Conserved Energy in gravitational paradigms conflates actual time, mimed time and detached time operations.

rreferring page: ... "Actual Time, Detached Time and Controlled Time / Physical Paradigms and Energy Constructions."

Constructions of Conserved Energy (CE) in gravitational paradigms use three distinct kinds of energy: (1) kinetic energy carried by a moving body; (2) work performed in moving a body upward against the force of gravity; and (3) potential energy that is stored in a relationship between the body and a presumed "gravitational field" during such an upward movement.

Kinetic energy occurs in actual time and causes changes in actual movements of colliding bodies; such changes directly depend on the relative speed between bodies. A work process [W = ∫ F × dx] occurs in mimed time; the formulation does not involve time and the speed of movement can change without affecting the result. Potential energy, detached from movement, exists in in a "field" structure described by a mathematical group. Movements in the potential energy structure occur in detached time or mimed time as needed..

Thus, in basic gravitational paradigms, three different kinds of energy appear to be convertible into each other and conversions are presumed to occur perfectly and automatically. E.g., in Atwood's machine (see the Times and Paradigms project, § II.A.1), potential energy is converted into kinetic energy. The sum of energy before a conversion is equal to the sum after the conversion. The sum remains constant during conversions.

Problems with such paradigms are illustrated by the launch of a rocket carrying a satellite into orbit around Earth. Suppose that we reduce an actual launch to a paradigm. Rearward projection of hot expanding gases produces force that lifts the rocket. First, a large force must be produced that is equal to the weight of the rocket and that puts the rocket into dynamical balance. Then "something more" must be produced to accelerate the rocket. There is a considerable period of time between "ignition" and "liftoff" during which forces are insufficient to put the rocket into balance. Energy in fuel burned during this period is not converted into work, potential energy or kinetic energy - but is "dissipated." Similar dissipations are required after liftoff to keep the rocket in dynamical balance. Such dissipations are not "wasted" energy. They are a necessary expenditure, They also require adjustments to a paradigm based on conservation principles.

To minimize dissipation in a rocket liftoff paradigm, it would be necessary at the start to instantaneously apply an upward force equal to the weight of the rocket, plus the "something more" that gets the rocket into actual motion. The amount of that "something more" would depend on the position and velocity of the rocket that is desired when the mission is finally accomplished by release of the satellite. Rates of fuel consumption at every moment during the flight would have to be calculated to find the most efficient trajectory towards that final moment. The entire trajectory must be determined before the first "something more" can be calculated.

Instantaneous application of a very large force is problematical. It would be like a collision, which is often damaging to soft structured bodies such as animal bodies. Bodies without structure — e.g., billiard balls — are said to be homogeneous. Collisions between rigid homogeneous billiard balls can be said to conserve energy and to be elastic. Only special classes composed of particles and rigid homogeneous bodies participate in elastic collisions.

Exact application of a start force is problematical. Physics paradigms treat a starting movement the same as subsequent movements: m × Δv = F × Δt regardless of v. In actual life, v = 0 is special. Additional force must be applied at the start to overcome sticking. A start force begins at a higher level and then quickly drops to a lower level, e.g., we feel a jerk when a train starts.

In sum, conversions of force into kinetic energy or potential energy, e.g., during a satellite launch, always include dissipations that require limitations and adjustments to the paradigm.

Similar problems beset conversions of kinetic energy into work or potential energy, e.g., with gunshot ballistics as an exemplar; and likewise with conversions of potential energy to other kinds of energy, e.g., by dropping a mass from a height or by means of a waterwheel.

Dissipative conversions present problems for a conservation principle. It might be thought that problems could be overcome by constructing a fourth kind of energy called "dissipated energy." E.g., when a bullet is fired into the ground, its kinetic energy is converted into dissipated energy. Then, four kinds of energy would add up to a constant. However, there does not appear to be any way to convert dissipated energy into kinetic energy, work or potential energy. Dissipated energy becomes "waste energy" or whatever is needed to support assertions that a constant is being maintained. To avoid such problems, basic CE paradigms minimize or ignore dissipation.

referring page: ... "Actual Time, Detached Time and Controlled Time / Physical Paradigms and Energy Constructions."

May, 2017

Copyright © 2017 Robert Kovsky