On Physical Lines of Force/Part IV/Why magnetism must be rotatory
On Physical Lines of Force → Part IV → The argument
The evidence from currents
Electric currents are known to produce effects of transference in the direction of the current. They transfer the electrical state from one body to another, and they transfer the elements of electrolytes in opposite directions, but they do not cause the plane of polarization of light to rotate when the light traverses the axis of the current.
Two transference effects and one absence. A current carries charge from place to place; it carries the constituents of a dissolved compound to opposite electrodes. It does not twist light. By the principle set out in the opening, the cause is longitudinal.
The evidence from magnetism
On the other hand, the magnetic state is not characterized by any strictly longitudinal phenomenon. The north and south poles differ only in their names, and these names might be exchanged without altering the statement of any magnetic phenomenon; whereas the positive and negative poles of a battery are completely distinguished by the different elements of water which are evolved there. The magnetic state, however, is characterized by a well-marked rotatory phenomenon discovered by Faraday — the rotation of the plane of polarized light when transmitted along the lines of magnetic force.
This is a sharp and unusual observation, and it is worth dwelling on.
The two poles of a battery are physically distinguishable. Put them in water and one evolves hydrogen, the other oxygen. Nature marks them differently, and the marking is longitudinal — it distinguishes one end of a direction from the other.
The two poles of a magnet are not. "North" and "south" are labels. Swap every occurrence of the two words throughout the whole of magnetism and no statement changes its truth value. There is no experiment that picks out a north pole in the way electrolysis picks out an anode.
But magnetism does produce a genuine handed effect: it turns the plane of polarized light. So the asymmetry magnetism carries is rotatory, not longitudinal. That fits a spinning thing and does not fit a flowing thing.
The experimental facts of the rotation
When a transparent diamagnetic substance has a ray of plane-polarized light passed through it, and if lines of magnetic force are then produced in the substance by the action of a magnet or of an electric current, the plane of polarization of the transmitted light is found to be changed, and to be turned through an angle depending on the intensity of the magnetizing force within the substance.
The direction of this rotation in diamagnetic substances is the same as that in which positive electricity must circulate round the substance in order to produce the actual magnetizing force within it; or if we suppose the horizontal part of terrestrial magnetism to be the magnetizing force acting on the substance, the plane of polarization would be turned in the direction of the earth's true rotation, that is, from west upwards to east.
In paramagnetic substances, M. Verdet has found that the plane of polarization is turned in the opposite direction, that is, in the direction in which negative electricity would flow if the magnetization were effected by a helix surrounding the substance.
Note, once again, the translation of an algebraic sign into something a person could check with an apparatus on a bench: "from west upwards to east."
The decisive distinction: magnetic rotation is not optical activity
Quartz and turpentine also rotate the plane of polarized light. Maxwell separates the two phenomena carefully, and the separation is the crux of his argument.
In both cases the absolute direction of the rotation is the same, whether the light passes from north to south or from south to north,— a fact which distinguishes this phenomenon from the rotation produced by quartz, turpentine, &c., in which the absolute direction of rotation is reversed when that of the light is reversed. The rotation in the latter case, whether related to an axis, as in quartz, or not so related, as in fluids, indicates a relation between the direction of the ray and the direction of rotation, which is similar in its formal expression to that between the longitudinal and rotatory motions of a right-handed or a left-handed screw; and it indicates some property of the substance the mathematical form of which exhibits right-handed or left-handed relations, such as are known to appear in the external forms of crystals having these properties. In the magnetic rotation no such relation appears, but the direction of rotation is directly connected with that of the magnetic lines, in a way which seems to indicate that magnetism is really a phenomenon of rotation.
| optical activity (quartz, turpentine) | magnetic rotation (Faraday) | |
|---|---|---|
| reverse the light's direction | the rotation reverses | the rotation does not reverse |
| what it is tied to | the handedness of the substance itself | the direction of the magnetic lines |
| shows up in | crystals with handed external forms | any transparent substance, given a field |
Send light through a sugar solution and back again through a mirror, and the two rotations cancel. Send light through a magnetized medium and back again, and they add. That non-reciprocity is the fingerprint of a medium that is already in motion, and it is the property exploited in every optical isolator built since.
Maxwell states his reason for the whole model
The transference of electrolytes in fixed directions by the electric current, and the rotation of polarized light in fixed directions by magnetic force, are the facts the consideration of which has induced me to regard magnetism as a phenomenon of rotation, and electric currents as phenomena of translation, instead of following out the analogy pointed out by Helmholtz, or adopting the theory propounded by Professor Challis.
Two experimental facts, named, as the reason for the architecture of a four-part paper. This is as close as Maxwell comes to explaining his own choice of model, and it is a good deal more specific than "it occurred to me."
The theory that electric currents are linear, and magnetic forces rotatory phenomena, agrees so far with that of Ampère and Weber; and the hypothesis that the magnetic rotations exist wherever magnetic force extends, that the centrifugal force of these rotations accounts for magnetic attractions, and that the inertia of the vortices accounts for induced currents, is supported by the opinion of Professor W. Thomson. In fact the whole theory of molecular vortices developed in this paper has been suggested to me by observing the direction in which those investigators who study the action of media are looking for the explanation of electro-magnetic phenomena.
Thomson's symmetry argument
Professor Thomson has pointed out that the cause of the magnetic action on light must be a real rotation going on in the magnetic field. A right-handed circularly polarized ray of light is found to travel with a different velocity according as it passes from north to south, or from south to north, along a line of magnetic force. Now, whatever theory we adopt about the direction of vibrations in plane-polarized light, the geometrical arrangement of the parts of the medium during the passage of a right-handed circularly polarized ray is exactly the same whether the ray is moving north or south. The only difference is, that the particles describe their circles in opposite directions. Since, therefore, the configuration is the same in the two cases, the forces acting between particles must be the same in both, and the motions due to these forces must be equal in velocity if the medium was originally at rest; but if the medium be in a state of rotation, either as a whole or in molecular vortices, the circular vibrations of light may differ in velocity according as their direction is similar or contrary to that of the vortices.
The argument deserves unpacking, because it is one of the best pieces of physical reasoning in the paper and it is entirely Thomson's.
- A circularly polarized ray traces a helix in the medium. Send it north or send it south: the shape traced is identical. Only the sense in which it is traced differs.
- Forces between the parts of a medium depend on configuration. Same configuration, same forces.
- So if the medium is at rest, the two rays must travel at the same speed. There is nothing to distinguish them.
- But experiment says they travel at different speeds.
- Therefore the medium is not at rest. Something in it is turning.
That is a proof, from an optical measurement, that there is real rotation in a magnetic field — obtained without any commitment to what is rotating. It is the strongest support Maxwell's model ever received, and he says plainly that it is Thomson's.
The question Part IV then sets
We have now to investigate whether the hypothesis developed in this paper — that magnetic force is due to the centrifugal force of small vortices, and that these vortices consist of the same matter the vibrations of which constitute light — leads to any conclusions as to the effect of magnetism on polarized light. We suppose transverse vibrations to be transmitted through a magnetized medium. How will the propagation of these vibrations be affected by the circumstance that portions of that medium are in a state of rotation?
The answer is the six results.
Next: The six results · Previous: Part IV
Modern derivation: Faraday rotation today