Trouton-Rankine experiment
Encyclopedia
The Trouton–Rankine experiment was an experiment designed to measure if the Lorentz–FitzGerald contraction of an object according to one frame (as defined by the luminiferous aether
) produced a measurable effect in the rest frame of the object, so that the ether would act as a "preferred frame
". The experiment was first performed by Frederick Thomas Trouton
and Alexander Oliver Rankine in 1908.
The outcome of the experiment was negative, which is in agreement with the principle of relativity
(and thus special relativity
as well), according to which observers at rest in a certain inertial reference frame, cannot measure their own translational motion by instruments at rest in the same frame. Consequently, also length contraction cannot be measured by co-moving observers. See also Tests of special relativity.
theory needed to be modified. FitzGerald
and Lorentz
, independently of each other, proposed a length contraction of the experimental apparatus in the direction of motion (with respect to the Luminiferous aether
) that would explain the almost null result of the Michelson Morley experiment. The first attempts to measure some consequences of this contraction in the lab frame (the inertial frame of reference
of an observer co-moving with the experimental apparatus) were made in the Experiments of Rayleigh and Brace
(1902, 1904), though the result was negative. By 1908, however, the then-current theories of electrodynamics, Lorentz ether theory
(now superseded) and Special Relativity
(now generally accepted, and doesn't include an aether at all), predicted that the Lorentz–FitzGerald contraction is not measurable in a co-moving frame, because these theories were based on the Lorentz transformation
.
Frederick Thomas Trouton
, (after conducting the Trouton–Noble experiment in 1903), instead did the calculations using his own interpretation of electrodynamics, calculating the length contraction according to the velocity of the experimental apparatus in the aether frame, but calculating the electrodynamics by applying Maxwell's equations and Ohm's law
in the lab frame. According to Trouton's view of electrodynamics, the calculations then predicted a measurable effect of the length contraction in the lab frame. Together with Alexander Oliver Rankine, he set out to verify this in 1908 by attempting to measure the change of the resistance of a coil as they changed its orientation to the "aether velocity" (the velocity of the lab through the luminiferous aether). This was done by putting four identical such coils in a Wheatstone bridge
configuration which allowed them to precisely measure any change in resistance. The circuit was then rotated through 90 degrees about its axis as the resistance was measured. Because the Lorentz–FitzGerald contraction is only in the direction of motion, from the point of view of the "Aether frame" the length of the coils depended on their angle with respect to their Aether velocity. Trouton and Rankine therefore believed that the resistance as measured in the rest frame of the experiment should change as the device was rotated. However their careful measurements showed no detectable change in resistance.
This showed that if the Lorentz–FitzGerald contraction existed, it was not measurable in the rest frame of the object – only theories containing the complete Lorentz transformation
, like special relativity
, are still valid.
Luminiferous aether
In the late 19th century, luminiferous aether or ether, meaning light-bearing aether, was the term used to describe a medium for the propagation of light....
) produced a measurable effect in the rest frame of the object, so that the ether would act as a "preferred frame
Preferred frame
In theoretical physics, a preferred or privileged frame is usually a special hypothetical frame of reference in which the laws of physics might appear to be identifiably different from those in other frames....
". The experiment was first performed by Frederick Thomas Trouton
Frederick Thomas Trouton
Frederick Thomas Trouton FRS was an Irish physicist known for Trouton's Rule and experiments to detect the Earth's motion through the luminiferous aether.- Life and work :...
and Alexander Oliver Rankine in 1908.
The outcome of the experiment was negative, which is in agreement with the principle of relativity
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....
(and thus special relativity
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
as well), according to which observers at rest in a certain inertial reference frame, cannot measure their own translational motion by instruments at rest in the same frame. Consequently, also length contraction cannot be measured by co-moving observers. See also Tests of special relativity.
Description
The famous Michelson–Morley experiment of 1887 showed that the then-accepted aetherLuminiferous aether
In the late 19th century, luminiferous aether or ether, meaning light-bearing aether, was the term used to describe a medium for the propagation of light....
theory needed to be modified. FitzGerald
George FitzGerald
George Francis FitzGerald was an Irish professor of "natural and experimental philosophy" at Trinity College in Dublin, Ireland, during the last quarter of the 19th century....
and Lorentz
Hendrik Lorentz
Hendrik Antoon Lorentz was a Dutch physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for the discovery and theoretical explanation of the Zeeman effect...
, independently of each other, proposed a length contraction of the experimental apparatus in the direction of motion (with respect to the Luminiferous aether
Luminiferous aether
In the late 19th century, luminiferous aether or ether, meaning light-bearing aether, was the term used to describe a medium for the propagation of light....
) that would explain the almost null result of the Michelson Morley experiment. The first attempts to measure some consequences of this contraction in the lab frame (the inertial frame of reference
Inertial frame of reference
In physics, an inertial frame of reference is a frame of reference that describes time homogeneously and space homogeneously, isotropically, and in a time-independent manner.All inertial frames are in a state of constant, rectilinear motion with respect to one another; they are not...
of an observer co-moving with the experimental apparatus) were made in the Experiments of Rayleigh and Brace
Experiments of Rayleigh and Brace
The experiments of Rayleigh and Brace were aimed to show whether length contraction leads to birefringence or not. They were some of the first optical experiments measuring the relative motion of Earth and the luminiferous aether which were sufficiently precise to detect magnitudes of second order...
(1902, 1904), though the result was negative. By 1908, however, the then-current theories of electrodynamics, Lorentz ether theory
Lorentz ether theory
What is now often called Lorentz Ether theory has its roots in Hendrik Lorentz's "Theory of electrons", which was the final point in the development of the classical aether theories at the end of the 19th and at the beginning of the 20th century....
(now superseded) and Special Relativity
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
(now generally accepted, and doesn't include an aether at all), predicted that the Lorentz–FitzGerald contraction is not measurable in a co-moving frame, because these theories were based on the Lorentz transformation
Lorentz transformation
In physics, the Lorentz transformation or Lorentz-Fitzgerald transformation describes how, according to the theory of special relativity, two observers' varying measurements of space and time can be converted into each other's frames of reference. It is named after the Dutch physicist Hendrik...
.
Frederick Thomas Trouton
Frederick Thomas Trouton
Frederick Thomas Trouton FRS was an Irish physicist known for Trouton's Rule and experiments to detect the Earth's motion through the luminiferous aether.- Life and work :...
, (after conducting the Trouton–Noble experiment in 1903), instead did the calculations using his own interpretation of electrodynamics, calculating the length contraction according to the velocity of the experimental apparatus in the aether frame, but calculating the electrodynamics by applying Maxwell's equations and Ohm's law
Ohm's law
Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points...
in the lab frame. According to Trouton's view of electrodynamics, the calculations then predicted a measurable effect of the length contraction in the lab frame. Together with Alexander Oliver Rankine, he set out to verify this in 1908 by attempting to measure the change of the resistance of a coil as they changed its orientation to the "aether velocity" (the velocity of the lab through the luminiferous aether). This was done by putting four identical such coils in a Wheatstone bridge
Wheatstone bridge
A Wheatstone bridge is an electrical circuit used to measure an unknown electrical resistance by balancing two legs of a bridge circuit, one leg of which includes the unknown component. Its operation is similar to the original potentiometer. It was invented by Samuel Hunter Christie in 1833 and...
configuration which allowed them to precisely measure any change in resistance. The circuit was then rotated through 90 degrees about its axis as the resistance was measured. Because the Lorentz–FitzGerald contraction is only in the direction of motion, from the point of view of the "Aether frame" the length of the coils depended on their angle with respect to their Aether velocity. Trouton and Rankine therefore believed that the resistance as measured in the rest frame of the experiment should change as the device was rotated. However their careful measurements showed no detectable change in resistance.
This showed that if the Lorentz–FitzGerald contraction existed, it was not measurable in the rest frame of the object – only theories containing the complete Lorentz transformation
Lorentz transformation
In physics, the Lorentz transformation or Lorentz-Fitzgerald transformation describes how, according to the theory of special relativity, two observers' varying measurements of space and time can be converted into each other's frames of reference. It is named after the Dutch physicist Hendrik...
, like special relativity
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
, are still valid.
External links
- On the Electrodynamics of Moving Bodies Einstein's 1905 paper
- Electromagnetic phenomena in a system moving with any velocity smaller than that of light Lorentz's 1904 paper
- Sfarty, A., The Trouton Rankine Experiment and the End of the FitzGerald Contraction, http://www.mrelativity.net/Papers/29/Trouton_Rankine.pdf.