Can humans know absolute position in space relative to the aether?

Can humans know absolute position in space relative to the aether?

Newton’s laws of motion does not supply any criterion to distinguish rest from uniform motion

If the laws of motion are applicable when the position of bodies is referred to any particular set of axes, they will be equally applicable when position is referred to any other set of axes which have a uniform motion of translation relative to these.

The older theories of electrostatics, magnetism, and electrodynamics were based on the concept of action at a distance. They are concerned only with relative configurations and motions, and are therefore useless in the search for a basis of absolute reckoning.

But the existence of an aether, seems at first sight to involve the conceptions of rest and motion relative to it. It thus affords a way to specify absolute position.

If a disturbance is generated at any point in free aether, this disturbance will spread outwards in the form of a sphere..

The centre of this sphere will for all subsequent time occupy an unchanged position relative to the aether.

In this way, or in many other ways, we might hope to determine, by electrical or optical experiments, the velocity of the earth relative to the aether.

The failure of such experiments led FitzGerald[84] to suggest that the dimensions of material bodies undergo contraction when the bodies are in motion relative to the aether.

By the transformation of Lorentz and Larmor, this hypothesis got a new form; namely that the equation of the figure of the body, referred to a frame of reference moving with it, is always the same, but that frames of reference which are in notion relative to each other are based on different standards of length and time.

This way of regarding the matter brings into prominence the fundamental questions involved.

Before speaking of lengths and velocities, it is necessary to examine the nature of systems of measurement of space and time.

Of the events with which Natural Philosophy is concerned, each is perceived to happen at some definite location at some definite moment.

When a material object has been observed to occupy a certain position at a certain instant, the same object may again be observed at a subsequent instant.

But it is impossible to determine whether the object is or is not in the same position, since there is no obvious means of preserving the identity of any location from one moment to another.

The physicist, however, finds it convenient to construct a framework of axes in space and time for the purpose of fitting his experiences into an orderly arrangement. The question at issue is whether experience furnishes the means of determining a framework completely and uniquely by absolute properties, or whether the selection inevitably rests on arbitrary choice and accidental circumstance.

In attempting to answer this question, it may first be observed that the choice is always made so as to simplify the description of natural phenomena as much as possible; thus, the variable which is to measure time is so chosen that its increment in the interval between any two consecutive beats of a pendulum is the same as its increment in the interval between any other two consecutive beats.

If the selection of the 4 variables (x, y, z, t) is well made, it should be possible to express the laws of nature by statements of a simple character, e.g., that a body isolated from the influence of external agents moves through equal intervals of space in equal intervals of time.

Accepting, then, the principle that the framework of axes is to be chosen so as to furnish the simplest possible expression of the natural laws, it becomes of importance to determine which of the natural laws are entitled, by reason of their primary importance, to receive the greatest consideration.

Now many indications point to the probability that the various types of forces which are observed in ponderable bodies—forces of cohesion, of chemical union, and so forth—are ultimately electric in their nature. Such an assumption would have the great advantage of explaining the contraction postulated by Fitz Gerald, since it would represent the contraction as actually produced by the notion.

But if this assumption be correct, the theory of electricity and aether is without doubt the fundamental theory of Natural Philosophy, and the framework of space and time should be chosen with a view chiefly to the expression of electrical phenomena.

This may most naturally be done by stipulating that the wave-fronts of disturbances generated in free aether shall, in the system of length and time adopted, be accounted spheres whose centres are at the origins of disturbance and whose radii are proportional to the times elapsed since their initiation. Referred to axes of (x, y, z, t) which satisfy these conditions, the fundamental equations of the electric field assume the form which has been taken as the basis of all our theoretical investigations.

Imagine now a distant star which is moving with a uniform velocity w or o tanh a relative to this framework (x, y, z, t).

The theorem of transformation shows that there exists another framework (x1, y1, z1, t1), with respect to which the star is at rest, and in which moreover the condition laid down regarding the wave-surface is satisfied. This framework is peculiarly fitted for the representation of the phenomena which happen on the star; whose inhabitants would therefore naturally adopt it as their system of space and time.

Beings, on the other hand, who dwell on a body which is at rest with respect to the axes (x, y, z, t) would prefer to use the latter system, and from the point of view of the universe at large, either of these systems is as good as the other.

The equations of motion of the aether are the same with respect to both sets of coordinates, and therefore neither can claim to possess the only property which could confer a primacy—namely, an absolute relation to the aether.[85]

To sum up, we may say that the phenomena whose study is the object of Natural Philosophy take place each at a definite location at a definite moment; the whole constituting a four-dimensional world of space and time. To construct a set of axes of space and time is equivalent to projecting this four-dimensional world into a three-dimensional world of space and a one-dimensional world of time, and this projection may be performed in an infinite number of ways, each of which is distinguished from the others only by characteristics merely arbitrary and accidental.[86]

In order to represent natural phenomena without introducing this contingent element, it would be necessary to abandon the customary three-dimensional system of coordinates, and to operate in four dimensions.

Analysis of this kind has been devised, and has been applied to the theory of the aether; but its development belongs to the twentieth century, and consequently falls outside the scope of the present work.

In the closing years of the 19th century, electrical investigation was chiefly concerned with systems in motion. The theory of electrons was, however, applied with success in other directions, and notably to the explanation of a new experimental discovery.

The last recorded observation of Faraday[87] was an attempt to detect changes in the period, or in the state of polarization, of the light emitted by a sodium flame, when the flame was placed in a strong magnetic field. No result was obtained.

But the conviction that an effect of this nature remained to be discovered was felt by many of his successors. Tait[88] examined the influence of a magnetic field on the selective absorption of light; impelled thereto, as he explained, by theoretical considerations.

For from the phenomenon of magnetic rotation it may be inferred[89] that rays circularly polarized in opposite senses are propagated with different velocities in the magnetized medium; and therefore if only those rays are absorbed which have a certain definite wave-length in the medium, the period of the ray absorbed from a beam of circularly polarized white light will not be the same when the polarization is right-handed as when it is left-handed. “Thus,” wrote Tait, “what was originally a single dark absorption-line might become a double line.”

The effect anticipated under different forms by Faraday and Tait was discovered, towards the end of 1896, by I. Zeeman.[90] Repeating Faraday’s procedure, he placed a sodium fame between the poles of an electromagnet, and observed a widening of the D-lines in the spectrum when the magnetizing current was applied.

A theoretical explanation of the phenomenon was immediately furnished to Zeeman by Lorentz.[91] The radiation is supposed to be emitted by electrons which describe orbits. within the sodium atoms.

If e denote the charge of an electron of mass m, the ponderomotive force which acts on it by virtue of the external magnetic field is e [‘i.K], where K denotes the magnetic force and r denotes the displacement of the electron from its position of equilibrium; and therefore, if the force which restrains the electron in its orbit be κ2r, the equation of motion of the electron is

The motion of the electron may (as is shown in treatises on dynamics) be represented by the superposition of certain particular solutions called principal oscillations, whose distinguishing property is that they are periodic in the time. In order to determine the principal oscillations, we write

for r, where r0, denotes a vector which is independent of the time, and n denotes the frequency of the principal oscillation: substituting in the equation, we have

This equation may be satisfied either (1) if r0, is parallel to K, in which case it reduces to

so that n has the value κm- 1 2 , or (2) if r0 is at right angles to K, in which case by squaring both sides of the equation we obtain the result

which gives for n the approximate values κm-

When there is no external magnetic field, so that K is zero, the three values of n which have been obtained all reduce to κm- 1 2 , which represents the frequency of vibration of the emitted light before the magnetic field is applied. When the field is applied, this single frequency is replaced by the three frequencies. κm-

1 2

• eK/2m; that is to say, the single line in the spectrum is replaced by three lines close together. The apparatus used by Zeeman in his earliest experiments was not of sufficient power to exhibit this triplication distinctly, and the effect was therefore described at first as a widening of the spectral lines.[92]

We have seen above that the principal oscillation of the electron corresponding to the frequency κm-

is performed in a direction parallel to the magnetic force K.

It will therefore give rise to radiation resembling that of a Hertzian vibrator, and the electric vector of the radiation will be parallel to the lines of force of the external magnetic field.

It follows that when the light received in the spectroscope is that which has been emitted in a direction at right angles to the magnetic field, this constituent (which is represented by the middle line of the triplet in the spectrum) will appear polarized in a plane at right angles to the field; but when the light received in the spectroscope is that which has been emitted in the direction of the magnetic force, this constituent will be absent.

We have also seen that the principal oscillations of the electron corresponding to the frequencies κm-

± eK/2m are ​performed in a plane at right angles to the magnetic field K. In order to determine the nature of these two principal oscillations, we observe that it is possible for the electron to describe a circular orbit in this plane, if the radius of the orbit be suitably chosen; for in a circular motion the forces κ2r and

would be directed towards the centre of the circle; and it would therefore be necessary only to adjust the radius so that these furnish the exact amount of centripetal force required. Such a motion, being periodic, would be a principal oscillation. Moreover, since the force

changes sign when the sense of the movement in the circle is reversed, it is evident that there are two such circular orbits, corresponding to the two senses in which the electron may circulate; these must, therefore, be no other than the two principal oscillations of frequencies κm-

When the light received in the spectroscope is that which has been emitted in a direction at right angles to the external magnetic field, the circles are seen edgewise, and the light appears polarized in a plane parallel to the field; but when the light examined is that which has been emitted in a direction parallel to the external magnetic force, the radiations of frequencies κm-

are seen to be circularly polarized in opposite senses. All these theoretical .conclusions have been verified by observation.