# The Equivalence Principle -- Is this a way to distinguish between a gravitational field and an accelerated rocket?

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## Summary:

Is this a way to distinguish between a gravitational field and an accelerated rocket?
If we are in a cabine in a gravitational field and inside, we have a racket and a ball. We put strings in each side of the racket and we connect the racket to the ceiling of the cabine. This strings only allows us to keep the weight of the racket. Then, we drop a ball to the racket.
We do this exactly in an accelerated cabine. Will the ball reach the same height in both scenarios after the collision?
In the cabine in gravity, the ball will hit the racket, and in the accelerated cabine the racket will hit the ball. The ball has a mass of 0,1 kg and the racket 1kg.

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Ibix
I can't understand your experimental set up, so I can't really comment on the specifics. Are you basically asking if a dropped ball will bounce to the same height under the two circumstances?

More generally, there are many ways to tell the difference between being in an accelerating room or on a planet's surface. They all depend on detecting the non-uniformity of the gravitational field - i.e., tidal effects, which won't be present in the rocket. The point about the equivalence principle is that, given any particular experimental precision, you can find a small region of spacetime that is too small for such effects to be detectable.

I can't understand your experimental set up, so I can't really comment on the specifics. Are you basically asking if a dropped ball will bounce to the same height under the two circumstances?

More generally, there are many ways to tell the difference between being in an accelerating room or on a planet's surface. They all depend on detecting the non-uniformity of the gravitational field - i.e., tidal effects, which won't be present in the rocket. The point about the equivalence principle is that, given any particular experimental precision, you can find a small region of spacetime that is too small for such effects to be detectable.
What i mean is when you drop the ball in the cabine in gravitational field, to make it a collision between the ball and the racket, the ball will bounce less than if you are in the accelerated cabine and do the same thing. So, is this a way to distinguish between a gravitational field and an accelerated frame?

phinds
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... when you drop the ball in the cabine in gravitational field, to make it a collision between the ball and the racket, the ball will bounce less than if you are in the accelerated cabine and do the same thing.
Why do you think this is true? Would it matter how far the ball drops? Would it matter the precision to which you measure the bounce?

Why do you think this is true? Would it matter how far the ball drops? Would it matter the precision to which you measure the bounce?
Wouldn't that mean it is a way to distinguish between a gravitational field and an accelerated frame?

phinds
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2019 Award
Wouldn't that mean it is a way to distinguish between a gravitational field and an accelerated frame?

DaveC426913
Gold Member
Wouldn't that mean it is a way to distinguish between a gravitational field and an accelerated frame?
How do you think it would be distinguishable?

If you were to accelerate the rocket at 9.8m/s^2, the ball would bounce just as high.

I actually answered you, you said would that matter? I said yes, because Wouldn't that mean a way to distinguish between them?

How do you think it would be distinguishable?

If you were to accelerate the rocket at 9.8m/s^2, the ball would bounce just as high.
In the accelerated cabine scenario, the racket of 1kg will hit the ball of 0,1kg, in the cabine in gravity scenario, the ball of 0,1kg will hit the racket of 1kg, Doesn't that mean it will be a difference?

phinds
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2019 Award
I actually answered you, you said would that matter? I said yes, because Wouldn't that mean a way to distinguish between them?
Ah, good point. I wasn't clear. I meant HOW specifically would any of those things be used as distinguishing characteristics.

Ah, good point. I wasn't clear. I meant HOW specifically would any of those things be used as distinguishing characteristics.
You mean the example i gave?

phinds
Gold Member
2019 Award
You mean the example i gave?
Nuts. I missed that. Sorry.

Ibix
Doesn't that mean it will be a difference?
No. You can use both those descriptions to describe either scenario.

phinds
Gold Member
2019 Award
In the accelerated cabine scenario, the racket of 1kg will hit the ball of 0,1kg, in the cabine in gravity scenario, the ball of 0,1kg will hit the racket of 1kg, Doesn't that mean it will be a difference?
Why? What would make it different? It looks like you are describing exactly the same phenomenon, just from different frames of reference. Underlying facts of reality do not depend on the frame of reference used to describe them. Nature doesn't care how we humans talk about it, it just does what it does.

sophiecentaur
Gold Member
Wouldn't that mean it is a way to distinguish between a gravitational field and an accelerated frame?
You could ask yourself if such an experiment that you propose would enable you to tell the difference then where would the Equivalence Principle come in? It would be discredited from the very start. The EP tells us there is no way of telling the difference when the gravitational field is uniform.
If you want to introduce practical situations then they could be outside of the EP and you could tell the difference. It's like saying two sticks are the same length but then someone uses a better ruler and shows they aren't. Both could be looked upon as true within the limits of the experiment.

Why? What would make it different? It looks like you are describing exactly the same phenomenon, just from different frames of reference. Underlying facts of reality do not depend on the frame of reference used to describe them. Nature doesn't care how we humans talk about it, it just does what it does.
Well, something of 1kg hitting another of 0,1kg, the effects of collision won't be the same as if something of 0,1kg hit another of 1kg, for example, the velocity after collision of that "thing" of 0,1kg, won't be the same in both cases.

You could ask yourself if such an experiment that you propose would enable you to tell the difference then where would the Equivalence Principle come in? It would be discredited from the very start. The EP tells us there is no way of telling the difference when the gravitational field is uniform.
If you want to introduce practical situations then they could be outside of the EP and you could tell the difference. It's like saying two sticks are the same length but then someone uses a better ruler and shows they aren't. Both could be looked upon as true within the limits of the experiment.
I don't undestand what you mean by this.

Ibix
Well, something of 1kg hitting another of 0,1kg, the effects of collision won't be the same as if something of 0,1kg hit another of 1kg, for example, the velocity after collision of that "thing" of 0,1kg, won't be the same in both cases.
So? You've switched frames from one where the racket is stationary to one where it's moving. If the initial velocities are different the final ones certainly will be. On the other hand, in both cases, you can pick a frame where the racket is stationary - this is the correct way to compare your two scenarios.

You can use this experiment (in principle) to detect whether you are on Earth or in a rocket. In the first case, the acceleration of the ball will change very slightly with height (and I do mean very slightly - a few tenths of a ##\mu\mathrm{ms^{-2}}## per metre of height change), and will not in the second case. But this is nothing to do with the reason you state.

Tomorrow i'm going to explain myself more.

Ibix
I don't undestand what you mean by this.
The point @sophiecentaur is making, I think, is that your interpretation of your experiment (if true) would invalidate the equivalence principle. It would be surprising if such a trivial experiment had not been considered in the last 100 years. Of course, it has been considered (for far more than 100 years) and it does not invalidate the equivalence principle. What you are actually doing is using incompatible descriptions of your two experiments and confusing yourself.
Tomorrow i'm going to explain myself more.
I don't think you need to. You are saying that a ball of mass 0.1kg striking a racket of mass 1kg with some speed ##v## is different from a racket of mass 1kg striking a ball of mass 0.1kg with that same speed. This is incorrect. They are simply two different descriptions of the same interaction and you can use either one for either the rocket or planet experiment. In both cases the first description is more natural for someone at rest with respect to the cabin and the second is more natural for a free falling observer.

The point @sophiecentaur is making, I think, is that your interpretation of your experiment (if true) would invalidate the equivalence principle. It would be surprising if such a trivial experiment had not been considered in the last 100 years. Of course, it has been considered (for far more than 100 years) and it does not invalidate the equivalence principle. What you are actually doing is using incompatible descriptions of your two experiments and confusing yourself.
I don't think you need to. You are saying that a ball of mass 0.1kg striking a racket of mass 1kg with some speed ##v## is different from a racket of mass 1kg striking a ball of mass 0.1kg with that same speed. This is incorrect. They are simply two different descriptions of the same interaction and you can use either one for either the rocket or planet experiment. In both cases the first description is more natural for someone at rest with respect to the cabin and the second is more natural for a free falling observer.
Man if you think because it's a simple way can't be true and also because no one thought about it, Get out of this post.
Are you really telling me that a racket of 1kg hitting a ball of 0,1kg it's equal as if it happens otherwise??? It's surprising me since i assume everyone here knows physics.

weirdoguy
PeterDonis
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Man if you think because it's a simple way can't be true and also because no one thought about it, Get out of this post.
Are you really telling me that a racket of 1kg hitting a ball of 0,1kg it's equal as if it happens otherwise??? It's surprising me since i assume everyone here knows physics.
This is not a productive attitude towards someone that is (a) trying to help you, and (b) doing so by giving you correct information.