Marble on a Wigner-rotated floor In space there is a spaceship. On the floor of the spaceship there is a marble. The underside of the floor is filled with rocket motors. The rocket motors start thrusting simultaneously in the spaceship frame. The marble does not start rolling.
Same viewed from another frame:
In space there is a spaceship. On the floor of the spaceship there is a marble. The underside of the floor is filled with rocket motors. The rocket motors start thrusting non-simultaneously in this frame. The floor becomes tilted. The marble does not start rolling.
The question is: Why does the marble not roll on the tilted floor?
 A: 
The question is: Why does the marble not roll on the tilted floor?

In a sense, it does. It does not roll relative to the floor, but it does accelerate in that direction.
Specifically, let's use units where c=1 and let's say that the rocket motors are oriented in the $y$ direction and that the other frame is boosted in the $x$ direction. So the marble has a worldline of $$r^\mu = \left(t,0,\frac{1}{2}g t^2, 0\right)$$ then the four-velocity and four-acceleration are respectively $$u^\mu=\left(\frac{1}{\sqrt{1-g^2 t^2}},0,\frac{g t}{\sqrt{1-g^2 t^2}},0\right)$$$$a^\mu=\left( \frac{g^2 t}{(1-g^2 t^2)^2},0, \frac{g}{(1-g^2 t^2)^2} ,0 \right)$$Note that since there is a $t^2$ in both the $t$ and $y$ components, the worldline is curved in both of those directions.
Boosting to a frame moving at $v$ in the $x$ direction the marble has a worldline of $$r'^\mu=\left( t', v t',\frac{1}{2}g t'^2(1-v^2),0 \right)$$ the four-velocity and four-acceleration are pretty messy, but if we write them to first order in $v$ and second order in $t'$ we get $$u'^\mu\approx \left( 1+\frac{g^2 t'^2}{2},v+\frac{g^2 t'^2}{2} v, g t',0 \right)$$$$a'^\mu \approx \left( g^2 t', g^2 t' v, g+2g^3 t'^2,0 \right)$$
Note, in particular, that the four-acceleration in the $x$ direction is non-zero. The marble is gaining momentum in that direction in response to the force in that direction due to the floor being tilted. However, that increase in momentum does not correspond to movement relative to the floor. Instead, it is a simple reflection of the fact that the worldline which is curved in $t$ and $y$ in the unprimed frame is curved in $t'$, $x'$, and $y'$ in the primed frame.
