# Force of gravity at quantum level is indetermined?

Newton's law of Universal Gravitation states that any two bodies in the universe attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

$$F = \frac{GmM}{R^2}$$

$F$ is the force of gravity.

$m$ is the light mass.

$M$ is the heavy mass.

$R$ is the distance.

$G$ is a gravitational constant = 6.67384 $\times$ 10-11 m3 kg-1 s-2.

From the above mentioned equation the force of gravity $F$ becomes stronger if any of the mass increases, since nerds love to treat elementary particles (they have mass) as point-like if we reduce the distance $R$ to $0$ we will get $F = \infty$ (sound weird).

Question

Can't I apply Newton's laws of universal gravitation at quantum level? Or do these particles actually have radius?

• "Can't I apply Newton's laws of universal gravitation at quantum level?" What do you mean by that? You don't "apply the Coulomb law of electrostatic force at quantum level", either. Apr 11, 2015 at 14:33
• @ACuriousMind therefore this is how classical physics becomes weird when applied to point-like particles? I simply want to find the gravitational force between these two elementary particles as they close in on each other. Apr 11, 2015 at 14:38
• Quantum mechanically, the force would become an operator like eveything else. See Force in quantum mechanics Apr 11, 2015 at 14:41
• Possible duplicate of Does Newton's Law of Universal Gravitation work when particles are very close? May 4, 2018 at 10:23