Particles vs Fields vs Standard Model

The Standard Model of particle physics describes atomic physics in terms of 

• fermions as matter particles like electrons and protons 
• bosons as force carriers like (massless) photons and gluons.

While matter particles as electrons and protons carrying charge intuitively appear to connect to some reality, the idea of photon as carrier of electromagnetic force is more difficult to grasp. In fact, in all of electromagnetics so well described by Maxwell's equations, photons as carrier of electromagnetic force do not appear. 

In particular the electric force appears as the gradient $\nabla\phi$ of an electric potential $\phi (x,t)$ as a continuous function or field depending on a Euclidean space coordinate $x$ and $t$ a time coordinate. 

Similarly, in Newtonian gravitation, the gravitational force appears as the gradient of a gravitational potential field. There is here no need to worry about a carrier of gravitational force in the form of some hypothetical particle named graviton, which has evaded all form of detection. 

In field theories there is thus no need to introduce particles as force carriers, since forces come out as gradients of fields. 

In particular, the idea of photon as carrier of electric force has no role to serve in electromagnetics described by Maxwell's equations. 

Confronted with this fact, a modern physicist would say that particle theory and field theory in fact are just the same with a particle simply a fluctuation of a field and so to say that the photon is the carrier of electric force makes perfect sense. 

In particular, modern physics insists that both blackbody radiation and the photoelectricity must be understood in terms of a stream of photons as particles of light, and then not in terms of fields even if particle and field is the same. 

Computational BlackBody Radiation offers an alternative Maxwellian field theory, where radiative heat transfer appears as a resonance phenomenon and photoelectricity is a threshold phenomenon, both free of particles.  

In summary, there does not seem to be any real need to view a photon to be a particle carrying electromagnetic force, and so the whole idea of fundamental particles as force carriers may lack sound reason. Yet it is a fundamental part of the Standard Model and so may be a suspect behind the crisis of modern physics witnessed by leading physicists.