What if Coulomb's Law Used Different Constants for Quantum Forces?

[kurious]

If the classical attraction between two coulomb charges was
constant x q1 x q2 / r ^3 or another constant x q1 x q2/ r^4 instead of
k x q1 x q2 / r ^2 (perhaps the constants could still be the
same-though I doubt it)
what would be the force relations on a quantum scale using coupling
constants?
Also what are the force relations if the r terms are on the top line
so force increases with distance?


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[Antonio Lao]

In 1785 memoir to the French Academy of Sciences, Charles Augustine Coulomb (1736-1806) presented his experimental apparatus called the torsion balance.

This device was used by Coulomb to determined that the force of attraction or repulsion of electric charges obeys the inverse square law.

F \propto \frac {1}{r^2}

Later in 1798, Cavendish used a similar arrangement of the torsion balance to measure gravitational attractions of two masses quantifying Newton's (circa 1685) 114 years old law of universal gravitation.

The inverse square law was theoretically formulated by Newton but experimentally verified by Cavendish and earlier applied by Coulomb for electrostatic forces of charge particles.

Because of the uncontestable results of the experiments, it was never felt the need to check for inverse 3rd power or inverse 4th power law of the distance r.

Inverse square law is applied the same way in the quantum domain except when r=0. This is where the force becomes infinite and renormalization technique comes to the rescue.

In particle physics, the strong force seems to be directly proportional to the distance, r.

strong force \propto r

This property of the strong force is partly describe by asymptotic freedom and infrared slavery.

Asymptotic freedom says that the force between the quarks gets weaker as the quarks come closer to each other.

Infrared slavery says that under normal conditions, the quarks can never get far from each other no matter how hard they try to separate by divorcing its partneship.

 

[kurious]

quantum field theory

When r=0 renormalization makes the force finite.
But what is the size of the bare charge at r= 0?
Also if a 1s electron in a proton emits a photon and absorbs it again later it reduces the effective force acting on it.How? what would be the effect if it emits a graviton too? Presumably the feynman diagrams get rather complicated if gravity is included.

 

[Antonio Lao]

I am not knowledgeable in the details of quantum field theory. I don't know the answers to your questions. I'm sorry that I cannot help you further.

I do seem to recall that there is no 1s electron in proton or maybe I misunderstand what you are getting at.