Dictionary of the History of Ideas Studies of Selected Pivotal Ideas |

II. |

II. |

II. |

VI. |

VI. |

VI. |

VI. |

III. |

I. |

VI. |

VI. |

I. |

VIII |

VI. |

VI. |

VI. |

VI. |

VI. |

IV. |

IV. |

II. |

IV. |

V. |

III. |

VI. |

III. |

III. |

V. |

VI. |

III. |

III. |

VI. |

VI. |

VI. |

V. |

V. |

VII. |

V. |

I. |

I. |

V. |

VI. |

VII. |

III. |

III. |

III. |

VII. |

III. |

I. |

III. |

VI. |

II. |

VI. |

I. |

V. |

III. |

I. |

VII. |

VII. |

II. |

VI. |

V. |

V. |

I. |

II. |

II. |

IV. |

V. |

V. |

V. |

II. |

II. |

V. |

V. |

IV. |

Dictionary of the History of Ideas | ||

*VIII*

By analogy with water waves and sound waves, and

more specifically because of Maxwell's equations, we

can expect light waves to travel through free aether

with a fixed speed. If, in our laboratory, we find that

light waves have different speeds in different directions,

we can conclude that we are moving through the

aether. Suppose, for example, that we find that their

greatest speed is 186,600 miles per second in this di-

rection → and their least speed 186,000 miles per

second in this direction ←. Then we can say that our

laboratory is moving through the aether in this direc-

tion → at 300 miles per second (half the difference

of the speeds), and that the light waves are travelling

through the aether at 186,300 miles per second (half

the sum). Thus we shall have discovered our absolute

velocity, and this despite Fresnel. But in speaking of

Fresnel's so-called aether drag, we said it implied that

every *feasible* first order experiment would fail. The

above is not feasible. The direct laboratory methods

of measuring the speed of light have involved not

one-way but round-trip speeds.

Shortly before his death, Maxwell outlined a way

to measure the earth's velocity through the aether by

comparing not one-way but round-trip speeds of light

in various directions in the laboratory. But since there

would be only a residual effect of the second order—if

*v* is the earth's orbital speed and the sun is at rest *v*2/*c*2

is about 10-8—he dismissed the effect as “far too small

to be observed.”

In 1881, however, Michelson succeeded in perform-

ing the experiment with borderline accuracy for de-

tecting the orbital speed. And in 1887, with Morley,

he repeated the experiment, this time with ample

accuracy. It gave a null result, and thereby precipitated

a crisis. For it suggested, and this was indeed Michel-

son's own interpretation, that the earth carries the

nearby aether along with it. But aberration implied

that the earth does not.

To resolve the conflict, FitzGerald, and later Lorentz

independently, proposed that objects moving through

the aether contract by an amount of the second order

in the direction of their motion.

Lorentz, assuming a fixed aether, untrapped and

undragged, had nevertheless obtained an electromag-

netic derivation of Fresnel's formula far more con-

vincing than that given by Fresnel. Thus Lorentz could

account for the null results of the feasible first-order

experiments to detect absolute motion. His task was

to express Maxwell's equations in a reference frame

moving uniformly through the aether with velocity *v,*

and to do so in such a way that, to the first order,

the *v* did not show up. But the Maxwell equations were

far from being pliable. In the moving frame they more

or less forced Lorentz to replace the *t* representing

the time by a new mathematical quantity that he called

“local time” because it was not the same everywhere.

By incorporating the contraction of lengths, he was

able to account for the null result of the Michelson-

Morley experiment without spoiling the theory of ab-

erration. But again the Maxwell equations forced his

hand, causing him to introduce with the contraction

a corresponding dilatation, or slowing down, of the

local time. Specifically, he found in 1904 what we now

call the *Lorentz transformation,* a name given it by

Poincaré in 1905. Consider two reference frames simi-

larly oriented, one at rest in the aether and the other

moving with uniform speed *v* in the common *x*-direc-

tion. Ordinarily one would have related the coordinates

(*x, y, z*) of the former to the coordinates (*x*′, *y*′, *z*′) of

the latter by what P. Frank named the Galilean trans-

formation:

*xʹ*=

*x*-

*vt*,

*yʹ*=

*y*,

*zʹ*=

*z*

. But the Lorentz transformation relates (

*x, y, z*) and the

true time

*t*to (

*x*′,

*y*′,

*z*′) and the local time

*t*′ of the

moving frame as follows:

*x*′ = (

*x*-

*vt*)/√1 -

*v*2/

*c*2,

*y′*=

*y*,

*z*=

*z*

*t′*= (

*t*-

*vx*/

*c*2/√1 -

*v*/

*c*2.

By means of these equations, Lorentz succeeded, ex-

cept for a small blemish removed by Poincaré in 1905,

in transferring the Maxwell equations to the moving

reference frame in such a way that they remained

unchanged in form. Since no trace of the

*v*survived,

neither the Michelson-Morley nor any other electro-

magnetic experiment could now be expected to yield

a value for

*v.*

It is of interest that the Lorentz transformation, (2),

had already been obtained on electromagnetic grounds

by Larmor in 1898, and its essentials by Voigt on the

basis of wave propagation as early as 1887, the very

year of the Michelson-Morley experiment.

Dictionary of the History of Ideas | ||