If I have an accelerometer at rest on Earth, and another placed inside a rocket which is accelerating, we will find that the observer in the rest frame and the one in the rocket both agree that the rocket shows acceleration on the accelerometer, while the Earth accelerometer does not. This is what would happen in real life: acceleration is an absolute event, and this solves the Twin Paradox for me.
I have seen the answers here: Difference between relative acceleration and absolute acceleration? but I don't understand why we conclude that the Earth observer is in fact the inertial frame, as if this a "privileged" frame of reference. What medium "preferentially" considers the Earth frame inertial while the other rocket frame non-inertial? Because in the rocket frame, we see the Earth as the accelerating object.
Yes acceleration is not relative as an "event," but when considering frames of reference as purely mathematical coordinate transformations, we could see either the Earth or the rocket as non-inertial depending on who we consider at "rest," so acceleration is mathematically "relative." I know we cannot consider the rocket to be at rest - it is always non-inertial, but the question is why? What "medium" is it accelerating through?
Theoretically speaking, why is acceleration absolute? More importantly, what medium does acceleration occur in if it is absolute, and what is its mathematical description?
