The main problem with Minkowski space is related to your "spooky action at a distance". Evidently, Minkowski didn't buy into quantum entanglement either (and his student was having difficulties with it also). That is why it was Minkowski who probably related that "we are living in a world of events".
It is true that we are living in a world of events. Some of those events are simultaneous, relative to a frame that is at rest, but by and large, simultaneity would make little difference to objects and events surrounding us. We don't care because even if simultaneity changes when things start to move, they don't change very much at the rate most motion on this planet proceeds. The trains will still run on time no matter how fast we drive or walk to the train station. Except for those pesky Euclidean solids that are material objects (like trains). These were near and dear to Minkowski. In fact, all of his quasi-Euclidean geometry was based on them. Why is this a problem for relativity?
Because Minkowski thought that there is no equivalent to the speed of light in a solid. Solids were treated as though infinitely rigid; as though when you push on the front part of a block of iron, or pull on the back part of it, the whole block moves SIMUTANEOUSLY. He didn't really believe that E=mc^2, I suppose.
Think of an infinitely rigid solid bar of iron or better yet, a braided iron rope (something you can tug on) that is sufficiently long for relativity to play a part in what the whole object does when you tug on the front or the back of it, say a light hour in length, or about three times the distance from the Earth to the Sun; 270 million miles. And you have a laser you can turn on right next to it that you can use to signal someone on the other end that you have just tugged on it. Which gets to the other end faster, the beam of light, or the pull on the braided iron rope? If relativity is to be believed (and it is more solid than Euclidean geometry ever was), the signal from the laser gets to the far end of the rope a considerable amount of time before the tug on the rope is felt. This would probably be true because the speed of sound in an iron rope is about 5130 meters per second, a far cry from 186,000 meters per second which is the speed of light.
But breaking the sound barrier in air is a trick that is done by military fighter jets all the time. In 1920s era physics, before the sound barrier in air at high altitude was actually broken, this was believed to be impossible, USING THE SAME SORT OF REASONING THAT MINKOWSKI USED TO COME UP WITH HIS IDEA OF 4D INTERVALS. It is in part because of the spectacular failure of the calculations that prohibited the sound barrier from being broken that some people believe that relativity physics is in error when it predicts that neither matter nor energy can exceed the speed of light, or the "light barrier". These people are wrong. The speed of light is a much harder limit than anything like a sound barrier. There will never be warp engine powered starships like Enterprise that will be able to break that barrier. The transporter (matter teleportation by means of quantum entanglement) may be a different matter, but it is a fact that the Enterprise, in the process of beaming someone to a planet's surface, would be blown halfway across the galaxy if the process did not cause the energy of each atom transported to stop and instead of continuing to bombarding a planet as a beam of a 200 kg chunk of matter converted completely to energy (widest possible dispersion). I suppose they could solve the problem by beaming an equal mass into empty space in the opposite direction, but Newton's third law evidently still works for the Enterprise, or else it wouldn't be able to actually go anywhere, other than somewhere else no man has seen before, and come back to tell anyone about it. Star Trek physics is a pinch of science along with a planet sized mass of fantasy, as one might expect.
Nevertheless, there is something definitely wrong with Minkowski's conception of solid objects as having dimensions that are the same as "events", but it's difficult to figure out exactly what that is until you add the element of entanglement. The energy in the vacuum is entangled everywhere.
A block of iron is a sculpture that is comprised of iron atoms. Each one of those atoms is a combination of electric, electroweak, and strong nuclear fields, and they form a lattice that is bound by entangled electrons. Yes, ENTANGLED electrons are a part of the mix of what we consider to be solid matter. The electrons, quarks, W and Z bosons, and their antiparticles (about 2% of the total mass of each atom, in actual fact) all derive their inertial mass from the Higgs mechanism, something that derives from the energy of the vacuum. The part of atomic mass that is NOT serviced by the inertia imparting Higgs mechanism consists of gluon-quark color charge energy exchanges. Also, if one is to believe QCD, getting most of that other 90% of the energy imparted to atomic mass from the vacuum.
It is certainly true that pulling on one end of a 270 million mile braided iron rope is nothing like exploiting the entanglement of the electron gas within the rope to communicate, there is nothing wrong with the idea of breaking the iron braid into two separate conductors and using it to create the first 270 million mile old style telegraph. And the telegraph signal would arrive at the other end at about the same time as the laser.
One would be very surprised, to say the least, if when moving your average chunk of iron, the electrons that move so easily in metallic solids to communicate over long distances just decided that they would remain in the space the iron previously occupied. So part of what it means for something to be solid means that it also contains energy, and not all of that energy is mechanical in nature, nor does it behave as though it were. No matter how quickly you tug on that long braided iron cable, the electrons contained within it are not likely to vacate either end.
There is more to solids than Minkowki's rigid Euclidean mechanical conception. Solids are dynamic structures. That includes many events going on inside of them that are entangled, and they also impart a property to solid objects that is in many respects faster than if that solid object were to break the equivalent of the speed of sound inside of itself. A solid traveling at relativistic speed relative to something else already breaks that particular barrier, and it does not need to deform mechanically in order to do so. But it does appear to contract in the direction it is traveling relative to an observer at rest, along with all of the entangled events it carries along with it.
