# I Yet another simultaneity paradox

1. May 26, 2017

### Arkalius

I thought of yet another simultaneity paradox that I find even more confusing:

We're just in space with spaceships. There's a ship moving past us at some relativistic speed. On the front and back of the ship there are thrusters at the top that can be activated by a pulse of laser light striking them. As the ship flies past me, I shine two lasers like in the original scenario at the same time (for me) such that they hit the front and back sensors simultaneously (for me), thus turning on the engines. From my perspective they ignite at the same time, thus the ship should start adding a downward component to its velocity relative to me.

From the ship's perspective, the front should ignite first, then the back. Now, we've established that the orientation can be different in different frames, but here's what I find puzzling. because the ship will spend some time with an unbalanced force at the front, there will be a torque creating angular momentum. Then, the force is balanced when the back fires, eliminating that torque, but the angular momentum remains. Furthermore, due to the rotation, the engines are firing along the same vector as observed from the other frame. The ship should continue to rotate as it accelerates, which would have it move on a completely different trajectory compared to what would be observed in the other frame.

I'm sure there's something I'm missing here, so I hope someone can shed some light on this one.

Last edited by a moderator: May 26, 2017
2. May 27, 2017

### Erland

Why downward? Which direction is downward in space?
As I see it, the effects of the engines should cancel each other out, so the ship will not accelerate, at least relative to you.

3. May 27, 2017

### jbriggs444

As stated, the thrusters are pointed to the side, not fore and aft. We are expected to visualize the craft moving left to right (or right to left) in front of us with the thrusters pointed "up" and the resulting ship velocity pointing "down".

4. May 27, 2017

### Erland

Ok, but then, the argument about torque is valid only if the ship is considered as a rigid body. But there are no truly rigid bodies, and if the ship is so long that relativistic effects are noticeable, then it cannot be considered as rigid.

5. May 27, 2017

### SlowThinker

What I've learned from various threads on rotation at relativistic speeds is that analysing rotation in a frame that is not co-moving with the center of mass, is a waste of your time. Even the most knowledgable people here struggle with it.
My guess is that the ship will start to rotate in your scenario, because that's what happens in the frame where the ship is stationary, but I have no idea how to explain it in "your" frame.
You can have a multizillion thrusters all along the bottom of the ship, fired by an on-board computer so that it looks simultaneous in Arkalius's frame. How do you explain the rear end of the ship bending up, when viewed from our frame? And more importantly, how is this simpler than explaining the ship's rotation?

6. May 27, 2017

### jbriggs444

Torque applies to non-rigid bodies too.

7. May 27, 2017

### Janus

Staff Emeritus
The force of thrusters firing has to propagate through the ship and can not do so at greater than c. So in the frame initially at rest with respect to the ship, the ends begin to move and then points closer to the center begin to move. The ship will bend with the with the maximum deflection being at the midpoint of the ship.
In your frame, the forces can't propagate faster than c relative to you. the trailing thruster will fire and the force will propagate forward. But before this force can get even to the midpoint, the front thruster will fire and its force will propagate backwards. due the way velocities add in relativity, by your perspective, the force moving backwards travels faster with respect to the ship than the force moving forward and even though the force from the trailing thruster started first, they will still meet at the midpoint. The ship bends just like it does in the ship's original rest frame. No torque or rotation will be applied to the ship in either frame. That conclusion only comes from assuming that the entire ship will react to the firing of either thruster instantaneously, which is in of itself a violation of Relativity.

8. May 27, 2017

### jbriggs444

Come again? By your perspective (standing outside the ship), the forces start simultaneously, the resulting waves propagate differently and fail to meet at the midpoint. By a rider's perspective (standing inside the ship), the forces started out of synch, the waves propagate identically and fail to meet at the midpoint.

9. May 27, 2017

### Janus

Staff Emeritus
Sorry, my mistake, I was working from a scenario where the thrusters fired simultaneously in the ship frame.