Note the mention of the aether. Then we have the mention of Lorentz and Poincare, there should also be a mention of Riemann. This period, of a major crisis in physics, is popularly called the aether wars. It didn't end an outright victory for Einstein's relativity but as something akin to the situation in Korea.
It did get rather ugly at thee time, and it got uglier still with the rise of the Nazi party in Germany.
People had to make the choice between two relativistic theories. Einstein's theories seemed less bizarre than than an idea of an aether, so were chosen. if the solar system, the galaxy, group of galaxies, are moving through a stationary aether, then this aether has to have strange properties. Light travels through at light speed. it therefore has to be trillions of times denser than steel. yet a flea can walk through it, without any drag.
In its favour, we have a prefered frame of reference, there's no reciprocity. No ladder paradox. Time and space are absolutes, and time is not another spacial dimension at right angles to x,y, and z. (The ladder paradox is, that a ten foot ladder fired at near the speed of light should fit into a six foot barn but the barn also shrinks, so it can't)
So, now let's take a particle, an electron say, and accelerate it up to near the speed of light. Virtual particle pairs should form in its path. One of the pair can find itself on the wrong side of an event horizon. The upshot is that mass is created by this particle becoming "real" rather than "virtual."
It gets stranger yet. We are now making materials which have negative refractive index. In these metamaterials we can do odd stuff, we can stop light, we can have negative light and we can produce phonons; sound particles that travel at near the speed of light.
In short the aether is back in vogue but nobody is going to call it that. it's not stationary, and the idea that it was ever that is something of a straw man. All matter particles have their own "atmosphere" of aether particles, call that zpe or Higgs, suit yourself.
Gravity acts instantaneously, or nearly so. This is so in both Lorentzian an Einsteinian relativity. Let's take a lump of gravitational "space" and a lump of electromagnetic "space" and pop them into a blender. The grav space is informationally the same "size" as the e.m. space, yet it's volume is huge. it's energy appears very small therefore. lend this stuff up and we end up with a viscoelastic material, rather like mayonnaise. But mayo with a difference i.e. it has negative refractive index. you can run across at speed. You can walk though it. Walking through a swimming pool full of mayo is going to be hard work, the mayo finds it hard to get out of your way. With negative mayo however, the particles get out of your way and go round to you back and push.
One thing to stress with that, these would not be reverse time particles, or tachyons, They would simply be phase change particles.