Books and publications on the
interaction of systems in real time by A. C. Sturt
b. Definition of force
d. Possible interactions
4.Uniform motion in a circle
f. Definition of force
h. Possible interactions
4.Uniform motion in a circle
j. Definition of force
l. Possible interactions
4.Uniform motion in a circle
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 m1 and m2 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
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 Q1 and Q2 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 K0 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 mv2/r. By analogy with the basic equation for force, v2/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, rω2 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
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 current-carrying 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
no force, no mass, no
newton of force defined at low accelerations and velocities
extension of definitions to electric charges and magnetic poles
electric charges movable
but interactions possible
gravity all pervasive
Faraday – medium of space under strain
forces inside the atom
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
Copyright A. C. Sturt 27 September 2001