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How is it that particles affect each other—for example, the repulsion of like charges, or attraction of unlike charges?  

How is it that particles affect each other—for example, the repulsion of like charges, or attraction of unlike charges?  

Field theory can incorporate "action at a distance" models by the direct incorporation of an external potential field, e.g. V(x) where x is the distance from a fixed, unmoving charge, and V is the potential energy of the interaction. However, such models are of limited use because x becomes dependent on the motion of the other particle, if the other particle moves; and in addition this method ignores fluctuations of virtual particles expected from [[Heisenberg's Uncertainty Principle]]. Thus, most commonly field theory employs other methods.

Field theory can incorporate "action at a distance" models by the direct incorporation of an external potential field, e.g. V(x) where x is the distance from a fixed, unmoving charge, and V is the potential energy of the interaction. However, such models are of limited use because x becomes dependent on the motion of the other particle, if the other particle moves; and in addition this method ignores fluctuations of virtual particles expected from [[Uncertainty principle|Heisenberg's Uncertainty Principle]]. Thus, most commonly field theory employs other methods.

The forces of nature are mediated by particles called field [[bosons]]. Particles exert forces on each other, which appears to be action at a distance, by passing back and forth between them virtual field bosons, which exchange their momenta.  As an analogy, consider two people on ice skates on an ice rink, playing football. The first throws a football, and the reaction force of the throw pushes him backward. The second catches the football, and the catch pushes her backward. The two ice skaters are now "repelled" and moving away from each other, with the football as mediator of the force. Thus, virtual bosons mediate attractive and repulsive forces.

The forces of nature are mediated by particles called field [[bosons]]. Particles exert forces on each other, which appears to be action at a distance, by passing back and forth between them virtual field bosons, which exchange their momenta.  As an analogy, consider two people on ice skates on an ice rink, playing football. The first throws a football, and the reaction force of the throw pushes him backward. The second catches the football, and the catch pushes her backward. The two ice skaters are now "repelled" and moving away from each other, with the football as mediator of the force. Thus, virtual bosons mediate attractive and repulsive forces.

The weak nuclear force is mediated by particles called W and Z bosons. These are very massive particles, as massive as a heavy atomic nucleus.  The W particles are charged (W+ and W-) and Z is uncharged.

The weak nuclear force is mediated by particles called W and Z bosons. These are very massive particles, as massive as a heavy atomic nucleus.  The W particles are charged (W+ and W-) and Z is uncharged.

The electromagnetic and weak forces have been mathematically unified into a single formalism, called [[Electroweak Theory]].<ref>Chris Quigg. ''Gauge Theories of the Strong, Weak, and Electromagnetic Interactions'' Chapter 6; Benjamin/Cummings Co. (1983).</ref> The unification means that photons, W and Z bosons are all considered to be different aspects of a more fundamental doublet of field bosons.  The electroweak theory can describe electromagnetic and weak phenomena with fewer tuneable free parameters—as the single most important goal of physics is to describe all forces with as few free parameters as possible. Electroweak Theory has been extremely successful, and predicted the existence and approximate mass of the Z boson before its observation in experiments.

The electromagnetic and weak forces have been mathematically unified into a single formalism, called Electroweak Theory.<ref>Chris Quigg. ''Gauge Theories of the Strong, Weak, and Electromagnetic Interactions'' Chapter 6; Benjamin/Cummings Co. (1983).</ref> The unification means that photons, W and Z bosons are all considered to be different aspects of a more fundamental doublet of field bosons.  The electroweak theory can describe electromagnetic and weak phenomena with fewer tuneable free parameters—as the single most important goal of physics is to describe all forces with as few free parameters as possible. Electroweak Theory has been extremely successful, and predicted the existence and approximate mass of the Z boson before its observation in experiments.

The strong nuclear force is mediated by particles called gluons. Particles such as quarks are said to have "color charge", which gives them an ability to exchange gluons, in the same way that particles with electrical charge can exchange photons. The theory that describes quarks and gluons is called Quantum Chromodynamics, or QCD.<ref>Chris Quigg. ''Gauge Theories of the Strong, Weak, and Electromagnetic Interactions'' Chapter 8; Benjamin/Cummings Co. (1983).</ref> A major complication in QCD is that the gluons themselves have "color charge", unlike, say, photons which have no electrical charge. This makes QCD calculations extremely difficult.  On the other hand, it has the advantage of eliminating the "screening problem" identified by Landau. Also, the coupling between quarks and gluons (color charge) is, measured in absolute units, much larger than the electrical charges of charged particles like electrons.  

The strong nuclear force is mediated by particles called gluons. Particles such as quarks are said to have "color charge", which gives them an ability to exchange gluons, in the same way that particles with electrical charge can exchange photons. The theory that describes quarks and gluons is called Quantum Chromodynamics, or QCD.<ref>Chris Quigg. ''Gauge Theories of the Strong, Weak, and Electromagnetic Interactions'' Chapter 8; Benjamin/Cummings Co. (1983).</ref> A major complication in QCD is that the gluons themselves have "color charge", unlike, say, photons which have no electrical charge. This makes QCD calculations extremely difficult.  On the other hand, it has the advantage of eliminating the "screening problem" identified by Landau. Also, the coupling between quarks and gluons (color charge) is, measured in absolute units, much larger than the electrical charges of charged particles like electrons.