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 indispensible 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 l920's. This knowledge is based on the great synthesis of the
information about electric and magnetic phenomena which James Clerk Maxwell
published in the l850'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 Ð 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 Ð 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 electomagnetic 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
involve 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 in 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 mid-point 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 electomagnetic 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, (l86,000 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 affect 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 Schrodinger'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" \(me 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 assymmetric flux from the universe superimposd on the assymmetric
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.
Copyright © 1983 J.N.P. Hume All rights in this book reserved