


Further reading

;History * 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
TOCpref.intro-I12intro-II34refs
* ;Textbooks * * * * *
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External links

* Kevin Brown,
Trouton-Noble and The Right-Angle Lever
at MathPages. * Michel Janssen,
The Trouton Experiment and ''E'' = ''mc''2
," ''Einstein for Everyone'' course at UMN (2002). {{DEFAULTSORT:Trouton-Noble experiment Aether theories Physics experiments 1901 in science 1902 in science 1903 in science Physical paradoxes