CHAPTER 8
THE ENERGY CRISIS
Newton's studies of the way that objects
interact with each other showed that the ratio of the accelerations of the
interacting objects was a constant, independent of the distance between them
and their velocities at the time of their interaction. In the last chapter I described the
interaction between electric charges and indicated that this interaction does
not fit the Newtonian idea of interaction. Because the interaction is not instantaneous,
whenever there is a relative motion of the interacting charges, the effect is
complicated. In an attempt to try to simplify the calculation about what
happens, we introduce the idea of an electromagnetic field. At any time the field at particle
number one (if you call the interacting particles "one" and
"two") is due to particle number two's position and motion (velocity
and acceleration) at an earlier time, called the retarded time. The position of particle two at the retarded
time is called the retarded position.
The duration of the retardation is the time required for the
electromagnetic effect to travel in a straight line from particle two, at its
retarded position, to particle one in
its present position. The
speed of electromagnetic interaction is a constant; we name it c. Its value, as I said before, is 186,000
miles per second which is 3 hundred million meters per second. This is an extremely high speed and you
can see that, unless particle two is moving fairly rapidly, it will not have
moved very far from the retarded
position in the interval between the retarded time
and the present.
It is very difficult to think about the
interaction between charged particles and not think, as Maxwell did, that there
must be something travelling from particle number two to particle number one
(and, of course, vice versa). This
something I have called "messengers" although I have not yet made any attempt to quantify this
messenger model of electromagnetic
interaction. One of the reasons
for putting this off is because there is a competitor for what is travelling in electromagnetic
interaction and that competitor is called "energy". I have entitled this chapter "The
Energy Crisis" because, if I am to make any serious progress with a messenger
model, I must first dispose of the energy model.
Energy started as a concept, like force
or field, which helps make calculations about the behavior of interacting
particles simpler. But it has, by
degrees, been invested with more and more significance until now it has become
to many people not only a part of nature, a reality, but, to many, the very
basis of all reality. As an
example of the most extreme reification (if not deification) of energy I quote
Werner Heisenberg:
Energy is in fact the substance from which all
elementary particles, all atoms and therefore all things are made, and energy
is that which moves. Energy is a
substance, since its total amount does not change, and the elementary particles
can actually be made from this substance as is seen in many experiments on the
creation of elementary particles. Energy can be changed into motion, into heat,
into light and into tension.
Energy may be called the fundamental cause for all change in the world.
[1]
I quote this to show you just how far very
respectable physicists get carried away in their regard for energy. If it is not energy itself that grips
scientists, it is usually the general law called the "law of conservation
of energy". I will outline
how this law fits in with Newtonian interaction and electromagnetic interaction
in turn so that you can appreciate just what it is about, but first I quote a
typical enthusiast for the law - Professor R.P. Feynman:
There is a fact, or if you wish, a law , governing
all natural phenomena that are known to date. There is no known exception to this law Ð it is exact as far
as we know. The law is called the conservation
of energy. It states that there is a certain quantity, which we call
energy, that does not change in the manifold changes which nature undergoes...
It is not a description of a mechanism, or anything concrete; it is just a
strange fact that we can calculate some number and when we finish watching
nature go through her tricks and calculate the number again, it is the same.[2]
To Feynman, the law of conservation of energy is a
fundamental part of nature's bag of tricks. It is to him part of the grand design, one of the rules of
the game, perhaps the most basic rule since it "governs all natural phenomena
that are known to date".
The law of conservation of energy, and
with it the concept of energy itself, must be attacked directly if the notion
that the existence of laws governing (or describing) the physical world is to
be believed to be an illusion. The
metaphysical power of any conservation law is very great. Here is Mach:
... the notions of the constancy of the quantity of
matter, of the constancy of the quantity of motion, of the indestructibility of
work or energy, conceptions which
completely dominate modern physics, all arose under the influence of
theological ideas. [3]
As Mach says, constancy within change is a deeply
rooted theological idea. Do you
know the famous hymn "Abide with me"?
Change
and decay
In
all around I see
Oh
Thou who changest not
Abide
with me.
Not only is the unchanging element within a
constantly changing environment important to us theologically, it is important
to every accountant. Books must
balance; if something disappears, it must be explained. Whether it is our orderly accountant's
attitude in science or a deep-seated yearning for the eternal, somehow the law
of conservation of energy has cast its spell over us and we see it as general
and fundamental.
Where did it all start? It started with what is known as the work-energy
theorem. This is really a
restatement of the definition of velocity and acceleration combined with
Newton's second law of motion. I
will show you what it is. Suppose
that an object is moving along in a straight line with constant acceleration a. This means its velocity is changing uniformly with
time. Suppose that it starts at
time zero with a velocity zero (from rest as they say). As time goes on, its velocity will
increase. At a later time t its velocity v will be v=s*t (where the
asterisk means multiplied by).
This is the definition of constant acceleration. In time t it will
travel a certain distance d. If it were travelling at constant
velocity v, it would travel a
distance d = v * t (that is the
definition of constant velocity v). In
the accelerated case, the velocity is not constant but changes from 0 to v. The
distance travelled will be d=(average
velocity)*t. The average velocity
will be v/2. So d=v*t/2. Using the value for the time of the trip from the
other equation v=a*t, or t=v/a, we get
d~=~( v * v ) / 2 * a
We can rewrite this equation as
a * d~=~( v * v ) / 2
or
a * d~=~v 2 / 2
If the acceleration is varying, we multiply the
instantaneous acceleration by the small distance travelled when the
acceleration has that value and add this up over the whole trip. The right-hand side of the equation
stays the same. I will just stick
with the constant acceleration case because all that adding up of little pieces
involves calculus.
Now comes the time to stir in Newton's
second law of motion which is
F = ma
I do not write arrows over F and a here because they are both along the
straight line where the motion is taking place. From this equation and the previous one we get
F * d / m~=~v sup 2 / 2
or
F * D~=~m v sup 2 / 2
Now we are ready for the work-energy theorem. We define a new concept
"work" which is the force exerted multiplied by the distance over
which it is exerted. So here by
definition
"Work"~=~F * d
We then define a second quantity which we call the
"energy" of the moving object which is its mass multiplied by its
velocity squared all divided by two.
"Energy"~=~m v sup 2 / 2
Having defined these two quantities, we now see that
our equation says that the work done (by exerting a force over a distance) is
equal to the energy of the object that has been accelerated. Sometimes the energy of the moving
object is called energy of motion or kinetic energy.
We have introduced (defined) two new
concepts: work done by a force and energy of motion. We say, as if these concepts had some existence independent
of these definitions, that if you do work on an object, its energy
increases. This has no more
information than Newton's law has, namely, that if you act on an object with a
force, it will be accelerated.
This is well understood by all scientists. Here is a quote from one of the most widely used university
physics textbooks by Resnick and Halliday:
The work-energy theorem does not represent a new,
independent law of classical mechanics.
We have simply defined
work and kinetic energy and derived
the relation between them from Newton's second law. The work-energy theorem is useful, however, for solving
problems in which the work done is easily computed and in which we are
interested in finding the particle's speed at certain positions. [4]
The principal use of this new law is to
make calculations about the speed (velocity) of an object that has been
subjected to a force where we can make the calculation of the work easily. A
force is exerted only if our object is near another object or, as we say, is in
the field (of influence) of the other object. According to Newtonian mechanics,
if an object is at a certain position in the field of another object and
released, it will move in an accelerated manner either towards the object, or
away from the object, depending on what the two objects are. If they are both
electrons, they will move apart. If one is an electron and one a proton,
they will move together.
For certain kinds of fields, called
conservative fields, the work done by the force on an object released at one
point A in the field and moving to another point B is independent of the
particular path that the object takes from A to B. The work done can then be expressed as the difference
between two quantities that depend only on the positions of the two points A
and B in the field. If we call
these two quantities potential energy, then the work done on a moving particle
which travels from A to B is just
(Potential Energy at A)-(Potential Energy at B)
This is the definition of the term potential energy
(P.E.). Now if we go back to the
work-energy theorem we see that, if the object starts from rest at A and is
accelerated to B where it has a speed v, then
(K.E. at B) = (P.E. at A) - (P.E. at B)
Since the Kinetic Energy (K.E.), as defined, is zero
at A (where v = 0), we can write
(K.E. at B)-(K.E. at A) = (P.E. at A) - (P.E. at B)
or regrouping the terms in the equation
(K.E. at B)+(P.E. at B) = (K.E. at A)+(P.E. at A)
This is the first appearance of the idea of energy
conservation. If we say that the
total energy of the object is the sum of the potential energy and the kinetic
energy then this equation says that
(Total Energy of object at B) = (Total Energy of
object at A)
The energy of the object is conserved and this is the
law of conservation of energy. As
an object moves in a conservative field, there is a quantity (Feynman calls it
"a number") which we have named energy which does not change. We say it is an invariant of the
motion. How wonderful nature is!
Descartes is quoted by Mach as saying:
Therefore, it is wholly rational to assume that God
since in the creation of matter he imparted different motions to its parts, and
preserves all matter in the same way and condition in which he created it, so
he similarly preserves in it the same
quantity of motion [sometimes
energy]. [5]
Having gone to the trouble of defining all these new
concepts: work, kinetic energy, potential energy, total energy, in order to
disguise Newton's law of motion, we stand back and pronounce it as part of the
grand design.
I said that it is only for certain
Newtonian type interactions that this law of conservation of energy holds. These include gravitation and
electrostatic interactions and actions of this sort that happen in isolation of
other nearby objects. These must
of course be the limitations, since conservation of energy is really Newton's
second law in disguise. Perhaps I
should say that the same facts about interaction can be expressed in different
"guises"; but the
information content is the same in each guise.
I have said that the conservation law
idea is very gripping. You begin to believe that energy is something that
really exists. Gradually you are led to believe that an object can possess
certain kinds of energy and that the total amount that it possesses does not
change. This is the way we analyze
what happens when an object moves in the field of another object which itself
remains fixed. What happens when both interacting objects can move? How do we
analyze the situation then?
Suppose object number one is moving at speed v directly
toward object number two, initially at rest, and that the two objects repel one
another. Suppose also that the two
objects are identical. In the
interaction, we know, using Newton's third law, that the forces are equal and
opposite at all times. This does
not immediately mean that the energy lost by one object is equal to the energy
gained by the other since the equal forces may be exerted over different
distances. We do know that they
are exerted for the same length of time (the time for the interaction to take
place). So we define a new quantity called "impulse" which is the
product of force multiplied by the time over which the force is exerted. If a constant force F is exerted on an object for time t, the impulse is F*t. Using Newton's second law this is m*a*t. But, if the body changes from a velocity 0 to a
velocity v under the influence of the constant force, v=a*t, so that the impulse is equal to m*a which we call the "momentum" of the
object. Just as we had the
work-energy theorem, we now have the impulse-momentum theorem. The impulse
given to an object equals the momentum of the object.
F * t = m * v
One of the big differences between the two theorems
is that work and energy are just numbers that have a certain size (the numbers
may be positive or negative). But
impulse and momentum are quantities that have both size and direction.
Using Newton's third law we can show
that, if two objects interact, the change in momentum of one object is equal in
size and opposite in direction to
the change in momentum of the other.
This means that the total change in momentum is zero. Momentum is conserved in an
interaction. This is called the
law of conservation of momentum and is a direct consequence of Newton's laws of
motion. It is not new
information. It is necessary to
use both conservation laws to analyse an interaction since between them they
give the same information as contained in both Newton's laws of motion.
Using the conservation laws you can tell
that if two identical objects (balls) collide by having one start at rest and
the other come toward it with a speed v that after collision the speeds will be reversed. If each has a mass m, before collision the energy is m*v2/2. The potential energy is zero both before and after
collision because the objects are assumed to start and finish out of range of
any interaction. This means that
the only energy before and after is kinetic energy. It seems that the energy of the system is passed from the
incoming ball to the outgoing ball during the collision. As far as momentum is concerned, before
collision it is m*v+0; after
collision it is 0+m*v. Both velocities are in the same
direction so momentum is also
conserved. Momentum is passed from the incoming ball to the outgoing ball.
Neither momentum nor kinetic energy are
quantities that are independent of the frame of reference that you use for
observing the collision. Suppose you imagine the collision between the two
identical objects from a frame of reference that is moving along with the
incoming object at a speed v
relative to the first frame we spoke about. In this moving frame the incoming object from frame one
would seem to be at rest. But the
object that was at rest in frame one would be moving towards the first object
with a speed v. The whole collision would seem to be
the other way around. If you think
of energy: in frame one the kinetic energy of object one is passed over on
collision to object two; in frame two the kinetic energy of object two is
passed over on collision to object one.
How can energy as we have described it be anything real when, depending
on our frame of reference, it is passed in opposite directions? And one frame is as good as another for
viewing the event. They are both
inertial frames and inertial frames are equivalent.
The same remarks can be made about
momentum although, strangely enough, no one seems to speak of momentum as a
thing. Perhaps the reason is that we introduce a great many properties all
called energy, the sum of which remains constant in an interaction. I have
already spoken about kinetic energy and potential energy but there are more. Another is heat energy. Kinetic energy "shows"
because the object is moving; potential energy "shows" because the
object is in a certain position in the field. But heat energy does not "show"; it is internal to
the object. The object is
hotter. We now know heat is
related to the internal motions of the constituents that make up the
object. The constituents of the
object have an increase in kinetic energy which shows up as a higher
temperature of the object.
An example of where energy apparently
disappears, is when two identical objects collide, as before, but stick
together after collision. The law
of conservation of momentum tells us that the stuck-together objects must move
off with speed v/2 in order that
the momentum after collision, namely 2*m*v/2, is the same as the momentum before, namely m*v.
The kinetic energy before collision is m*v2/2 whereas after collision it is (2*m)*(v/2)2/2 since the mass of the outgoing object is 2*m and its speed is v/2. (Remember kinetic energy is the mass multiplied by
the velocity squared all divided by two.)
If you simplify this expression for the energy after collision you see
that it is m*v2/4, only half of
what it was before collision. It would seem that energy had disappeared. We call this kind of collision an
inelastic collision which just means one in which the total of the potential
and kinetic energies is not conserved. These two kinds of energy are called
mechanical energy. I said that it
was found that, when mechanical energy disappeared, heat appeared. This was discovered by Joule; he found
the exact relationship between the unit for measuring mechanical energy and the
unit for measuring heat, the calorie.
We now call the unit for measuring any kind of energy after Joule.
Joule's discovering where energy
disappeared to in an inelastic collision was very important and made scientists
believe that the law of conservation of energy was very fundamental. Since it is merely a restatement of
some of the information in Newton's laws of motion we would expect that it
holds as long as Newton's laws hold.
But I guess they forgot about Newton and began to put their trust in
energy conservation. The reason
that energy conservation includes heat energy is that if you look
microscopically at the collision it is not between two objects but between two
systems of particles which are moving about randomly as well as having their
centers of mass move along systematically. When we say that object number one moves at speed v, we really mean that the center of mass of the
system of particles that we call object one is moving at speed v. The
other object is at rest before collision but its particles are also moving
about at random; but their center of mass stays fixed. After collision, each center of mass
moves at speed v/2, but the
random motions of each system are intensified. This shows up as heat, but is
really mechanical energy of the particles. So, in fact, mechanical energy is conserved, at the
microscopic level, even when it seems that it is not when we just look
macroscopically.
So we emerge from all this with an
alternative way of expressing the information in Newton's laws: as the laws of
conservation of momentum and energy.
But more than that, scientists found the conservation law form of the
information more appealing. It is
undoubtedly good to have alternative ways of reasoning about physical
situations but this alone would never have been enough to raise conservation
laws to the prominence they now enjoy without metaphysical feelings on the part
of scientists. The idea of
conservation seems to support the idea of design in the physical world.
I have indicated in the last chapter that
Newton's laws do not describe the interactions between electric charges. We need Maxwell's laws of
electromagnetism or their information equivalent. Newton is just plain
incorrect as far as the interactions between fundamental particles go. Does that mean that the laws of
conservation of energy and momentum are also incorrect? The answer is yes, if we stick to the
same definitions of momentum and energy. But if we are willing to change the
meanings of the words we can get laws that have the form of the old laws.
I will concentrate first on the law of
conservation of energy. The person responsible for manipulating Maxwell's laws
of electromagnetism into a conservation of energy law was Poynting. His
equation is sometimes called Poynting's theorem (like the work-energy
theorem). Poynting defined energy
in such a way that it was a property of the fields (electric and magnetic)
rather than a property of the charges causing the fields. If the fields were static, that is, not
changing with time, the energy just stayed in space wherever there was a
field. When the field changed with
time because a charge was moving, the energy stored at any position could
change and this according to Poynting was accompanied by a flow of energy from
one point to another. If an
electric charge was oscillating back and forth there would be a flow of energy
from it outward into space.
I did not write down Maxwell's equations
as I did Newton's equations because they are mathematically more
difficult. But remember they are
equations that relate the way that the electric and magnetic field components,
which describe the electromagnetic field, depend on each other and on the
source of the fields, namely electric charges. The emphasis in Maxwell's equations is the field and when
you perform mathematical operations on these equations just as we did on
Newton's equations, to get a theorem that can be given an energy
interpretation, it is natural that the energy will be associated with the field
rather than with the charges.
Jammer describes it this way:
[Maxwell and Poynting have shown that] the field is
the seat of the energy and matter ceases to be the capricious dictator of
physical events. [6]
An earlier energy interpretation which involved only
static electric or magnetic fields, found that a valid conservation law could
be obtained either by associating the energy with the charges or with the
field. But Poynting's assignment
to the fields is necessary in the most general case.
The main thing to realize is that the law
of conservation of energy for electromagnetic fields does not contain any
information whatsoever not contained in Maxwell's equations. From the point of view of worrying
about whether or not the energy conservation law proves the existence of design
in nature, the question can be decided by looking at Maxwell's equations.
The fact that energy is an artifact, an
invention of man and not a part of nature is made completely explicit in the
high school textbook on physical science prepared for non-science students (by
PSNS project staff):
Much of the usefulness of the energy concept arises
from the fact that, when properly defined, the total energy in the Universe is
constant. This statement is so
fundamental to man's model of the world about him that it has become known as
"the principle of conservation of energy". We will discover that if this principle is to apply to all
physical interactions and to all situations whatsoever, it will be necessary to
invent a number of different kinds of energy. We will also see the need to invent rules for assigning
numerical values to the various forms of energy we invent. These rules will tell us how to compute
the values of each kind of energy in terms of the properties of objects under
any situation imaginable
The rule for determining this number has already been
set for kinetic energy:
"K.E."~=~( 1 / 2 ) m * v sup 2
But we must establish other kinds of energy and give
the rules for determining a given amount of each kind if we are going to be
able to develop the principle of conservation of energy. That principle is the accounting system
of the energies as objects interact with one another. If we assume that energy is conserved in each interaction,
then if objects do interact in such a way that the energy of one decreases, the
energy of some other must increase.
It is possible, of course, for the energies of each of the interacting
objects to decrease, but only if they lose energy to the surroundings. Objects can also gain energy from the
surroundings.
By this reasoning, we are at liberty to invent as
many energies as we wish and in any way we see fit in order to accomplish our
objective of producing an energy conservation principle. The principle will only be useful,
however, if the number of separate rules necessary to specify all kinds of
energy is reasonably small. Generating the law would not be worth the effort if
every new phenomenon investigated required a new kind of energy calculated by a
new rule. If, however, we can
describe all interactions in terms of the exchange of only a few kinds of
energy, then the energy conservation principle would provide a new relationship
between properties of interacting bodies.
Fortunately, it is possible, by identifying only six or eight distinct
kinds of energy, to arrive at a principle which turns out to be enormously
powerful as an aid in thinking about how bodies interact. Once we are persuaded we have
established a principle that is valid for all events, we can use it with
confidence to predict what results we shall obtain from experiments we have not
yet performed. [7]
From this you can see that my point of view
about energy is completly orthodox; but I am not sure that it is the view held
by most scientists. It is
certainly not the view held by the general public, particularly when the words
"energy crisis" are on everyone's lips. Energy becomes more than a concept when we think of running
out of fossil fuels.
If you take the scientific view, energy
is always conserved; it can neither be "destroyed nor created" as is
often said. Why are we constantly
being told to conserve energy? The
reason is that some things that we "assign" energy to are more useful
than others as a source of energy.
It is easier to "transfer" energy from oil to a motor car to
accelerate it than to "transfer" energy from air. The energy from oil is more
available. When we lose energy
from our houses to the air we say it is dissipated; it is not concentrated in a
way that keeps our bodies warm.
That is why we insulate our houses: to prevent the transfer. There are different classes of
energy. High class energy, like
that assigned to oil or to the heat in a warm house, is more useful. We call energy that is dissipated by
nuclear power plants into the lake water used to cool them "thermal pollution". The energy is unwanted.
There is no doubt that the concept of
energy is a very good way to describe the changes that are occurring around us
but we must constantly remember its roots as an invention of man; as the PSNS
book says:
Energy itself is a creation of the human mind. Our confidence that we can find a small
number of simple rules for assigning energies so that the sum of all kinds is
constant has established the conservation principle as a basic premise of
science. [8]
Conservation laws are a form that we want and we give
meaning to all kinds of things like work, potential energy, kinetic energy,
energy density, energy flow, and so on to keep our beloved form. And so far we have been
successful. But the thought that
we have a general law of nature is an illusion.
SUMMARY
All the ideas expressed in this chapter are orthodox although perhaps not uniformly held by all scientists.
Copyright © 1983 J.N.P. Hume All rights in this book reserved