An enquiry concerning the principles of natural knowledge

by Alfred North Whitehead

The dynamical theory of this investigation does not depend on the existence of any material body other than the earth. Suppose that the rest of the material universe were annihilated, or at least any part of it which is visible to our eye-sight. Why not? For after all there is a very small volume of visible matter compared to the amount of space available for it. So there is no reason to assume anything very essential in the existence of a few planets and a few thousand stars. We are left with the earth rotating. But rotating relatively to what? For on the relational theory it would seem to be the mutual relations of the earth's parts which constitute space. And yet the dynamical theory of the bulge does not refer to any body other than the earth, and so is not affected by the catastrophe of annihilation. It has been asserted that after all the fixed stars are essential, and that it is the rotation relatively to them which produces the bulge. But surely this ascription of the centrifugal force on the earth's surface to the influence of Sirius is the last refuge of a theory in distress. The point is that the physical properties, size, and distance of Sirius do not seem to matter. The more natural deduction (on the theory of Newtonian relativity) is to look on the result as evidence that the theory of any empty space is an essential impossibility. Accordingly the absoluteness of direction is evidence for the existence of the material ether. This result only reinforces a conclusion which has already been reached on other grounds. Thus space expresses mutual relations of the parts of the ether, as well as of the parts of the earth.

[9. Motion through the Ether]. 9.1 The existence of the material ether should discriminate between the consentient sets of the Newtonian group. For one such set will be at rest relatively to the ether, and the remaining sets will be moving through it with definite velocities. It becomes a problem to discover phenomena dependent on such velocities.

Can any phenomena be detected which are unequivocally due to a quasi-absolute motion of the earth through the ether? For this purpose we must put aside phenomena which depend on the differential velocities of two bodies of matter, e.g. the earth and a planet, or a star. For such phenomena are evidently primarily due to the relative velocity of the two bodies to each other, and the velocities relatively to the ether only arise as a hypothetical intermediate explanatory analysis. We require phenomena concerned solely with the earth, which are modified by the earth's motion through the ether without reference to any other matter. We have already concluded that the bulging of the earth at the equator is one such required instance, unless indeed (with Newton) we assume absolute space.

9.2 The effects on the observed light due to the relative motions of the emitting body and the receiving body are various and depend in part on the specific nature of the assumed disturbances which constitute light. Some of these effects have been observed, for example, aberration and the effect on the spectrum due to the motion of the emitting body in the line of sight. Aberration is the apparent change in the direction of the luminous body due to the motion of the receiving body. The motion of the luminous body in the line of sight should alter the wave length of the emitted light due to molecular vibrations of given periodicity. In other words, it should alter the quality of the light due to such vibrations. These are the effects which have been observed, but they are of the type which we put aside as not relevant to our purpose owing to the fact that the observed effect ultimately depends merely on the relative motion of the emitting and receiving bodies.

9.3 There are effects on interference fringes which we should expect to be due to the motion of the earth. In six months the velocity of the earth in its orbit is reversed. So that such effects as the earth's motion produces in the interference fringes of a certain purely terrestrial apparatus at one time can be compared with the corresponding effects in the same apparatus which it produces after the lapse of six months and—as the experiments have been carried out—the differences should have been easily discernible. No such differences have been observed. The effects, which are thus sought for, depend on no special theory of the nature of the luminous disturbance in the ether. They should result from the simple fact of the wave disturbance, and the magnitude of its velocity relatively to the apparatus.

It will be observed that the difficulty which arises from the absence of this predicted effect does not discriminate in any way between the philosophic theories of absolute or of relative space. The effect should arise from the motion of the earth relatively to the ether, and there is such relative motion whichever of the alternative spatial theories be adopted.

9.4 Electromagnetic phenomena are also implicated in the theory of relative motion. Maxwell's equations of the electromagnetic field hold in respect to these phenomena an analogous position to that occupied by Newton's equations of motion for the explanation of the motion of matter. They differ from Newton's equations very essentially in their relation to the principle of relativity. Newton's equations single out no special member of the Newtonian group to which they specially apply. They are invariant for the spatio-temporal transformations from one such set to another within the Newtonian group.

But Maxwell's electromagnetic equations are not thus invariant for the Newtonian group. The result is that they must be construed as referring to one particular consentient set of this group. It is natural to suppose that this particular assumption arises from the fact that the equations refer to the physical properties of a stagnant ether; and that accordingly the consentient set presupposed in the equations is the consentient set of this ether. The ether is identified with the ether whose wave disturbances constitute light; and furthermore there are practically conclusive reasons for believing light to be merely electromagnetic disturbances which are governed by Maxwell's equations.

The motion of the earth through the ether affects other electromagnetic phenomena in addition to those known to us as light. Such effects, as also in the case of light, would be very small and difficult to observe. But the effect on the capacity of a condenser of the six-monthly reversal of the earth's velocity should under proper conditions be observable. This is known as Trouton's experiment. Again, as in the analogous case of light, no such effect has been observed.

9.5 The explanation [the Fitzgerald-Lorentz hypothesis] of these failures to observe expected effects has been given, that matter as it moves through ether automatically readjusts its shape so that its lengths in the direction of motion are altered in a definite ratio dependent on its velocity. The null results of the experiments are thus completely accounted for, and the material ether evades the most obvious method of testing its existence. If matter is thus strained by its passage through ether, some effect on its optical properties due to the strains might be anticipated. Such effects have been sought for, but not observed. Accordingly with the assumption of an ether of material the negative results of the various experiments are explained by an ad hoc hypothesis which appears to be related to no other phenomena in nature.