What I meant was, the origin of the object may have been in a different inertial frame of reference to our solar system, so the 'spin' as far as it is concerned is not spin.
You've got the right general idea, but the principle of relativity only applies to constant velocity motion. If two astronauts float past each other in space, either of them can claim that they're motionless and the other is moving past them. However, if one of them is accelerating or spinning, they'll both agree on who it is.
To add on to this, here's a simple thought experiment to explain why spinning is different from constant velocity:
Imagine you're off somewhere space. You're holding a ball in each hand.
1. You're motionless with reference to the Earth. You let go of the balls. They stay put.
2. You're moving away from the earth with a constant velocity. You let go of the balls. They continue to move at the same velocity as you do: This is indistinguishable from case 1.
3. You're accelerating away from the Earth (using rocket boots). You let go of the balls. They do not continue to accelerate with you.
4. You're motionless with respect to Earth, except that you're spinning. Think of the fastest you've ever spun. You'll be really dizzy when you stop. You let go of the balls. They fly off into space, because in order to stay spinning, they need acceleration toward the center of the spin plane. By letting them go, you stop that acceleration, and their trajectory changes (or really, their trajectory change stops).
Velocity is all relative, but acceleration is not. Spinning is acceleration.
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Here's another example:
You occupy a cosmos consisting only of you and an apple. You accelerate away from the apple for a moment, then stop accelerating. You now have a constant velocity away from the apple, but it's meaningless to say which of you is actually moving. You each perceive the other as moving away at constant velocity.
Now imagine you start spinning. You feel like you're spinning, and visually, you perceive the apple orbiting you at a bizarrely fast rate. From the apple's perspective, you are spinning. These two perceptions are not symmetric.
I’m really interested in understanding this. So please indulge me...
So, I’m Oumuamua rocking my way through interstellar space. I see nothing around me so as far as I know I’m not spinning. Then, all of a sudden I happen upon a solar system that is spinning around me. Who is spinning? Me or the solar system?
Is the point here that I’m spinning with reference to my direction of motion?
Yes. You are aware that you are spinning even without external reference because your outer parts are accelerating toward your inner parts. This is the feeling of spinning in a circle on earth too.
This is how plausible simulated gravity works too. A ship spins. It doesn’t require a reference to know whether it’s spinning.
You seem to know that the rules of physics should hold in any inertial (i.e. non-accelerating) reference frame. But the thing you missed is that a spinning reference frame cannot be inertial. There is centripetal acceleration when something spins.
