What are the theoretical/experimental problems with using negative gravitational energy and positive EM energy of the vacuum to balance one another?
Energy is :
In physics, energy is the quantitative property that must be transferred to an object in order to perform work on, or to heat, the object. Energy is a conserved quantity; the law of conservation of energy states that energy can be converted in form, but not created or destroyed.
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The total energy of a system can be subdivided and classified into potential energy, kinetic energy, or combinations of the two in various ways. Kinetic energy is determined by the movement of an object – or the composite motion of the components of an object – and potential energy reflects the potential of an object to have motion, and generally is a function of the position of an object within a field or may be stored in the field itself.
Note the words "object" and "system. It refers to things that can be described by coordinates (x,y,z,t) . In classical physics energy cannot belong to the vacuum, by definition of the word vacuum, which means no objects or systems in a vacuum.
In the quantum frame the existence of objects at (x,y,z,t) has become probabilistic, the only calculations that can be done give the probability of a system to interact, there is no determinism. This mathematical system has lead to the use the word "vacuum" for the mathematical description of the interactions in a specific way to make it consistent with measurements and observations at the quantum framework.
The model called field theory of quantum mechanics, fills up everything with fields that correspond on the elementary particles in the table of the model. electron fields neutrino fields etc , and creation and annihilation operators on these fields generate the interactions given in the mathematical integrals of the theory, which are depicted by Feynman diagrams.
The fields have a vacuum expectation value (VEV)of zero, except for the Higgs field which has one at 246 GeV. This will be true for all interactions, whether electromagnetic or gravitational.
It means that no electron positron pairs can be created from vacuum due to the conservation of energy. The pair production loops have to be connected to real four vectors entering the interaction so that real particles may appear.
The often misused vacuum loops are higher order corrections in the integrals that give particle interaction and decays. Without input energy and momentum, the VEV is zero.
A combination of electromagnetic and gravitational forms is even more forbidden by conservation of energy. The standard model of physics, which fits existing data and is very predictive, cannot be fitted using your hypothesis and the present tools.
There do exist off the main stream proposals to give a value to the VEV, but this site is not the place to discuss them. To propose such a model as you do, needs a lot of mathematical justifications and effort not to destroy existing verified models.