Field Infinites when distance is zero

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The discussion centers on the behavior of electric and gravitational forces as one approaches a point mass or charge, highlighting the theoretical implications of these forces becoming infinitely strong due to their inverse square nature. It questions the validity of this model, suggesting that forces may actually behave more like a function of 1/(arctan(constant/distance))^2 rather than 1/x^2, positing that finite interactions, such as the emission of gravitons, would limit the force experienced. The breakdown of these forces into weaker interactions at close distances is also noted, challenging traditional high school physics teachings. The conversation seeks clarity on the equations governing these forces and the appropriate distance scales for their application. Ultimately, it raises fundamental questions about the nature of force at quantum levels and the limits of classical physics.
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So in high school we are taught the equation for force from electric fields or gravity is proportional to the distance squared. This implies that this force can become arbitrarily high as you approach closer to the point mass/charge.

In practice I realize that the point mass/charge does not exist, the electric force breaks down to the weak force and gravity may not be a force at all.

I always assumed that the real function is closer to a 1/(arctan(constant/distance)^2, just because that made more sense in my head. Basically if "gravitons" spontaneously come into existence at the point mass heading in a random direction at the speed of light from time to time then one would expect that as you get closer you cannot be hit by more than all of the gravitons and only a finite amount are sent out in a finite amount of time thus there are no infinites.

I have never read anywhere about whether this is true or not. Do we believe that the electric/gravitational force should behave more like 1/arctan^2 or more like 1/x^2.
 
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Why would the force become arbitrarily high? Whats the equation for it and what scale for distance would you use?
 

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