The discussion of static magnetism in Chapter 19 was addressed to the type of two-dimensional rotational vibration known as ferromagnetism. This is the magnetism known to the general public, the magnetism of permanent magnets. As noted in that earlier discussion, ferromagnetism is present in only a relatively small number of substances, and since this was the only type of magnetism known to the early investigators, magnetism was considered to be some special kind of a phenomenon of limited scope. This general belief undoubtedly had a significant influence on the thinking that led to the conclusion that magnetism is a by-product of electricity. More recently, however, it has been found that there is another type of magnetism that is much weaker, but is common to all kinds of matter.
For an understanding of the nature of this second type of static magnetism one needs to recall that the basic rotation of all material atoms is two-dimensional. It follows from the previously developed principles governing the combination of motions that a two-dimensional vibration (charge) can be applied to this two-dimensional rotation. However, unlike the ferromagnetic charge, which is independent of the motion of the main body of the atom, this charge on the basic rotation of the atom is subject to the electric rotation of the atom in the third scalar dimension. This does not alter the vibrational character of the charge, but it distributes the magnetic motion (and force) over three dimensions, and thus reduces its effective magnitude to the gravitational level. To distinguish this type of charge from the ferromagnetic charge we will call it an internal magnetic charge.
As we have seen, the numerical factor relating the magnitudes of quantities differing by one scalar dimension, in terms of cgs units, is 3×1010. The corresponding factor applicable to the interaction between a ferromagnetic charge and an internal magnetic charge is the square root of the product of 1 and 3×1010, which amounts to 1.73×105. The internal magnetic effects are thus weaker than those due to ferromagnetism by about 105.
The scalar direction of the internal magnetic charge, like that of all other electric and magnetic charges thus far considered, is outward. All magnetic (two-dimensional) rotation of atoms is also positive (net displacement in time) in the material sector of the universe. But the motion in the third scalar dimension, the electric dimension, is positive in the Division I and II elements and negative in the Division III and IV elements. As explained in Chapter 19, the all-positive magnetic rotations of the material sector have a polarity of a different type that is related to the directional distribution of the magnetic rotation. If an atom of an electropositive element is viewed from a given point in space—from above, for example—it is observed to have a specific magnetic rotational direction, clockwise or counterclockwise. The actual correlation with north and south has not yet been established, but for present purposes we may call the end of the atom that corresponds to the clockwise rotation its north pole. This is a general relation applying to all electropositive atoms. Because of the reversals at the unit levels, the north pole of an electronegative atom corresponds to counterclockwise rotation; that is, this north pole occupies a position corresponding to that which is occupied by the south pole of an electropositive atom.
When electropositive elements are subjected to the field of a magnet, the orientation of the poles is the same in both the atoms and the magnet (which is similarly positive). The atoms of these elements therefore tend to orient themselves with their magnetic axes parallel to the magnetic field, and to move toward the stronger part of the field; that is, they are attracted by permanent magnets. Such substances are called paramagnetic. Electronegative elements, which have the reverse polarity, are oriented with the poles of their atoms opposite to those of a magnet. This puts like poles together, causing repulsion. These atoms therefore tend to orient themselves perpendicular to the magnetic field, and to move toward the weaker part of the field. Substances of this kind are called diamagnetic.
In present-day magnetic theory diamagnetism is regarded as a universal property of matter, the origin of which is unexplained. “All materials are diamagnetic,”98 says one textbook. On this basis, paramagnetism or ferromagnetism, where they exist, simply overpower the basic diamagnetism. Our finding is that each substance is either paramagnetic or diamagnetic, depending on the scalar direction of the rotation in the electric dimension. Ferromagnetic substances are paramagnetic with an additional two-dimensional rotational vibration of the kind previously described.
All elements of the electropositive divisions I and II, except beryllium and boron, are paramagnetic. As in the case of other properties previously discussed, the positive preference carries over into some of the adjoining elements of Division III. All other elements of the electronegative divisions III and IV, except oxygen, are diamagnetic.
The abnormal behavior of some of the elements of Group 2A is a result of the small size of this 8-member group, which permits the constituent elements, in some instances, to function as members of the inverse division of the group. Boron, for example, is normally the third member of the positive division of Group 2A, but it can alternatively act as the fifth member of the negative division of this group. Boron and beryllium are the positive elements nearest to the negative division in this group, and therefore the most subject to whatever influences tend to cause the polarity reversal. Just why oxygen is the element of the negative division in which the polarity reversal takes place is not yet known.
As brought out in Volume I, all chemical compounds are combinations of electropositive and electronegative components. The presence of any significant amount of motion in time (space displacement) in a molecular structure prevents establishment of the positive magnetic orientation. All compounds, except those that are ferromagnetic, or heavily weighted with paramagnetic elements, are therefore diamagnetic. This overwhelming preference for diamagnetism in the compounds is probably what led to the currently accepted hypothesis of a universal diamagnetism.
The intensity of the magnetic effect in a magnetic material is measured in terms of magnetization, symbol M, which was defined in Chapter 20. The magnetization and the intensity of the applied field are additive. Both therefore have the dimensions of magnetic field intensity, t2/s4, but for historical reasons the field intensity is customarily identified with the vector H, which has the dimensions 1/t. Since the magnetization must have the same dimensions as the field intensity, it is also expressed in terms of a unit with the 1/t dimensions. As we saw in Chapter 20, the actual physical quantities are µM and µH, rather than M and H, but the permeability, µ, entering into these definitions is the “permeability of free space,” µ0, which has unit magnitude. The dimensional error therefore does not affect the numerical results of calculations.
From the foregoing, the net total magnetic field intensity, B, is the sum of µ0M and µ0H. For some purposes it is convenient to express this quantity in terms of H only. This is accomplished by introducing the magnetic susceptibility, χ, defined by the relation χ = M/H. On this basis,
B = (1+χ)µ0H.
As indicated earlier, the internal magnetic effects are relatively weak. The susceptibilities of both paramagnetic and diamagnetic materials are therefore low. Those of the diamagnetic substances are also independent of temperature. Some studies of the factors that determine the magnitude of the internal magnetic susceptibility were undertaken in the early stages of the theoretical investigation whose results are here being reported, and calculations of the diamagnetic susceptibilities of a number of simple organic compounds were included in the first edition of this work. These results have not yet been reviewed in the light of the more complete understanding of the nature of magnetic phenomena that has been gained in the past several decades, but there are no obvious inconsistencies, and some consideration of these findings will be appropriate at this time.
As would be expected, since the internal magnetic charge is a modification of the magnetic component of the rotational motion of an atom, the magnetic susceptibility is the reciprocal of the effective magnetic rotational displacement. There are, of course, two possible values of this displacement for most elements, but the applicable value is often indicated by the environment; that is, association with elements of low displacement generally means that the lower value will prevail, and vice versa. Carbon, for instance, takes its secondary displacement, one, in association with hydrogen, but changes to the primary displacement, two, in association with elements of the higher groups.
Another source of variability is introduced by the fact that the susceptibility, like most other physical properties, has an initial level, and this level is also influenced by environmental factors. At the present stage of the investigation we are not able to evaluate these factors from purely theoretical premises, but they vary in a fairly regular way in the various families of compounds. We can therefore establish what we may call semi-theoretical values of the diamagnetic susceptibility of many relatively simple organic compounds with the aid of series relationships.
The experimental values of the susceptibility of these compounds vary over a substantial range. It was found, however, in the original investigation, that, except for certain differences in the initial levels, the diamagnetic susceptibility has the same value as a constant, which we are calling the refraction constant, that determines the index of refraction. The properties of radiation will not be covered in this volume, but the measurements of the refractive index are much more accurate than those of the magnetic susceptibility. It will therefore be desirable to use the refraction constant as a base in the calculation of the susceptibilities. and some explanation of the manner in which that constant was derived will be required.
Like the internal susceptibility, the refraction constant is the reciprocal of the effective magnetic rotational displacement, the total displacement minus the initial level. As in the case of the susceptibility, the determination of this constant is complicated by a variability in the initial levels, especially those of the most common elements in the organic compounds, carbon and hydrogen. For convenience, both in calculation and in emphasizing the series relationships, a value of the refraction constant is first calculated on the basis of what we may regard as “normal” values. The deviation of the constant from the normal value is then determined for each compound.
Table 33 shows the derivation of the refraction factors in three representative organic families of compounds. In the acids, for example, the normal rotational displacement of the oxygen atoms and the carbon atom in the CO group is 2, while that of the hydrogen atoms and the remaining carbon atoms is 1. The normal initial level is 2/9 in all cases. The normal refraction factors of the individual rotational mass units are then 0.778 for the displacement 1 atoms, and half this value, or 0.389 for those of displacement 2. All of the acids from acetic (C2) to enanthic (C7) inclusive have normal initial levels (no deviations), and the differences in the individual refraction factors are due entirely to a higher proportion of the 0.778 units as the size of the molecule increases. The normal initial level in the corresponding hydrocarbons, however, is only 1/9, and when the molecular chain becomes long enough to free some of the hydrocarbon groups at the positive end of the molecule from the influence of the acid radical at the negative end, these groups revert to their normal initial levels as hydrocarbons, beginning with the CH3 end group and moving inward. In caprylic acid (C8), the three hydrogen atoms in the end group have made the change, those in the adjoining CH2 group do likewise in pelargonic acid (C9), and as the length of the molecule increases still further the hydrogen in additional CH2 groups follows suit.
The deviations from the normal values (expressed in numbers of 1/9 units per molecule) are shown in the first column of Table 33. The second column shows the refraction constants, kr, calculated by applying the deviations in column 1 to the normal values. In columns 3 and 4 the product 0.697 kr is compared with the quantity (n-1)/d, where n is the refractive index at the sodium D wavelength and d is the density. The refraction constant is related to the natural unit wavelength rather than to the wavelength at which the measurements were made, but the difference is incorporated in the factor 0.697 that is applied before the comparison with the values derived from observation . An explanation of the derivation of this factor and the reason for making the correlation in this particular manner would require more discussion of radiation than is appropriate in this volume, but the status of the calculated refraction constants as specific functions of the composition of the compounds is evident.
In the paraffins the initial levels increase with increasing length of the molecule rather than decreasing as in the acids. As brought out in Volume I, the hydrocarbon molecules are not the symmetrical structures that their formula molecules would seem to represent. For example, the formula for propane, as usually expressed, is CH3 CH2 CH3, which indicates that the two end groups of the molecule are alike. But the analysis of this structure revealed that it is actually CH3.CH2.CH2.H, with a positive CH3 group at one end and a negative hydrogen atom at the other. This negative hydrogen atom has a zero initial level, and it exerts enough influence to eliminate the initial level in the hydrogen atoms of the two CH2 groups, giving the molecule a total of 5 units of deviation from the normal initial level. When another CH2 group is added to form butane, the relative effect of the negative hydrogen atom is reduced, and the zero initial level is confined to the CH2 H combination, with 3 hydrogen atoms. The deviation continues on this basis up to hendecane (C11), beyond which it is eliminated entirely, and the molecule as a whole takes the normal 0.889 refraction constant.
Also shown in Table 33 is a representative sample of the monobasic esters, which, as would be expected of acid derivatives, follow the same pattern as the acids. The only new feature is the appearance of a -3 deviation in some of the lower compounds. This appears to be due to a reversal of the influences that are responsible for the additional positive deviations in the lower paraffins, an interpretation that is supported by the fact that both end groups of the esters are positive.
The objective of Table 33 is merely to show how the refraction constants that are used in the susceptibility calculations are derived from the molecular composition and structure, and the number of compounds listed has been limited to those required for this purpose. The refraction constants used in application to the greater number and variety of compounds included in Table 34, which shows the kind of results that are obtained from the susceptibility calculations, are determined in the same manner.
As noted earlier, the diamagnetic susceptibility of an organic compound is equal to its refraction constant with an adjustment for a difference in the initial levels. The magnetic initial level is generally the same as that in refraction except in certain groups in which the level is modified by some factor not yet specifically identified, but apparently geometric. In the compounds listed in Table 34, the CH3, CH2OH, and OH end groups have initial levels 1/9 unit higher, per unit of rotational mass, than the refraction levels. Interior CH2 groups are subject to a similar modification, half as large (1/18 unit) at certain points, as the molecular chains lengthen The sum of the individual differences in initial level, ΔI, is m’/9, where m’ is the number of rotational mass units in the modified end groups of the molecule, plus half of the number of units in the modified interior groups, with appropriate adjustments in special cases.
The average difference in initial level for a molecule of rotational mass m is then m’/9m. In Table 34 this value, shown as ΔI/m, is applied to the refractive constants of representative groups of simple organic compounds to arrive at the internal magnetic susceptibilities. The corresponding values from observation are listed in the last three columns of the table. Values marked with asterisks are taken from a recent compilation.99 Where no measurement was available from this source, a representative value from the earlier reports is shown in the same column. The last two columns shown the range of results reported from the earlier measurements.
In the normal paraffins the association between the CH2 group and the lone hydrogen atom at the negative end of the molecule is close enough to enable the CH2.H combination to act as the end group. This means that there are 18 rotational mass units in the end groups of each chain. The value of ΔI for these compounds is therefore 18/9 = 2. Branching adds more ends to the molecule, and consequently increases ΔI. The 2-methyl paraffins add one CH2 end group, raising DI to 3, the 2,3-dimethyl compounds add one more, bringing this quantity up to 4, and so on. A very close association, similar to that in the CH2.H combination, modifies this general pattern. In 2-methyl propane, for instance, the CHCH3 combination acts as an interior group, and the value of DI for this compound is the same as that of the corresponding normal paraffin, butane. The C(CH3)2 combination likewise acts as an interior group in 2,2-dimethyl propane, and as a unit with only one end group in the higher 2,2-dimethyl paraffins.
Each of the interior CH2 groups with the higher initial level adds nine rotational mass units rather than the 8 corresponding to the group formula. This seems to indicate that in these instances a CH2.CH2 combination is acting geometrically as if it were CH3.CH. In the ring compounds the CH2 and CH groups take the normal 8 and 7 unit values respectively.
The behavior of the substituted chain compounds is similar to that of the paraffins, but there is a greater range of variability because of the presence of components other than carbon and hydrogen. The alcohols, a typical family of this kind, have a CH3 group at one end of the molecule and a CH2OH group at the other. The value of ΔI for the longer chains is therefore 26/9 = 2.89. In the lower alcohols, however, the CH2 portion of the CH2OH group reverts to the status of an interior group, and ΔI drops to 2.00. The methyl alcohol molecule goes a step farther and acts as if it has only one end. A similar pattern can be seen in other organic families, such as the esters. Since we have found that the effective units of some of these compounds in certain of the phenomena previously examined are double formula molecules, it appears likely that the magnetic behavior of methyl alcohol and other compounds with similar characteristics can be attributed to the size of the effective molecule.
No similar studies of paramagnetic materials have yet been made. Unlike diamagnetism, paramagnetism is temperature dependent. For an explanation of this dependence we need to recall that magnetism is a motion. One of the significant advantages of recognizing its status as a motion is that its effect on other motions can be evaluated in terms of a direct addition or subtraction, rather than having to be approached circuitously by means of some hypothetical mechanism. Diamagnetism, which is motion in time (negative) has no connection with the thermal motion, which is motion in space (positive). But paramagnetism is positive, and has an imputed direction opposite to that of the thermal motion. Thus an increase in temperature reduces the paramagnetic effect.
The internal magnetism, which has been the principal subject of discussion thus far in the present chapter, is of interest primarily because of the light that it sheds on the nature and properties of magnetism in general. From a practical standpoint, “magnetism” is synonymous with ferromagnetism. No systematic study of ferromagnetism in the context of the theory of the universe of motion has yet been undertaken. There are, however, a few points about the place of this phenomenon in the general physical picture that should be noted.
Ferromagnetism exists only below a temperature, the Curie point, which is specific for each substance. Inasmuch as this type of magnetism is restricted to positive elements and some of their compounds, ferromagnetic materials are also paramagnetic, and exhibit their paramagnetic properties above the Curie temperature. In this range, the susceptibility is linearly related to the temperature, but the relation is inverse; that is, the relation is between temperature and 1/χ.
In one respect there is a significant difference between the magnetic susceptibility and most of the physical properties discussed in the earlier pages. The specific heat of any given substance, for instance, decreases with decreasing temperature, and reaches zero at a particular temperature level. There is no negative specific heat. Consequently, the specific heat of the individual atom is zero at all temperatures below this level. But magnetic forces act upon magnetic substances at all temperatures below the critical temperature, as well as above it. What we have here is a difference in the significance of the zero point.
As explained in Volume I, the true datum of physical activity, the natural zero, is unit speed, the speed of light. Natural physical magnitudes extend from this natural zero to the natural unit of speed in space (our zero) in one direction, and to unit speed in time (inverse speed) in the other. These two speed ranges are identical, except for the inversion. Most of the physical magnitudes with which we deal are in the range from our zero to the speed of light, but there are some quantities that extend beyond the natural zero levels. This introduces some modifying factors into the physical relations, as the natural zero levels are limiting magnitudes of the kind discussed in Chapter 17; that is, points at which an inversion of most physical properties takes place.
For example, a property such as thermal radiation that increases with the temperature up to the unit temperature level (the natural zero) does not continue to increase as the temperature rises still farther. Instead, as we will see in Volume III, it undergoes a decrease symmetrical with the increase that takes place between zero and unit temperature. A somewhat similar reversal occurs in the case of those properties that extend into the region inside unit space, the time region, as we have called it, because all changes in this region take place in time, while the associated space remains constant at the unit level.
Ferromagnetism is a phenomenon of the time region, and its natural zero point (the Curie temperature) is therefore a boundary between two dissimilar regions, rather than a center of symmetry, like the speed of light, the natural zero of speed. Instead of following the kind of a linear relation that is characteristic of the properties of the regions outside unit space, the relation of ferromagnetism to temperature has a more complex form due to the substitution of the spatial equivalent of time for actual space in this region where no change in actual space takes place.
No detailed studies in this area have yet been undertaken, but it seems evident that in the more regular elements the magnetization is subject to the (1-x2)1/2 relation that applies to other time region properties examined earlier, and to a square root factor, which may also be inter-regional. It can therefore be expressed as M = k(1-T2)1/4. If the magnetization is stated as a fraction of the initial magnetization, and the temperature is similarly stated as a fraction of the Curie temperature, the constant k is eliminated, and the values derived from the equation apply to all substances that follow the regular pattern.. Within the limits of accuracy of the experimental data, the reduced magnetizations thus calculated are in agreement with the empirical values, as reported by D. H. Martin.100
Because the internal magnetic charge is applied against the basic rotational motion of the atom, its force is symmetrically distributed in the same manner as the gravitational force. But, as we have seen, ferromagnetism is a motion of an individual, specifically located, component of the atom. The directional distribution of the ferromagnetic force in the reference system is therefore determined by the atomic orientation. If each atom acted independently, the orientation of the atoms of an aggregate would be random, but, in fact, each magnetically charged atom exerts a force on its magnetic neighbors, tending to line up these neighboring atoms with its own magnetic directions. This orienting effect encounters mechanical resistance, and is ordinarily limited in scope. For this reason, and because the relation of each magnetic aggregate to its magnetic environment changes from time to time, the magnetic orientation of an aggregate is not usually uniform. Instead, the aggregate is subdivided magnetically into a number of sections, generally called “domains.”
Ordinarily, the domains are randomly oriented, and the effective magnetic force is reduced by the distribution over the different directions. Application of an external field forces a reorientation of the atoms to conform with the direction of the field, the extent of which depends on the strength of the field. This reorientation concentrates the magnetic effect in the direction of the field, and results in an increase in the effective magnetic force, reaching a maximum, the saturation level, when the reorientation is complete.