Is there a smallest possible gravitational wave?

[Cato]

An accelerating mass produces gravitational waves. Is there a smallest possible gravitational wave? Is there some quantum energy level lower than which a wave will not be produced? For example, would a slowly accelerated electron produce any gravitational waves at all?

 

[phyzguy]

This is an interesting question that we debated in my GR class. I think that since we don't have a theory of quantum gravity, nobody knows for certain. Presumably gravitational waves come in gravitons, which are quanta of energy = ħω. Then if the mass acceleration is too small to produce a single graviton, a graviton would be produced with some probability less than 1. I'll be interested to hear what others have to say.

 

[Cato]

Thanks for your response, phyzguy. I'm interested in hearing what others might say, too. Possibly we don't know enough to answer definitively?

 

[Hornbein]

An accelerating mass produces gravitational waves. Is there a smallest possible gravitational wave? Is there some quantum energy level lower than which a wave will not be produced? For example, would a slowly accelerated electron produce any gravitational waves at all?

If there is a smallest possible, it is very small indeed. The energy of quanta depend on geometry. It's a relationship between two objects. The further apart two objects are, the smaller the minimum energy. Ten billion light years of wave length? Why not.