The very claim that there are "four fources" is an approximation. We know that the electromagnetic and the weak force have to be unified to an electroweak theory. So counting the electroweak theory as one force, there are just three known elementary forces.

The electroweak theory is based on the $SU(2)\times U(1)$ group which has two factors, but these two factors are not in one-to-one correspondence with the electromagnetism and the weak force, respectively.

The strong force with its $SU(3)$ group is another seemingly independent factors, except that there is evidence that all three non-gravitational forces get unified into a grand unified force of a GUT theory at high energies.

String theory unifies the non-gravitational forces with gravity, too.

Every vacuum of string theory predicts gravity described by GR plus extra non-gravitational forces. The number of factors and their Higgs-like breaking patterns are essentially random properties of the string vacua. According to the anthropic picture of the world, the number of low-energy forces is an accidental property of our world that could be different in different parts of the multiverse.

According to non-anthropic reasoning, the precise selection of our vacuum - including the fact that it has 4 low-energy forces - could be derivable from some more unique theoretical principles. However, this research program remains a wishful thinking as of 2011.

welcome to physics.SE

How are decays related to forces, what is meant by particle X decays through the, say, strong force?

It means that particle X was bound by the strong force to particle Y to form particle Z for a delta(t) and then it parts company.

The way I understand forces is by how they change the acceleration of particles with the right charge (mass, electric etc), through F=ma, how does it cause one particle to turn into other?

Your understanding is about the classical domain of forces.

Elementary particles necessarily belong to the quantum domain, one uses relativistic four vectors to describe them and forces are mediated by other elementary particles, graphically shown with Feynman diagrams, which are a short hand for the way one can calculate the probability of the decay. One can think of the mediating particle as a carrier of delta(p), where p is the four momentum, which transfers momentum and energy to the decay products from the binding energy of the original particle.

From a teacher site here is the Feynman diagram of the decay of a lambda baryon to a proton and a pion, mediated by the weak interaction:

Lambda contains a strange quark which is not stable under weak interactions. For a time the three quarks are bound together by the strong force, with gluon exchanges ( Not shown) but then the s quark decays into an up quark which is bound into a proton, and a W- weak boson off mass shell goes into an anti up and a down quark making a pi- .

How is it determined which force is responsible for which decays?

It has been determined experimentally and theoretically encoded into the Standard Model

Can a particle decay through the gravitational interaction?

We have not found elementary particles or resonances bound by the gravitational interaction so the answer is that experimentally it cannot. The reason is that the gravitational force is many orders of magnitude weaker than the other three forces that reign in the particle domain.

## Best Answer

https://physics.stackexchange.com/a/200/7924 gives a competent and fairly complete answer to your question.

Let me add that locality is implemented automatically into the quantum field concept by the demand that the fields satisfy (weak operator) differential equations, which define the changes at some point in terms of values at the same point. Thus the fields in some region (such as those occupied by a particle = a localized lump of energy) changes with time without ever using information from elsewhere except the region itself an its boundary.

The forces are gradients of the fields and are ''there'' all the time with their right strength. The transmission of energy (perceived colloquially as transmission of forces) happens according to the laws derived from the differential equation. This are hyperbolic for systems with finite propagation speeds. This implies that pulses of energy spead in a wave-like manner to everywwhere where they can have an effect.

The transmission is completely analogous to that of gravitational forces by the gravitational field. Thus you can study the details in a framework much simpler than the standard model.