I Galilean relativity for 2 frames

[jbriggs444]

@jbriggs444 So everything I said is correct ? Right ? Just to be sure.

It was too verbose. I was left wondering what the point was. The part about something moving backward, but not really but yes, moving backward relative to the train frame was very off-putting. Here is that passage:

to me(observer in the train), while ball is dropping, it moves backward, but not in real sense, because while ball is in the air(dropping), train still accelerates, so it moves with increased speed, but ball in the air doesn't feel this increased speed.

There is no such thing as a "real sense". All motion is relative. There is no need to waffle. Pick a frame and describe the ball's motion in that frame. Don't handwave about other frames that you could have used but did not.

Do you mind explaining what you mean here ?

Your conclusion was that:

So Landau’s argument that in all inertial frames, equation of motion of the same system takes the same form seems to be correct if my analysis is correct.

But a conclusion about inertial frames has nothing to do with reasoning that involves accelerating frames. So your talk about accelerating frames was irrelevant.

Reasoning that only addresses the $x$ component of position is one dimensional. You only reasoned about one dimension. So your reasoning was restricted to one dimensional inertial frames of reference that may be in relative motion in that single dimension.

You've dealt with the case of a single object in force-free motion as described in two different one dimensional inertial frames and reasoned that the same force law (no force) applies in both frames.

That is a weak basis on which to conclude that the principle of [Galilean] relativity holds good for all physical force laws and does so in three dimensions.

 

[gionole]

There is no such thing as a "real sense". All motion is relative. There is no need to waffle. Pick a frame and describe the ball's motion in that frame

Ok then we say in train’s frame, ball moves backward and that’s it. Correct ? Hope everything else is correct too ?

That is a weak basis on which to conclude that the principle of [Galilean] relativity holds good for all physical force laws and does so in three

True, but I had to start somewhere and learn. But it holds true for even 3 dimensions and multiple particles right ? I mean Landaus argument

 

[A.T.]

Ok then we say in train’s frame, ball moves backward and that’s it. Correct

We describe the motion of the ball in a frame quantitatively.

In inertial frames that quantitative description matches all 3 of Newton's Laws of Motion.

In non-inertial frames it doesn't. But we can introduce inertial-forces, which violate Newton's 3rd Law, but allow us to match Newton's Laws 1 & 2.