Do we actually feel fictitious forces acting on our bodies? My conclusion is that yes we do, since when I am accelerating upwards in an elevator, I feel a lot of pressure on my knees. I have an example though (that certainly has some logical error in it) that proves the opposite:
A car is moving at constant velocity u=100km/h with a passenger on the back seat. The passenger is sitting on ice so that the friction between the car and passenger is 0. The car crashes on a wall, and stops completely in t=0.1s.
Inertial frame of reference:
An observer outside of the car, sees the passenger moving at constant speed of u=100km/h after the crash, so the net force acting on him continues to be 0. When the passenger eventually hits the wall he stops moving as well.
Non inertial frame of reference:
There is a camera placed on the window of the back seat focusing on the passenger. As the car crashes, the people watching from the camera see the passenger accelerating from 0 to 100km/h relative to the camera. Since there is no other way to explain this, they assume that a force acted on the passenger, causing his acceleration. Since the passenger accelerated 100 km/h in 0.1 seconds we have a great rate of change of momentum, causing an enormous force.
In the inertial frame of reference we expect the passenger to be damaged after hitting the wall.
In the non inertial frame of reference we expect the passenger to be damaged instantly, due to the force acting on him.
The second conclusion can't possibly make any sense, cause if it did I could hurt people by moving next to them very quickly. What's the difference between the fictitious force in an elevator and the one in the crashing car?