The Non-Conservation of Energy

1. Mechanics

The historical development of physics started with natural philosophy. In present day terminology, this became the field of mechanics. Since mechanics is concerned with the motion of natural objects, Newton's laws of motion form the basis of the study.

Aside from the laws of momentum and inertia which are encompassed in the work of Galileo, Newton's third law is concerned with work and energy. From this law evolved the concept that energy could neither be created nor destroyed. This immediately raises the question: How did it get there in the first place?

The concept demands that energy is additive. Energy can be added to an object which in turn can transfer energy to another object only in such a way that the total is conserved. Again, we raise the question: What is the source of the energy which was added in the first place?

We are forced to take a closer look at the three laws of motion. The first law is due to Galileo. It is: An object in motion tends to remain in motion in a straight line at constant velocity in the absence of external influences. Also, an object at rest remains at rest. This appears innocuous but assumes that motion and rest and linearity can be defined. These supposed facts are assumed without proof.

The second law is a quantitative law generally expressed in the form

This law defines force as a time rate of change of momentum of an object under the influences of the applied force. Thus, it defines cause by the effect. The source of the force is not defined and no reaction on the source is considered.

Newton's third law involves action and reaction. It is written

The interpretation is: In the interaction of two objects, forces of action and reaction are equal in magnitude and oppositely directed.

In the case of contact forces, we have the work integral

The zero result indicates that no energy was gained or lost by the system considered as a unit. Then we write

where the second integral is rendered positive by the fact that equation (1.2), F₂₁ must be the negative of F₁₂. In terms of work we have

In this case we find that the work done by object 1 on object 2 is exactly equal to the work done by object 2 on object 1. The conclusion is that no net amount of energy was transferred in either direction.

We find: In the absence of impact heating and radiation loss, the energy of an object is not changed by the action of contact forces. The analysis indicates the necessity of an internal reservoir of energy that can be invoked in the case of an object accelerated from rest by the action of a contact force. The kinetic energy of motion can be imposed only at the expense of a reduction in the internal energy in such a way as to conserve the total.

The second law can be true only in case there exists a source of energy in a field to be released to augment a mass particle. If the field energy is

we write

and

The equality of (1.7) and (1.8) is then

If we use the integrating factor M, we have

In this case the increased mass is given by

where C₀ represents the uncontracted velocity of light. Then we find the second law of motion applies only to the action of a particle accelerator in which field energy is released to augment the energy of the accelerated particle.

2. Quantum Theory

The basic energy law of quantum theory is

where h is Planck's Constant and f is frequency. This implies a radiation element, but in the event that matter is formed from radiation we may write

as applied to the positron and to the electron as the primary particles of matter.

The implication is that there exists in the electron or positron at rest an internal circulation velocity equal to that of the uncontracted velocity of light. Then we may write

where r is the radius of the unit. As opposed to Newtonian mechanics in which volumes and masses are constant, let us suppose a radius contracted by the factor N. Then (2.3) becomes

The energy of a single unit in the contracted state is

and the energy of N such units forming a single group is

The neutron (1) consists of 930 electrons and 930 positrons with a mass defect of 20 electron mass units and a measured mass of 1840 electron mass units. Neglecting the mass defect, the neutron energy is given by

where M_n is the neutron mass. It follows that the simple mass-energy relation does not apply to the neutron or the proton or to mass in any aggregate.

3. Electromagnetic Theory

The energy of electrical charge depends on the square of the charge. The charge energy of the electron or positron is then

in the electromagnetic system of units. The energy of N equal charges isolated from each other is then

If the charges are closely associated in a single group, there exists a mutual energy between them. In EMU, this is

where r is the radius of the group. If the self energy of N isolated charges is added as given by (3.2), we find

Then we have

to agree with (2.7). The form (3.3) is applied to the calculation of the stability of an atomic nucleus. Considering the difference between (3.2) and (3.5) we may ask: What is the source of the energy excess?

4. Toroidal Matter

The electron is a toroid with a volume given by

If the charge is in motion around the ring, the magnetic field is

where e is the charge and f is the frequency. The total energy is then

The use of (2.3) then gives

to repeat (3.1)

By analogy, the neutron volume has the form (4.1) if the

neutron radius is assumed. The magnetic field is given by

since the reversal of charge is compensated by the reversal of current flow. Then we have

to agree with (3.5). The excess of energy over that given by (3.2) is confirmed but not explained. We conclude that the law of energy conservation never did apply to electromagnetic theory.

5. Electron Clusters

The experimental study of electron clusters is almost entirely due to the work of Kenneth Shoulders (2). The cluster is toroidal in nature with a volume given by (4.1). For stability, the equation

must apply. The magnetic field is

and v is given by

The energy equation is

where the radius is given by

The use of (5.3) and the value of H derived from equation (5.2) yields

so that the radius of the cluster is directly proportional to the number of electrons in the group. To appear in the visible range, an order of magnitude of 10¹³ electrons per cluster is required.

The output energy is given by

by the use of (5.6). If we use the input ballistic energy

we find the ratio of output to input to be

Claims of excess energy have been given in the past. There exists a "Free Energy" cult which plans to tap into the source of excess energy. Various names such as vacuum energy have been

applied. Let it be stated once and for all time that most of these efforts are a matter of wishful thinking. Even so, the present article establishes the fact that existing laws of energy conservation are not valid. No claim is made that the source of excess energy is revealed. Kenneth Shoulders himself claims that excess energy appears but attributes it to induced nuclear decay.

References

(1) The Energy of Physical Creation, Copyright 1985, by Robert L. Carroll: 94 pages, Hard Cover

(2) Kenneth Shoulders, P.O. Box 243, Bodega, CA, 94922

ABSTRACT

It is shown that Newton's second law is valid only as applied to a particle in which a collapsing field releases energy that goes into a mass increase. The third law applies to mechanics but requires that contact forces are conservative. The kinetic energy is increased at the expense of the internal energy.

Analysis indicates that energies are not additive in quantum theory or in electromagnetic theory. Toroidal matter is introduced and a study of electron clusters is made. The decay energy of the cluster is shown to be in excess of the ballistic energy of formation. This fact is in accord with reported experimental results. The implication is that contraction energy is involved. No explanation of the sources of the added energy is attempted.