I.3 Natural Analysis of Newton's definition of potential energy

To stipulate conservation of energy, Newton has introduced potential energy as an invisible equivalent of kinetic energy. Although the concept of energy is introduced from the very beginning of physics courses, it remains an non-natural mathematics operator which has been introduced as follow:

In English terms, potential energy corresponds to the work of a force along the path that has brought a material system from a position to another. Conversely, this makes any force at a distance as the gradient of a potential energy.

Although all physicists are fully satisfied with these definitions, Natural Analysis must consider with suspicion this introduction of artificial concepts. Let's refer to a major predicate of Natural Analysis to bring analysis of forces at a distance:
  • Nothing can act at a distance without a natural medium that propagates pressure and information
Pressure is a natural and easy understood concept that any child can intuitively perceive. Pressure is force per surface which work establishes the following relationships:

 It successfully appears a very close definition between potential energy and pressure: potential energy is nothing else than the sum of pressures exerted on a volume.

Energy and Newton law of conservation lose therefore any magic, it is naturally understandable that any material object is pushed toward any area of lesser pressure - no need to introduce the mathematics concept of potential wells.

Natural analysis can therefore shed a new light on forces at a distance like electrostatic or gravitation forces: material objects are not attracted by any miraculous force but just pushed toward areas of lesser pressures from the surrounding medium.

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