This train example is interesting too. I'm trying to grasp the key concept here. So when the carriage is at rest then denser air is at the bottom and less denser is on top.
Objects will fall from up to bottom according to pressure layers. Atmosphere is working against objects. Fine. When carriage starts to accelerate then back wall will compress air and locomotive facing wall will decompress it causing horizontal layers of air forming so that I feel weight towards the seat I'am sitting because is more dense there. Good so far?
Basically, yes.
Lets say that the locomotive accelerates 9.8 m/s^2 for the sake of simplicity so we experience the same weight towards the seat than we do towards ground. If we look how pressure layers are stacked they appear to be in 45 degree angle so if something is dropped from the center of the carriage it will eventually drop to back lower corner if we assume carriage to be square shaped. Correct?
Only if the locomotive is accelerating. Not if it was at a constant speed.
So we can say hypothetically that if we could locally engineer a closed body of air that has more dense air on top and less dense at the bottom then objects inside it would fall towards sealing? Hypothetically speaking of course. I'am sure that engineering such conditions is much hard as creating a vacuum where that same object would float relative to the walls.
Ok, let's clarify so we don't get our wires crossed.
You're never going to get less dense at the bottom. Air pressure is dependent on stacking. It's like saying that we can turn a skyscraper upside down and balance it on its spire and all will be fine. It's not.
But what can you say about the nature of this body of stacked air? What is the relation of acceleration to pressure or differences in pressure? In normal atmospheric conditions at sea level we observe lets' say one unit of pressure at sea level and gradual change to lets' say 0.5 units at some height. Now what determines the acceleration? Is it the 0.5 unit difference or absolute values of pressure or what?
Let me make this easier for you. You seem to want to understand it.
Imagine you're in that train carriage with the full front cut off it so when it accelerates, all the air inrushes and fills that carriage. Naturally you feel your hair and face take that wind pressure, plus it pushes you into your seat.
As that carriage accelerates, the air pressure builds up and it can't simply flow because the back of the carriage is closed off.
Because of this, you would find that breathing is hard and also your face is getting air blasted.
That air wants to tear that carriage apart but the carriage is strong and resists it but the inrushing air has to go somewhere, which it does, eventually once it's built up a pressure equal to outside which can only happen once that carriage takes a constant speed.
You still feel the force on your body because of the wind hitting the back and rebounding around the carriage and squeezing back out once you are constant.
Now if you stick the front back onto that carriage and do the very same thing, you find that the air that hits the carriage front is now rebounded off it and around the outside of it....but it also seeps into the carriage yet you don't realise this because it's a pressure seep. It's a pressure build up as the carriage smashes into the air from the back as the air in front pressures the front and starts to compress all that is in the carriage on acceleration. You feel it by being pushed into your seat. You can see it by watching your drink slide towards you.
Your body is a lot more mass so it takes more of the pressure and pushes you back into your seat.
Once that carriage goes a constant speed, everything inside of that carriage equalises and you feel that by being slowly balanced again, yet you are still under a bit more pressure due to the speed.
The thing is, at those speeds it's barely noticeable.
Now imagine the carriage brakes are pulled. Once this happens you feel yourself being pushed forward violently. This is because the air pressure has been unbalanced inside and the air at the front is compressed into the back and rebounded right onto your back which pushes you forward. Once that carriage stops, you get shoved back into your seat again because now the pressure has to even up, meaning it now pushes back against you as it heads to the back to even up.
See what I'm saying?
There's no inertia and no gravity. It's simply atmospheric pressure that is responsible for everything.
For every action there is an equal and opposite reaction. There has to be an action first. An energy before a reaction, always.
If you borrow 10 you pay it back, always.