- #1

only1god

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Thanks to anyone who takes time and responds.

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- #1

only1god

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Thanks to anyone who takes time and responds.

- #2

Nugatory

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You can do this using only ordinary high-school physics, no relativity or fancy math needed:Like i said, i know I'm wrong but i can't see where.

Try actually writing down the equations of motion for the rocket and the box assuming a constant force from the motor, then solving for the position relative to some arbitrarily chosen fixed point in space of each as a function of time. Compare the position of the rocket and the floor of the elevator, as this is what the person inside the elevator is observing. Do this for both the free-fall-in-gravity and at-rest-no-gravity case, and you will find that the motion of the rocket relative to the elevator is the same in both cases.

Constant speed relative to what?Another thing, if the rockets goes up to the ceiling at a constant speed

- #3

only1god

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to earthConstant speed relative to what?

- #4

only1god

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I have troubles thinking there would not be any difference, maybe someone can help me doing the math and showing me with it, there's no difference.

- #5

Nugatory

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So we have a rocket moving upwards at constant speed relative to earth, meaning that its engines are producing exactly the right amount of thrust to balance the earth’s gravity (constant speed means zero acceleration by definition, zero acceleration means zero net force by ##F=ma##). That is, of course, exactly the amount of thrust needed to accelerate the rocket at 1g in empty space with no gravity.to earth

So in empty space the thrust from the rocket engine accelerates the rocket towards the ceiling at 1g.

In an elevator freefalling in the earth’s gravitational field the ceiling of the elevator is accelerating towards the rocket, or at least that’s how someone standing on the surface of the Earth watching the elevator accelerating downwards will describe the situation. But someone inside the elevator, freefalling with it and therefore at rest relative it, will interpret the rocket’s motion relative to the elevator as the rocket accelerating towards the ceiling at 1g - just as in the empty space case.

- #6

Dale

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For simplicity, consider the rocket engine to deliver a constant thrust force, ##F## to the constant mass, ##m## vehicle. The rocket starts at rest wrt the box on the floor, ##y=0##, and travels under the constant thrust until it hits the ceiling, ##y=h##. The amount of fuel consumed is determined by the thrust ##F## and the time between when the rocket launches from the floor ##t_0=0## and when it reaches the ceiling ##t_h##.

From the usual SUVAT equations $$s=ut+\frac{1}{2}at^2$$ $$h=0+\frac{1}{2}\frac{F}{m} t_h^2$$ $$t_h=\sqrt{\frac{2hm}{F}}$$

Any questions so far?

- #7

PeterDonis

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An essential thing to do in these types of thought experiments is to carefully specify the exact conditions, as they would be measurable to the observer inside the "box", and to make sure that the conditions arei know I'm wrong but i can't see where.

It is a lot easier to keep track of things if you label them. So let's do that:

Case S: A box floating freely in deep space, far away from all gravitating bodies. A rocket is floating freely in the exact center of the box. Then, at some instant of time ##t = 0## according to the clock carried by the observer at the center of the box, the rocket's engine turns on and it accelerates towards one of the box walls, which we will call wall U. The observer inside the box observes the rocket's acceleration, relative to him at the box's center, to be a constant value ##a##. The distance from the center of the box to wall U is ##d##, so the time required, by the observer's clock, for the rocket to reach wall U is ##sqrt(2 d / a)##.

Case E: A box freely falling towards the Earth (either above the atmosphere or inside a large evacuated vertical tower, so air resistance can be ignored). A rocket is floating freely in the exact center of the box. (Note: what does this imply about how the rocket is moving relative to the Earth?) Then, at some instant of time ##t = 0## according to the clock carried by the observer at the center of the box, the rocket's engine turns on and it accelerates towards one of the box walls, wall U, which is the wall that is at the "top" of the box relative to Earth (i.e., the "upper" wall, hence the label U). The observer inside the box observes the rocket's acceleration, relative to him at the box's center, to be a constant value ##a##. The distance from the center of the box to wall U is ##d##, so the time required, by the observer's clock, for the rocket to reach wall U is ##sqrt(2 d / a)##.

As you can see, the calculation of the time required for the rocket to reach the wall (which in turn tells us how much fuel the rocket uses, since the rocket's fuel consumption rate is the same in both cases--the rockets are identical and have the same acceleration) is the same in both cases.

- #8

PeterDonis

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Since the Earth is only present in one of the two cases, you can't specifyImagine we take 5 m/s upwards from Earth as an example velocity.

- #9

PeterDonis

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If the rocket's engine is on, it is accelerating relative to the box in both cases. See my previous post #7.Wouldn't the person inside free fall box notice the acceleration of the ceiling to the rocket? something that doesn't happen in the space-box.

- #10

only1god

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What if there is no acceleration of the rocket and it goes at constant speed? The same speed in both cases.If the rocket's engine is on, it is accelerating relative to the box in both cases. See my previous post #7.

- #11

PeterDonis

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The only way for the rocket to go at constant speed relative to the box is if it is in free fall, with its engine off. It should be obvious that its motion relative to the box will then be the same in both cases.What if there is no acceleration of the rocket and it goes at constant speed?

- #12

only1god

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i meant the rockets going at constant speed up to the ceiling, with the same speed in both cases.The only way for the rocket to go at constant speed relative to the box is if it is in free fall, with its engine off. It should be obvious that its motion relative to the box will then be the same in both cases.

- #13

PeterDonis

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Go read my post #11 again. It already says "constant speed relative to the box". That's what you're talking about.i meant the rockets going at constant speed up to the ceiling

- #14

PeterDonis

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Or, if constant speed relative to the box ist already says "constant speed relative to the box". That's what you're talking about.

- #15

only1god

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Look, i mean constant speed of the rockets going up to the ceiling in both cases with the same speed. Your explanation was about acceleration.Go read my post #11 again. It already says "constant speed relative to the box". That's what you're talking about.

- #16

PeterDonis

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Constant speed relative to what?i mean constant speed of the rockets

If it's constant speed relative to the box, my post #11 applies: the rocket must be in free fall. (Note that it can be in free fall and still move relative to the box: it just needs to have some initial velocity relative to the box.)

If it's constant speed relative to the Earth, my post #8 applies: speed relative to the Earth is irrelevant to the equivalence principle because it's not local: the Earth isn't in the box, and is only present to begin with in one of the two cases.

I strongly suggest that you take a step back and think very carefully about the above.

No, it wasn't. You aren't reading carefully enough. My post #11 explicitly said "constant speed relative to the box", and the word "acceleration" doesn't even appear in it. See above.Your explanation was about acceleration.

- #17

only1god

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Ok, but RELAXConstant speed relative to what?

If it's constant speed relative to the box, my post #11 applies: the rocket must be in free fall. (Note that it can be in free fall and still move relative to the box: it just needs to have some initial velocity relative to the box.)

If it's constant speed relative to the Earth, my post #8 applies: speed relative to the Earth is irrelevant to the equivalence principle because it's not local: the Earth isn't in the box, and is only present to begin with in one of the two cases.

I strongly suggest that you take a step back and think very carefully about the above.

No, it wasn't. You aren't reading carefully enough. My post #11 explicitly said "constant speed relative to the box", and the word "acceleration" doesn't even appear in it. See above.

- #18

Dale

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Any questions about the math in post 6?

- #19

PeterDonis

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My tone was in response to yours:Ok, but RELAX

That's why I advised you to take a step back. Your questions are being answered. If you can't immediately see how our responses answer your questions, you should not assume that we've simply failed to understand you. You should take a step back and think carefully about what we are saying, making sure that you are reading carefully what we have posted.Look, i mean...

- #20

only1god

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I see you a little bit nervous answering, so either you relax an we have a normal discussion in which obviously i will ask and you will answer because I'm the one who don't understand, or you better get out of this thread and i'll ask another one.My tone was in response to yours:

That's why I advised you to take a step back. Your questions are being answered. If you can't immediately see how our responses answer your questions, you should not assume that we've simply failed to understand you. You should take a step back and think carefully about what we are saying.

- #21

PeterDonis

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I'm not nervous at all. I'm just getting the impression that you think the responses you have gotten so far in this thread have not addressed your question. That's why I emphasized that they have. I suggest that you stop worrying about how I or anyone else feel (all of the people responding to you in this thread are moderators, and we have very thick skins, I can assure you ) and focus on understanding why the responses you have gotten in this thread do address your question.I see you a little bit nervous answering

- #22

only1god

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- #23

PeterDonis

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You keep assuming that we somehow don't understand your scenario. We do. That's not the issue. In fact, we understand it better than you do, since you keep leaving out crucial information: see below.i'll make this clear as possible.

Constant speed relative to what? "Speed" makes no sense unless you specify what it is relative to.if the rockets are going at constant speed from the initiation to the ceiling,

Please specify what "constant speed" is relative to. Until you do that, the rest of your post is simply not well-defined.

- #24

Bandersnatch

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The same acceleration that you picture pulling the ceiling towards the rocket, is also pulling the rocket away from the ceiling. The two cancel out exactly.

- #25

only1god

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I've never said you don't understand at all.You keep assuming that we somehow don't understand your scenario. We do. That's not the issue.

Constant speed which means there is no acceleration, a = 0, it just means that whatever is the speed (it should be a little big to notice the effects), from the initiation of the propulsion until reaching the ceiling, the speed remains the same.Constant speed relative to what? "Speed" makes no sense unless you specify what it is relative to.

Please specify what "constant speed" is relative to. Until you do that, the rest of your post is simply not well-defined.

- #26

PeterDonis

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No acceleration relative to what?Constant speed which means there is no acceleration

Constant speed/no acceleration relative to the box is very, very different from constant speed/no acceleration relative to the Earth.

- #27

PeterDonis

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Then why do you keep repeating what "constant speed" means in the abstract, without answering the question I have repeatedly asked you about it?I've never said you don't understand at all.

- #28

PeterDonis

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As I have already pointed out:Constant speed/no acceleration relative to the box is very, very different from constant speed/no acceleration relative to the Earth.

If you mean constant speed relative to the box, the rocket is in free fall. (And @Bandersnatch in post #24 has now given you a simple intuitive way to understand what is going on in that case with respect to the Earth.)

If you mean constant speed relative to the Earth, the rocket's engine is on and it has some nonzero acceleration ##a## relative to the box. And that scenario is easily reproduced in the "floating in empty space" case by firing the rocket's engine with the same thrust, to give it the same acceleration ##a## relative to the box.

- #29

only1god

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ok expert, define the difference between constant velocity and accelerationThen why do you keep repeating what "constant speed" means in the abstract, without answering the question I have repeatedly asked you about it?

- #30

only1god

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Imagine 5 m/s here in Earth as an example, that velocity aplies it in both cases.

- #31

Dale

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The Earth only exists in one scenario. So there is no way to match the scenarios if you measure it relative to the Earth in one of them.Imagine 5 m/s here in Earth as an example, that velocity aplies it in both cases.

Stick with things inside the box for the setup.

- #32

only1god

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Ok, that's why i said constant velocity no matter what velocity it is, it just has to be constant in both cases, no matter what's the reference frame is.The Earth only exists in one scenario. So there is no way to match the scenarios if you measure it relative to the Earth in one of them.

Stick with things inside the box for the setup.

- #33

PeterDonis

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It's impossible for the rocket's velocity to be constant relative to the boxt just has to be constant in both cases, no matter what's the reference frame is.

- #34

only1god

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i don't understand why to be honest.It's impossible for the rocket's velocity to be constant relative to the boxandconstant relative to the Earth.

- #35

Dale

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It doesn’t make sense to offer constant relative to Earth as an option since there is no Earth in one scenario. The only thing in both scenarios is the box and rocket. So it has to be constant relative to the box.It's impossible for the rocket's velocity to be constant relative to the boxandconstant relative to the Earth. So which one is it?

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