# On Einstein inertial systems - Can you tell if you go upwards or downwards in a vertically "shot" elevator?

if we look at an elevator which is shot into the air - it is clear to me that e.g. two particles don't stay where they are (relative to one another) since the gravitational force points towards the earths center (and thus the two particles aren't accelerated parallel). They will close up and also move upwards (in the elevator).

I was wondering if it would be noticable for somebody in this elevator (without windows) if the elevator is still going upwards or has already changed direction (as an obeserver on earth would explain).

Clearly it must not be noticable, since the view of the elevator as an einstein inertial system doesn't consinder speeds at all (or it just makes no difference). I have tried to explain it better but I just can't do it. Can anyone state a more precise explanation for this?

So the main question is: As seen from inside the elevator: does it make a difference if the elevator is (relative to the ground) moving upwards or if it is already falling towards earth again - e.g. if you somehow can notice the velocity (relative to earth) of something inside the elevator or if this velocity cannot be noticed.

• Can we ignore air resistance in this thought experiment? That is, after the initial acceleration of the shot, the elevator is moving perfectly ballistically, with no other acceleration apart from the acceleration due to Earth's gravity? Mar 10, 2021 at 13:36
• Yes I thank that is how I mean it :) Mar 10, 2021 at 16:57
• Search about parabolic flight. Wikipedia is not in English for this, the German is this de.wikipedia.org/wiki/Parabelflug Mar 11, 2021 at 5:20
• Danke für den Hinweis! :) Thanks for the advice! :) Mar 11, 2021 at 8:55

I'm not sure if I've interpreted your question correctly, but you seem to be talking about tidal forces, which are ruled out when considering the equivalence principle by the requirement of locality. See the wiki for a longer discussion here.

In short, in a freely falling laboratory, tidal forces (the variations in strength and direction of a gravitational field) are assumed to be negligible. Therefore you're correct that these forces shouldn't be noticeable, so long as we're only performing local measurements/experiments.

• I think I meant it another way. I am unsure about wether someone inside the elevator could (somehow) tell if the elevator is moving away from the sun or towards it (regarding a velocity $v$ relative to the ground which is (firstly) positive, then negative. Or is that what you tried to explain to me? Maybe I got your answer wrong... Mar 10, 2021 at 17:43
• @manuel459 No, you wouldn't be able to tell whether you were moving up towards the Sun or down towards the Earth. You'd feel weightless. If you released two particles, they'd just float there in front of you. Because of tidal effects, the 2 particles would move very slightly towards each other, but it would be hard to tell because the angle between them to the Earth's centre is so tiny. Similarly, a spherical soap bubble would be slightly distorted into an egg-shaped ellipsoid (but its volume wouldn't change). Mar 10, 2021 at 17:58

the main question is: As seen from inside the elevator: does it make a difference if the elevator is (relative to the ground) moving upwards or if it is already falling towards earth again - e.g. if you somehow can notice the velocity (relative to earth) of something inside the elevator or if this velocity cannot be noticed.

Elevator is moving upwards: tidal forces are decreasing, situation inside the elevator is becoming more like vacuum of space far from all masses.

Elevator is moving downwards: tidal forces are increasing, situation inside the elevator is becoming less like vacuum of space far from all masses.

This is Einstein's equivalence principle: gravity is indisguishable from acceleration. Hence a body in free-fall is equivalent to a body being in a gravity free area.

Now, once you throw a ball into the air, even though it is going upwards initially, it is still in free fall as no force apart from gravity is acting on it. Eventually of course the ball will reach it's maximum height and then start to drop, amd then it actually looks like it is in free fall.

The same goes for your elevator. It makes no difference that initially it is "shot up" so long as there is no other force acting upon it (apart from gravity of course).