The way out to your concerns seems to be given in the conclusions of the paper that I mentioned before (arXiv:1001.2718):
"Paraphrasing the Newton’s law of inertia and the de Broglie hypothesis we assume that elementary free bosonic fields have intrinsic space-time periodicities T_\mu = h / p^\mu[ where h is the Planck constant and p^\mu is the four momentum, that is time curled up with length T=h/E]. These Periodic Boundary Conditions satisfy the variational principle and the theory is in agreement with SR. As much as the Newton’s law doesn’t imply that every point particle goes in a straight line, our assumption does not mean that the physical world should appear to be periodic. According to Special Relativity, these periodicities can vary through interactions (energy exchange) or by changing the reference system. Furthermore the combination of two or more periodic phenomena with irrational ratio of periodicities results in ergodic (nearly chaotic) evolutions. Remarkably, from this assumption of dynamical intrinsic periodicity the usual Quantum Mechanics emerges under many of its different formulations and for several nontrivial phenomena. This could open a new scenario where Special Relativity and Quantum Mechanics are unified in a deterministic field theory. After all, the notion of time is strictly related with the assumption of periodicity: our usual -non compact- time axis is defined by counting the number of cycles of phenomena supposed to be periodic, in particular with reference to the Cs-133 atomic clock. “We must assume, by the principle of sufficient reason”,4 periodicity to define a relativistic clock. Indeed, every elementary field can be regarded as having a relativistic de Broglie internal clock. For massless (electromagnetic or gravitational) fields these periodicities can in principle be infinite whereas in massive fields they are bounded by the inverse of their masses. As in a calendar, the combination of the “ticks” of all these different internal clocks is sufficient to fix uniquely events in time and the usual exter- nal time axis can be dropped. In these relativistic internal clocks “all that happens in a given period is identical with all that happens in an arbitrary period”[Einstein 1910] Thus, in a full relativistic generalization of acoustic fields, every field can be regarded as characterized by dinamical compactified space-time dimensions. Massless fields with low frequency provide long space-time scales whereas non-relativistic massive fields can be regarded as localized inside the Compton length, but with nearly infinite spatial period and microscopic time compactification, i.e. as classical 3D point-like particles."
