How to distinguish force from accelerating frame of reference?

Question

So in this question Is this the reason why acceleration is said absolute?, author asks is his reasoning about absolute acceleration right, and he concludes that we can measure absolute acceleration of the ball because of the fact that the ball begins to deviate from the y-axis, but now my question is, what is the reason that we conclude that this deviation is not caused by some other force? Is this the fact that before there were only two forces?

Answer 1

In order to be indistinguishable from an accelerating reference frame, a force should give the same acceleration to all matter. Gravity does that. Electromagnetism and all other forces do not.

Answer 2

Newton's III law assumes our forces always come in pair in our physics world in an inertial frame - for every observed force, there must be another opposite force.

So in your example of "a ball begins to deviate from the y-axis", something else will be acted by an reaction force, hence being deviated or accelerating as well, if you are in an inertial frame.

However, "forces in pair" is not necessary at all in an accelerating frame. There can be "one force" in an accelerating frame.

Answer 3

In classical mechanics, the observations made by a traveler inside a uniformly accelerating rocket in outer space are almost identical to those made by a traveler in that same rocket, hovering permanently one metre about the ground of planet Earth (say), as long as the traveler does not look out of the window. The results of most experiments inside such a rocket are the same in the two cases. Suppose our traveler releases an apple. In both cases they observe it to "fall" to the ground of their rocket, accelerating as it falls. But we, looking in, might choose to say that in the first case the apple did not accelerate at all, but floated freely, while the floor of the rocket accelerated towards it. So who is right? This illustrates the sense in which, even in classical physics, acceleration can, in some respects, be a relative not an absolute concept. That is, we can assert that there is relative acceleration between apple and floor, but we cannot easily say which item was 'really' accelerating and which was not.

There are two ways to restore a sense of absoluteness about acceleration. The first way is to imagine a rocket or cabin located far from all other things. We say that the cabin provides a local inertial frame of reference as long as things released inside the cabin, and experiencing no force from anything inside the cabin, move at constant velocity relative to the cabin. Now you can define acceleration absolutely as that sort of motion which is not constant-velocity relative to such an inertial frame (and it does not matter which inertial frame you pick).

The second way to get some absolute acceleration is to look at relative acceleration between nearby trajectories. Ultimately in G.R. this leads to a way to determine spacetime curvature, which is an absolute not relative concept. In my rocket example, there are detectable differences between the two cases, such as whether apples released from all points have parallel trajectories. Earth being spherical, in the rocket hovering above Earth two apples dropped from the same height but separated horizontally will move together a little as they fall. This is called a tidal effect.