Fig.
98 Electric
and magnetic fields linked by induction.
This is, of course, only
a rough description of the process, which actually
propagates itself in all directions continuously. Later we
shall sketch a better picture.
What particularly
interests us here is the following: We know from mechanics
that the finite velocity of propagation of elastic waves is
due to the delays that occur as a result of the inertia
which comes into play when the forces are transmitted in the
body from point to point. We have formulated this in
equation (36) pb =
pf and with (37) c2
= p
p
we get
b
=c2f. (36a)
Here c2 means
the square of the velocity of the elastic waves, b
the acceleration of the mass particles in the elastic
body
(i.e., the secondorder differential coefficient with
respect to time), and f is the secondorder
differential coefficient with respect to space.
Now, in the
electromagnetic field, the case is nearly the same. The only
difference is that instead of the dependency of the
displacement on space and time in the elastic case we have
two quantities
/ Page 186 /
E and H
depending on space and time. The rate of change of the
electric field E
t
first determines the magnetic field H, and then the
rate of change H of
the latter determines the electric field E at a
t
neighbouring point. The equations (64) contain only
differential quantities of the first order, for instance
E ,
t
a firstorder differential coefficient with respect to time,
and curl H, a first order differential coefficient
with respect to space. One gets an equation similar to (36)
by the following procedure: To begin with, take the
firstorder differential coefficient of equation (64a) with
respect to time. Then we have on the lefthand side the
secondorder differential coefficient of E with
respect to time which is analogous to b in
(36a) and which we will
call bE. On the righthand
side we have a mixed second order differential coefficient
(forming first the difference in space and then in time or
vice versa). One gets the same mixed coefficient
from (64b) by forming the firstorder differential
coefficient with respect to space. Then one sees that the
mixed coefficient is equal to the product of c into
the secondorder differential coefficient in space of E,
which is analogous to f in
(36a) and may therefore be called fe.
Now one can eliminate the mixed coefficient in the equations
and
one gets bE = c2 f E.
(65)
This equation is in complete analogy with (36a) and shows
the existence of electric waves with
velocity c. By the same method one may
derive a corresponding equation for the magnetic
field H(bH=c2fH). If
one of the two partial effects would happen without loss of
time, no propagation of the electric force in the forms of
waves would occur. This helps us to realize the importance
of Maxwell's
displacement current, for it provides just this rate of
change E of the electric
field." t
And so, guided by the good brother Born, and the
intermittent company of Elders. The Alizzed, Scribe, and
shaded glow of those socalled, followed the good
brother to the best of their abilities, through the trick
and treat of the hear, there, and everywhere, of that long
subterranean nights journey into light. Holding within that
minds eye the golden thread of eventual escape.
The page continued to
read.
"We shall now give a
description of the propagation of an electromagnetic
wave which is somewhat nearer to the actual
process. Let two metal spheres have large, opposite, equal
charges + e and  so that a b electric field exists
between them Next let a
/ Page
187 /
spark occur between the
spheres. The charges then neutralize each other; the field
collapses at a great rate of change E
. The figure shows how the magnetic and electric
lines of force then encircle each other alternately
(Fig.
99).
t
In our diagram the magnetic lines of
Fig
99 The
electromagnetic field surrounding a discharge spark between
two spheres. This field expands with velocity c of
light in all directions.
force are drawn only in the median plane between the
spheres, the electric lines of force only in the plane of
the paper, perpendicular to the median plane. The whole
figure is, of course, radially symmetrical about the line
connecting the centre of the spheres. Each successive loop
of the lines of force is weaker than its immediate
predecessor because it lies further outwards and has a
larger circumference. Accordingly, the inner part of a loop
of electric force does not quite counterbalance the outer
part of its predecessor, especially since it enters into
action a little late.
If we pursue the process
along a straight line which is perpendicular to the line
connecting the centers of the spheres, say along the xaxis,
then we see that the electric and magnetic forces are always
perpendicular to this axis; moreover, they are
perpendicular to each other.
/ Page
188 /
FUNDAMENTAL LAWS OF
ELECTRODYNAMICS
"This is true of any
direction of propagation. Thus, the electro
magnetic wave is precisely transversal. Furthermore, it is
polarized,
but we still have the choice of regarding either the
electric or the
magnetic intensity of field as the determining factor of the
vibration.
Thus we have shown that the velocity of the waves is equal
to the
constant c and the waves are
transversal. Further since according
to Weber and Kohlrausch the value of c is equal to
that of the
velocity of light c, Maxwell was able to
conclude that light waves are
nothing other than electromagnetic waves."
The Alizzed had yonder
scribe count in descending order of a kind , the number of
the lines on which dances the following
words "light
waves are nothing other than electromagnetic
waves."
The scribe noted in passing, that if the title of the
Chapter v, counted as line 1 then the phrase
occupied lines
9
and 10
or alternatively
if the heading
be discounted az
iz usually the case Edgar,
then
lines
8
and
9 carry the
crown.
Either way the reference contains
9
lines
And we all know what that means, writ the scribe,
wonderingly wandering.
Page 188 continues
" One of the inferences
which Maxwell drew was soon confirmed experimentally to a
certain extent, for he calculated the velocity of light
c1 for the case of an insulator
(o
= O) and no free charge (p = O).
Maxwell's equations (62c and d) show that
we get nearly the same equations as (64) but with other
cvalues. In (64a) c is to be released by
c
*
and in (64b) by c . The same reasons which
led us to equation (65) show now that the square of the
velocity c 1 2 of the
electromagnetic waves must be equal to the product of
c and c : c 1 2 =
c2 .
u *
u
*u
Many materials are not noticeably magnetizable, so we can
set u = 1, which means that the velocity of light in an
insulator with dielectric constant * is given by c1
= c. This leads to
the value n =
c = / *
/
* c1
for the refractive index.
Thus it should be possible to
determine the refrangibility of light from the dielectric
constant as given by purely electrical measurements. For
some gasesfor example, hydrogen, carbon dioxide, airthis
is actually the case, as was shown by L Boltzmann. For other
substances Maxwell's relation n = / * is not
correct, but in all these cases the refractive index is not
constant but depends on the colour (frequency) of the light.
This shows that dispersion of the light introduces a
disturbing effect. We shall return to this fact
later and deal with it from the point of view of the theory
of electrons. At any rate, it is clear that the slower the
vibrations or the longer the waves of light that is used,
the more closely the dielectric constant as determined
statically, agrees with the square of the refractive index.
Waves of an infinite time of vibration are,
of" /
The nightmare transition of mind realization that out is
in within the womb of the mother.
The scribe recorded the 7 lettered name
Page
189
1 x 8 x 9 =
72 7 +
2 =
9 1+ 8
+ 9 =
18
1 + 8 =
9
"course identical with a
stationary state. Researches into the region of long waves
(lengths of the order of centimeters) have completely
confirmed Maxwell's formula.
Concerning the more
geometrical laws of optics, reflection, refraction, double
refraction, and polarization in crystals and so forth, the
electromagnetic theory of light resolves all the
difficulties that were quite insuperable for the theories of
the elastic ether. In the latter, the greatest obstacle was
the existence of longitudinal waves which appeared when
light crossed theboundary between two media and which could
be removed only by making quite probable hypotheses about
the constitution of the ether. The electromagnetic waves are
always strictly transversal. Thus this difficulty
vanishes.
Maxwell's theory is almost identical formally with the ether
theory of MacCullagh, as we mentioned above (IV,6. P 117);
without repeating the calculations we can take over most of
his deductions.
We cannot here enter
into the later development of electrodynamics. The bond
between light and electromagnetism became ever closer. New
phenomena were continually being discovered which showed
that electric and magnetic fields exerted an influence on
light. Everything proved to be in accordance with Maxwell's
laws, the certainty of which continued to grow.
But the striking proof
of the oneness of optics and electrodynamics was given by
Henrich Hertz (1888) when he showed that the velocity of
propogation of electromagnetic waves was finite and when he
actually produced electromagnetic waves. He made sparks jump
across the gaps between two charged spheres and by this
means generated waves such as are represented by our diagram
(Fig
99
). When they encountered a circular wire with a small gap in
it, they produced in it currents which manifested themselves
by small sparks at the gap. Hertz succeeded in reflecting
these waves and in making them interfere. This enabled him
to measure their wave length. He knew the frequency of the
oscillations and thus could calculate the velocity of the
waves which came out equal to c, that of light.
This directly confirmed Maxwell's hypothesis. Nowadays the
Hertzian waves of wireless stations travel over the earth
without cessation and bear their tribute to the two great
scientists Maxwell and Hertz, one of whom predicted the
existence of electromagnetic waves while the other actually
produced them.
Page
190
1 x
9
x
0 =
9
1 +
9 =
10
10 The
Electromagnetic Ether
From this time on there
was only one ether, which was the carrier of all electric,
magnetic, and optical phenomena."
Either or either, either or neither, writ yon
scribe.
Page
190
"We know its laws,
Maxwell's field equations, but we know little of its
constitution. Of what do the electromagnetic fields
actually consist, and what is it that executes vibrations in
the waves of light ?
We recall that Maxwell
took the concept of displacement as the foundation of his
argument, and we interpreted this visually as meaning that
in the smallest parts or molecules of the ether, just as in
the molecules of matter, an actual displacement and
separation of the electric (or magnetic) fluid occur. So far
as this idea concerns the process of electric polarization
of matter, it is well founded: it is also adopted in the
modern modifications of Maxwell's theory, the theory of
electrons, for numerous experiments have rendered certain
that matter has a molecular structure and that every
molecule carries displaceable charges. But this is by no
means the case for the free ether: here Maxwell's idea of
displacement is purely hypothetical, and its only value is
that it provides a visualizable image for the abstract laws
of the field.
These laws state
that with every change of displacement in time there is
associated an electromagnetic field of force. Can we form a
mechanical picture of this relationship ?
Maxwell himself designed mechanical
models for the constitution of the ether and applied them
with some success. "...Kelvin was particularly
inventive in this direction and strove unceasingly to
comprehend electromagnetic phenomena as actions of concealed
mechanisms and forces."
Good Lord! exclaimed the scribe at all this
activity.
Page 190
"The rotational character
of the relationship between electric currents and magnetic
fields, and its reciprocal character, suggests that we
regard the electric state of the ether as a linear
displacement, the magnetic state as a rotation about an
axis, or conversely. In this way we arrive at ideas that are
related to MacCullagh's ether theory. According to this the
ether was not to generate elastic resistences against
distortions in the ordinary sense, but resistances against
the absolute rotation of its elements of volume. It would
take us too far to count the numerous and sometimes very
fantastic hypotheses that have been put forward about the
constitution of the ether. If
/ Page 191 /
we were to accept them
literally, the ether would be a monstrous mechanism of
invisible cogwheels, gyroscopes, and gears intergripping in
the most complicated fashion, and of all this confused mass
nothing would be observable but a few relatively simple
features which would present themselves as an electronic
field.
There are also less
cumbersome, and in some cases, ingenious theories in which
the ether is a fluid whose rate of flow represents, say, the
electric field, and whose vortices represent the magnetic
field. Bjerknes has sketched a theory in which the electric
charges are imagined as pulsating spheres in the ether
fluid, and he has shown that such spheres exert forces on
one another which exhibit considerable similarity with the
electromagnetic forces.
If we inquire into the meaning and
value of such theories, we must grant them the credit of
having suggested (though rather seldom) new experiments and
of having led to the discovery of new phenomena. More often,
however, elaborate and laborious experimental researches
have been carried out to decide between two ether theories
equally improbable and fantastic. In this way much effort
has been wasted. Even nowadays there are people who regard a
mechanical explanation of the electromagnetic ether as
something demanded by reason. Such theories continue to crop
up, and naturally they became more and more abstruce as the
abundance of facts to be explained grows; hence the
difficulty of the task increases without cessation. Heinrich
Hertz deliberately turned away from all mechanistic
speculations. We give the substance of his own words:
"The interior of all bodies, including the free ether, can,
from an initial state of rest, experience some disturbances
which we call electrical and others which we call magnetic.
We do not know the nature of these changes of state, but
only the phenomena which their presence calls up." This
definite renunciation of a mechanical explanation is of
great importance from the methodical point of view. It opens
up the avenue for the great advances which have been made by
Einstein's researches. The mechanical properties of solid
and fluid bodies are known to us from experience, but this
experience concerns only their behaviour in a crude sense.
Modern molecular researches have shown that these visible,
crude properties are a sort of appearance, an illusion, due
to our clumsy methods of observation,
/ Page
192
1 x 9 x 2 +
18 1
+ 8 =
9
/
whereas the actual
behaviour of the smallest elements of structure, the atoms,
molecules, and electrons follows quite different laws. It is
therefore, naïve to assume that every continuous
medium, like the ether, must behave like the apparently
continuous fluids and solids of the crude world accessible
to us through our coarse senses. Rather, the properties of
the ether must be ascertained by studying the events that
occur in it independent of all other experiences. The result
of these researches may be expressed as follows: The state
of the ether may be described by two directed magnitudes,
which bear the names electric and magnetic
strength of field, E and H, and whose
changes in space and time are connected by Maxwell's
equations. Under certain circumstances such an ether
phenemon produces mechanical, thermal, and chemical actions
in matter that are capable of being observed.
Everything that goes beyond these
assertions is superfluous hypothesis and fancy. It may be
objected that such an abstract view undermines the inventive
power of the investigator, which is stimulated by visual
pictures and analogies, but Hertz's own example contradicts
this opinion, for rarely has a physicist been possessed of
such wonderful ingenuity in experiment, although as a
theorist he recognized only pure abstraction as
valid."
