Field Infinites when distance is zero

[meadbert]

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.

 

[granpa]

http://en.wikipedia.org/wiki/Renormalization

 

[meadbert]

Thank you.

 

[Drakkith]

Why would the force become arbitrarily high? Whats the equation for it and what scale for distance would you use?

 

[PJC01]

The concept of field infinites when distance is zero is a common misconception. In reality, the force between two objects is not infinite at zero distance, but rather becomes undefined. This is because the equations for electric and gravitational force rely on the concept of a point mass or point charge, which do not exist in reality.

As you mentioned, at very small distances, the effects of the weak force and other fundamental forces come into play, making the concept of a point mass or charge even less applicable. Therefore, it is not accurate to assume that the force between two objects will behave like 1/x^2 or 1/(arctan(constant/distance)^2).

In the field of physics, we use mathematical models and equations to describe and predict the behavior of objects and forces. These models are constantly being refined and updated as we gain more knowledge and understanding of the physical world. So while it may be helpful to think of the force behaving like 1/(arctan(constant/distance)^2) in your mind, it is important to rely on the established equations and theories in our current understanding of physics.

In summary, the concept of field infinites when distance is zero is not accurate and is based on a simplified model that does not accurately reflect the complexities of reality. As scientists, it is important to continue questioning and refining our understanding of the physical world, but we must also rely on established theories and equations in our current understanding of physics.