I often hear that gravitational force is much "weaker" than electroweak and strong forces. But how can you compare the strength of interactions without the parameters like mass, charge on which it depends? Surely the gravitational force can be made as (practically) strong as one wants by increasing the mass?
Answer
For forces that can be expressed in terms of a quantum field theory, you can compare the size of the coupling constants (which are dimensionless). In short this means that perturbative expansions of weaker forces are well represented by a small number of leading terms because the series converges quickly, while those of stronger forces require more terms (or in the case of the strong interaction don't converge at all in the naive application).
This spares us the philosophical quandary of comparing dimensional coefficients in force laws.
So far, however, there is no quantum field theory of gravity. But it is possible to work out the scale of the gravitational coupling constant by observing scattering problems for which there is a close analogy in E&M. I suppose that this in effect this means that we are comparing the force-law coefficients written in natural units ($c = \hbar = G = 1$).
No comments:
Post a Comment