
Books and publications on the
interaction of systems in real time by A. C. Sturt 


An Electrodynamic Model of Atomic Structure 


by
A. C. Sturt 




2. An alternative
physical model a. Gravity b. Definition of force c. Electrical charges and magnetic poles d. Possible interactions 4.Uniform motion in
a circle 5.Proposed model of
the simplest atom b. Displacement
of the electron 6. Magnitude of
electromagnetic quanta b. Ellipse
in an inclined plane a. Proposed
structure of helium nucleus c. Magnetic
field in the helium atom e. Potential
interaction of helium atoms 9. Atomic structures
from lithium to neon 12. Atomic radii and
chemistry 2. An alternative
physical model e. Gravity f.
Definition of force g. Electrical charges and magnetic poles h. Possible interactions 4.Uniform motion in
a circle 5.Proposed model of
the simplest atom d. Displacement
of the electron 6. Magnitude of
electromagnetic quanta d. Ellipse
in an inclined plane f.
Proposed structure of
helium nucleus h. Magnetic
field in the helium atom j.
Potential interaction
of helium atoms 9. Atomic structures
from lithium to neon 12. Atomic radii and
chemistry 2. An alternative
physical model i.
Gravity j.
Definition of force k. Electrical charges and magnetic poles l.
Possible interactions 4.Uniform motion in
a circle 5.Proposed model of
the simplest atom f.
Displacement of the
electron 6. Magnitude of
electromagnetic quanta f.
Ellipse in an inclined
plane k. Proposed
structure of helium nucleus m. Magnetic
field in the helium atom o. Potential
interaction of helium atoms 9. Atomic structures
from lithium to neon 12. Atomic radii and
chemistry 

3. The Equivalence of Forces
It was Newton who first defined quantitatively the forces
which underpin the units used today. Brought up to date, the line of
reasoning starting with his and others’ observations on gravity, was as
follows.

Objects fell to earth, and at an accelerating rate,
because there was a force pulling them down, the force of gravity. 
Objects of the same weight but different bulk
densities, such as cannonballs and feathers, fell side by side at the same
rate in vacuo. They must be separately pulled down by forces of the same
magnitude. 
For this to happen they must have in common some
inherent property on which gravity acted to produce acceleration. This
property he called mass. 
Cannon balls of different weights, and so different
masses, also fell at the same rate. 
The forces on them must be different, and so force
must be proportional to mass to produce the same acceleration i.e. twice the
mass, twice the force. 
The Earth also had mass, because this was the
origin of the force which caused the objects to fall. 
The mass of the Earth was subject to the same law
as the objects which were falling i.e. the force of attraction which the
Earth exerted was also proportional to its mass. 
The objects attracted the Earth with the same force
as the Earth attracted the objects, by the law of action and reaction. 
The force between them was therefore proportional
to the product of the two masses, which is (the mass of the Earth) x (the
mass of the object). 
The mass of the Earth or any other object could be
considered as acting at a point called the centre of gravity. 
The force between two masses was proportional to
the inverse of the square of the distance between their centres of gravity.
This was subsequently verified by experiment. 
The force between two objects was not affected by
other masses, or by the gravitational force between other masses i.e. it was
one to one. Thus the gravitational force between two masses could be treated
quite independently of other masses. 
There was no limit to the number or magnitude of
masses towards which an individual mass could exert gravitational attraction. 
There was no distance at which the force of
gravitational attraction ceased to operate. 
The corollary was that every mass in the Universe
exerted gravitational attraction on every other mass. This allowed him to formulate an equation which described
the force between any two masses m_{1} and m_{2}
a distance d apart, wherever located in the Universe i.e. where G is the
Universal Gravitational Constant.
The argument then broadened even further to a definition
of force in the abstract. No force can operate in the absence of gravity, by
the equation above, but a theoretical situation can be imagined in which its
effect can be ignored. 
The effect of force is to produce acceleration, as
with objects accelerating towards Earth. 
Force is proportional to acceleration i.e. twice
the force, twice the acceleration, and vice versa. 
Since force is also proportional to mass: force =
mass x acceleration from which our definition
of force. The implications of this are: if there is no force, there
is no acceleration; if there is no mass, there is nothing to accelerate; and
if a mass does not accelerate, it is because no resultant force is being
applied. However, the next step is to consider the force of gravity
on a mass at rest. Force is experienced by a mass which is not even moving,
let alone accelerating. Any mass resting on a platform, or anybody sitting on
a chair can testify to that. The answer was to extend the term acceleration
to include the acceleration which a mass would have if it were free to fall.
Bodies which are not moving nevertheless experience a “g” force. The conclusion was that the force of gravity on a mass at
rest was identical to the force on the mass if it were free to fall. In other
words the acceleration produced by a force is independent of the velocity of
the body. In fact the Inertial Field analysis (3) suggests that the
force required to produce unit acceleration increases as a hyperbolic
function of velocity, which is why it is impossible for a mass to reach the
speed of light. Hence the need to introduce a factor R into the Second
Law of Motion, which then becomes F
= mRa
The consequence for units is that the standard unit of
force which causes unit acceleration, the newton, is the force exerted by
unit mass at extremely low accelerations, even down to zero, which is rest mass.
Increasing resistance to acceleration with velocity is not observed in
practice because the effect of R is negligible except at magnitudes of
velocity great enough to be a significant fraction of the speed of light,
which is outside ordinary experience.
The next stage of the argument was to apply the definition
of force to torsion by applying torque to a rod of material by means of known
rest masses running over pulleys. In the form of a torsion balance, torque can
be applied to the measurement of forces of other origins. So, 
An apparatus was constructed in which electrical
charges Q_{1} and Q_{2} repelled each other so
as to produce a torque which was counteracted by weights on pulleys. 
When the weights exactly compensated for the
repulsive forces of the charges, the force of repulsion was calculated from
the known masses of the weights. 
The force of repulsion between the two charges was
found to be in inverse proportion to the square of the distance d
between them. 
The equation for force was therefore: where the constant K_{0} was
required to maintain the dimensions the same on both sides of the equation
i.e. MLT^{2}. The same method was used for magnetic poles. There was the same assumption as with gravity that the
interaction between the charges or poles is one to one. They all act
independently on all other charges. There is no limit to the number of other
charges with which each can interact. Since charges come as units in the form
of electrons, as far as we are aware, charges of different magnitude are the
sum of the unit charges of which they consist. However, unlike gravitational forces, electrical charges
can move on a conductor and concentrate at particular points on its surface.
They can be screened from interaction by enclosing them completely in a
conductor, whereas gravity acts on each individual particle of mass in a
structure, even though it is conveniently referred to as a summation acting
at a centre of gravity. Electrical charges can neutralise each other, and
discharge through space. This says something about the nature of the two phenomena;
there is no gravitational permittivity or permeability. There are no
gravitational conductors; there are no mobile particles of gravity to transfer
the property from one corpuscle to another. The probable conclusion is that
there are no particles of gravity at all, because sooner or later they would
be found to move. Gravity is a kind of tension set up between masses in the
medium of space. The comparison of forces exerted by these phenomena
resulted in a definition of electrical force which included neither
acceleration nor mass, far from the original components of the definition of
force.
There is no doubt that these various forces are equal in
magnitude under the circumstances under which they are compared, which is
essentially static. However, it cannot be assumed that the relationships are
always identical under all circumstances. Since they too are interactions with
the medium of space, charge and pole strength may not be independent of their
velocity through it. Their responses as they approach the speed of light
might be different from what is observed at rest. In support of this caveat
it is noted that it is a fundamental tenet of classical physics that
electrical and magnetic phenomena interact when electrical charges move at
constant velocity as in electric current, or accelerate as in electromagnetic
phenomena. There are two other points to note. First, every process
at every level takes place in the presence of gravity; nothing can be
shielded from it. Thus whatever transmits gravitational attraction may also
influence the spatial transmission of other phenomena. It is worth noting
that Newton himself was in no doubt that there was a medium which transmitted
gravitational attraction (4). Secondly, the medium of space permeates the
interstices between all structures i.e. everything but the entity of
fundamental particles. Any interaction between a phenomenon and the medium of
space will occur at any size of particle or structure. Faraday himself thought the medium in an electric field
was under stress or strain, and essentially different from the same medium
when no field existed. As far as he was concerned, the intervening medium
between electric charges played an essential part in the action. If experiments eventually reveal that there are velocity
effects on forces of electrical origin, it is possible that electric charges
may not be independent of mass with its inertial field effects e.g. in the
electron and the proton. It ought to be possible to confirm whether or not
mass and charge interact by measurements over a range of velocities. In the absence of experimental
evidence the assumption must be that forces of different origin are best
treated as equivalent forces in the conditions under which they were
compared. The reason for this detailed
scrutiny of equivalence of forces is that the forces inside the atom relate
to particles with velocities which are significant with respect to the speed
of light. Velocity through the medium of space may have significant and
differential effects, like that on inertial resistance. 4.
Uniform Motion in a Circle An extension of these arguments
is to consider uniform motion in a circle. Acceleration in a straight line is
given by the equation: force = mass x acceleration If a mass moving along the
straight line at an even rate covers distance dl in time dt, then its
velocity v is and its acceleration a is The term a relates force, which
is expressed in terms of mass, time and distance, to the change in the rate
at which the mass cuts the medium of space. This might be called line
acceleration (not linear, which may have a different connotation); it is the
change in the number of points of the medium of space cut per unit time. To find the force required to
keep mass m moving uniformly in a circle of radius r, the methodology is to
transfer the force by vector calculations from a tangential straight line to
a radial component, which results in the expression for force of mv^{2}/r.
By analogy with the basic equation for force, v^{2}/r is then called
the acceleration. A further geometrical transformation shows that: where ω is the angular
velocity, which is the number of radians covered per second. Again by analogy
with the equation for force, rω^{2} is called the acceleration
in uniform circular motion. However, when “acceleration”
consists of a constant angular velocity in a circle of constant radius, there
is no change with time in the rate at which the mass cuts the medium of
space. The line traversed per second is the number of rotations multiplied by
2πr, the circumference of the circle, neither of which changes. So if v
is the velocity through the medium of space, v = rω and But r is constant, and
dω/dt = 0 because the motion is uniform, and so a = 0. Thus there is no line
acceleration in uniform circular motion. Therefore the equation for circular
motion is not relevant when phenomena depend on changes of the rate at which
the medium of space is cut i.e. line acceleration. In fact the force required
to maintain uniform motion in a circle may be construed as the force required
to prevent any increase in line acceleration. I have proposed that when a mass
is accelerated towards the speed of light, the vibration of bonds causes the
emission of quanta of electromagnetic radiation. The acceleration in question
is line acceleration, because the phenomenon results from interaction with
the medium of space, and therefore depends on change in the rate at which the
length of space is cut. Similarly the analysis suggests
that the emission of radiation from an electron also depends on line acceleration,
when the electron cuts the medium of space at an increasing rate. Thus there
is no reason why an atomic electron moving in a circle at a uniform rate
should give off radiation and lose energy. There is no reason on this count
why it should not go on circling the nucleus indefinitely. The concept of line acceleration
is consistent with Laplace’s Law of magnetic intensity due to a
currentcarrying conductor. It is also compatible with the classical laws of
physics governing emission of electromagnetic radiation by a conductor when
electrons are caused to accelerate back and forth in oscillation. 

Inverse square law
force
no force, no mass, no
acceleration inertial field R newton of force
defined at low accelerations and velocities extension of
definitions to electric charges and magnetic poles dimensional
adjustment electric charges
movable neutralise permittivity but interactions
possible gravity all pervasive Faraday – medium of
space under strain forces inside the
atom classical analysis predicts loss of
energy by atom’s electron as radiation because of acceleration and so model of
circulating electron could not be sustained structure of atom
would collapse classical analysis
wrong new analysis says no
loss of energy because no line
acceleration through medium of space Laplace 
Copyright A. C. Sturt 27 September 2001 

Churinga
Publishing 