After showing mathematically that the energy equation is in error, there needs to be an explanation of what the error means. This page explains some of that.

What is the Definition of Energy.

Energy takes many forms. The first to be identified was kinetic energy. It is somewhat of a reference for defining energy, because it is tangible and easy to conceptualize.

Energy has been misdefined in that the formula for kinetic energy is incorrect as shown mathematically on other pages. On this page, the logic is described apart from the mathematics.

The formula is KE = ½mv². It indicates that the energy of motion is in proportion to mass times velocity squared. Squaring the velocity is the problem, because no mass can move at velocity squared. As a result, the formula is an abstraction apart from the motion of the mass. explanation

A similar contradiction in logic shows up in the force-distance form of the analysis. Supposedly, kinetic energy is proportional to force times distance for an accelerating mass. However, the force does not move through any distance relative to the mass it acts upon. Distance relates to the starting point, which the force does not act upon.

As indicated elsewhere (including collision analysis) transformations of kinetic energy need to be analyzed relative to the point where the energy acts (impact points), while force times distance creates a reference frame relative to the starting point. Errors result from the incorrect reference frame.

Kinetic energy should be represented as mv, which is called momentum. It is proportional to force times time for an accelerating mass.

This material is reduced to simple logic not to be pedantic but to show how the logic changes as the concepts are corrected. It also allows some original analyses to be derived from the logic.

Original Concepts.

The original basis for defining kinetic energy in terms of mv² was that momentum is supposedly not a conserved quantity. Later, momentum was considered to be conserved. So the historical basis for the definition of energy contradicts modern concepts.

It also contradicts the logic of Newton's laws which indicate that the force-time combination must be conserved through all interactions, because otherwise forces would not be equal and opposite. Force times time produces a defined amount of mv, not ½mv².

Shortly before Newton's time (1642-1727), Rene Descartes (1596-1650) drew the conclusion that there is a fixed amount of momentum in the universe, because it is conserved during interactions (momentum being mass times velocity, mv). From his studies of collisions, he concluded that changes in motion are produced by force, and force is quantitated in proportion to momentum divided by time (F = mv/t).

Newton then extended the concept stating three important laws. They are:

1. Force equals mass times acceleration.

2. For every force, there must be an equal and opposite force.

3. An object at rest stays at rest, or an object in motion maintains its motion unless a force acts upon it. (Which is inertia.)

At around that time, Leibniz (Gottfried Wilhelm von -) published a paper (in 1686) claiming to prove that momentum is not the conserved quantity of motion—mv² is. Eventually, Leibniz's view became the concept of kinetic energy in spite of contradictions with Newton's laws.

The issue was how to relate force to motion in order to get a quantity which is conserved. While force creates motion, one additional factor must be known to quantitate the results. One must know how long the force acts upon the mass. There are two alternatives for completing the quantitation. One alternative is to measure the time that the force acts; and the other is to measure the distance that the mass moves while the force is acting upon it. To multiply the force times time yields the resulting momentum (Ft = mv). To multiply the force times the distance yields the resulting ½mv² (Fs = ½mv²).

Eventually, the conclusion was drawn that both quantities are conserved, even though Leibniz directly stated that his analysis does not conserve momentum. During elastic collisions, both mv and ½mv² are conserved. But during inelastic collisions, both cannot be conserved simultaneously. The applications of energy function by the dynamics of inelastic collisions, because the force moves with the mass it is acting upon.

Some persons claimed that the disagreements were nothing but semantics. But in fact, the issue is not semantics, because energy is used in discrete quantities as fuel. Fuel will only produce a definable amount of mv, not ½mv².

For example, the rate at which energy is added to a system (energy divided by time) is called power. With mv divided by time, power becomes force only (mv/t = F). With ½mv² divided by time, power becomes force times velocity (½mv²/t = Fv).

The Relativeness of Power.

Power thereby varies with velocity. But velocity is a relative concept. Everything has an infinite number of velocities simultaneously depending upon reference points. For example, a spacecraft might be moving at ten thousand miles per hour relative to the earth, and twenty thousand miles per hour relative to a comet. Therefore, if energy as ½mv² were being added through a rocket engine, the rate of energy addition would be twice as much relative to the comet as to the earth. But the fuel going through the engine would have the same rate relative to the earth as to the comet. The rate of fuel use must correlate with the rate of energy acquired by the mass, because energy is supposed to be a definable, discrete quantity which is conserved through transformations.

When kinetic energy is defined as momentum, and power becomes the equivalent of force, the force is the same relative to all reference points; so the rate of energy addition to the mass correlates with the rate of fuel use.

Conceptualize the Error.

Kinetic energy is the energy of motion. Therefore it must be in proportion to motion, and more motion must mean more energy. Squaring the velocity destroys that set of relationships.

Squaring velocity creates a nonlinear increase in energy, while distance increases linearly. This results in a inconsistent set of relationships.

To visualize this, consider one meter of distance. At the beginning, start a mass accelerating. At the end of one meter, so much energy was added. Now move the starting point back ten meters. As the mass accelerates through the previous distance, there is much more energy added than the first time. It depends upon where the starting point is.