Surely a true time lord deserves a more exotic name than Dave.
Thanks, QuarkHead. Maybe they will give me a proper timelord name when they recognize my contributions on Galifrey. Maybe something like, Tim.
I'm still thinking about whether Osiak relativity predicts a backwards-time transmitter can be built. I think I have a way to approach the issue, at least, and tentatively, it seems like there's not a good reason to think an antenna that focuses waves at a distant point at a future time would also focus waves at a point in the past. Also, I believe it's an engineering problem that current antenna design techniques can be applied to, to possibly prove that Osiak relativity isn't actually paradoxical. I will try to explain how these techniques can be modified to incorporate Osiak relativity, and so definitively answer the question.
At the same time, a benefit of there being a simple experimental test of whether Osiak relativity is true, or not, is that it becomes rather beside the point whether it's paradoxical or not (unless the objective is to get paid to debate the issue ad infinitum). Even if it can be proven one way or the other whether Osiak relativity is paradoxical, it's arguably better for both the yay and nay sayers that the test should be done before spending a lot of effort trying to settle the paradoxy issue.
It's notable that when we see positrons being influenced in an understandable way by an electron current in a cloud chamber, we are seeing the influence of a constant magnetic field set up by steady-state currents in the electromagnet windings. So, not a transmitter antenna and also a process that behaves very predictably under time inversion. It's basic electrodynamics that magnetic fields sign-invert under time inversion. That's the only difference for a steady current.
More generally, in electrodynamics there are closed-form solutions to the inhomogenous electromagnetic wave equation for arbitrary motion of a point charge. These are so-called Green's functions and make it possible to determine the field distributions for an arbitrary time-dependent current, which could represent (say) the current distribution in a wire antenna, by linear superposition of these solutions. Engineers will pretty invariably represent such a time-dependent current distribution based on its Fourier transform representation, which is representing it in terms of its sinusoidal components at all frequencies and including relative phases between them.
It turns out there are two Green's function solutions to the EM wave equation, in traditional (i.e. non-Osiak) electrodynamics for a point charge undergoing oscillatory motion at a fixed frequency, that are called the retarded, and the advanced wave solutions. The retarded waves are representing radiation of energy away from the field-source charge, and make construction of a radio transmitter possible. The term "retarded" is describing the propagation delay that occurs in radio transmission, where a charge oscillating in the transmitter antenna causes a field disturbance that propagates toward the receiver and arrives at a time later in accordance with the speed of radio transmission, which is equal the speed of light. On the other hand, the advanced wave solutions describe what is happening at the receiver where the retarded wave causes motion of the charges in a receiving antenna. They describe spherical waves converging on a point charge in the receiving antenna. So, the retarded and advanced wave solutions together are needed to describe radio communication.
There is a famous physics paper by Wheeler and Feynman from 1945, "Absorption as the mechanism of radiation," that argues the process of absorption of an EM wave by an absorbing medium involves a back reaction on the field-source charge by advanced waves reradiated by the absorber charges. They were able to derive the formula for radiation damping from this assumption. What's interesting about radiation damping is that it's needed to explain the back force on a charge when it's accelerated, that accounts for the work that the field may do on other charges, but isn't obviously inherent in Maxwell-Lorentz electrodynamics. They showed that the advanced waves, arriving simultaneously with the accelerating force but phase-delayed by pi/2 radians, could account for the radiation reaction force which is not otherwise explainable in classical electrodynamics. (It can also be derived from energy conservation expectations, but this arguably constitutes putting it in "by hand.") The philosopher Huw Price wrote a book (in the aughts, I think), Times Arrow and Archimedes Point, that related a lot of this stuff, including Wheeler-Feynman Absorber theory and quantum nonlocality, to the direction of time. I think he was really on to something, but that it takes Osiak relativity to make it all work.
As I have already mentioned, Osiak relativity allows that an EM field may carry temporal momentum (which is identifiable with energy in Einstein relativity, as ensconced in the energy-momentum four-vector in Einstein relativity, but not so in Osiak relativity) from the present to the past. Letting the temporal momentum become negative implies the existence of imaginary EM fields and charges. However, the inhomgenous EM wave equation solutions for the imaginary fields are the same as for the real fields, except for the imaginary constant. So there are advanced and retarded imaginary EM fields just like there are advanced and retarded real EM fields, and from symmetry considerations it's clear that a time-forward advanced wave has to appear to a time-reversed observer as a retarded wave, and vice versa for time-forward retarded waves. So, this provides the procedure to determine if a time-reversed field from a transmitting antenna can focus coherently on a receiving antenna in the past. I guess probably it can't, but the process of doing the calculation might have some surprises.
Sorry if this is vague and unclear, I just didn't want people to think I really believe time-reversed communication is likely or trivial. It's a rabbit hole to pursue it seriously right now, though. We should just do the test, and let the chips fall where they may.