Thus far we have considered three general types of motion: unidirectional linear motion, unidirectional rotational motion, and vibratory linear motion. To complete the coverage in this respect we now turn to the fourth of the basic types: vibratory rotational motion. Such a rotational vibration, which is identical with the basic linear vibration except in direction, will be identified as a charge. Since the primary rotations of the atoms and other rotational combinations are either one-dimensional or two-dimensional it follows that the corresponding rotational vibrations are also one dimensional and two-dimensional respectively. A one-dimensional rotational vibration will be identified as an electric charge and a two-dimensional motion of the same character as a magnetic charge.
The rotational vibration has the same general characteristics as the linear atomic vibration (thermal motion) previously discussed, including the fact that it is opposite in direction to the rotation with which it is associated. The electric rotational displacement of an electropositive element, for instance, is in time, and such an element therefore takes a vibrational space displacement. This introduces an awkward question of terminology. From a logical standpoint the vibrational space displacement should be called a negative charge since its direction is opposite to that of the positive rotation. On this basis the term “Positive” would always refer to a time displacement and the term “negative” to a space displacement. Adoption of such a system of nomenclature would have some very definite advantages, but so far as this presentation is concerned it does not seem advisable to run the risk of adding further confusion to explanations which are already somewhat handicapped by the unavoidable use of unfamiliar terminology to express relationships not previously recognized. For present purposes, therefore, current usage will be followed and a vibrational space displacement will be called a positive charge and a vibrational time displacement a negative charge. This means that the significance of the terms “positive” and “negative” with reference to rotation is reversed in application to charge. An electropositive element (net time displacement) takes a positive charge (space displacement) whereas an electronegative element, which can assume either a positive or negative orientation, may take either charge. Normally, however, the negative charge is restricted to the most negative elements of this class: those of Division IV.
Electric charges do not participate in the basic motions of the material and sub-material combinations, but they are easily produced in almost any kind of matter or sub-material particle and can be detached from these units with equal case. In a low temperature environment such as that on the surface of the earth the electric charge plays the part of a temporary appendage to the relatively permanent rotating system of motions.
The simplest type of charged particle is produced by imparting one unit of one-dimensional rotational vibration to the electron which, as we have found, has only one unbalanced unit of one-dimensional rotational displacement. Since the rotational displacement is in space the electron takes a vibrational displacement in time: a negative charge. The production of a charged electron in a conductor involves merely the transfer of sufficient energy to the uncharged electron to bring the existing kinetic energy of translation, which is also a time displacement (opposite to the thermal space displacement of matter), up to the total energy equivalent of a unit charge. If the electron is to be projected into space an additional amount of energy is required to break away from the solid or liquid surface and overcome the surrounding gas pressure. The necessary energy can be supplied in a number of different ways, each of which therefore constitutes a method of producing charged electrons.
A convenient and widely used method furnishes the additional energy by means of an electrical potential. Here the translational energy of the uncharged electron is increased by the electromotive force until it meets the requirements of a charged electron. In many cases the increment of energy is minimized by projecting the newly charged electrons into a vacuum rather than requiring them to overcome gas pressure. The cathode rays used in x-ray production are streams of charged electrons propagated into a vacuum. The use of a vacuum is also a feature of the thermionic production of electrons in which the necessary energy is imparted to the uncharged electrons by means of heat. In the photoelectric effect the energy is absorbed from radiation.
Existence of the electron as a free charged unit is usually of brief duration. Within a short time after it has been produced by one transfer of energy and ejected from matter into space it again encounters matter and enters into another energy transfer by means of which the charge is converted back into thermal energy or radiation and the electron reverts to the uncharged condition. In the immediate neighborhood of an agency which is producing charged electrons both the creation of charges from kinetic energy and the reverse process which transforms the charge back into kinetic energy are going on simultaneously and one of the principal reasons for the use of a vacuum in electron production is to minimize the loss of charge which occurs in this manner.
The ability of the charged electron to move through space is a result of the neutralization of the rotational space displacement by the time displacement of the charge. In the uncharged condition the electron was a rotating unit of space and could move only through time, which meant that we could observe it only by means of its effects on matter. Now that the single unit of rotational space displacement has been balanced by a single unit of vibrational time displacement (charge) the particle is neutral from the space-time standpoint and it can move freely through either space or time, although it is still blocked by insulators, which are space-time combinations that do not have the necessary open dimensions in either space or time. Furthermore, the electric charge enables us to control the motion of the charged electron through space and unlike its mysterious and elusive uncharged counterpart this electron becomes a tangible entity which can be subjected to observation and can be manipulated as a tool to produce physical effects of various kinds.
It is not feasible to isolate and examine the individual charged electrons in matter as we do in space, but we can recognize the presence of these particles by evidence of freely moving charges within the material aggregate. Aside from the special characteristics due to the electric charges, these charged electrons in matter have the same properties as the uncharged units. They travel readily through good conductors, less readily through poor conductors, are restrained by insulators, move in response to potential differences, and so on. In their various activities within aggregates of matter these charged electrons are known as static electricity.
On undertaking an examination of the basic mathematical relationships in static electric phenomena it will first be necessary to define and evaluate the units in which we will express the various electrical magnitudes. Unlike the common mechanical systems of units, which are clearly defined and mutually consistent, differing only in the arbitrary sizes assigned to the basic units, the electrical and magnetic measurement systems now in use present an extraordinary picture of confusion in which different units are applied to separate manifestations of the same quantity, the same units are used in application to different quantities, and the various systems cannot even agree on the dimensions of the quantities involved.
Failure to recognize tl-le difference between the charged and uncharged electron is one of the items of this nature that has introduced some confusion in the electrical system. No distinction has been made between charge and quantity and the numerical value of the natural unit of electric charge is therefore 4.8069×10-10 e.s.u., the same expression that was used as the natural unit of quantity. Ordinarily the two different usages are entirely separate and under these circumstances no error is introduced into the calculations by utilizing the same expression for both quantities, but a clear distinction is necessary in any case where both units enter into the same calculation as they are not equivalents and cannot be treated as such.
As an analogy we might assume that we are undertaking to set up a system of units in which to express the properties of water. Let us further assume that we fail to recognize that there is any difference between the properties of weight and volume and consequently express both in cubic centimeters. Such a system is equivalent to using a weight unit of one gram and as long as we deal separately with weight and volume, each in its own context, the fact that the expression “cubic centimeter” has two entirely different meanings will not result in any difficulties. If we have occasion to deal with both quantities simultaneously, however, it is essential to recognize the difference in dimensions. Dividing cubic centimeters (weight) by cubic centimeters (volume) does not result in a pure number as the calculations seem to indicate; the quotient still has the dimensions weight/volume.
Similarly we may use the identical electrical charge and quantity units in a normal manner as long as they are employed independently and in the right context, which is the normal situation, but whenever the two enter into the same mathematical expression or are employed individually in the wrong context it is necessary to take into account both the dimensional difference and the numerical ratio of the two quantities. Charge has the dimensions t/s, but is numerically equal to t since s = 1 in the local environment. Quantity is space, s. The ratio of s to t is unit velocity, 3×1010 cm/sec, which for this purpose is reduced to 1010 cm/sec by the fact that the charge of the electron, a one unit displacement applicable to a three-dimensional particle is the equivalent of three purely one-dimensional quantity units.
One place in which both charge and quantity units are involved simultaneously is in the calculation of the natural unit of capacitance. This quantity is normally expressed in farads, which are equal to coulombs (e) per volt. The volt is one joule per coulomb (q). In computing the natural unit the first requirement is to put the coulomb values on the same basis and we therefore multiply coulombs (e) by 1010 to change them to coulombs (q). The natural unit of electric charge, now in coulombs (q), is then divided by the natural unit of potential in volts. This gives us the value 0.5137×10-17 farads for the natural unit of capacitance. The expression coulombs (e) per volt equals capacitance can be broken down into space-time terms as follows: t/s × s2/t = s. Capacitance is therefore one-dimensional space and its magnitude in centimeters can be calculated from geometrical measurements where conditions are favorable. From such measurements the centimeter has been found to be equal to 1.1126×10-12 farads. We may then divide 0.5137×10-17 by 1.1126×10-12 to obtain the value of the natural unit of capacitance in centimeters. The result is 0.462×10-5 cm. Within the limits of accuracy of the measurements this agrees with the value of the natural unit of space as previously determined and serves as a confirmation of the values computed for the units in both the electric current and electrostatic systems, since both were involved in the capacitance calculations.
The electron has an effective rotational displacement in one dimension. In this dimension only it has the gravitational characteristics of an atom; that is, it is rotating in the direction opposite to that of the space-time progression. This progression in the macroscopic material universe (the time-space region) is outward toward infinite space. On the opposite side of the neutral axis (the space-time region) it is outward toward infinite time. Since the net rotational displacements are in the opposite directions, these displacements are in time (positive rotation) in the time-space region and the direction of motion is inward toward zero space. Gravitational force in this region is therefore a force of attraction. The direction of a positive rotational vibration (positive charge) is opposite to that of the positive rotation and it is outward toward infinite space. Two such positive charges are therefore moving apart, and in terms of force we may say that they repel each other. The same situation prevails where the rotations and the charges are all negative. Here the space and time relations are reversed but gravitation always opposes the space-time progression and consequently it is still a force of attraction. The oppositely directed force between the charges is a force of repulsion.
It should be recognized that the several space-time regions as previously defined are not localized in space and phenomena of two or more regions, such as positive and negative charges, may therefore exist in close proximity. If one of two interacting charges is positive and the other negative, the space-time direction of the motion is outward in both cases but because of the space-time inversion outward in each region is inward with respect to the other, hence the motions of unlike charges are directed toward each other. We therefore arrive at the general principle that the vibrational motions which we identify as charges create forces of repulsion if they are alike and forces of attraction if they are unlike.
Except for the dimensional difference, the force between electric charges is identical with the gravitational force. As in the latter, the motion is numerically equal to the displacement because the associated magnitude of the opposite kind is unity. Three-dimensional displacement t3 results in mass, t3/s3, which from a numerical standpoint reduces to t3 again since s = 1. Similarly one-dimensional displacement (electrical quantity) t or Q results in energy, t/s, which also reduces to the numerical value t because of the unit value of s. The gravitational force relations can therefore be adapted to the electrical system by placing acceleration with reciprocal space, which gives us
t/s2 = t/s × 1/s,
or in the usual terms,
|Fe = E/s|| |
From the facts brought out in the discussion of the analogous gravitational relation, equation 2, it is obvious that the expression for the force between two charges takes the same form as the gravitational equation. We may therefore state this relation as:
|Fe = ee’/s2|| |
As indicated in the general discussion of the sub-material particles, the electron has no primary rotational mass. When it acquires a charge, however, a gravitational force is produced by the effect of the rotational vibration on the basic linear frequency. We have already seen how the existence of this frequency in the atom modifies the secondary mass per effective rotational mass unit from 1/128 unit to 1/137.48 unit. In the electron the original 1/128 mass unit, which is merely the three-dimensional distribution of the rotational mass unit, does not exist and only the difference between 1/128 and 1/137.48 appears as mass. As in the atoms the secondary effect increases this mass by the factor 2/137.48. The total electronic mass is then:
|me = (1/128 - 1/137.48) (1 + 2/137.48) = 0.0005458||(124)|
This figure, 0.0005458 natural units, may be expressed as
or as 1/1823.28 amu.
Two additional electrostatic quantities should be mentioned briefly, as it will be of interest to compare their dimensions with those of the corresponding magnetic quantities which will be considered later. The electric field intensity is the potential gradient and is expressed in volts per meter or similar terms. The space-time dimensions are t/s2 × 1/s = t/s3. The flux density is expressed in terms of flux (charge) per unit area, which is t/s × 1/s2 = t/s3. These two quantities are therefore essentially the same thing seen from two different viewpoints, and the justification for the use of two different units is rather questionable.
Electric charges are not by any means confined solely to electrons. They may also be imparted to any other particles with electric rotational displacement or its equivalent, including material atoms as well as sub-material particles. The process of producing charges in matter is known as ionization and the charged atoms or molecules are called ions. Like the electrons, matter can be ionized by any of a number of different agencies including radiation, thermal collisions, electron impacts, etc. Essentially the ionization process is simply a transfer of energy and any kind of energy will serve the purpose if it can be delivered to the right place in the necessary concentration. There is, however, one other requirement to be taken into consideration. Mechanical principles indicate that translational velocity can be converted into rotational velocity only through the agency of a force couple. The atom or sub-material particle to be ionized must therefore be associated with some unit of the opposite space-time character so that a couple is in existence at the time the translational impact occurs.
An important consequence of this requirement is that in gases and liquids ions are normally produced in pairs. In solids any atoms that acquire charges retain their fixed positions and the only mobile units produced are the charged electrons, but in fluids all of the constituent units are free to move and each ionization therefore produces both positive and negative mobile particles. The effective couple in the simple gases is normally between the atom (or molecule) and an uncharged electron. Ionization under these conditions results in the production of a positively charged atom and a negatively charged electron. Any atom can take a positive charge (space displacement), as the net rotational displacement of all elements is in time, but as a practical matter positive ions are rarely formed in a low temperature environment by the lower Division IV elements, which are strongly electronegative. In gases these elements can produce negative ions, normally as members of ion pairs since positrons are not usually available for the force couple. The electron, being a unit of space displacement, can take only a negative charge.
One of the sources from which the ionization energy can be obtained is the thermal energy of the ionizable matter itself. Because of the high temperature required for this process thermal ionization of gases is of minor importance in the terrestrial environment, but at the high temperatures prevailing in the sun and other stars thermally ionized atoms, including positively charged ions of Division IV elements, are plentiful. The ionized condition is, in fact, normal at these temperatures, and we may consider that at each location there is a general ionization level, determined by the temperature. At the surface of the earth the electric ionization level is zero and any atom or sub-material particle which acquires a charge while in the gaseous state is in an unstable condition. It therefore eliminates the charge at the first opportunity. In some other region where the prevailing temperature corresponds to an ionization level of two units, for example, the doubly ionized state is the stable condition and any units which are above or below this degree of ionization tend to eliminate or acquire charges to the extent necessary to reach this stable level.
Since the rotational vibration which we call ionization is basically a motion in opposition to the rotation of the atom, the ionization cannot exceed the net effective rotational displacement (the atomic number). In a region of high ionization level the heavier elements therefore have a considerably greater content of space displacement in the form of ionization than those of smaller mass. This point has an important bearing on the life cycle of the elements and will be discussed in detail later.
Although thermal ionization of gases in the local environment is negligible, it does occur freely in liquids. At first glance it may seem contradictory to explain the relatively small amount of thermal ionization in gases as a result of insufficient temperature when it is widespread in liquids where the temperature is still lower. It should’ be recognized, however, that the determining factor is not the temperature as ordinarily measured but the temperature on the basis of the appropriate regional scale. A gas temperature of 2000° K, for example, is very low in a region where unit temperature is 3.62×1012 degrees. A liquid temperature of 400° K, on the other hand, is a very high level in a region where unit temperature is only 510 degrees.
The process of ionization in the liquid is essentially the same as in the gas. A compound such as HNO3 consists of two components, in this case a hydrogen atom and a NO3, radical group, held together by forces arising from the atomic rotations and the space-time progression. The effective rotation of the hydrogen atom is positive (displacement in time) while the effective rotation of the NO3 group is negative (displacement in space). The two components are therefore able to take positive (displacement in space) and negative (displacement in time) charges respectively, and the combination constitutes the kind of a positive-negative force couple which is a prerequisite for ionization. The thermal motion of the liquid itself supplies the necessary ionizing energy.
Because of the fact that positive rotation and positive charge are opposite in direction the charge acquired by the hydrogen atom neutralizes the single active positive valence and enables the atom to lead an independent existence as a neutral one-atom molecule. Similarly the charged NO3 group becomes independent. By means of this process the HNO3 molecule has now been split into a H+ molecule and a NO3- molecule.
The proportion of the total number of molecules which will be ionized in any particular aggregate is a probability function, the value of which depends upon a number of factors, including the strength of the chemical bond, the nature of the other substances present in the liquid, the temperature, etc. Where the bond is particularly strong, as in the organic compounds, the molecules often do not ionize or dissociate at all within the range of temperature through which the substance is liquid. Substances such as the metals in which the atoms are joined by positive bonds likewise cannot be ionized in the liquid state since there is no positive-negative couple on which the translatory impact can act.
The presence or absence of ions in the liquid is an important factor in many physical and chemical processes and for this reason chemical compounds are often classified on the basis of their behavior in this respect as polar or non-polar, electrolytes or non-electrolytes, etc. This distinction is not as fundamental as it might appear since the difference in behavior is merely a question of whether the bond strength is greater or less than the value necessary to prevent ionization. The position of the organic compounds in general as non-electrolytes is primarily due to the extra strength of the two-dimensional bonds which are characteristic of these compounds. It is worthy of note in this connection that organic compounds such as the acids which have one atom or group less strongly attached than normal are frequently subject to an appreciable degree of ionization.
Ionization of a liquid is not a process which is completed when the substance is first exposed to the appropriate conditions; it is a dynamic equilibrium similar to the vapor-liquid equilibrium. The electric force of attraction between unlike ions is always present and if an ion of the opposite kind is encountered at a time when the thermal energy is below the ionizing level, recombination will occur. This elimination of ions is offset by the ionization of additional molecules whose energy reaches the ionizing level. If conditions are stable an equilibrium is ultimately reached at a point where the rate of formation of new ions is equal to the rate of recombination.
Any change of conditions which affects either the ion formation or the recombination will, of course, alter the point of equilibrium. An important change of this kind is initiated if two conducting surfaces or electrodes are placed in contact with the ionized liquid or electrolyte and a potential difference is maintained between the two by some outside agency. For an explanation of the action which takes place we turn to the Principle of Inversion. According to this principle the charge of the negative ion, a rotational vibration with a displacement in time, is equivalent to and in equilibrium with a similar but opposite motion of the space unit in which the ion is located. This inverse motion is therefore a unit rotational space displacement. As long as it is associated with the ion it is a unit vibration, the inverse of the atomic vibration, but if it is detached from the ion for any reason the vibrational characteristics disappear as a single displacement unit is not vibratory when independent. Under these circumstances the motion manifests itself as an uncharged electron: a single unit of electric rotational displacement.
The external energy source acts as an electron pump, withdrawing electrons from the anode and forcing them into the cathode. Since the electrolyte is not a conductor of electrons, the electrical equivalent of a vacuum is produced at the anode and the equivalent of a pressure at the cathode. The ion, which is an atom or molecule of matter, cannot enter an electrode, but this prohibition does not apply to the coexisting space motion, and since the inverse motion of a negative ion is equivalent to an electron it is subject to the differential forces at the electrodes. When a negative ion comes in contact with the anode, therefore, the space motion leaves the ion and enters the anode as a free particle, an electron. The negative ion, deprived of its rotational vibration (charge), reverts to the neutral state. This leaves an excess of positive charge in the immediate vicinity of the anode and causes a movement of negative ions in this direction.
A similar process is simultaneously taking place at the cathode. Here the electric potential is the equivalent of a pressure and this tends to force the electrons out of the cathode whenever the opportunity arises. The electron cannot enter the liquid, which is not a conductor, but it can enter a positive ion if the latter makes contact with the cathode, since the ion is an atom of matter. When this occurs the electron and the oppositely directed rotational vibration (charge) of the space unit associated with the ion destroy each other and the ion becomes a neutral atom. As in the analogous situation at the anode, this leaves an excess charge of the opposite kind, in this case negative, and a movement of positive ions toward the cathode results.
Inasmuch as the electrons in the external conductor appear at the anode, flow through the conductor, and disappear again at the cathode, it would seem on first consideration that they must be carried from the cathode to the anode through the liquid. Examination of the movement within the liquid, however, indicates that this is incorrect, as all of the movement is from the body of the liquid to the electrodes; there is no movement from cathode to anode. The positive and negative charges created by the ionization process move to the cathode and anode respectively, where they are destroyed in the manner described. This lowers the ion concentration below the equilibrium value and further ionization then occurs. If the ionizable matter is finally exhausted and there are no more ions available the electrolytic action ceases, regardless of the potential difference between the two electrodes.
When the cycle which originated with the ionization of the molecule of the electrolyte is completed by the neutralization of the positive and negative ions a complete electronic balance has been accomplished and no net change has occurred from the electronic standpoint. The result of the process has been a chemical change. By means of energy supplied from the external source of potential the cohesive forces within the molecule have been overcome and the positive and negative components have been physically separated. Because of this separation it is not possible to reconstitute the original compound when the charges are neutralized and the ions deprived of their charges therefore combine with others of the same kind, where this is chemically possible. Metals plate out on the cathode and hydrogen gas escapes from the liquid. In some instances a gas is similarly formed at the anode, as in the electrolysis of water, but negative radicals such as SO4, for example, cannot combine and they normally attack the metal of the anode.
It is also possible to utilize the same process to accomplish the inverse objective; that is, to obtain electrical energy from a chemical change. Let us assume, for instance, that copper and zinc electrodes are inserted into a suitable electrolyte and connected externally by a metallic conductor. Because of the difference in contact potential, electrons flow from the zinc electrode through the conductor to the copper electrode to achieve an electronic equilibrium. This leaves the zinc anode in the condition of an electronic vacuum relative to the electrolyte and similarly creates an electronic pressure at the cathode. The situation is then identical with that existing when the potential difference is created by an outside agency and the same kind of motion takes place.
In order to arrive at the condition of space-time equilibrium required for the independent existence of ions it is necessary for each component of the molecule to acquire a charge equal in magnitude but opposite in direction to the net effective rotational displacement. The number of units in the ionic charge is therefore equal to the effective valence of the atom or group which carries it. This enables us to compute the relation between the quantity of electricity and the mass involved in electrolytic action. Each ion of valence n carries n units of charge. Since a unit of charge is transformed into a unit of electrical quantity by the process at the anode the total number of ions of each sign corresponding to a current of quantity Q is Q/n. If n is one and the ion is monatomic the number of atoms is equal to the number of units of electric quantity. We may evaluate this one to one relationship in cgs units by dividing the unit of electric quantity by the unit of atomic mass.
|4.8069×10-10 e.s.u. / 1.66124×10-24 g |
= 2.8936×1014 e.s.u./g-equiv.
This is the Faraday Constant. It tells us that each 2.8936×1014 e.s.u. will remove from solution one gram of a univalent substance of unit atomic weight or m/n grams of a substance of atomic weight m and valence n. The determination of this constant is a much simpler and more direct process than the experimental evaluation of the electronic charge and since it is advisable to base the conversion constants on the most firmly established value, the Faraday constant is listed in Appendix A as the basis of the conversion ratios in the electrical system. As indicated by equation 125 the currently accepted experimental value of this constant, 2.8936×1014 e.s.u./g.-equiv., is equivalent to Millikan’s value of the electronic charge, on which the previous calculations were based.
In all of the discussion in the foregoing pages the direction of movement of the electric current has been indicated in terms of electron flow and reference to the direction of “flow of current” has been avoided because of the unfortunate convention which pictures the flow in the wrong direction. Inasmuch as some rather basic changes in the concept of the nature of electric currents will be necessary in view of the findings of this work, it would seem that this is an opportune time to discard this erroneous and confusing flow convention. No change will be necessary in the designations positive and negative as they apply to battery terminals, etc. It will, in fact, be quite desirable to retain the present nomenclature as long as we continue to regard the electronic charge as negative. All that is required is an understanding that current flow is from negative to positive, or from more negative to less negative in wires connecting terminals of the same sign. On this basis the terms “positive” and “negative” in application to electric currents will refer to the electronic “pressure” or potential, the higher potential being the more negative.