The Brace Principle

Keywords

Founded in Mechanics

If we stretch a real spring; we need some way of keeping it stretched. The spring might be lying on the work bench and we might stretch it between two clamps. In the ideal world of classical mechanics, the workbench and the clamps remain perfectly rigid. However in the real world, the clamps and the workbench bend a little. The act of stretching the spring and hooking it to the clamps not only stores energy in the spring, but it also stores a small amount of energy in the workbench and the clamps. We can formalise this in the Brace Principle.

It is impossible to store energy in a single component. The component must always be hooked to one or more other components which act as a brace. Energy will also be stored in the brace.

Dielectric stress

The point to be made is that when we store energy in a dielectric medium, we generate internal electric forces which would crush the medium if it were not a rigid structure. The storing of electrical energy in the dielectric has to be braced against the mechanical strength of its crystal structure. It is impossible to store electrical energy without also storing mechanical energy in the crystal structure which acts as a brace.

Combing forces

We expected to store an amount of energy equal to 0.5 x 100 x 1 = 50 Joules, but the extension is only 0.999 m and the force only 99.9 N, so that we only store 49.90005 Joules in the first spring.

We also distort the frame 1 mm thus storing 0.5 x 99.9 x 0.001 = 0.04995 Joules of energy in the frame.

When the second spring is attached, the frame distorts by another 1 mm and we end up with each spring exerting a force of 99.8 N, so that the energy stored in them is now 2 x 0.5 x 99.8 x 0.998 = 99.6004 Joules. The energy stored in the frame has increased to 1.996 Joules. These calculations are not absolutely accurate because we have ignored the fact that the amount the frame distorts is affected by the reduced force of the springs, but the effect is very small.

If we round the numbers to 4 figures to make it easier to think about them, we see that the important thing to notice is that the frame being a thousand times stiffer than the springs stores only one thousandth of the amount of energy as the spring. We thought we we going to store 50 joules but we only succeeded in storing 49.95 Joules. That is 49.9 in the spring and 0.05 in the frame. We have not had to store the other 0.05 J. When a second spring is added, the amount of energy stored in the frame increases by a factor of 4 and so does the shortfall.

This amount of energy which we have saved is available to generate other effects which depend on the exact nature of the system.

A system can be described in which the brace is provided by a pair of parallel rails. When two springs are stretched and hooked between the rails near to one another, the distortion they impart to the brace results in the applied forces no longer being perfectly perpendicular to the rails. This gives a very small component of force acting along the rails between the hooks.

We can can formulate the full Brace Principle.

The Brace Principle

1. It is impossible to store energy in a single component. The component must always be hooked to one or more other components which act as a brace. Energy will also be stored in the brace.
   
2. When energy is stored in a single component hooked to a brace, the energy stored in the component and in the brace are in inverse proportion to the relative stiffness of the component and the brace..
3. When a number of components are hooked between the the same points of a brace, the energy stored in the brace is proportional to the square of the number of components hooked to it.
4. When energy is stored in a component, we can identify with each hook point a region in which the brace is distorted. Where the hook points of two components are within each others distortion regions they experience a force between the the hook points. This force is small compared with the forces exerted on the brace. In the special condition where the forces exerted upon the brace by the components are parallel we can determine the forces between the hook points, by considering the changes in total energy stored in the components and the brace, caused by small movements in the hook points.
5. The force exerted on component B by component A is proportional to the product of the two forces exerted by the components on the brace times the rate of change of the distortion caused by spring A at the locus of spring B, with respect to the distance from A.

Gravity

In the absence of a physical media, an electric field still has energy stored in it. That energy density field must create an internal tension in the fabric of space. The electric field must be braced against the fabric of space. Space itself acts as the brace and energy must be stored in it.

I had one advantage over Einstein, he did not know about quarks and for him, just over half the mass of Newton's apple and over half the mass of the earth was composed of neutrons which possessed no charge. I now knew that the apple and the earth were composed entirely of charged particles.

Matter is composed of charged particles, namely electrons, up quarks and down quarks. An atom consists of one or more electrons orbiting a nucleus composed of protons and neutrons. Protons and neutrons each consist of 3 quarks. When we say that an atom has mass, we are referring to a property which is proportional to the total energy content of the electric and magnetic fields of its electrons and quarks. The energy content of these energy density fields has to be braced against the fabric of space. This does not occur in three dimensional space but in a fourth non extended dimension which is perpendicular to each of the three dimensions of space. Space is distorted in this fourth dimension giving it a property of slope-y-ness. The tendency to slide down this slope-y-ness is experienced as gravity.

Gravitational mass and inertial mass are not quite the same thing! Consider the pure charge model of a hydrogen atom. Its gravitational mass comes from the total energy content of the electric fields of its electron and three quarks. It is the potentials of these charges which add together, ignoring their signs, to give the total energy hooked to the fabric of space. The inertial mass comes from the generation of magnetic fields of motion around the charge generated by its velocity. When we consider the whole atom, we have to take into account the fact that the magnetic intensities caused by the motion of their electric fields adds together. In regions where the combined magnetic intensity is not dominated by a single charge, it will be less than the sum of the magnitudes of the individual magnetic intensities. This means that the kinetic energy stored in the fields of motion of the component charges of an atom will be less than it would be if the component charges were separate. This effect is similar to the classical explanation of the reduced mass of the atom in which the electric fields combine to give a reduced energy content.

What we find is that inertial mass corresponds to the reduced mass predicted by classical physics, but gravitational mass remains equal to the sum of the individual masses. This should be totally and absolutely impossible to test experimentally!