Chapter IX

The States of Matter

Under the conditions prevailing in our local environment, a static equilibrium of the kind described in the preceding chapter never exists other than momentarily, as the individual atoms are able to acquire translational motions of their own, independent of both the space-time progression and the opposing scalar effect of the atomic rotation. This translational or thermal motion is readily transferred from atom to atom by any one of several processes and hence any motion of this kind that may exist in a particular region is promptly distributed among all of the atoms present. The study of the behavior of matter—of its properties—therefore deals with atoms in motion rather than static atoms, and these properties depend upon the magnitude of that motion as much as they do upon the characteristics of the atoms themselves, often more so.

As mentioned previously, the original development of the theoretical structure which is being presented in this work did not take the short and easy route that was followed by the hypothetical race of super-men in Chapter IV, but was the result of a long and difficult process of fitting together bits of information gathered by study and analysis of many separate physical phenomena. Because of the large amount of detailed and reasonably accurate quantitative information that is available regarding the physical properties of matter, the investigation of these properties has been one of the principal areas of concentration and the theoretical development has been extended into great detail throughout this field.

In each of the areas covered, including the thermal expansion, specific heat, compressibility, resistivity, crystal structure and melting point of solids, the volume, specific heat, compressibility, surface tension, viscosity, refractive index, magnetic susceptibility and boiling point of liquids, and the PVT relations, critical constants and viscosity of gases, the general principles governing the property in question have been worked out by a further development of the consequences of the postulates of the Reciprocal System, and the validity of the conclusions thus reached has been verified by calculating the theoretical values for many different substances under many different conditions and comparing these with the results of experiment. Because of the tremendous scope of this field and the finite amount of time that has been available for the task, the coverage of the different items has not been uniform. In some instances it is reasonably complete. The solid compressibility calculations, for instance, have reproduced practically all of the experimental values available in the range above 1000 atmospheres where the compressibility is great enough to be significant. Another property that has been given a very comprehensive treatment is liquid volume. The theoretical volumes for nearly a thousand liquids have been calculated, many over extensive ranges of temperature and pressure. Since the agreement between the theoretical and experimental values is within the margin of uncertainty of the experimental results in both the liquid volume and the compressibility comparisons, the validity of the theoretical relations in these areas is definitely established. In some other areas, particularly where the experimental data are meager and unreliable, the “fine structure” of the theory is less certain, but even in these cases there is every reason to believe that the general relations deduced from the theoretical foundations are correct.

Obviously a presentation of the immense amount of numerical data accumulated in support of the conclusions reached in these studies is far outside the limits that have been established for this present volume, and publication of these quantitative results will therefore have to be deferred to subsequent volumes in the series. The qualitative agreement between these conclusions and the results of observation is, however, very striking in itself, and the orderly and systematic way in which hitherto recalcitrant phenomena fall into line in this new development is quite impressive. A brief survey of some of the principal findings in this field, particularly the new information that has been developed as to the nature and origin of the different states of matter, should be quite appropriate in the present context.

The thermal motion, like the scalar effect of the rotation, necessarily opposes the space-time progression, for the same reason, and the addition of motion of this type therefore displaces the equilibrium in the outward direction. The first effect of the motion is thus an expansion of the solid structure. This direct and positive result is particularly interesting in view of the fact that previous theories have always been rather vague as to why such an expansion occurs. These theories visualize the thermal motion of solids as an oscillation around equilibrium positions, but they fail to shed much light on the question as to why the equilibrium positions should be displaced. A typical “explanation” taken from a physics text says, “Since the average amplitude of vibration of the molecules increases with temperature, it seems reasonable that the average distance between the atoms should increase with temperature.”⁹⁰ But it is not at all obvious why this should be “reasonable.” As a general proposition, an Increase in the amplitude of a vibration does not, of itself, change the position of equilibrium. Some explanation other than increased amplitude must be found to account for the expansion. In the RS universe the connection between the thermal motion and the expansion is explicit. Any such motion, however small, adds to the outward-directed forces and hence displaces the inter-atomic equilibrium outward.

Pressure displaces the equilibrium in the opposite direction and thus reduces the inter-atomic distance and the corresponding atomic volume. Here, as in so many other physical phenomena examined during the course of this project, the actual mechanism turns out to be much simpler than has ever been suspected heretofore. The development of theory indicates that the solid volume under compression is not properly represented by the kind of a complex function that has usually been employed by those who have attacked this problem—a function generally involving some fanciful concept such as that of an inverse sixth power force—but follows a very simple relation analogous to Boyle’s Law, except that in the solid the volume is inversely proportional to P½ rather than to P; that is, for the solid structure PV² = k. Unlike the gaseous aggregate that conforms to Boyle’s Law, however, the solid is subject to the equivalent of a pressure even when no external pressure is applied, as the excess inward force that causes the equilibrium to be established somewhere inside unit distance has the same kind of an effect as the external pressure. The solid is thus partially compressed before the external pressure is applied, and the total pressure represented by the symbol P in the expression PV² = k is the sum of the initial pressure and the external pressure. If we use the symbol P to refer to the external pressure only, in accordance with the usual practice, the compressibility equation becomes (P₀ + P)V² = k.

It is the effect of this initial pressure that is responsible both for the wide differences in compressibility between different substances and for the seemingly complex nature of the mathematical relation between solid volume and pressure. The compressibility curves for very compressible substances and relatively incompressible substances are not altogether different curves, as they appear to be; they are merely different segments of the same curve. The observed sodium curve, for example, is nearly complete and has the characteristic exponential shape, whereas the observed platinum curve is practically linear, but this difference is simply due to the variation in the magnitude of the section of the theoretical curve that is cut off by the initial pressure. Calculations indicate that the initial pressure for sodium is only 18,000 atmospheres, and the pre-compression of solid sodium is therefore relatively small, whereas the platinum initial pressure has the extremely high value of 1,295,000 atmospheres, which means that this metal is already highly compressed before any external pressure is applied.

This concept of pre-compression by the forces responsible for solid cohesion, one of the necessary consequences of the postulates of the Reciprocal System, is typical of the new ideas through which the system is able to accomplish a drastic simplification of the entire solid and liquid picture. There is nothing remarkable about the idea itself; it is the kind of thing that seems practically self-evident after it is once pointed out. But it enables treating the resistance to compression as a simple force subject to accurate evaluation independently of the compression process, rather than having to postulate some purely ad hoc and mathematically complicated force for the purpose. Of course, the compression pattern for the solid does not have the extreme simplicity of the relations obeyed by the compression of diffuse gases, but this cannot be expected in view of the more complex nature of the solid structure. Most of the changes to which the solid structure is subject, including not only the discontinuous first order transitions but also the more subtle second order transitions, alter the effective initial pressure and thus modify the compression curve. However, this modification does not replace the simple curve by a complex and mathematically difficult relation; it merely means that instead of one simple curve amenable to easy and accurate mathematical treatment we now have a series of simple curves equally amenable to the same kind of treatment.

If the magnitude of the thermal motion is progressively increased, a point is ultimately reached at which the sum of the outward-directed motions, the thermal motion and the scalar effect of the atomic rotation, exceeds the sum of the inward-directed motions, the space-time progression and the equivalent of the external pressure. The inter-atomic force of cohesion then vanishes in one dimension. The atom is still restricted to vibratory motion within one unit of space of its nearest neighbors in two dimensions, but it is now free to move in space in the third dimension. The result of this one-dimensional freedom that is acquired when the atom reaches what we will identify as the melting point is a continuing realignment of the inter-atomic forces, as a consequence of which the atoms (or molecules) move about at random through the aggregate and no longer have any permanent neighbors.

Even though this freedom of motion acquired by an atom or molecule which reaches the one-dimensional limit is a rather restricted sort of liberty, it is enough to cause a very substantial modification of the physical properties of the unit: a change of sufficient magnitude to justify looking upon this new condition as a different state of matter. In this liquid state the aggregate still has a definite volume, just as it did in the solid state, since the constituent molecules maintain a fixed average inter-molecular distance, but it no longer has a specific form, as the freedom in one dimension allows the molecules to change their relative positions under the influence of external forces and the liquid aggregate therefore conforms to the requirements imposed by these external forces. In general this means that it assumes the shape of its container.

As is evident from the foregoing, the development of the Reciprocal System introduces a totally new concept of the nature of the liquid state. In current thought this state is v dewed as a property of the aggregate; it is a “state of aggregation.” As ordinarily explained, the atoms or molecules are able to maintain the fixed average positions of the solid structure until the thermal energy reaches a certain magnitude, but beyond this point the inter-atomic forces of attraction are unable to return them to the equilibrium positions and the orderly arrangement of the crystal gives way to the random arrangement of the liquid. Development of the consequences of the postulates of the new system now indicates that this viewpoint is wrong; that the liquid state is basically a property of the individual atom or molecule, and the state of the aggregate is simply a reflection of the state of the majority of its constituent molecules.

There are many items of evidence, which demonstrate the validity of the new concept. One direct confirmation can be obtained from an examination of some of the properties of solutions. It has long been recognized that these properties are quite sensitive to the melting point of the solute; that is, the properties of a liquid-liquid solution often differ materially from those of the corresponding solid-liquid solution. Some of the less soluble substances, particularly, show a very marked change at the melting point, separating into the two-layer structure characteristic of many of the liquid-liquid solutions. In preparing a liquid-liquid solution of this kind it makes no difference whether we put the solid into the liquid and then raise the temperature of the solution beyond the melting point, or whether we liquefy the solid independently and add the solute to the solvent. In each process there is a very decided change in properties at a specific temperature, and in both cases this is the same temperature: the solute melting point. The logical conclusion is that the process in the solution is the same as that outside the solution; in other words, that the solute is in the solid state below its melting point regardless of its environment and it makes the transition to the liquid state at its normal melting temperature in solution as well as out of solution.

The significance of these points in relation to the present subject lies in the fact that the solute is known to exist in units of molecular or ionic size in the solution. If the solute is in the solid state below its melting temperature and in the liquid state above this temperature, this means that it exists in the form of solid molecules (or ions, which will be included in the term “molecule” for purposes of this present discussion) and liquid molecules respectively. Obviously the existence of distinct solid and liquid molecules under any conditions precludes the possibility that the liquid and solid states are “states of aggregation” and establishes the fact that physical state is essentially a property of the individual molecule, as required by the principles developed in this work.

The most conclusive verification of the validity of the new concept comes, however, from the accurate calculation of the numerical values of the properties of both the solid and the liquid aggregates in the vicinity of the melting point that is made possible by its application. Because of the distribution of molecular velocities due to probability effects, the thermal energy of the individual molecules of an aggregate varies over a substantial range, and hence a liquid aggregate at any temperature in the neighborhood of the melting point contains a specific proportion of molecules whose temperature is below the melting point and which, as a consequence, are individually in the solid state and have the properties—volume, specific heat, etc.—appertaining to that state. Similarly a solid aggregate at a temperature in the neighborhood of the melting point contains a specific proportion of molecules whose temperature is above the melting point and which, accordingly, are individually in the liquid state. It has been found in this investigation that most of the temperature-dependent properties of solids and liquids are either inherently linear with respect to temperature or can be mathematically stated in such a manner that they can be graphically expressed in linear form. When these linear curves approach the melting point they invariably bend toward the values appropriate to the alternate state.

This is, in itself, a significant qualitative confirmation of the new theory, but mathematical analyses of the patterns of these deviations from the linear relation have supplied a large amount of quantitative data to support the qualitative conclusions. In the course of the present study the observed values of the physical properties of hundreds of solid and liquid substances in the vicinity of their melting points have been reproduced by applying the percentage of “foreign” molecules determined from the probability principles to the appropriate magnitudes of the properties of the pure solid and pure liquid. The correlation between the theoretical and experimental values is particularly striking in the case of such properties as liquid volume and solid specific heat where the experimental results have a high degree of accuracy.

A set of values that is of special interest is obtained where the property in question is theoretically applicable to only one of the two states. For instance, the property of fluidity is incompatible with the basic nature of a solid. Some true solids will flow or “creep,” under external pressure, but the distinctive feature of the solid state is a thermal energy less than that required to overcome the inward-directed forces, and the relative positions of the molecules of a true solid therefore cannot change under the influence of thermal forces alone; that is, a true solid cannot have any fluidity. It follows that the observed fluidity of certain solid aggregates is actually the fluidity of the liquid molecules in the solid aggregate, and the magnitude of this property is a direct reflection of the proportion of such liquid molecules in the aggregate. The validity of this conclusion has been corroborated by calculations of the type described in the preceding paragraph.

The situation with respect to the vapor pressure of solid aggregates is similar. It is evident that a true solid, as herein defined, cannot have a vapor pressure. If a molecule does not have enough thermal energy to attain the restricted freedom of movement characteristic of the liquid state, it obviously cannot have the still larger amount of energy necessary to become a vapor. Here again it is clear that the observed property of the solid aggregate is not a property of the solid itself but of the liquid molecules within the solid aggregate. The vapor pressure of a solid at any specific temperature is therefore a function of the proportion of liquid molecules in the solid at that temperature.

Present-day textbooks tell us that “there is no sharp line of demarcation between solids and liquids,”⁹¹ but aside from the glasses, which are a special class of substances whose unusual properties are due to certain peculiarities of their structure that we will not have space to discuss in this volume, the examples that are cited in support of this pronouncement are substances that contain significant percentages of both solid and liquid molecules throughout the temperature range in which they are commonly encountered. The difficulty in classifying these substances as solids or liquids results from the fact that they are not homogeneous; they are neither solids nor liquids, but are intermediate between the two states.

There is a “sharp line of demarcation” between true solids and true liquids; that is, between solid molecules and aggregates of solid molecules on the one hand, and liquid molecules and aggregates of liquid molecules on the other. Consequently, the melting points of pure substances (other than the glasses) are sharply defined. In fact, the range of melting or freezing temperatures is commonly used as a criterion of purity. Timmermans, for example, considers that a freezing range greater than one-tenth of a degree indicates that the sample in question is impure.⁹² This is rather difficult to reconcile with the currently accepted view of the nature of the melting process, but it is entirely in harmony with the concept of melting as a phenomenon of the individual molecule that takes place at a sharply defined energy level.

The new theory also makes it clear why a solid aggregate cannot exist above the melting point, although it is possible, under favorable conditions, to carry the liquid down to temperatures considerably below the normal freezing point. The change of state of the individual molecule always takes place at the appropriate melting point (which, for the molecule, is also the freezing point) and there are no superheated solid molecules or sub-cooled liquid molecules. Superheated solid aggregates are also ruled out, as the melting of the aggregate requires nothing more than an excess of liquid over solid molecules, hence the solid aggregate automatically melts when the normal melting temperature is reached. Freezing, however, is a more complicated process, and presence of the required number of solid molecules in the aggregate is not sufficient in itself. The molecules must also make contact with each other and must maintain that contact against the disruptive thermal forces long enough to enable additional molecules to link up with the original combination so that a stable solid nucleus can be formed. Where conditions are not favorable for this process the liquid aggregate may be cooled well below the normal freezing point before it solidifies. If the freezing point is approached by way of increased pressure rather than decreased temperature, the formation of a stable solid nucleus is still more difficult as the pressure constitutes an additional disruptive force tending to break up any momentary association between solid molecules before it can be built up into a permanent solid structure.

Two characteristic properties of the liquid state are surface tension and fluidity (viscosity). The nature of these properties is clearly indicated by the theoretical development. At the melting point adjoining atoms in the liquid are held together by a cohesive force of the same kind as that which exists in the solid, but effective in only two dimensions. This cohesive force, the surface tension, decreases as the temperature rises, since the additional thermal energy gradually cuts down the excess inward forces in the two dimensions that retain the characteristics of the solid. Fluidity is the inverse quantity, a result of the mobility resulting from the freedom to move in the limited liquid manner. It increases as the temperature rises, and reaches a maximum at the upper end of the liquid temperature range. We may regard the surface tension as a measure of the extent to which the liquid still retains the character of a solid and the fluidity as a measure of the extent to which it has acquired the character of a gas.

Surface tension, as the name implies, is commonly pictured as a surface phenomenon. “The existence of this surface tension,” says Kimball, “suggests that the surface of a liquid may be regarded as a stretched membrane enclosing the bulk of the liquid.”⁹³ But even those who use such an analogy realize that the same forces must be effective throughout the liquid, and this author goes on to say, “Surface tension must have its origin in the attractive forces between molecules which hold the liquid together.” The new light obtained from the Reciprocal System shows clearly that this view is correct and that the surface phenomena are simply differential effects due to the presence of adjoining molecules inside the surface but not outside.

The upper limit of the liquid is the critical temperature. At this temperature the molecule has enough thermal energy to overcome the cohesive forces in all three dimensions, and it therefore breaks away from its neighbors and moves independently through space. The molecule is then in the gaseous state.

Since the probability principles necessitate a distribution of molecular velocities above and below the average which determines the temperature of the aggregate, there are individual molecules passing out of the liquid state at all temperatures, the number of those escaping being determined by the molecular velocity distribution corresponding to the existing average temperature of the aggregate.

This is essentially the same condition that prevails in the vicinity of the melting point, where a certain proportion of liquid atoms is present in the solid aggregate and a certain proportion of solid atoms in the liquid aggregate. In the solid-liquid situation, however, the paths of motion for the two states are intermingled and both the solid and liquid molecules are distributed uniformly throughout the aggregate. The presence of the minor component can be recognized only by its effect on the properties of the aggregate. But when the high-energy molecules in the liquid break their ties with their neighbors they spread out in all directions and diffuse into all available space. The result is a physical separation between the molecules in the two different states.

Escape of the vapor molecules from the liquid aggregate reduces the proportion of high energy molecules in that aggregate below the level required by the probability relations and the energy inter changes within the liquid therefore bring other molecules up to the critical temperature. These molecules then also make their escape. The loss of high energy molecules reduces the average temperature of the remaining liquid, but under normal conditions there is an inflow of heat from the surroundings to compensate for this energy loss, and if the energetic molecules are escaping into free space the process is repeated over and over again until no more liquid remains. This process we identify as evaporation.

If the evaporated molecules enter a region whose temperature is below the critical level, they lose energy and conform to the ambient temperature, but this does not necessarily mean that they revert to the liquid state. The energy increment corresponding to a given temperature difference is much smaller for the free motion of the gaseous type than for the liquid motion, and the evaporated molecule may still retain sufficient kinetic energy to continue the free gas-type motion even at the lower temperature. The definition of the gaseous state is usually set up in such a manner as to include these free-moving molecules that are below the critical temperature, but from a theoretical standpoint there is enough difference in properties between these molecules and those above the critical temperature to justify considering them as being in a distinct state of matter: the vapor state.

In the theoretical RS universe the solid state is the state which exists where the motion of the molecule is confined entirely within one unit of space. The gaseous state is the state, which exists where the molecule is completely free to move in the region outside unit space. The liquid and vapor states are those, which exist in the intermediate region where the molecule is partially, free to move and partially restricted. We may regard the liquid state as an extension of the solid state into this intermediate region and the vapor state as an extension of the gaseous state into the same region.

The coexistence of the liquid and vapor states shows that the relation between these two is quite different from that between any other pair of states. Within the energy range of the solid no other state can exist. Likewise, the gaseous state is the only one that can exist within its range. Whether or not a molecule is in either of these states is therefore purely a question of its net energy balance. But if the energy level of a molecule is between the upper limit of the solid state and the lower limit of the gaseous state, the question as to whether this molecule is in the liquid state or the vapor state is not determined by the energy level; it is a matter of probability. In a relatively low-energy environment a state or condition requiring less energy is ordinarily more probable than one requiring more energy, where either can exist, but in the liquid-vapor situation the probability considerations which determine the distribution of molecular velocities interfere with the operation of this rule. As long as any significant portion of the velocity distribution curve of the liquid extends up to the critical temperature the molecular transitions from liquid to vapor continue to take place regardless of the fact that the liquid state requires less energy.

If the liquid-vapor system is confined to a limited space, the velocities of the individual vapor molecules are likewise distributed over a range of values. This range extends down to condensation temperatures and some of the vapor molecules therefore revert to the liquid state. Increased evaporation creates a pressure, which accelerates condensation of the vapor and retards evaporation of the liquid, and eventually an equilibrium point is reached. Here the evaporation of the most energetic liquid molecules is exactly balanced by the condensation of the least energetic vapor molecules, and the relative proportions of liquid and vapor remain constant.

An increase or decrease in temperature changes the probability factors and shifts the equilibrium point up or down. Application of external pressure similarly displaces the equilibrium in the direction of more liquid and less vapor. By using sufficient pressure this process can be carried to the point where substantially the entire vapor aggregate has been condensed into liquid. This property of condensing under pressure is a direct result of the fact that the vapor state exists only by virtue of probability considerations, and it is one of the major points of difference between the vapor and the gaseous states. The gas cannot be condensed by pressure as the aggregate is in the gaseous state by virtue of the average energy level of the constituent molecules, a property which, unlike the relative probability, is not altered by pressure.

The concept of physical state as a property of the individual molecule which we derive by development of the consequences of the postulates of the Reciprocal System is another idea that, in itself, is neither extraordinary nor remarkable. It involves a distinct change in the previously existing viewpoint, to be sure, but not what would ordinarily be considered a revolutionary change, particularly since the transition from the liquid to the gaseous state in the evaporation process quite obviously takes place on an individual molecule basis and the new concept can therefore be regarded merely as a generalization of an already recognized process rather than something entirely new. Nevertheless, the practical consequences of this innovation are of major importance, as they open the door to a full qualitative and quantitative understanding of the properties of liquids: a field in which the best efforts of scientific investigators have hitherto been distinguished by a very conspicuous lack of success. As expressed by Pitzer, whose comments apply specifically to the volumetric situation but are equally apropos in application to liquid properties in general, “The quantitative representation of the volumetric behavior of fluids over both gas and liquid regions has proven to be an unusually difficult problem.”⁹⁴ The practical value of bringing system and order to this hitherto confused field of liquid properties is ample justification for considering this phase of the theoretical development as Outstanding Achievement Number Eight.

From a qualitative point of view the results of this change in the concept of the nature of physical state are immediate and direct, but from the quantitative standpoint one of its most important effects is to clear the ground for another general principle of wide applicability. This principle, another of the many unexpected results obtained by deduction from the basic postulates of the Reciprocal System, is that the temperature and pressure dependent properties of the fluid states of matter—liquid, vapor, and gas—are linear with respect to both temperature and pressure.

As long as physical state is viewed as a “state of aggregation” recognition of the linear nature of these relations is precluded, since the observed curves for the properties in question come in a great variety of shapes. Some are approximately linear, but many others show no linear tendencies at all. In the new physical picture the deviations of the properties of an aggregate of any particular fluid state from the theoretical linear relation are due to the presence of certain specific proportions of molecules which are individually in other states. The observed non-linear curves then result from superimposing the probability curves expressing the proportion of “foreign” molecules upon the standard linear curves for the pure state. Disentangling the two kinds of mathematical relations is sometimes a rather long and involved operation, but it is a relatively straightforward process that is practically certain to produce the correct results if sufficient time and effort are applied, and it therefore has a very wide potential field of practical application.

A collateral aspect of the new viewpoint as to the nature of the liquid state is that it gives us a simple and logical explanation of solid-liquid solutions. If a water aggregate, for example, can contain a certain proportion of solid ice molecules, as asserted by the new system and confirmed by analysis of the numerical values of the properties of the aggregate, then the presence of solid molecules of a different composition is easily explained as a phenomenon of the same general nature.

Another interesting and important aspect of the new physical picture originates from the inequalities that usually exist between the different inter-atomic force systems within the solid or liquid aggregate. In a crystal of an isotropic element all inter-atomic forces are alike, and the thermal energy required to overcome the cohesive force is therefore the same for all force systems in the aggregate. A term commonly employed in this connection refers to the cohesive force as a “bond”, between the molecules, and if we use this term in the context of the explanation of atomic cohesion outlined earlier in this chapter, we may say that the bonds between the atoms of this homogeneous and isotropic aggregate are all alike. The same is true of many compounds of isotropic elements where the only bond that exists in the structure is that between element A and element B. The great majority of material substances, however, are either anisotropic, so that they have stronger bonds in some directions than in others, or have more than two components, so that there are different inter-atomic combinations within the aggregate.

In the compound KCN, for instance, the C-N bond is much stronger than either the K-C or the K-N bond. When the melting point is reached and the weakest bond gives way in one dimension, the C-N force system retains the solid characteristics in all three dimensions and, so far as the liquid motion is concerned, the CN combination acts as a single unit. In this respect the conclusions of the Reciprocal System do not differ materially from those of previous theories, but the existence of solid-type force systems in the liquid and the existence, for similar reasons, of both solid and liquid-type force systems in the vapor and gaseous states is a new finding that has a significant bearing on some of the properties of these fluid states.

Still another contribution of the new system in this area is a clarification of the observed localization of the atomic force of repulsion: the reason why “the repulsive forces are quite suddenly encountered when the inter-molecular separation is decreased.”⁹⁵ A “sudden encounter” with a new force is very difficult to explain by means of a theory which interprets the phenomenon in question as being the result of a gradual approach to the point of origin of the force—a “decrease in the inter-molecular separation“—and much of the difficulty which previous theories have experienced in this area is due to the inherent incompatibility between the nature of the observed facts and the type of theory utilized for their explanation. What is needed in order to explain the sudden onset of the repulsive force is an equally sudden change in the inter-atomic force characteristics, and this is what the Reciprocal System now provides. Outside unit distance the force due to the rotational motion of the atoms manifests itself as gravitational attraction. At unit distance the force directions are suddenly reversed and the former force of attraction becomes a force of repulsion.

In closing this brief survey of the application of the new theoretical system to the physical states of matter it may be appropriate, in view of the incredulity with which this idea of a force reversal at unit distance is often greeted, to emphasize the point that this reversal, like all of the other new concepts that have been discussed in this chapter, is a necessary and unavoidable consequence of the Fundamental Postulates of the Reciprocal System. However strange such an idea may seem to those who encounter it for the first time, it is a deduction, not an invention; it is a necessary result of the properties of space and time that were extrapolated from experience in Chapter IV. Although the idea of a force reversal may seem incongruous when it is encountered in an unexpected place such as this, force reversals are not at all uncommon in the physical realm and, significantly, the theoretical effects of this reversal are completely in harmony with the observed facts. Furthermore, it will be shown in Chapter XIV that the Particular kind of a force reversal that takes place at unit distance is not even a unique phenomenon; there are two other locations in the universe where essentially the same kind of thing occurs.