# 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. – ACuriousMind Apr 11 '15 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. – user6760 Apr 11 '15 at 14:38
• Quantum mechanically, the force would become an operator like eveything else. See Force in quantum mechanics – ACuriousMind Apr 11 '15 at 14:41
• Possible duplicate of Does Newton's Law of Universal Gravitation work when particles are very close? – sammy gerbil May 4 '18 at 10:23