Acceleration in a Closed Box: Uniform or Varied?

[Buckleymanor]

It's said that it is not possible to tell the difference between acceleration of objects within a closed box and acceleration due to gravity.
Is this allways the case.Does the acceleration of objects within a closed box act uniformly or does this depend on the gradual acceleration of the objects.
In other words if objects of different mass within the box are subjected to a violent or sudden acceleration will they still react as if they were in a gravitational field.

 

[MikeGomez]

It's said that it is not possible to tell the difference between acceleration of objects within a closed box and acceleration due to gravity.
Is this allways the case.

Yes, this is always the case.

In other words if objects of different mass within the box are subjected to a violent or sudden acceleration will they still react as if they were in a gravitational field.

Yes, it will feel like you fell on the ground, or jumped off a building, etc.

 

[HallsofIvy]

Yes, locally, it is impossible to distinguish between motion of an object because the closed box is accelerating, constantly around an object or the object is acted on by a "gravitational" force. Since the acceleration is constant, I do not know what you mean by "gradual" or "sudden".

 

[Vahsek]

Yes, locally, it is impossible to distinguish between motion of an object because the closed box is accelerating, constantly around an object or the object is acted on by a "gravitational" force. Since the acceleration is constant, I do not know what you mean by "gradual" or "sudden".

What do you mean by "locally"?

 

[1977ub]

In Gravity, if you build a tower and climb up, you will find up there that the force of gravity is less as you get further from the surface of the Earth. In a closed space, this doesn't happen, and you would know you are not in gravity (or that you just haven't climbed far enough up to detect the difference). In Gravity, if you drop a plumb line, and then if you move off along the floor some distance and do it again, you will find that that these two plumb lines are not pointing in the same precise direction, since both are pointing toward the center of the earth. In your accelerating room, this doesn't happen. The plumb lines should be completely parallel.

 

[danR]

What do you mean by "locally"?

Essentially, in the box.

 

[Buckleymanor]

Yes, locally, it is impossible to distinguish between motion of an object because the closed box is accelerating, constantly around an object or the object is acted on by a "gravitational" force. Since the acceleration is constant, I do not know what you mean by "gradual" or "sudden".

By gradual I mean a slow or steady constant acceleration.
Sudden acceleration would be caused by a violent or explosive acceleration.
Say you had a bowling ball and a pool ball side by side within the box and there was an explosive force underneath the box which propelled it upwards.
Presumeing the floor of the box was able to withstand the propellant force, would the bowling ball being more massive than the pool ball make more of an indenture in the floor and therefore take off from the floor at a slower speed than the pool ball.
If the pool ball and the bowling ball were just released at the same time in a gravity field they would fall at the same rate.

 

[mfb]

would the bowling ball being more massive than the pool ball make more of an indenture in the floor

Depends on details of the floor.

and therefore take off from the floor at a slower speed than the pool ball.

You are considering the situation after they bounced on the floor? Probably, but that is exactly the same in a gravitational field then.

If the pool ball and the bowling ball were just released at the same time in a gravity field they would fall at the same rate.

That is true in the accelerated box, too. It is even more obvious there, as the balls stay at rest (and at the same relative position), while the box accelerates.

 

[MikeGomez]

In Gravity, if you build a tower and climb up, you will find up there that the force of gravity is less as you get further from the surface of the Earth. In a closed space, this doesn't happen, and you would know you are not in gravity (or that you just haven't climbed far enough up to detect the difference). In Gravity, if you drop a plumb line, and then if you move off along the floor some distance and do it again, you will find that that these two plumb lines are not pointing in the same precise direction, since both are pointing toward the center of the earth. In your accelerating room, this doesn't happen. The plumb lines should be completely parallel.

It seems to me you have a fairly common misconception regarding gravity and acceleration.

The problem is that the proposed experiment is from the start not valid if it sets out to compare gravity from a source point acting radially (in all directions) and a force of acceleration which is acting in parallel.

The reason gravity (usually) falls off with distance is due to the fact that it is originated from a spherical body, not because of the inherent nature of gravity. It has to do with the nature of 3-dimensionality, not the nature of gravity. You can calculate the gravitational flux within a closed surface, but at a greater distance from the source the area is greater and with the same amount of flux there is less flux per area.

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A couple of ways you could make the experiment valid would be…

You can make the gravitational lines be parallel so that they match the parallel acceleration of the “elevator”. You could do that by using a rectangular plate for your gravitational source instead of a sphere.

If you wish to keep that spherical gravitational source, you could also make the adjustment on the acceleration side of the experiment if you could construct it so that the “lines of acceleration” extend radially such that they match the spherical gravitation.

 

[Buckleymanor]

Depends on details of the floor.

Not sure if it does, unless it's made of unobtanium.Perfect rigid bodies not allowed.

You are considering the situation after they bounced on the floor? Probably, but that is exactly the same in a gravitational field then.

Trying not too. I am considering the situation as the box starts to accelerate and causes a bounce.

That is true in the accelerated box, too. It is even more obvious there, as the balls stay at rest (and at the same relative position), while the box accelerates.

That's not the case I am describeing It might be if it's a slow acceleration but maybe it's not true when objects are accelerated quickly.
It might also be not be true when objects are accelerated slowly but not obviouse.

 

[Buckleymanor]

In Gravity, if you build a tower and climb up, you will find up there that the force of gravity is less as you get further from the surface of the Earth. In a closed space, this doesn't happen, and you would know you are not in gravity (or that you just haven't climbed far enough up to detect the difference). In Gravity, if you drop a plumb line, and then if you move off along the floor some distance and do it again, you will find that that these two plumb lines are not pointing in the same precise direction, since both are pointing toward the center of the earth. In your accelerating room, this doesn't happen. The plumb lines should be completely parallel.

The plumb lines not pointing in parallel might be a tidal effect. Which in this situation is usualy acceptable.

 

[MikeGomez]

MFB addressed this, but please allow me to reiterate.

Say you had a bowling ball and a pool ball side by side within the box and there was an explosive force underneath the box which propelled it upwards.
Presumeing the floor of the box was able to withstand the propellant force, would the bowling ball being more massive than the pool ball make more of an indenture in the floor and therefore take off from the floor at a slower speed than the pool ball..

If there is an indentation on the floor due to the bowling ball, it is due only to the nature of the floor and the bowling ball. There will be no difference between the cases of gravity or acceleration. The dent in the floor will be the same in both cases.

The speed of acceleration will also be the same in both cases, assuming you have set up your experiment to withstand the forces you are putting on it without breaking your experiment.

If the pool ball and the bowling ball were just released at the same time in a gravity field they would fall at the same rate.

Yes, and in an acceleration field they would hang motionless for the same amount of time as that of the freefall time in the gravitational field (until the accelerated floor catches up with them). Again the situation is exactly the same in both cases.

 

[MikeGomez]

The plumb lines not pointing in parallel might be a tidal effect. Which in this situation is usualy acceptable.

That's right.

 

[1977ub]

The plumb lines not pointing in parallel might be a tidal effect. Which in this situation is usualy acceptable.

It is an example where not keeping your tests sufficiently local reveals which situation you are in.

 

[1977ub]

It seems to me you have a fairly common misconception regarding gravity and acceleration.

The problem is that the proposed experiment is from the start not valid if it sets out to compare gravity from a source point acting radially (in all directions) and a force of acceleration which is acting in parallel.

The reason gravity (usually) falls off with distance is due to the fact that it is originated from a spherical body, not because of the inherent nature of gravity. It has to do with the nature of 3-dimensionality, not the nature of gravity. You can calculate the gravitational flux within a closed surface, but at a greater distance from the source the area is greater and with the same amount of flux there is less flux per area.

-----------------------------------------------------------------------
A couple of ways you could make the experiment valid would be…

You can make the gravitational lines be parallel so that they match the parallel acceleration of the “elevator”. You could do that by using a rectangular plate for your gravitational source instead of a sphere.

If you wish to keep that spherical gravitational source, you could also make the adjustment on the acceleration side of the experiment if you could construct it so that the “lines of acceleration” extend radially such that they match the spherical gravitation.

Well yes I was assuming that generally when comparing gravity with accelerated box, the comparison is done between the accelerating box vs Earth's (or some other planet's) surface. The nature of gravity (nearly always encountered and thought-experimented on) is in the context of a sphere. It won't remain constant.

 

[Buckleymanor]

If there is an indentation on the floor due to the bowling ball, it is due only to the nature of the floor and the bowling ball. There will be no difference between the cases of gravity or acceleration. The dent in the floor will be the same in both cases.

The speed of acceleration will also be the same in both cases, assuming you have set up your experiment to withstand the forces you are putting on it without breaking your experiment.

No it can't be the dent on the floor will be variable because you won't be able to maintain both the speed of acceleration in the experiment (which will vary stop start etc,) to that caused by gravity.

 

[OCR]

Yes, this is always the case.

That's correct.

http://en.wikipedia.org/wiki/Genera...rom_classical_mechanics_to_general_relativity



OCR

 

[Nugatory]

It's said that it is not possible to tell the difference between acceleration of objects within a closed box and acceleration due to gravity.
Is this always the case.Does the acceleration of objects within a closed box act uniformly or does this depend on the gradual acceleration of the objects.
In other words if objects of different mass within the box are subjected to a violent or sudden acceleration will they still react as if they were in a gravitational field.

Yes, this always the case, as long as:
1) the acceleration of the closed box is constant
2) the closed box is small enough that tidal forces and other large-scale gravitational effects cannot be observed.

 

[OCR]

It's said that it is not possible to tell the difference between acceleration of objects within a closed box and acceleration due to gravity.

Here's a bit more...

http://en.wikipedia.org/wiki/Equivalence_principle#Development_of_gravitation_theory


http://en.wikipedia.org/wiki/Uniform_acceleration#General_relativity

Unless the state of motion of an object is known, it is totally impossible to distinguish whether an observed force is due to gravity or to acceleration—gravity and inertial acceleration have identical effects.

Well, this is a 108 page pdf... I guess that's a bit more, than a bit more...

http://faculty.luther.edu/~macdonal/EGR.pdf





OCR

 

[MikeGomez]

Well yes I was assuming that generally when comparing gravity with accelerated box, the comparison is done between the accelerating box vs Earth's (or some other planet's) surface. The nature of gravity (nearly always encountered and thought-experimented on) is in the context of a sphere. It won't remain constant.

Understood. The gravitational effect is the weakest force and is normally only a concern regarding celestial bodies.

The problem is that confusion often arises with regards to the equivalence principle. Based on your original post, that seems to be at the heart of the disscussion here. That’s where care must be taken to insure that a proper comparison is made. The deeper meaning behind the equivalence principle is completely lost if confusion arises due to misunderstandings of tidal forces or the inverse square law.

Didn’t mean any disrespect. Cheers.

 

[Buckleymanor]

The problem is that confusion often arises with regards to the equivalence principle.

Yes there does seem to be a lot of confusion.Haveing read over the posts I get the impression that some posters imagine that as long as the box is accelerating at a constant velocity then it's not possible to tell the difference between the two.
If you read wiki the implication is that the velocity has to be a constant 1g.
Which if true actualy bounds the experiment to a very precise perameter probably difficult to obtain in any pratical experiment.

 

[mfb]

@Buckleymanor: I think you mean acceleration where you write velocity.

To be indistinguishable from gravity in general, the acceleration can take any value.
To be indistinguishable from gravity on the surface of earth, the acceleration has to take the same specific value (~9.81m/s^2). But that is nothing fundamental, it is just a special case of the more general statement.

 

[Buckleymanor]

@Buckleymanor: I think you mean acceleration where you write velocity.

To be indistinguishable from gravity in general, the acceleration can take any value.
To be indistinguishable from gravity on the surface of earth, the acceleration has to take the same specific value (~9.81m/s^2). But that is nothing fundamental, it is just a special case of the more general statement.

Yes I mean acceleration thanks.
(~9.81m/s^2)=1g.
I would imagine there would be a presumption that you would probably know the region of space the box was being accelerated in and therefore gravity's value.

 

[MikeGomez]

Yes there does seem to be a lot of confusion.

Not really. The only confusion is yours.

Haveing read over the posts I get the impression that some posters imagine that as long as the box is accelerating at a constant velocity then it's not possible to tell the difference between the two.

Yes, I was under the impression that that is what all the posters here believe. I know that is what I believe. An accelerometer in a box will not be able to distinguish between acceleration due to gravity or by any other source. If you want to simulate the situation we have from the surface of the earth, starting at the surface and then moving higher in elevation, then you would need to gradually taper off the acceleration to simulate weaker gravity at higher elevation.

If you read wiki the implication is that the velocity has to be a constant 1g.
Which if true actualy bounds the experiment to a very precise perameter probably difficult to obtain in any pratical experiment.

Srory, but that’s not the implication at all. The place where you read is referring to the development of the equivalence principle. There Einstein compares the acceleration due to gravity at the surface of the Earth with an equivalent acceleration (1g) due to a rocket ship. The more general point (and far more important) is that acceleration due to any gravitation field (not just the earth) is indistinguishable from acceleration due to any other method.

(~9.81m/s^2)=1g.

Mfb knows perfectly well that (~9.81m/s^2)= 1g. He was trying to explain to you that 1g at the surface of the Earth is only one out of an infinity of possible values for gravitation. Your original post seemed to be with concerned gravity and acceleration in general, not gravity at the surface of the earth.

I would imagine there would be a presumption that you would probably know the region of space the box was being accelerated in and therefore gravity's value.

Usually the "accelerated" box is imagined to be in space, far removed from any gravitational field.

I put the quotes there because I personally don't think there is any difference between acceleration and gravitation. They are just two different ways of looking at the same phenomena. That's just me. I don't know if that is a consensus though.

 

[Buckleymanor]

Not really. The only confusion is yours.

Well if you can't find any other confusion from any other poster in this thread it must be a first.

Yes, I was under the impression that that is what all the posters here believe. I know that is what I believe. An accelerometer in a box will not be able to distinguish between acceleration due to gravity or by any other source. If you want to simulate the situation we have from the surface of the earth, starting at the surface and then moving higher in elevation, then you would need to gradually taper off the acceleration to simulate weaker gravity at higher elevation.

It depends on what the constant velocity is and where.

Srory, but that’s not the implication at all. The place where you read is referring to the development of the equivalence principle. There Einstein compares the acceleration due to gravity at the surface of the Earth with an equivalent acceleration (1g) due to a rocket ship. The more general point (and far more important) is that acceleration due to any gravitation field (not just the earth) is indistinguishable from acceleration due to any other method.

Yes and why is he making the comparison.Because if you had a set of scales you could tell the difference.

Mfb knows perfectly well that (~9.81m/s^2)= 1g. He was trying to explain to you that 1g at the surface of the Earth is only one out of an infinity of possible values for gravitation. Your original post seemed to be with concerned gravity and acceleration in general, not gravity at the surface of the earth.

I know Mfb knows that what I did not know was why he substituted 1g for that.
Yes my original post was concerned with gravity and acceleration in general and has been slightly sidetracked I will try to remember my original concern.

Usually the "accelerated" box is imagined to be in space, far removed from any gravitational field.

I put the quotes there because I personally don't think there is any difference between acceleration and gravitation. They are just two different ways of looking at the same phenomena. That's just me. I don't know if that is a consensus though.

If that's the case then you certainly would be able to arrive at the conclusion that the gravity you felt was due to acceleration and not a gravity field.

 

[OCR]

... any difference between acceleration and gravitation.

Often... it seems difficult to define definitions, definitively.

http://en.wikipedia.org/wiki/Acceleration#General_relativity

http://en.wikipedia.org/wiki/Gravitational_acceleration#General_relativity

http://en.wikipedia.org/wiki/Fictitious_force#Gravity_as_a_fictitious_force

http://en.wikipedia.org/wiki/General_theory_of_relativity#Definition_and_basic_properties
OCR

 

[MikeGomez]

Often... it seems difficult to define definitions, definitively.

Thanks OCR. That made me laugh…

Regarding your references, I think the most appropriate considering the current state of this thread is from the first one…

“Unless the state of motion of an object is known, it is totally impossible to distinguish whether an observed force is due to gravity or to acceleration—gravity and inertial acceleration have identical effects. Albert Einstein called this the principle of equivalence, and said that only observers who feel no force at all—including the force of gravity—are justified in concluding that they are not accelerating.”

The other references are great, but in my opinion we need to get to an understanding of the equivalence principle before we discuss gravity as a fictitious force, or gravity curving space.

 

[MikeGomez]

If that's the case then you certainly would be able to arrive at the conclusion that the gravity you felt was due to acceleration and not a gravity field.

No you wouldn’t. That’s the whole point.

Assuming you are inside the box and can’t see which situation you are in, what method would you use to be able to tell one from the other (gravity at the surface of a body, or acceleration of a box in space)?

 

[Buckleymanor]

No you wouldn’t. That’s the whole point.

Assuming you are inside the box and can’t see which situation you are in, what method would you use to be able to tell one from the other (gravity at the surface of a body, or acceleration of a box in space)?

Sorry but you seem to be contradicting yourself now.

Usually the "accelerated" box is imagined to be in space, far removed from any gravitational field.

That was comment I was replying to.You state quite clearly that it's removed from any gravity field.
The above is a different assumption which I will need time to look at.

 

[danR]

Sorry but you seem to be contradicting yourself now.

That was comment I was replying to.You state quite clearly that it's removed from any gravity field.
The above is a different assumption which I will need time to look at.

I can't speak for Mike, but I assume he means is that we (Bob) remove the box and its contained observer (Alice) to a (hypothetical) gravity-free region (yes I know that's impossible), but we don't tell Alice we did that (we are very sneaky Bobs). We also give Alice a powerful sedative before we turn on the drive (which is an extra-sneaky quiet drive), so she wakes up and says:

"Hey! I'm in a gravity field! My rocket ship must have landed on a distant planet!"
​

Now, I know I've given enough rope for you to hang me with, but please don't hang the others.