It is possible that some of the physicists who can not dispute the validity of the capacitor anomaly may think that this is just another similar case of Zeno's paradox.

Such an attitude can be summarized by the following. "I can't disprove it, but I know it can't be true" kind of line of justification which can not really be a logical thinking. "But if it is true, it is entirely over my head". Hence, the chain of the rational mind stops working entirely.

This kind of similar situation happens when you discuss the religion of Islam with a Muslim. As soon as you get to the point where you have to seriously challenge the authority of the religious leader of Islam, the discussion ends abruptly because you can not go any further unless he/she has to disavow his/her religion.

What is remarkable about the science is that we have the tool known as mathematics that can prove or disprove a line of a statement on a certain quantitative phenomenon without a shadow of doubt.

For a reminder, Zeno's paradox runs like in the following hypothetical problem.

Zeno's Paradox: The Motionless Runner

A runner wants to run a certain distance - let us say 100 meters - in a finite time. But to reach the 100-meter mark, the runner must first reach the 50-meter mark, and to reach that, the runner must first run 25 meters. But to do that, he or she must first run 12.5 meters.

Since space is infinitely divisible, we can repeat these 'requirements' forever. Thus the runner has to reach an infinite number of 'midpoints' in a finite time. This is impossible, so the runner can never reach his goal. In general, anyone who wants to move from one point to another must meet these requirements, and so motion is impossible, and what we perceive as motion is merely an illusion.

Where does the argument break down? Why?

And also, where is the mathematical proof on this?

Now, let's examine the physical nature of the capacitor anomaly. The physical mechanism of the capacitor anomaly can be explained more clearly by the following physical observation(s).

The force lines that define the conventional energy stored in the concentric spherical capacitor are radial which means they are coming out of the center of the concentric spheres. On the other hand, the force lines that define the repulsive self energy is tangential to the sphere's surface.

This means that the force lines from the attractive electrostatic potential energy and the force lines from the repulsive electrostatic potential energy are "**orthogonal**" to each other. This indicates that the two types of the energy can not be mixed together.

The proof of the orthogonality between the two independent vector quantities is an excellent mathematical argument on the separate nature of the two seemingly related yet mysterious vector quantities in physics.

One can draw a spherical Gauss plane in between the two concentric spherical shell to calculated the field in between the shells, but then one can also draw a Gauss plane cut across in half of the inner sphere and there will still be net charges inside the Gauss plane which represents the source inside the Gauss plane. This proves that there IS electric field within the conducting metal which was totally neglected in the conventional theory of Electricity and Magnetism.

Of course, this means that the conventionally known energy (1/2)*Q^2/c in the capacitor does not include the repulsive self energy from each of the spherical shells.

Also, I tend to isolate the discussion of the space energy extraction using the gravitational dipole moment as I discussed in my other papers from that of the capacitor anomaly. However, once you add these two phenomena together, the case of the space energy extraction becomes an indisputable scientific fact, making the law of the local energy conservation a serious scientific misidentification.

I like the expression, **"INDISCRIMINATE, OVER GENERALIZATION"** of a principle obtained from one specific branch of physics (Thermodynamics) to all other more advanced branches of physics (theory of Electricity and Magnetism, General relativity) without serious investigation.