Acceleration: Effects on Matter & Observers

[Android17]

1) Is acceleration relative?
2) Can an observer in an accelerating body assume that he's at rest and everything else is accelerating except him and the object he's on?
3)Earth is accelerating and decelerating in its orbit around the sun all the time and yet we don't feel it, why? Is it only because these changes are small?

 

[Dale]

1) Is acceleration relative?

There are two kinds of acceleration: proper acceleration which is not relative and coordinate acceleration which is relative.

2) Can an observer in an accelerating body assume that he's at rest and everything else is accelerating except him and the object he's on?

Yes. An observer with non zero proper acceleration may still use a reference frame where he has zero coordinate acceleration.

3)Earth is accelerating and decelerating in its orbit around the sun all the time and yet we don't feel it, why? Is it only because these changes are small?

They are small, but in addition they are coordinate accelerations which you don’t feel anyway. You only feel proper acceleration which is zero for an object in free fall, like the Earth orbiting around the sun.

 

[Android17]

They are small, but in addition they are coordinate accelerations which you don’t feel anyway. You only feel proper acceleration which is zero for an object in free fall, like the Earth orbiting around the sun.

Please explain what coordinate acceleration is? Earths velocity and direction changes in its orbit around the sun at various continously. So why is it not considered proper?

What is the difference between proper acceleration and coordinate acceleration?

If Earth was revolving around the sun at 99.999% speed of light, would it still be just coordinate acceleration? Is speed a factor? Here?

 

[Ibix]

Please explain what coordinate acceleration is?

Your coordinates are changing at a changing rate. Since you are free to use coordinates that are not evenly spaced this may or may not correspond to anything you might feel.

Earths velocity and direction changes in its orbit around the sun at various continously. So why is it not considered proper?

"Proper" has changed meaning in English. It's being used here in its Latin sense of "its own", rather than its modern sense of "correct". Proper acceleration is one you can measure in a closed room because your accelerometers will read non-zero.

Gravity is not a force in general relativity, it's spacetime curvature. Things in free fall are, therefore, not experiencing forces. You can tell by the way you let go of a ball and it doesn't fall. There's no proper acceleration here.

If Earth was revolving around the sun at 99.999% speed of light, would it still be just coordinate acceleration?

There's no proper acceleration for a body in free fall, full stop. There may or may not be coordinate acceleration depending on your choice of coordinates.

 

[Android17]

What makes objects follow the curvature of space? Can we even ask such a question?

 

[Ibix]

You can ask the question, but there's no meaningful answer. Why do you think an object shouldn't follow the geometry of spacetime?

Quantum gravity may provide more helpful answers, but we don't have a working theory yet. And even when we do, it'll almost certainly have some other underlying question with no helpful answer. Hopefully, though, it'll have fewer "just because" answers than current theory.

 

[PeterDonis]

What makes objects follow the curvature of space?

As @Ibix notes in his response, it's curvature of spacetime, not space. Thinking of it as just curvature of space won't work.

 

[Dale]

Please explain what coordinate acceleration is?

In order to have a numerical position you have to have a coordinate system. The rate of change of an object’s position is called velocity, and the rate of change of an object’s velocity is called acceleration. Because it is based on the coordinates originally chosen, this is “coordinate acceleration”.

Earths velocity and direction changes in its orbit around the sun at various continously. So why is it not considered proper?

Proper acceleration is the acceleration measured by an accelerometer carried by the object. It is proper in the sense of “property”. It is a property of the object that does not depend on the choice of coordinates.

The earth’s acceleration in orbit is not a proper acceleration because it cannot be detected by an accelerometer on the earth. You have to choose a coordinate system and measure the velocity wrt that coordinate system and see that it changed over time. So it is coordinate acceleration.

 

[sweet springs]

1) Is acceleration relative?

Yes and No.
Say a rocket is thrusting and passing a space station nearby. Rocket is accelerating in the station system. The station is free-falling thus accelerating in the rocket system reciprocally. Gravity works on the rocket. However it does not on the space station.

 

[sweet springs]

2) Can an observer in an accelerating body assume that he's at rest and everything else is accelerating except him and the object he's on?

Yes.

3)Earth is accelerating and decelerating in its orbit around the sun all the time and yet we don't feel it, why? Is it only because these changes are small?

The Earth is free falling in the gravity of the Sun though it seems and actually is circling around it. Free falling system is roughly an inertial system with condition of neglecting tidal force generated from distance difference within the Earth from the Sun.

 

[Ibix]

Yes and No.
Say a rocket is thrusting and passing a space station nearby. Rocket is accelerating in the station system. The station is free-falling thus accelerating in the rocket system reciprocally. Gravity works on the rocket. However it does not on the space station.

This seems potentially rather confusing to me because you haven't made a clear distinction between coordinate acceleration and proper acceleration, nor made clear what you mean by "gravity works".

The rocket is under thrust; it is experiencing proper acceleration and all frames agree what its on-board accelerometers (spring balances with 1kg masses sitting on them) read. This is invariant, and is what I think you mean by "gravity works on the rocket" - loose objects will fall towards the rear of the rocket (or the rear of the rocket will accelerate up to meet loose objects depending on your point of view). It must be invariant because whether or not a coin crashes into the rear wall of the rocket is a fact, not open to interpretation.

In the (inertial) frame where the station is at rest, the rocket is undergoing coordinate acceleration. In the (non-inertial) frame where the rocket is at rest the station is undergoing coordinate acceleration. This type of acceleration is relative because it's specified relative to some frame.

 

[sweet springs]

Rocket is gaining speed in Station system.
Station is gaining speed in Rocket system.
I said this reciprocity in acceleration.

In Rocket system free body (it is in the rocket or in the station or anywhere it does not matter) falls.
In Station system free body stays still or keeps same speed.
I said this difference in gravity they feel.

 

[Dale]

I said this difference in gravity they feel.

Careful. Acceleration that you feel is proper acceleration. Gravity doesn’t produce proper acceleration. So you don’t feel gravity.

For example, gravity is almost as strong on the space station as it is on the surface of the earth. But astronauts do not feel it because it doesn’t produce proper acceleration.

 

[Ibix]

Rocket is gaining speed in Station system.
Station is gaining speed in Rocket system.
I said this reciprocity in acceleration.

In Rocket system free body (it is in the rocket or in the station or anywhere it does not matter) falls.
In Station system free body stays still or keeps same speed.
I said this difference in gravity they feel.

I think that's a muchh clearer statement, thank you. Although Dale makes a good point that you don't feel gravity, rather, you feel the normal force of the floor against your shoes.