CHAPTER 7
Electromagnetic Interaction
In the last chapter, I revisited Newton’s laws of motion and indicated that they were not fundamental laws in that they did not properly describe the interaction between fundamental particles. The fundamental particles that we are considering are the electron, proton, and neutron. The proton and neutron interact only at short range in such a way that they can be bound together in the nucleus of the atom but, as far as long-range interactions are concerned, the interaction between protons and electrons is all that need be considered. These particles are what we call electric charges—some say they have electric charge as if it is something that could be placed on an electron, for instance, or removed. When large-scale objects have an electric charge we mean, if the charge is negative, that they have more electrons than protons, or, if the charge is positive, that they have fewer electrons than protons. Since it is the electrons that are forming the outside parts of atoms, net electric charge of an object is a matter of electrons moving on or off the object—the protons are not migratory.
When I talk about the interaction between fundamental particles, I am taking a microscopic view of matter. When I talk of charged objects—which consist of a large number of fundamental particles—I am taking a macroscopic view. Newton’s laws apply to many macroscopic situations. It is a belief that is generally accepted that all macroscopic situations can be explained in terms of microscopic situations so that, in explaining laws, I need only concern myself with explaining the microscopic laws.
Darwin was trying to show that there were general laws behind evolution—nowadays we have a somewhat different view. We believe that the behavior of both inanimate and animate things in the universe can be explained in terms of these fundamental physical interactions. Thomas H. Huxley writes about it this way:
There is a wider teleology which is not touched by the doctrine of evolution, but is actually based on the fundamental proposition of evolution. This proposition is that the whole world, living and not living, is the result of the mutual interaction, according to definite laws of the forces possessed by the molecules of which the primitive nebulosity of the universe was composed. [1]
The forces between molecules are the forces described by the interaction between the fundamental electrically-charged particles. I am not sure why Huxley uses the word “teleology” here because that implies direction—or purpose—to which development is tending. As far as I am concerned, all that we can observe is the process. I am maintaining that in this process we cannot discern any evidence of design—there are no general laws. If there are general laws which transcend a large variety of particular things, we should be able to explain why these laws hold. Newton’s laws are general laws because they hold for all bodies, no matter what the bodies are made of: lead, or iron, or rubber. Newton believed that the existence of these general laws was evidence of design in the physical world. This is a reasonable conclusion unless you can explain how these laws happen to hold in terms of the behavior of the three basic fundamental particles: electrons, protons, and neutrons. The fundamental particles form atoms, the atoms form molecules and Newton’s bodies are made of atoms and molecules. Newton’s laws hold macroscopically because of the behavior of the fundamental particles. Newton’s laws of motion are not part of some grand design, or scheme of things.
At the present time, we explain the behavior of atoms and molecules using quantum theory. Here is a quotation from Hanson:
It is an indispensable condition of quantum theory that all electrons, all protons, all neutrons, must be identical; the successes of microphysics rest on this conception. [2]
I will be writing a lot more about quantum theory in later chapters, but one of its important components is the interaction between electrons and protons. This interaction might be called the electric interaction, but is, instead, more commonly called the electromagnetic interaction. If we understand how an electron and proton interact with each other, we can use this information over and over because of the natural recurrences of electrons and protons. What actually is a specific fact about two specific things—electrons and protons—acts like a general law. What exists is a specific fact, yet what we speak about are the laws of electromagnetism. The fundamental order in the universe stems from the fact that it is made up of fundamental particles—all electrons identical to each other, all protons, and all neutrons.
I am going to examine how an electron and proton interact with each other as far as scientists understood the interaction before quantum theory appeared in the 1920’s. This knowledge is based on the great synthesis of the information about electric and magnetic phenomena which James Clerk Maxwell published in the 1850’s. We call Maxwell’s theory classical electromagnetism. Maxwell was a theoretician and systematically organized all the bits and pieces of information available to him through the work of other pioneering scientists like Coulomb, Faraday, Oersted, Ampere, and Gauss.
One of the particularly worrying things about the interaction of two particles has always been—How do they do it? How does one affect the other without touching it? Newton brooded on the subject of action-at-a-distance in a letter to a friend:
It is inconceivable that inanimate brute matter, should, without the mediation of something else, which is not material, operate upon and affect other matter without mutual contact. [3]
Maxwell was faced with an additional problem when he determined that the electromagnetic interaction between two objects was not instantaneous, as Newton had assumed actions-at-a-distance were, but took a definite time. The speed of electric interaction Maxwell found was the same as what had been previously measured as the speed of light. At that time it was presumed that light travelled at a definite speed through space because it was a wave motion in a medium which was everywhere, a medium they called the ether—or aether. Here is Maxwell writing about electric interaction:
Now we are unable to conceive of the propagation [of electric action] in time, except either as the flight of a material substance through space, or as the propagation of a condition of motion or stress in a medium already existing in space. [4]
Maxwell decided that the explanation of a definite speed for electric action was that there was a medium in space—the ether—which was the same medium as light travelled in. He identified light as an electromagnetic wave on the basis of the fact that the speed of light waves was identical with what he calculated as the speed of his electromagnetic waves.
Since Maxwell’s death, experiments to detect the existence of the ether showed that whether there was an ether or not was an undecidable question. Einstein said that we should not speak about a thing that can never be established one way or the other; it was a waste of time and not scientific. That leaves Maxwell’s alternative “the flight of a material substance through space.” This explanation of the mode of transfer of electric action has been rejected on a variety of grounds. One reason for objecting to it is that Maxwell imagined that the messengers of the interaction would be “material” and thus would bump into each other and interfere with each other’s behavior, whereas the principle of superposition indicated that there was no interference between the actions of different charged objects. If we were seriously going to postulate this mechanism of interaction, we would have to have some non-interfering messengers of the interaction.
One of the present explanations of the electromagnetic interaction is that it is due to the exchange of virtual photons. A photon is a quantum of electromagnetic radiation so that this explanation is somewhat circular. What is being explained should not really be used as part of the explanation. Another reason for dropping the subject of a mechanism for electric interaction might be a general sympathy for Newton’s statement about not making hypotheses. But the real reason, I believe, for dropping it is the fact that having general laws like Maxwell’s laws of electromagnetism is now accepted as adequate explanation.
I am trying to argue that the general laws of electromagnetism come from the specific facts of interaction of two types of fundamental particles, electrons and protons. Since I believe that we cannot find evidence of design in nature—animate or inanimate—I must worry about an explanation of the specific interaction if that interaction has any sniff of design to it that cannot be explained.
Suppose we have an electron and a proton separated some distance from each other and held there—by what I don’t know. If we let go of them, then according to classical electromagnetism they will accelerate towards each other. The ratio of the accelerations will not depend on how far apart they are, and the acceleration of the electron will be nearly two thousand (1,840) times larger than the acceleration of the proton. If you could watch, you would see the electron accelerating towards what would seem like a fixed proton, because its acceleration is so small. The size of the actual accelerations would be smaller the larger the separation. This situation is what we call an electrostatic situation because the particles’ accelerations are measured just as they are released from a static position. This interaction was investigated by Coulomb, and the law of electrostatic interaction is called Coulomb’s law. Coulomb’s law is quite like Newton’s law of gravitation in that it is an inverse-square law. The mutual accelerations of the interacting particles decrease inversely as the square of their distance apart—as the distance increases the accelerations decrease.
The electrostatic interaction follows Newton’s laws of motion and was one of the interactions, besides gravitation and contact interactions between macroscopic objects, that confirmed the validity of Newton’s mechanics. But, when two charges interact while they are moving, Newton’s laws do not hold. The interaction is not instantaneous, as is required for Newton’s laws to be valid—and it is not independent of the velocities of the interacting particles. For the electrostatic interaction, the fact that interaction is not instantaneous does not show because the charges have been held fixed for a time interval before they are released. Since their velocities are both zero at the interaction time, the velocity dependence also does not show up.
Just as Newton introduced the idea of force in order to speak about the interaction of two objects, the idea of field was introduced to help to make calculations for electromagnetic interaction easier. The Coulomb law, being Newtonian in nature, could be expressed in terms of equal and opposite forces acting on the two charges. The idea of a field was introduced in order to be able to indicate even when there was just one stationary charge present —not two—that there was some kind of entity surrounding it. This entity was called the electric field. The size of the field at a point around the charge was just the force that another charge—of unit size—would experience if it were placed there. So if you knew what force there would be on a one-unit charge you could compute the force on a two-unit charge. It would be twice as much. The field idea introduced computational ease as well as the idea of an electric environment present around every charge, whether another charge was there to experience a force in the field or not. The electric field is called a force field. What the field consists of, if it has any reality, is anybody’s guess. Bridgman says:
The great virtue of the field concept is usually stated to be that it absolves us from accepting that intellectual monstrosity, action at a distance. It is felt to be more acceptable to rational thought to conceive of the gravitational action of the sun on the earth, for example, as propagated through the intermediate space by the handing on of some sort of influence from one point to its proximate neighbor, than to think of the action overleaping the intervening distance and finding its target by some sort of teleological clairvoyance. [5]
The environs of a stationary charge are characterized by this entity called the electric field. What about a moving charge? For one thing, the non-instantaneous character of electric interaction comes into play. When a charge is standing still, you do not care when the field at a point some distance away from the source charge was produced. It will continue to be the same if the charge that is the source of the field does not move. So you can just ignore the travel time of the effect. The value of the field actually depends on the charge as it was a time ago equal to the time for the effect to travel from the source point to the field point. But, since the field now is the same as it was at an earlier time, we just ignore the whole thing and treat it as if it were instantaneous—you get the same answer. But, when the source charge moves, that is a different story! The field at a field point at a certain time—say “now”—depends on where the source charge was at an earlier time. The effect is not instantaneous, but retarded due to the travel time. We call the spot where the source charge was at the retarded time—the time when it produced what is affecting the field point now—the retarded position. The field “now” depends on where the retarded position is relative to the field point and how the source charge was moving at the retarded time.
The field of the moving charge is not described by a simple quantity like the force field called the electric field of a static charge, but is characterized by what is called the electromagnetic field. The electromagnetic field can be given as two—apparently separate—parts, one called the electric field and the other called the magnetic field. When charges move, their field contains the part called the magnetic field as well as the part they have when stationary. Sometimes you hear that magnetic fields are produced by moving electric charges, and electric fields by stationary electric charges. But that is not quite accurate. A charge produces an electromagnetic field all the time. When it is stationary, the magnetic component has a zero value. When it is moving, you might expect that the electric component has a zero value, but this is not true. You might expect that the electric component is the same size, whether it is moving or stationary. But this is not true. And on top of all this the electromagnetic field depends on three things about the source charge at the retarded time—the position, the velocity, and the acceleration.
The acceleration produced by the source charge on a test charge which is at the field point depends on the velocity of the test charge—but not on its acceleration—and on the electromagnetic field at the field point. If the electromagnetic field has only an electric component, the acceleration of the test charge does not depend on how it is moving. Remember, to have only an electric component the source charge must be at rest and then the field at the field point is not changing with time.
Maxwell’s equations for electromagnetism are equations describing the connections between the electric and magnetic components of the electromagnetic field. Maxwell’s equations say things like: the way that the magnetic component at a field point changes with time depends on what the electric component is like in the neighborhood around the field point, and vice versa. The electric and magnetic components are interrelated. So you can see that the electromagnetic field is really a single entity, described in terms of these two components. As I have already mentioned, when the source is stationary, the electric component varies inversely as the square of the distance from the source point to the field point. When the source charge is moving, the way that the electromagnetic field depends on position, velocity, and acceleration at the retarded time, although more complicated, has this same kind of mathematical simplicity. By this, I mean that the mathematical formula has no factor in it that involves anything but integer powers of variables. As an example of an integer power, the square of the distance is distance to the power 2 —an integer—and as far as we know the value is precisely 2 , not approximately 2 .
When the size of a field component varies inversely as the square of the distance from the source point, it is only one-quarter as large at twice the distance, and one-sixteenth as large at four times the distance. In the formula for the electromagnetic field, we find that the contributions to the components connected with the acceleration of the source charge depend inversely on the distance rather than inversely on the square of the distance, as all the other parts in the formula do. So, at large distances, the effects due to the acceleration of the source charge are by far the largest contribution to the total field. When the distance from the source is increased tenfold, the field contribution due to the acceleration is one-tenth as much—that due to the other parts is one one-hundredth as much. You can see that the part due to the acceleration will dominate as distance from the source increases.
When a charge is oscillating back and forth in a periodic motion it is accelerating a lot of the time. Its acceleration is always a maximum at the ends of its oscillation as it is slowing down and starting up in the other direction, and zero as it passes through the midpoint of the oscillation, because there it has reached its maximum speed and is not accelerating anymore.
The field at a reasonably large distance from an oscillating charge is an oscillating field, where the components are all due to the acceleration of the source. Of course, the value of the field depends on what the source was doing at an earlier time. This particular kind of field we call electromagnetic waves. Electromagnetic waves are produced by an oscillating electric charge. At any point in the field of an oscillating charge there is an electromagnetic field whose electric and magnetic components oscillate together at the same frequency as that of the charge’s oscillation. At any particular time, if you move around in the field, the oscillations at different points will be at different stages—some will be at a maximum field, others at a zero field. The separation between nearest points that are in phase at any given time is called the wavelength of the electromagnetic waves. The whole field changes with time as if there were waves travelling out. Naturally, these waves travel at the same speed as the travel time of the electric interaction. This speed is the same for all frequencies of oscillation—we say that electromagnetic waves travel at this speed no matter what the frequency of the waves is. The value of the speed is approximately three hundred million meters per second (186,000 miles per second). Rather fast! This speed is represented by the letter c in all physics formulas. For what reason, I do not know.
A small range of frequencies of electromagnetic waves affects our eyes, and these waves are called light—some say visible light. The violet end of the spectrum of visible frequencies has the highest frequency, the red the lowest. Frequencies just higher than violet are called ultraviolet light but are not visible. They are what give us a suntan. Frequencies just lower than those we call red are named infrared and make us feel warm. Frequencies higher than ultraviolet are called various names depending on their source, that is, where the oscillating charges that produced them are. There are x-rays and gamma rays. Both of these radiations are more damaging to human cells than ultraviolet radiation is. Waves of lower frequencies than infrared can be produced by making charges oscillate in man-made electric circuits. We use these lower frequency waves to communicate with each other on radio or television.
Maxwell’s equations of electromagnetism tell us about the electromagnetic waves, but the fact of the existence of electrons and protons is not information present in the laws of electromagnetism. Bridgman says in his book The Way Things Are :
Given only Laplace’s equation [which can be derived from Maxwell’s equations] there would be no way whatever of predicting the physical occurrence of electrons. So far as I can see the same is true of Schrödinger’s equation for wave mechanics [quantum mechanics]. [6]
Nor is the explanation of why the electron and proton have equal and opposite charges contained in Maxwell’s equations. Certainly, if they were not equal in size, the net electric effect of an atom would be very strong and stability could probably never have been achieved. Possibly there is some interchange of something between charges which ensures that the exact balance is constantly being achieved as a natural consequence of the interaction, rather than by design decree. Certainly that must be one of the open questions for a person who does not believe in discernible design. The concept of behavior that ensures survival is not one that you normally associate with inanimate things like electrons or protons. The contrast between animate and inanimate is expressed by Reichenbach:
The living organism is a system functioning toward the aim of self-preservation and preservation of the species… Compared with the blind functioning of the inorganic world, the falling of stones, the flow of water, the blowing of the wind, the activities of living organisms appear to be controlled by a plan, to be directed towards a certain purpose. [7]
He goes on to say that the idea of a plan for animate things is erroneous; teleology contradicts causality. To have a future purpose means that things in the future influence the present. With causality, we believe that all the events which influenced the present happened in the past. Darwin is clear that chance events—the cause of which would have happened in the past—coupled with natural selection—the influence of the past or present environment—produces the order that we see in the animate world. Why should the inanimate world be radically different? Could not chance events and natural selection explain the occurrence of electrons and protons?
If the idea of continued existence—survival—is behind the behavior of charged particles, then the way that they accelerate when they interact must be a part of survival behavior. Scientists are inclined to say that they accelerate because a force is acting on them, but we could just as easily say they accelerate so that the environment they perceive remains the same as their natural environment is. Consider the two interacting electric charges, where we arbitrarily called one the test charge and the other the source charge. When the test charge accelerates in an inertial frame, it is subject to the superposition of the environment produced by the source charge, that is, its electromagnetic field, and the environment produced by the acceleration relative to the rest of the universe. If these superimposed environments added up to the same thing as the normal environment when the particle is at rest relative to the remainder of the universe, then the particle might continue to survive.
It might be a possibility, that the electric action of a source particle consists of a flow—or flux—of something through space. Remember Maxwell suggested this as an alternative to “a medium already existing in space”, the ether. The somethings cannot be “a material substance” or there would be collisions. To emphasize that they are not matter, I will call them messengers . These messengers, if they existed, would move outward, in all directions, from the source charge; some would fall on the test charge, after the retardation time. Perhaps the test charge might also be in receipt of messengers from all sides coming in symmetrically to it from the rest of the universe. How could it move so that this lopsided flux of messengers from the side where the source charge was located at the retarded time might be overcome? If it moved at constant speed in the inertial frame of the universe, we presume the inward flux from the universe to the charged particle would still be symmetric—remember all inertial environments are equivalent. It would have to accelerate in the inertial frame and this might produce just the right result. There would be an asymmetric flux from the universe superimposed on the asymmetric flux from the source charge, and these two might add up to a symmetric flux. All of this presumes that the messengers produced from the universe are indistinguishable from the messengers produced from a local source charge. And why not? What is out there except a lot of other electrons and protons? (I still am ignoring gravity.)
Summary
1. The general laws of electromagnetism come from the specific facts of interaction of the two types of fundamental particles: electrons and protons.
2. The way that charges accelerate when they interact is a part of survival behavior.
3. Charged particles emanate something that then forms the environment for other charged particles.
4. The something that charged particles emanate is probably the same something that is coming in from the rest of the universe and creating inertial environments.
5. The total environment is a superposition of all environments, from local charged particles and from the rest of the universe. This means that the somethings do not interfere with each other.
6. Charged particles will move in such a way as to experience a total environment that is inertial.
