B The Mini Rocket Experiment: A Test of Einstein's Equivalence Principle?

[only1god]

Alright, this is my idea of an experiment that could distinguish between the examples of the EP. Now, obviously I'm wrong (I don't say this because of your acceptance, i say this because I've tried with other ideas but they were wrong). The thing here is that i don't see where I'm wrong, and i hope someone show me where. Acording to Einstein's EP, one cannot know if he is in a free fall or suspended if there is no gravity, inside a box. What would happen if we propel a mini rocket inside the box? What i think is that, the mini rocket inside the free fall box would need more fuel than the mini rocket inside the box in space to reach the top, because it has to deal with gravity. Another thing, if the rockets goes up to the ceiling at a constant speed, the person inside the free fall box would see the rocket accelerating to the ceiling because the box is accelerating to the rocket, and the person inside the box in space would see the rocket going up to the ceiling in constant speed. Like i said, i know I'm wrong but i can't see where.
Thanks to anyone who takes time and responds.

 

[Nugatory]

Like i said, i know I'm wrong but i can't see where.

You can do this using only ordinary high-school physics, no relativity or fancy math needed:
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.

Another thing, if the rockets goes up to the ceiling at a constant speed

Constant speed relative to what?

 

[only1god]

Constant speed relative to what?

to earth

 

[only1god]

Imagine we take 5 m/s upwards from Earth as an example velocity. 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.
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.

 

[Nugatory]

to earth

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.

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.

 

[Dale]

Box floating in space

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?

 

[PeterDonis]

i know I'm wrong but i can't see where.

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 are exactly the same in both cases. You are having trouble seeing where you are wrong because you are implicitly allowing some conditions to be different between the two cases, without realizing it.

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.

 

[PeterDonis]

Imagine we take 5 m/s upwards from Earth as an example velocity.

Since the Earth is only present in one of the two cases, you can't specify anything relative to Earth and compare it between the two cases. The Earth is not inside the box, so nothing relative to the Earth can possibly have anything to do with the equivalence principle.

 

[PeterDonis]

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.

If the rocket's engine is on, it is accelerating relative to the box in both cases. See my previous post #7.

 

[only1god]

If the rocket's engine is on, it is accelerating relative to the box in both cases. See my previous post #7.

What if there is no acceleration of the rocket and it goes at constant speed? The same speed in both cases.

 

[PeterDonis]

What if there is no acceleration of the rocket and it goes at constant speed?

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.

 

[only1god]

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.

i meant the rockets going at constant speed up to the ceiling, with the same speed in both cases.

 

[PeterDonis]

i meant the rockets going at constant speed up to the ceiling

Go read my post #11 again. It already says "constant speed relative to the box". That's what you're talking about.

 

[PeterDonis]

t already says "constant speed relative to the box". That's what you're talking about.

Or, if constant speed relative to the box is not what you're talking about, but instead you mean constant speed relative to the Earth, then go read my post #8.

 

[only1god]

Go read my post #11 again. It already says "constant speed relative to the box". That's what you're talking about.

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.

 

[PeterDonis]

i mean constant speed of the rockets

Constant 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.

Your explanation was about acceleration.

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.

 

[only1god]

Constant 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.

Ok, but RELAX

 

[Dale]

Any questions about the math in post 6?

 

[PeterDonis]

Ok, but RELAX

My tone was in response to yours:

Look, i mean...

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.

 

[only1god]

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.

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.

 

[PeterDonis]

I see you a little bit nervous answering

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.

 

[only1god]

Ok, i'll make this clear as possible. What I'm trying to say is, if the rockets are going at constant speed from the initiation to the ceiling, Wouldn't the acceleration of the ceiling towards the rocket in the free fall box make the person notice he is in a free fall? In the space-box, the rocket would go at a constant speed.

 

[PeterDonis]

i'll make this clear as possible.

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.

if the rockets are going at constant speed from the initiation to the ceiling,

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.

 

[Bandersnatch]

Ok, i'll make this clear as possible. What I'm trying to say is, if the rockets are going at constant speed from the initiation to the ceiling, Wouldn't the acceleration of the ceiling towards the rocket in the free fall box make the person notice he is in a free fall? In the space-box, the rocket would go at a constant speed.

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.

 

[only1god]

You keep assuming that we somehow don't understand your scenario. We do. That's not the issue.

I've never said you don't understand at all.

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.

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.

 

[PeterDonis]

Constant speed which means there is no acceleration

No acceleration relative to what?

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

 

[PeterDonis]

I've never said you don't understand at all.

Then why do you keep repeating what "constant speed" means in the abstract, without answering the question I have repeatedly asked you about it?

 

[PeterDonis]

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

As I have already pointed out:

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.

 

[only1god]

Then why do you keep repeating what "constant speed" means in the abstract, without answering the question I have repeatedly asked you about it?

ok expert, define the difference between constant velocity and acceleration

 

[only1god]

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

 

[Dale]

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

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.

 

[only1god]

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.

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.

 

[PeterDonis]

t just has to be constant in both cases, no matter what's the reference frame is.

It's impossible for the rocket's velocity to be constant relative to the box and constant relative to the Earth. So which one is it?

 

[only1god]

It's impossible for the rocket's velocity to be constant relative to the box and constant relative to the Earth.

i don't understand why to be honest.

 

[Dale]

It's impossible for the rocket's velocity to be constant relative to the box and constant relative to the Earth. So which one is it?

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.

 

[PeterDonis]

i don't understand why to be honest.

Imagine you jump off a cliff, and let go of a rock just as you do so, so that the rock free falls downward with you. (Assume air resistance is negligible.) The rock's velocity relative to you is constant (assume you push the rock upward slightly as you let it go, so it has a small upward velocity relative to you). Is the rock's velocity relative to the Earth constant?

 

[only1god]

Imagine you jump off a cliff, and let go of a rock just as you do so, so that the rock free falls downward with you. (Assume air resistance is negligible.) The rock's velocity relative to you is constant (assume you push the rock upward slightly as you let it go, so it has a small upward velocity relative to you). Is the rock's velocity relative to the Earth constant?

I understand. But imagine that we fabricate here in Earth a mini rocket which only can go at 7 m/s from the start to the end, then we take this little rocket to the space. Wouldn't the velocity be the same?

 

[Dale]

Ok, so here is the math with constant velocity relative to the box. It is a rather silly scenario since no fuel is used for a constant velocity, $v_0$, relative to the box. But at least we can show that the time is the same:

Box feee floating in space:

Again, standard SUVAT equations give
$$ s = ut + \frac{1}{2}at^2 $$ $$ h = v_0 t +0$$ $$t=\frac{h}{v_0}$$

Box free falling near earth:

The equation for the “rocket” is $$ s_{rocket} = ut + \frac{1}{2} a t^2 $$ $$s_{rocket}= v_0 t -\frac{1}{2}gt^2$$

The equation for the ceiling of the box is $$ s_{ceiling}=h + ut + \frac{1}{2}at^2$$ $$ s_{ceiling}=h + 0 -\frac{1}{2}gt^2$$

The rocket reaches the ceiling when $$ s_{rocket}=s_{ceiling}$$ $$ v_0 t - \frac{1}{2}g t^2 = h -\frac{1}{2}gt^2$$ $$t=\frac{h}{v_0}$$

So it takes the same time in both cases. The equivalence principle holds.

 

[only1god]

I understand. But imagine that we fabricate here in Earth a mini rocket which only can go at 7 m/s from the start to the end, then we take this little rocket to the space. Wouldn't the velocity be the same?

Wouldn't the velocity remains also constant?

 

[PAllen]

I will add that your scenario has little to do with general relativity. Newton would have found your claims obviously wrong and ill informed. With the many detailed explanations here, I honestly don't understand what you fail to grasp. I actually think explaining what's wrong with what you claim about your scenario would be considered an easy exercise in a first course in physics. The only reason I don't offer yet another explanation is that others have already explained everything.

 

[PAllen]

Wouldn't the velocity remains also constant?

To repeat ad nauseum, velocity relative to what? Anyway, things you can manufacture into a rocket are e.g. amount of fuel, thrust profile, etc. Even if you clarify velocity relative to what, this is not a thing you can manufacture into a rocket. It is like saying, I have a widget that maintains a height of 5 meters. When I put in orbit around the Earth ? Just like height above something has no meaning without specifying the something, velocity, constant or otherwise has no meaning without a referent. This understanding goes back even centuries before Newton.

 

[PeterDonis]

imagine that we fabricate here in Earth a mini rocket which only can go at 7 m/s from the start to the end

This makes no sense. You can't specify the speed of the rocket since speed is relative. You can specify its thrust, but that doesn't equate to a specific speed.

 

[only1god]

This makes no sense. You can't specify the speed of the rocket since speed is relative. You can specify its thrust, but that doesn't equate to a specific speed.

Can something with uniform velocity relative to something, be non-uniform relative to another thing inertial?
In another words, Can a constant velocity relative to something be an acceleration relative to another thing at the same time? (If the thing is inertial)

 

[PAllen]

Can something with uniform velocity relative to something, be non-uniform relative to another thing inertial?
In another words, Can a constant velocity relative to something be an acceleration relative to another thing at the same time? (If the thing is inertial)

Only in one sense - something moving at constant velocity relative to something with proper acceleration can be accelerating relative to something inertial - because this thing must have proper acceleration in order to be at constant relative velocity to something else with proper acceleration. Proper acceleration is something measured with am accelerometer.

 

[PeterDonis]

Can something with uniform velocity relative to something, be non-uniform relative to another thing inertial?

Yes. The "inertial" qualifier is not necessary.

Can a constant velocity relative to something be an acceleration relative to another thing at the same time?

Yes.

(If the thing is inertial)

This qualifier is not necessary.

 

[only1god]

Yes. The "inertial" qualifier is not necessary.Yes.This qualifier is not necessary.

Doesn't that imply one of the two things are accelerating? This doesn't happen in the space-box because it's at rest, so something that have constant velocity relative to another thing would also have constant velocity relative to the space-box because it's at rest.

 

[PAllen]

@only1god , I notice you have made no response to either of @Dale ’s posts with simple calculations. I claim there is no point in any further discussion till you do so. If there is something you don’t understand in those, please ask. These posts are really elementary, so there is no point in discussing anything till you understand them

 

[PAllen]

Doesn't that imply one of the two things are accelerating? This doesn't happen in the space-box because it's at rest, so something that have constant velocity relative to another thing would also have constant velocity relative to the space-box because it's at rest.

In your original scenario, the rocket would be accelerating relative to the box by the same amount, whether it was in free fall near Earth or in free fall far away from any large mass. The fuel consumption would be identical.

 

[PeterDonis]

Doesn't that imply one of the two things are accelerating?

"Accelerating" is relative--at least, it is as you are using the term. For example, if you jump off a cliff and let a rock go just as you do so, you and the rock are accelerating relative to the Earth, but you are not accelerating relative to the rock and the rock is not accelerating relative to you.

There is a non-relative concept of acceleration called "proper acceleration", which basically means "feeling weight". This sense of "acceleration" is not relative to anything; it's something you can measure locally. For example, when you stand on Earth, you feel weight, and hence have nonzero proper acceleration; but if you jump off a cliff, you don't feel weight, and hence have zero proper acceleration. In your scenarios, the person at rest in the "box" feels no weight (they are in free fall), but the rocket does when its engine is on.

If we re-frame your scenarios using proper acceleration, it becomes even easier to see that the equivalence principle works. In each scenario, as just noted above, you have zero proper acceleration (you are weightless), and so does the box (since it is at rest relative to you), and the rocket has the same nonzero proper acceleration when its engine is on. Its proper acceleration and your lack of it (and the box's lack of it) in turn completely determines the rocket's motion relative to you (and the box) in both scenarios.

this doesn't happen in the space-box

Yes, it does. When the rocket's engine fires in the space-box, it accelerates relative to you and the box (in the first sense of "acceleration" above).

You appear to lack an extremely basic understanding of how rockets work.

because it's at rest

The box is at rest relative to you, but the rocket in the "space box" scenario is not when its engine fires.

Again, you appear to lack an extremely basic understanding of how rockets work.

 

[PeterDonis]

something that have constant velocity relative to another thing would also have constant velocity relative to the space-box because it's at rest.

If the rocket has constant velocity relative to the box, it is in free fall (weightless, engine not firing). This is true in both scenarios ("space box" and "box free-falling above the Earth"), as I have already said repeatedly.

In the "space box" scenario for this case (rocket moving at constant velocity relative to box), nothing at all has any acceleration anywhere.

In the "box free-falling above the Earth" scenario for this case (rocket moving at constant velocity relative to box), the Earth's surface has nonzero proper acceleration. This means the Earth is accelerating relative to the box and the rocket. You can phrase this either way: you can adopt the box frame and say that the Earth's surface is accelerating, or you can adopt the Earth's surface frame and say that the box and the rocket are both accelerating (and as @Bandersnatch pointed out a while back, both of their accelerations relative to Earth are the same, so they cancel out and the speed of the rocket relative to the box remains constant).