gentzen said:
Even classically, we talk about the electromagnetic field instead of saying that a particle here interacts with a particle there. So the question should rather be whether we favor photons over configurations of an electromagnetic field to just keep things local.
I read in "Do We Really Understand Quantum Mechanics?" by Franck Laloë that a version of Bohmian mechanics using field configuration trajectories for the electromagnetic field and particle trajectories for Fermions (with stochastic creation and annihilation events) works actually quite well. One of the main drawbacks of Bohmian mechanics (including this version) is its non-locality, so the answer to the adjusted question about keeping things local could actually be yes, in a certain sense.
This is really important. The point of introducing the field-point of view about interactions is the causality structure of relativistic spacetime, which leads to the fact that space-like separated events cannot be in a cause-effect relation. Opertionally that implies that there's no propagation of causal effects faster than light.
The field-point of view realizes this notion of the relativistic causality structure in the simple way that all interactions are local, i.e., the entire dynamics of a relativsitic (quantum) system is described in terms of local (quantum) fields. There's no notion of point particles on a foundational point of view.
It's easy to understand, why this solves the problem of action-at-a-distance theories as are the paradigm of Newtonian mechanics: For action-at-a-distance models for point particles within relativistic theory it's impossible that the momentum-conservation law may hold, but it should hold since Minkowski space of special relativity assumes the symmetry of the dynamical laws under spatial translations, and the corresponding conserved quantum theory a la Noether is momentum. In a local (Q)FT that's no problem since the fields are themselves dynamical degrees of freedom which carry momentum (as well as energy and angular momentum), and the conservation laws hold locally.
A formal way to see this is the fact that demanding that there's a relativistic Hamiltonian theory of classical point particles leads to the conclusion that this can only be fulfilled for non-interacting point particles.
The particle aspect comes into the game that in local QFT asymptotic free Fock states describe field excitations that behave in some sense like free relativistic particles. Particularly when preparing a single-particle asymptotic free Fock state it can be detected only once in a local interaction with a detector, leaving a "point-like trace" (think, e.g., in terms of a pixel detector, where a single electron always leaves one and only one spot). What's really observable according to QFT are space-time dependent probabilities for detecting "a particle" in this sense, and these probabilities are usually given in terms of expectation values of correlation functions that describe some kind of local density or a current density.
Photons are particularly special. They have no non-relativistic limit. Among other things that's due to the fact that as massless spin-1 particles one cannot construct a position observable from the representation theory of the Poincare group, i.e., photons cannot in any way be completely localized. That's easy to understand in the field picture: If you want to enclose the electromagnetic field within a region of space time all you can do is to create a cavity which is in as good an approximation as possible an ideal conductor, such that all em. radiation is reflected on the walls without energy loss. Then you learn in kindergarden that the corresponding eigenmodes of the electromagnetic field describe fields that are spread out over the entire volume of the cavity. There's no better way you can "localize" the em. field.
For massive particles you have at least a position operator, but even then if you try to localize particles, this you can do also only by somehow "confining them" in a "cavity" like a Penning trap for charged particles. The better you try to localize the particle in such a way the stronger em. fields you must impose, and at some point the involved energy transfers between these fields and the particle are so large that you rather create new particles (in accordance with the conservation laws) like in electron-positron pair creation, and it's impossible to distinguish the original particle from these other particles, particularly if you create particles of the same kind as this one. So even for massive particles, the localizability is constrained even more than within non-relativistic QM, where you also have the Heisenberg uncertainty relation between position and momentum (which you also have in relativistic QFT since the space-translation group is a subgroup of the space-time-symmetry group in both cases, and position operators are defined as obeying the usual commutation relations with the momentum operators, which generate spatial translations).
The problem with de Broglie-Bohm reinterpretations of the quantum formalism indeed is its non-local nature, which is at odds with the very foundations of local relativistic QFTs although there are some attempts in the literature that try do remedy this difficulty.
In my opinion, there's no need for such reinterpretations, because the probabilistic interpretation of the quantum state in the sense of the minimal statistical interpretation (Einstein, Ballentine,...) describes all observations very well, avoiding any confusing, unnecessary philosophical ballast which is just introduce to prevent people to admit that the classical, deterministic worldview suggested by our experience with macroscopic objects, simply is not the way Nature can be adequately described on a fundamental level. It's rather an emergent phenomenon, which is pretty well understood in terms of quantum many-body theory.
