My take:
The unifying theory
The famous equations involving Newton’s laws of gravity and the electrostatic force:
F=G*M*m/r^2
F=K*q1*q2/r^2
These two equations look similar. The first works in macroscopic conditions involving masses and the second one works in microscopic quantum states of electrons and charges.
To understand what looks like an incompatibility between these two equations, we need to find the link that is missing.
My guess is inclined to starting from the relationships between sizes of masses decreasing from macro state to the micro state. Gravity is well expressed as the mass of objects increases to the likes of planets and stars. As the masses decrease in size the gravitational attraction between them is almost non existent. The reason is simple. In general relativity, mass tells space time how to curve, while space time tells mass how to move. In the case of quantum particles, what’s direly lacking is mass. So, the way the microscopically invisible tiny quantum particles can curve space time is anyone’s guess; extremely feeble. The quantum state doesn’t follow the rules of general relativity because the particles, especially electrons, can be any where any time in their enormous space in comparison to their sizes. We can confidently say in the quantum state, there’s no mass but energy. The electrons may also move with the speed of light. Since the formula: E=mc^2 works with the speed of light, and electrons have charge, replacing mass, can we use the famous Einstein equation by replacing m by q? Even then, there’s still a dilemma about uniting both states with one formula: My guess is , this can only be done by changing parameters, instead of creating a unifying formula. A good analogy would be when algebraic functions with asymptotic boundaries come to mind.
Can we settle with the disconnect between the two worlds?
To resolve this discrepancy, we can think of a critical mass Mc and M0 where the boundaries of change can be observed.
For m less than Mc, gravity becomes insignificant while for m greater than Mc, gravity starts becoming tangible. For m less than M0, the rules change dramatically.
We can conclude from the above that gravity becomes insignificant when the curvature of space a mass makes is almost non existent.
This means as the masses become infinitesimally small, the degree of freedom is such that the phenomenon changes to include repulsion. This is where electric chargers replace masses and the attractions and repulsions between them replace gravity with an increased degree of freedom.
We can use the above assumptions to formalize the big think. We can derive a unifying formula for gravity by changing the parameters that make these transformations possible.
For m less than Mc, gravity becomes insignificant while for m greater than Mc, gravity starts becoming tangible. For m less than M0, the rules change dramatically.
We can conclude from the above that gravity becomes insignificant when the curvature of space a mass makes is almost non existent.
This means as the masses become infinitesimally small, the degree of freedom is such that the phenomenon changes to include repulsion. This is where electric chargers replace masses and the attractions and repulsions between them replace gravity with an increased degree of freedom.
We can use the above assumptions to formalize the big think. We can derive a unifying formula for gravity by changing the parameters that make these transformations possible.