Gravitational potential between two massive particles....

[R. E. Nettleton]

If my understanding is correct, all particles are sources of gravitational fields (albeit minor ones), and the gravitational potential energy between two bodies is given by:
U = -GMm/r

So, if we have two Z bosons (or any other bosons with mass but no repulsion due to charge) which are traveling toward one another and pass through the same space, their gravitational potential energies would increase as the distance between them approaches 0 -- and at 0, the value would be infinite. In accordance with E=mc², this would result in an increase of mass, tending to infinity.

However, infinitely massive particles seems implausible. Which part of this is incorrect?

 

[Vanadium 50]

Are you asking "Is the classical gravitational potential at r = 0 infinite?"?

The answer is yes. But it's also true that quantum mechanically you cannot reach a stationary state with r = 0.

 

[R. E. Nettleton]

Are you asking "Is the classical gravitational potential at r = 0 infinite?"?

The answer is yes. But it's also true that quantum mechanically you cannot reach a stationary state with r = 0.

Thanks. Does this increase in gravitational potential lead to a temporary increase in mass?

 

[PeroK]

If my understanding is correct, all particles are sources of gravitational fields (albeit minor ones), and the gravitational potential energy between two bodies is given by:
U = -GMm/r

So, if we have two Z bosons (or any other bosons with mass but no repulsion due to charge) which are traveling toward one another and pass through the same space, their gravitational potential energies would increase as the distance between them approaches 0 -- and at 0, the value would be infinite. In accordance with E=mc², this would result in an increase of mass, tending to infinity.

However, infinitely massive particles seems implausible. Which part of this is incorrect?

The GPE decreases as the particles get closer. In the classical model, this is compensated for by an increase in kinetic energy. The total energy of the system remains constant.

 

[Vanadium 50]

Does this increase in gravitational potential lead to a temporary increase in mass?

Your mixing Newtonian and relativistic mechanics here. The only thing that will make is a mess.