Experiments cannot determine the correct definition of energy, because elastic force cannot be separated from inelastic force in experimental results. So pure mathematics is needed. By using rockets as a substitute for gravity, simple mathematics shows the proof.

Physicists used a falling object test in an improper manner starting with false assumptions. Here is proof applying simple rocket math to the same test that physicists used proving that they were wrong and momentum (mv) is the real kinetic energy.

Explanation of Concept: Energy is defined as "that which is conserved during transformations." Conserved means totals stay the same when components are re-arranged. So the test for the definition of kinetic energy is to re-arrange the components and see which total stays the same.

Part 1: Kinetic energy is not ½mv²:

A 4kg object dropped 1m (meter) has the same amount of ½mv² as a 1kg object dropped 4m, because force times distance equals ½mv² for an accelerating mass. But a rocket accelerating the masses to those velocities requires twice as much energy as fuel for the large mass as for the small one.

Rocket burn time:
large mass: 1.77177876722800 seconds
small mass: 0.88588938361400 seconds

Therefore, both masses do not have the same energy; the rocket does not transform energy in proportion to ½mv²; ½mv² is not kinetic energy; and a gallon of fuel does not produce a consistent amount of ½mv².

Part 2: Kinetic energy is mv:

A 4kg object dropped for 1s (second) has the same amount of mv (momentum) as a 1kg object dropped for 4s, because force times time equals mv for an accelerating mass. A rocket accelerating the masses to those velocities uses the same amount of energy as fuel for both masses.

Rocket burn time:
large mass: 3.92400000000000 seconds
small mass: 3.92400000000000 seconds

Therefore, both masses have the same amount of energy; the rocket transforms energy in proportion to mv; mv is kinetic energy; and a gallon of fuel produces a consistent amount of mv.

All logic and evidence of energy point to the same conclusion. The logic created the need to derive the mathematical proof.

About ninety percent of physics is corrupted by the error.