@layman,
We are not talking about SR. This is basic Newtonian Physics.
1. You
wake up on a very smooth train. You have no idea whether it is moving or not. I am clearly having you wake up because I want to take away your ability to compare your motion to the Earth (which is either moving or not moving... but in this case it doesn't matter).
2. You don't know if the train is moving or not. You also don't know which direction it is moving or not. You are sitting in a direction you call "forward" half of the other passengers are sitting in a direction you call "backwards".
3. You fell an acceleration of 2 m/s/s in the direction you call "backwards" (it is slightly pulling you forward in your seat).
Now there are thee explanations for this.
A. The train was stopped when you woke up, and the acceleration you felt was the train starting to move in the direction you call "backwards".
B. The train was already moving in the direction you call "backwards" when you woke up, and the acceleration you felt was the train going faster.
C. The train was already moving in the direction you call "forwards" when you woke up, and the acceleration you felt was the train going slower (putting on the brakes).
Without comparing himself to the Earth (i.e. by looking out the window),
All experiments will give the same results whether A, B or C is true from the Earth frame of reference. In all three of these possibilities you will measure the exact same acceleration in the same direction. They are scientifically equivalent.
The case I am making is Isaac Newton. Just a heads up to where I am going with this... when you make a philosopical argument about "correct" or "really moving" I am going to ask you if the Earth is moving in this line of argument.