1. quick proof
4. Defining Energy
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.
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.
This is an intuitive concept. Intuitive concepts are just thoughts, but they are the starting point of science, and concrete proofs can be developed, as I showed.
The concept is this: The force in accelerating a mass acts upon the mass. If you push a roller-skate, the force is between your hand and the roller-skate. The force moves with the roller-skate. This is important, because real energy is transferred and transformed through force. It occurs where the force is located. It can only be represented mathematically by representing the actual interaction between force and mass. So there is no change of position between the force and mass. Distance creates a change in position.
As I state elsewhere (including collision analysis), real energy is transformed at impact points, which means where the force acts upon the mass. To add distance to force is to create an unreal situation, because there is no real distance involved. Starting points are unreal. Change in position is unreal. Distance is unreal. To understand this, conceptualize a spacecraft. What is a distance while a force acts? A reference frame is needed for distance, and any reference frame can be picked.
But force times time has a universal and stable reference frame, because time is defined in terms of atomic motion.
Kinetic energy should be represented as mv, which is called momentum. It is proportional to force times time for an accelerating mass.
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.
1. Force equals mass times acceleration.At around that time, Leibniz (Gottfried Wilhelm von -) published a paper (in 1686) claiming to prove that momentum is not the conserved quantity of motionmv² 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, the addition of energy as ½mv² would be twice as much relative to the comet as to the earth.
It is true that a constant powered rocket shows the same total power relative to all reference frames, because it is analyzed relative to the place where the force acts in the combustion chamber. But the contradiction shows up in the external reference frame as shown in the second proof.
If there were some other source of power, such as solar wind, the power would vary with reference frames. It is the separation velocity of the exhaust which holds the power constant for a rocket as reference frames change.