On the nature of fields
Abstract:
A fundamental analysis of attractive and repulsive fields yields an unexpected result.Analysis:
Let us assume that we have a collection of objects - which all repel each other with increasing force the more closely they are brought together. It is apparent that we have to expend energy to bring these repellent objects closer to each other, and that having done so that we can extract that energy (in the form of kinetic energy) by allowing the objects to freely move away from each other. We may postulate the existence of an 'energy field' around the objects; when we move the objects closer to each other we put energy into that field; we increase the strength of the field. When we allow the objects to repel each other so as to increase the distance between them we extract back from the energy field the energy which was put into it - which weakens the field. A collection of negative electric charges is an example of this sort of behavior. Let us now add to the picture a second type of object which while repelling others of its kind is attracted to the first type of objects more strongly, the closer that it gets to them. Adding a positive electric charge to our previous negative charges is a real world example of such a situation. We now have a somewhat different case than we had before: there are now more ways to affect the energy field: we can force the repulsive charges more closely together - which increases the energy in the field - just as it did before, or we can move attractive objects away from each other. Doing either one requires that we do work and put energy into the field - strengthening the field. If we allow an attractive object to freely approach the repellent objects we extract kinetic energy from the field and we weaken the field. This weakening occurs because we now make the force of repulsion between the repulsive quantities less because it is now partially canceled by the attractive object's ability to attract the otherwise repulsive objects. Certainly, positive and negative electric charges behave in just this fashion; adding a positive charge to a group of negative charges extracts energy from the electric field weakening it. Let us now examine the case of objects which all attract each other. As in the case of an electric field one does work on the attractive objects by attempting to move them away from each other, and one extracts work from them by allowing them to approach each other; drawing energy out of the field between them. A gravitational field is an example of a purely attractive case. However, there is a critical difference between the purely attractive case and the previous cases. When one extracts energy from the field in the purely attractive case the field gets stronger - not weaker! One extracts energy from the field by allowing the objects to move closer to each other; but the closer they get - the more strongly they attract each other, and the more strongly they attract each other the more energy may be extracted from the system. If there were no competing processes, such as the thermodynamic properties of the contracting material, a purely attractive system would run away by collapsing to an infinitely small point; producing an unbounded amount of energy in the process. Let us also notice that when one does work on a purely attractive field; adding energy to it by moving objects away - that the field becomes weaker. The only mathematical way to make sense of such a situation is to consider a purely attractive field such as gravity to be a negative energy field - while cases involving repulsive objects have a positive energy field. R.E. Canup II 4/4/2003