Understanding the relationship between Force, Energy and Fields.

Yet another time, mathematical formulas are correct but their expression and interpretation mislead everyone.
According our previous demonstration potential energy is a specific property of space field and its gradient generates field's force according the conservative law: dp/dt + gradE_field =0.

Forces and Forces learn to tell them apart

However, when an object is constrained by an external force that is not derivative of a field's energy, the general equation of dynamics: dp/dt=F_cons remains applicable.
Note that this kind of external forces, named constraint forces to be told apart, differs from field forces. They don't operate everywhere in space but:

• They only apply on material contact

• They only propagate through material supports, such as ropes or levers

• They influence the free motion of an object in space by providing or by removing kinetic energy not by carrying on potential energy

As shown through the two examples above, superposing constraint forces and fields leads to a more general expression (1) which integration leads to the well known energy conservative law (2).

• dp/dt + gradE_field = F_cons (1)

• ΔE_kinetik + ΔE_field = W_cons (2)

In order to preserve the energy balance the term W_cons has been introduced. It represents the work of a constraint force. It is equal to the constraint force time the distance along which it applies.

The work and the nature of a force

Note first that the notion of work is useless when only fields operate; it is to say that only constraint forces work.
Although mathematically correct, applying a work to a field force is a physical non-sense because field force is itself the derivative of energy. This kind of formalization has really hidden the real nature of a field: a space property that carries energy.

Second, the idea to unify every nature of forces in only one expression is a very bad one. According the point of view that takes into account the energy balance, we can classify them into several natures:

• The field's force which is the derivative of a space field energy (gravity, electric and magnetic forces)

• The constraint force that carries on a work through material contacts (pulling, pushing, rubbing)

• The reaction force that prevents an object to pass through one another or an object to be broken off. These forces are only passive, they can't interfere in no way with energy balance (bearing, retaining)

• The coherence force that keeps the stability of matter up to a certain level of energy. When a threshold of stress is reached, it suddenly frees or captures an amount of energy (weak and strong interactions, chemical links between atoms)

According Synergetics model, each of these natures has a physical meaning:

• The field's force is the derivative of fields' space energy according specific rules for each of the three cases - Gravitation, Electrostatics, Magnetostatics

• The constraint force is a macroscopic force that takes source from a material apparatus: muscles, engines, shocks

• The reaction force comes from the coherence force that holds atom together

• The coherence force corresponds to the wave resonance of energy. A resonant state maintains its energy up to a level where external stress is too strong. Inversely, a resonant state can suddenly occur when surrounding conditions allow it.

Why Physics ignore space medium, read more...