Gravity on Earth: Basic Qs Answered by Physicists

[Brooksie]

TL;DR

Relativity & Gravity

I passed O level Physics in 1983 and loved it but went down the arts route. Over the last 5 years or so I re-kindled my interest and have been reading a lot e.g. Hawkings, Al Khalili, Rovelli etc. I am still struggling with various things that relativity throws up.

For example I understand that gravity is not actually a force of attraction and that a body's natural state is to fall unless a force is exerted upon it (Newton - I understand this). Apparently therefore we are held on Earth not by the gravity pulling us down but by the Earth's thrust towards us.

I understand that acceleration and gravity are interchangeable, however if I am being held down here in the UK because of the Earth's acceleration underneath me, how come someone on the other side of the Earth is also held here, should they not fly off? Is it some type of force of attraction also being in operation as well or the revolution of Earth holding everyone down?

 

[phinds]

Summary:: Relativity & Gravity

I passed O level Physics in 1983 and loved it but went down the arts route. Over the last 5 years or so I re-kindled my interest and have been reading a lot e.g. Hawkings, Al Khalili, Rovelli etc. I am still struggling with various things that relativity throws up. For example I understand that gravity is not actually a force of attraction and that a body's natural state is to fall unless a force is exerted upon it (Newton - I understand this). Apparently therefore we are held on Earth not by the gravity pulling us down but by the Earth's thrust towards us. I understand that acceleration and gravity are interchangeable, however if I am being held down here in the UK because of the Earth's acceleration underneath me, how come someone on the other side of the Earth is also held here, should they not fly off? Is it some type of force of attraction also being in operation as well or the revolution of Earth holding everyone down?

The spacetime geodesic along which your body will travel if not interfered with by some force (such as that of the Earth preventing you from moving any further) points to the center of the Earth. A geodesic for someone in the antipodes ALSO points to the the center of the Earth.

 

[jbriggs444]

how come someone on the other side of the Earth is also held here, should they not fly off?

Curved space-time is the answer to why an outward proper acceleration in Sydney and an outward proper acceleration in London can leave the separation between those two cities constant.

Wrapping one's head around curved space-time is a learning process. One usually approaches it by analogy. Consider the surface (just the surface) of the spherical Earth. Consider two parallel lines going north from the equator along the surface of the Earth. Both lines are straight. Neither curves right or left. Yet they meet at the pole. The surface of the Earth is curved.

[Note that this is just a two dimensional analogy -- a two dimensional non-Euclidean space embedded in a three dimensional Euclidean space. It has nothing directly to do with the situation of the four dimensional curved pseudo-Riemannian space of General Relativity not embedded in anything else].

One might go from this introductory analogy to a discussion of "embeddings" and the distinction between intrinsic curvature and extrinsic curvature.

Eventually, one might arrive at a discussion of differential geometry, tensors and pseudo-Riemannian manifolds.

 

[Brooksie]

Curved space-time is the answer to why an outward proper acceleration in Sydney and an outward proper acceleration in London can leave the separation between those two cities constant.

Wrapping one's head around curved space-time is a learning process. One usually approaches it by analogy. Consider the surface (just the surface) of the spherical Earth. Consider two parallel lines going north from the equator along the surface of the Earth. Both lines are straight. Neither curves right or left. Yet they meet at the pole. The surface of the Earth is curved.

[Note that this is just a two dimensional analogy -- a two dimensional non-Euclidean space embedded in a three dimensional Euclidean space. It has nothing directly to do with the situation of the four dimensional curved pseudo-Riemannian space of General Relativity not embedded in anything else].

One might go from this introductory analogy to a discussion of "embeddings" and the distinction between intrinsic curvature and extrinsic curvature.

Eventually, one might arrive at a discussion of differential geometry, tensors and pseudo-Riemannian manifolds.

Thank you, unfortunately this is beyond me at this point.

 

[Ibix]

Thank you, unfortunately this is beyond me at this point.

Try this video by forum member A.T., which is a gentle introduction to straight lines in curved spacetime versus curved lines in flat spacetime.

 

[PeroK]

... if I am being held down here in the UK because of the Earth's acceleration underneath me ...

Two points:

1) that is a local acceleration, which applies only locally to you on your location on the Earth's surface. You canot assume the same acceleration (in terms of direction) globally across the Earth's surface.

2) Acceleration is not to be confused with motion. Although you are accelerating in a certain direction, that does not imply you are absolutely moving in that direction. You and an Australian may globally be accelerating in opposite directions, but that does not imply relative motion away from each other.

 

[Brooksie]

Try this video by forum member A.T., which is a gentle introduction to straight lines in curved spacetime versus curved lines in flat spacetime.

Thank you,

 

[A.T.]

if I am being held down here in the UK because of the Earth's acceleration underneath me, how come someone on the other side of the Earth is also held here,

The surface everywhere has a proper acceleration away from the center. See this posts:
https://www.physicsforums.com/threads/source-of-gravity-of-heavy-mass-as-per-gtr.998081/post-6440957
https://www.physicsforums.com/threa...ly-at-rest-begin-to-fall.995946/#post-6416452

 

[Dale]

Summary:: Relativity & Gravity

if I am being held down here in the UK because of the Earth's acceleration underneath me, how come someone on the other side of the Earth is also held here, should they not fly off?

This is a good question. It is because of spacetime curvature, but understanding the answer requires some background. Here is an article I wrote that should help you understand

https://www.physicsforums.com/insights/understanding-general-relativity-view-gravity-earth/