Understanding Gravity with GR: Beginner's Guide by Aerodyn

[Aerodyn]

Hi everybody.

I recently started to learn GR from a very begginer level. I would like to share with you some lines of discussion, to understand your approach to some specific topics which for me are key to better understand the whole story.

If a put an accelerometer on the floor it reads 9.8 m/S2. Does it mean I am in an accelerated frame of reference? Here on Earth surface

When objects are in free fall, they feel no force does it mean that it is on a geodesic curve? If I see them accelerating towards the ground and they are inertial, does it mean that I am accelerated?

Is gravity an inercial force we feel because of the aceleration of our frame of reference here on Earth surface?;on the radial direction pointing outside (the acceleration).

So gravity is just inertia, the same force that we feel backwards when we accelerate a car, o turn?

How is this aceleration no affecting the size of Earth (outwards aceleration of Earth surface)

Thank you everybody for this great forum

Regards,
Aerodyn

 

[Orodruin]

Does it mean I am in an accelerated frame of reference?

No. It means you have a proper acceleration of 9.8 m/s^2. It is a very common misconception to use language such as "am I in X and Y frame of reference?"
First of all, frames of reference in Special Relativity typically refers to inertial frames. Second, nobody "is in" a particular reference frame. Any object will be in all reference frames - however it will be stationary in its rest frame. Finally, accelerated frames are not as unambiguous in special relativity (and certainly not in general relativity) as they are in Newtonian mechanics. In order to talk about them reasonably one needs to be very careful in specifying what is intended by the phrasing.

When objects are in free fall, they feel no force does it mean that it is on a geodesic curve?

Yes, this is what free fall means.

If I see them accelerating towards the ground and they are inertial, does it mean that I am accelerated?

Yes. Although technically it is the ground that has the proper acceleration. The falling object is in free fall.

Is gravity an inercial force we feel because of the aceleration of our frame of reference here on Earth surface?;on the radial direction pointing outside (the acceleration).

In general relativity, gravity is not a force at all. It is the effects of the curvature of spacetime.

So gravity is just inertia, the same force that we feel backwards when we accelerate a car, o turn?

The locally experienced gravitation works much like that yes. However, that is not the full extent of the concept of gravity, which also includes how energy, momentum, and stress curves spacetime.

How is this aceleration no affecting the size of Earth (outwards aceleration of Earth surface)

Spacetime is curved. This means that you can have locally accelerated paths that do not deviate from each other. This is similar to latitudes on a sphere that are locally curved (except the equator, which is a geodesic) away from the equator yet still maintains the same distance to it.

I recently started to learn GR from a very begginer level.

Then probably A-level is not the level you want to select for your thread. Doing so indicates that you have graduate level knowledge of the subject and would like answers geared at that level of understanding.

 

[PeterDonis]

I recently started to learn GR from a very begginer level.

Moderator's note: Thread level changed to "I" based on this.

 

[Ibix]

Does it mean I am in an accelerated frame of reference? Here on Earth surface

No, but it does mean that any frame you can sensibly describe as your rest frame is a non-inertial frame. You do often see this written as "you are in a non-inertial frame", but that's sloppy terminology that is likely to mislead you. You are free to use any frame (or, better said, any coordinate system) whether you are at rest in it or not.

 

[PeroK]

How is this aceleration no affecting the size of Earth (outwards aceleration of Earth surface)

This is a good question. Basically, proper acceleration in a given direction does not imply absolute motion in that direction. Instead it implies changing relative motion between the accelerating object and a local inertial object. To understand the global picture, of course, you need the concept of curved spacetime. This allows two objects on opposite sides of the Earth to be constantly accelerating in opposite directions, but having no relative motion.

 

[Aerodyn]

Thank you very much for your ideas. (Sorry for the mistakes).

I have serious lack of root knowledge, but for me is incredible to think how can the curvature of the space make us feel this "force". How the curvature is transferred to the fact that we feel a force down. I think I should read good about proper acceleration as you mentioned. I am very Newtonian!

I also liked the comparison with the latitude in the sphere

Thank you very much for your feedback, also more ideas are welcomed.

Regards,
Aerodyn

 

[Orodruin]

How the curvature is transferred to the fact that we feel a force down.

It is not the curvature itself that transfers to that, it is the fact that the ground is preventing you from following your free fall geodesic. Much like, as you said, a car seat prevents you from staying behind the car when the car accelerates.

 

[Ibix]

I have serious lack of root knowledge, but for me is incredible to think how can the curvature of the spaced make us feel this "force,". How the curvature is transferred to the fact that we feel a force down. I think I should read good about about proper acceleration as you mentioned.

It doesn't make you feel a force. The only force you feel is the floor pushing up on your feet. That's why being in an accelerating lift, its floor pushing up on your feet, is indistinguishable from gravity locally. The curvature just changes the definition of "straight line" so that your natural movement is a curve downwards unlike in Euclidean space.

 

[PeterDonis]

How the curvature is transferred to the fact that we feel a force down.

As others have commented, you do not feel a force down. If you are moving solely under the influence of gravity, you feel no force at all. Astronauts on the International Space Station, for example. The force you feel standing on the surface of the Earth is up, not down, and is due to the ground pushing on your feet.

 

[Dale]

How the curvature is transferred to the fact that we feel a force down.

In GR gravity isn’t a real force. So you don’t feel a force down. The only real force you feel is pressure from the ground pushing up, so you accelerate up as indicated by an accelerometer.

The curvature does not press you down, it just keeps the surface of the Earth from expanding despite its acceleration outward.

 

[vanhees71]

As others have commented, you do not feel a force down. If you are moving solely under the influence of gravity, you feel no force at all. Astronauts on the International Space Station, for example. The force you feel standing on the surface of the Earth is up, not down, and is due to the ground pushing on your feet.

And this pushing is mostly due to the electromagnetic interaction as well as the fact that matter consists of fermions.