The Theory Of Aether And Electrons In The End of the 19th Century

Maxwell and Hertz tried to extend the theory of the electromagnetic field to the case in which ponderable bodies are in motion. But they were not successful.

Neither had taken account of any motion of the material particles relative to the aether entangled with them. In both investigations, the moving bodies were regarded simply as homogeneous portions of the aether medium which fills all space. They were distinguished only by special values of the electric and magnetic constants.

Such an assumption is inconsistent with the admirable theory by which Fresnel[3] had explained the optical behaviour of moving transparent bodies.

It was therefore not surprising that writers subsequent to Hertz should have proposed to replace his equations by others designed to agree with Fresnel’s formulae.

What is the evidence for and against the motion of the aether in and adjacent to moving ponderable bodies in the 1890s?

The phenomena of aberration had been explained by Young[4].

• He assumed that the aether around bodies is unaffected by their motion.

But Stokes[5] showed in 1845 that this is not the only possible explanation.

• The motion of the earth can communicate motion to the neighbouring portions of the aether.
• This is superposed on the vibratory motion which the aethereal particles have when transmitting light.

The orientation of the wave-fronts of the light will consequently be altered generally.

• The direction in which a heavenly body is seen, being normal to the wavefronts will thereby be affected.

But if the aethereal motion is irrotational, its elements do not rotate. Then the direction of propagation of the light in space is unaffected.

The luminous disturbance is still propagated in straight lines from the star, while the normal to the wave-front at any point deviates from this line of propagation by the small angle u/c, where u denotes the component of the aethereal velocity at the point, resolved at right angles to the line of propagation, and c denotes the speed of light.

If the aether near the earth is at rest relatively to the earth’s surface, the star will appear to be displaced towards the direction in which the earth is moving, through an angle measured by the ratio of the velocity of the earth to the velocity of light, multiplied by the sine of the angle between the direction of the earth’s motion and the line joining the earth and star.

• This is precisely the law of aberration.

H. A. Lorentz[6], and others, objected to Stokes’s theory.

• The irrotational motion of an incompressible fluid is completely determinate when the normal component of the velocity at its boundary is given.
• If the aether had the same normal component of velocity as the earth, it would not have the same tangential component of velocity.

Stokes’s theory had 2 conditions:

1. The motion of the aether is irrotational
2. At the earth’s surface its velocity is the same as that of the earth

It follows that no motion will in general exist which satisfies Stokes’s conditions. The difficulty is not solved by either of the suggestions:

1. The moving earth does generate a rotational disturbance which is being radiated away with the speed of light and so it does not affect the steadier irrotational motion.
2. Planck[7] suggested that Stokes’ 2 conditions may both be satisfied if the aether is:

• compressible in accordance with Boyle’s law, and
• subject to gravity

Around the earth, the aether is compressed like the atmosphere.

• The speed of light is supposed independent of the condensation of the aether.

Lorentz combined the ideas of Stokes and Fresnel. He assumed that:

• the aether near the earth is moving irrotationally (as in Stokes’s theory)
• but the aether at the surface of the earth the aethereal velocity is not necessarily the same as that of ponderable matter
• a material body imparts the fraction (μ2 - 1)/μ2 of its own motion to the aether within it (as in Fresnel’s theory).

Fresnel’s theory is a particular case of this new theory, being derived from it by supposing the velocity-potential to be zero.

Aberration is not the only astronomical phenomenon which depends on the speed of light.

• This velocity was originally determined by observing the retardation of the eclipses of Jupiter’s satellites.

Maxwell[10] said in 1879 that these eclipses theoretically help determine the velocity of the solar system relative to the aether.

• If the distance from the eclipsed satellite to the earth be divided by the observed retardation in time of the eclipse, the quotient then represents the speed of light in this direction, relative to the solar system.

This will differ from the speed of light relative to the aether by the component, in this direction, of the sun’s velocity relative to the aether.

By taking observations when Jupiter is in different signs of the zodiac, it should therefore be possible to determine the sun’s velocity relative to the aether, or at least that component of it which lies in the ecliptic.

The same principles may be applied to the discussion of other astronomical phenomena.

Thus, the minimum of a variable star of the Algol type will be retarded or accelerated by an interval of time which is found dividing the projection of the radius from the sun to the earth on the direction from the sun to the Algol variable by the velocity, relative to the solar system, of propagation of light from the variable. Thus, the latter quantity may be deduced from observations of the retardation.[11]

Another instance in which the time taken by light to cross an orbit influences an observable quantity is afforded by the astronomy of double stars.

Savary[12] long ago remarked that when the plane of the orbit of a double star is not at right angles to the line of sight, an inequality in the apparent motion must be caused by the circumstance that the light from the remoter star has the longer journey to make.

Yvon Villarceau[13] showed that the effect might be represented by a constant alteration of the elliptic elements of the orbit (which alteration is of course beyond detection), together with a periodic inequality, which may be completely specified by the following statement: the apparent coordinates of one star relative to the other have the values which in the absence of this effect they would have at an earlier or later instant, differing from the actual time by the amount

where m1, and m2 denote the masses of the stars, c the speed of light, and z the actual distance of the 2 stars from each other at the time when the light was emitted, resolved along the line of sight. In the existing state of double-star astronomy, this effect would be masked by errors of observation.

Villarceau also examined the consequences of supposing that the speed of light depends on the speed of the light source.

If the speed of light from a star occulted by the moon were less than the velocity of light reflected by the moon, then the apparent position of the lunar disk would be more advanced in its movement than that of the star, so that at emersion the star would first appear at some distance outside the lunar disk, and at immersion the star would be projected on the interior of the disk at the instant of its disappearance.

The amount by which the image of the star could encroach on that of the disk on this account could not be so much as 0″·71; encroachment to the extent of more than 1″ has been observed, but is evidently to be attributed for the most part to other causes.