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 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 ...

) produced a measurable effect in the rest frame of the object, so that the ether would act as a "

preferred frame In theoretical physics, a preferred frame or privileged frame is usually a special hypothetical frame of reference in which the laws of physics might appear to be identifiably different (simpler) from those in other frames. In theories that apply ...

". 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 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 thus

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 ...

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 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 ...

of 1887 showed that the then-accepted aether 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

) 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 In classical physics and special relativity, an inertial frame of reference (also called an inertial space or a Galilean reference frame) is a frame of reference in which objects exhibit inertia: they remain at rest or in uniform motion relative ...

of an observer co-moving with the experimental apparatus) were made in the

Experiments of Rayleigh and Brace The experiments of John William Strutt, 3rd Baron Rayleigh, Lord Rayleigh and DeWitt Bristol Brace (1902, 1904) were aimed to show whether length contraction leads to birefringence or not. They were some of the first optical experiments measuring th ...

(1902, 1904), though the result was negative. By 1908, however, the then-current theories of electrodynamics,

Lorentz ether theory What is now often called Lorentz ether theory (LET) has its roots in Hendrik Lorentz's "theory of electrons", which marked the end of the development of the classical aether theories at the end of the 19th and at the beginning of the 20th century. ...

(now superseded) and

(now generally accepted, and lacking any 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 In physics, the Lorentz transformations are a six-parameter family of Linear transformation, linear coordinate transformation, transformations from a Frame of Reference, coordinate frame in spacetime to another frame that moves at a constant vel ...

. 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 Ohm's law states that the electric current through a Electrical conductor, conductor between two Node (circuits), points is directly Proportionality (mathematics), proportional to the voltage across the two points. Introducing the constant of ...

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 it changed its orientation to the "aether velocity" (the velocity of the lab through the luminiferous aether). This was done by putting four identical coils in a

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. The primary benefit of the circuit is its ability to prov ...

configuration which allowed them to precisely measure any change in resistance. The circuit was then rotated 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

, like

, are still valid.

References

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 {{DEFAULTSORT:Trouton-Rankine experiment Tests of special relativity 1908 in science