The Meaning of Acceleration
We have no problem believing that a moving vehicle or vessel is stationary until it starts accelerating (gaining or losing speed, changing direction). Then we realize that we have been moving all the time, literally transported by our vehicle.
At that moment of acceleration we are as it were thrown back on earth with the velocity of the vehicle. Tragic cases of passengers flying through the windshield are the sad but perfect example.
The event is understandable if we consider that we were moving relative to earth, and that the change in velocity of the vehicle could not be passed on to us immediately. That is why cars and planes, however smooth their engines, experience vibrations of their different parts which are adjusting to the new speed one (group) after the other.
What would happen in "absolute" empty space? Would acceleration have the same consequences on objects or persons being transported at high velocities by a space ship? But that would mean that they then should be considered as also moving relative to space! That would breathe new life in the ether's concept.
Maybe the concept of inertia is enough to dispel such a possibility. A passenger would keep moving forward when the ship decelerates until his body catches up with the new speed. The speed of information, in this case, the change of velocity, can never be instantaneous, can it?
Let us take another example.
We have two points attached to each other and they are therefore, after an initial jerk whereby the first one pulls the second point along, moving at the same speed.
About that initial jerking movement. Why did that happen again? Inertia, right. In empty space? How are we supposed to understand that? When applied to objects on earth we are dealing with gravity and friction, both absent or at least negligible, or so the the theory goes, away from everything. The object would have to create its own resistance, because of its mass. It should therefore be more difficult to change the direction of a massive object than of a puny one. Just like on Earth. Of course a massive object creates its own gravitational field and would attract/pull the "pusher" instead of just reacting to the push.
That sounds like a good explanation to me. The passenger on the spaceship is subject to gravitational forces created by the motion of the ship. When the ship accelerates, the change is not instantaneous, and therefore the passenger, just like anybody on a train or a car, keeps moving forward until stopped by another object.
The passenger is therefore moving relative to the ship, and not relative to a hypothetical ether.
But what if the vessel and the passenger have the same mass? Something like an escape pod for one. If the passenger still moves forward when the pod decelerates, what would that mean?
Let us go back to the points attached to each other, maybe that will make the problem easier to analyze.
Let us say the Siamese points approach a denser medium in such a way that one point is hindered by the medium while the one above it is not. We can even imagine that it is one and the same object which collides with the medium halfway. Like wanting to jump a wall and not quite making it. In this case the speed of information would seem to be irrelevant. The lower part, unable to follow immediately the upper part would make it over the wall with a delay because it has to climb over it first.
That still does not solve our problem. A wall is a compact obstacle, while acceleration is much more elusive. Assuming that one part of the body is moving faster than the other part is exactly what we wish to explain. Why does that happen? Why does not the whole object stop instead of tumbling about its axis? 
We can equate deceleration with colliding with a more or less elastic object. The distinction we make about the vessel and the passenger is an anthropomorphic bias. As far as Physics are concerned, the passenger is a bundle of atoms just like the vessel. Since not all atoms are as strongly anchored to each other, they will react differently to a collision or acceleration.
That must be it. Except that it would change the way we look at acceleration on Earth, if that were true. 
Stragglers are always moving in the previous direction the forward atoms were moving in.
That, apparently, does not prevent trains from derailing. Or maybe that is why they can be derailed. I would assume that if the locomotive can take the curve, the rest would follow with no problem, unless they are made of lesser material, or the information does not reach them on time. [I am using the term information because it is verbally convenient. I certainly wouldn't want to suggest that we need Shannon to explain to us why trains get derailed. In fact, I would think it is the other way around. Understanding what makes trains derail would help us understand information theory better.]
This brings us to a seemingly different question, even if still closely related to our subject.
Why is there a limit to the speed an object can have in changing direction? Again, inertia. Good, we have given a name to the problem, now all we need to do is solve it.
Doesn't that mean by the way that particles in a linear accelerator would go much faster than the same kind of particles in a circular one? Imagine such a linear accelerator of infinite length. What could then stop the particles from going faster than c when they are already approaching c in an accelerator with a radius of just a few kilometers? Let us put this point aside for the moment.
Back to the previous question, the one leading to derailment. It is easier to take a large turn than a sharp one. Why is that? Why can't a speeding car take a 90º turn without tumbling about? We have seen that in a cyclotron higher speeds mean larger orbits. Talking about energy wouldn't be much help, we would just exchange one mystery for the other.
Let us play a computer game. A very simple one I'm afraid. I remember one of the first "apps" I had ever programmed myself. It consisted in a simple pixel moving in a horizontal line on my monochromatic 12" screen, on a very modern pc running at 4,7 MHz. Making the pixel suddenly change direction, let us say move vertically, would not have been very difficult. In fact, as far as the computer was concerned, it would take as many cycles to execute any of the (group of) instructions. Nature apparently does not work that way. She needs more "cycles" to have an object moving in a straight line, and suddenly change direction. She also needs more juice to do that.
Why? I know, science only cares about the how, or at least that's what everybody wants us to believe. In fact, scientists usually have already answered the why for themselves and therefore do not think that it is still relevant to the discussion. So, I will ask again. Why? Why should it be more difficult to make a sharp turn at high than at low velocities? It would be very tempting to speak of resistance. But what is doing the resisting? A kind of ether? How would that be a solution? We would still have to answer the same question: why is changing direction so difficult?
A particle has to move from one position to the other, followed by all other particles being part of the same atom. Instead of a train, we have a merry-go-round we want to move from one place to the other, without stopping it from rotating first. Certainly no easy matter, but why should it be more difficult to move it in one direction than the other? I have no idea, and I do not think our revered scientists have an answer either.
Here is a very speculative answer, just to give you an appetite. Imagine each particle, however small, is carried by a piece of the ether. Except, this ether of mine is not like a medium, everywhere present, but only there where there is matter. So, we have simply transfered the difficulty to this ether. It's his fault that particles do not want to change direction without a fight! Let's banish this ether once and for all! He is stealing our bread and seducing our women! Death to the ether! 
But whom shall we blame after he is gone? No, I don't want the ether back. I am just saying that it is not that simple. 
What about space? We could blame space, couldn't we? Hang space! I always knew he was a no good! Cut his ugly head!
Oh, I give up. You guys are so unreasonable. There is no talking to you.
Okay, one last time. Space curvature explains why a body would fall prey to gravity, but it would not explain why changing direction in the absence of massive objects should be an issue. What do you mean, maybe it isn't? Do you mean what I think you mean? That an object, away from any other massive body would have no problem changing abruptly its direction, even at very high speed?
That would certainly solve our problem. But how would that work?
When an object is moving in a straight line, according to Newton, no force is necessary to keep it moving, only to change its velocity. But that is where the troubles start. If the only force present is the one needed for a change of direction, then it shouldn't be any problem. So, maybe any object in the vicinity of other objects is subject to all kind of forces that sum up to an inertial field. Yes! That's it. It's gotta be it! In empty space there is no inertial field, therefore an object, or at least a particle, would be able to make a 90º or even a volte-face or turn-about, go in the opposite direction without stopping first. Just like my ancient computer pixel!
But is that true? How would I know? I have never been in outer space where no massive objects are present. I do not think such a place, if it even exists, has ever been observed by Hubble or any other human-made device.
The practical use of such a knowledge, if it can be called that, is highly questionable. Still, if it is true then it is an important piece of information.
For one, the fact that relative motion does not depend on another reference frame. To go back to our first example of an accelerating vehicle, the passenger does not keep moving forward because he is moving relative to earth, but relative to his vehicle. It keeps the idea intact that motions in a frame are physically neutral when considered from another frame. The passenger crashing to the windshield notwithstanding. He is leaving one reference frame and entering, rather brutally, another. Just like jumping from a moving train or sailing ship.
For two, spaceships away from massive stars should be more easily handled even at high speeds. But that's for later generations to worry about.
For three... I'll have to get back to you on that one. I think I'm going to take a nap first.

George: you do that, old man.
me: who you calling old? You can remember the Neanderthals!
George (sigh): it still feels like yesterday! But then, looking at you, nothing much has changed!
me: humph! And I know now what I wanted to say.
You: for three? For real?
me:  yes, for three. And of course for real. Oh wait. I forgot again.
George: ha!

It's because it is so difficult to remember the Nothing. If there is no ether, and no space, one direction is as good as another, and there is no reason for an object, except for the conditions it creates by its own presence, not to be able to change direction at any moment, and at any angle. These auto-generated conditions could put a serious limitation on the maneuverability of objects in empty space, but I will leave that to the experts to investigate further.