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So this question has been bothering me for several days now. I've seen many YouTube videos on how "Gravity is not a Force", but no one seems to offer a simple explanation on how does this "accelerating up" thing works for the entire planet. A person sitting in India is accelerating up and so is someone in the United States, for example? How does that actually work? In simple words, exactly what is it that makes us glued to the ground?

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    $\begingroup$ You are accelerating up because the earth's surface prevents you from falling toward its center of mass when you just follow a geodesic. $\endgroup$ – Jeanbaptiste Roux May 9 at 16:44
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    $\begingroup$ In Newton’s theory, falling apples on opposite sides of the Earth both accelerate down. Isn’t that just as strange? $\endgroup$ – G. Smith May 9 at 17:09
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    $\begingroup$ The equivalence principle is about local frames and it does not apply for frames as large as a planet. It does not take curvature of the object into account. $\endgroup$ – shai horowitz May 9 at 18:11
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If there were no forces acting between atoms, then all the particles making up the Earth (and us) would continue on their paths towards the Earth's center of mass. The Earth would get smaller and smaller, eventually forming a black hole, and everything would keep falling forever (roughly speaking... I don't want to get into black hole physics here).

Fortunately for us, there are other forces at play, such as electrostatic repulsion between atoms, forces due to the Pauli exclusion principle, and pressure due to heat. All of these provide an upward force that accelerates matter away from its normal path towards the center of mass. And these are what keep you glued to the ground... or more accurately, keep you from falling through the ground (which is what your atoms would naturally do, they "want" to follow a geodesic path through spacetime). The atoms in your shoes are repelled upwards by the atoms in the floor... those atoms in turn are repelled upwards by atoms in the ground, and so on all the way down.

Visualizing how the longest paths through spacetime all lead towards the center of the Earth is tricky, because spacetime is 4 dimensional (and the time dimension very much matters -- it's spacetime that is curved, not space alone). This video provides some images that might help a bit.

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Imagine a really deep hole in the ground (obviously this can be anywhere!). If you step into it you fall inwards (geodesic motion). If you activate your rocket pack you can return to ground level. By tuning the thrust you can remain level with the surface. That thrust is equal to the outward acceleration that the earth is imparting to everyone else on the surface, wherever they are.

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Since spacetime is curved due to Earth’s mass we have to visualise curvature to affect Earth from all sides and places therefore when we say that the ground is accelerating upwards to our feet irrespective of whichever location we are on Earth. We have to think about acceleration in these cases to be a deviation from a geodesic (path that an object in inertial motion tends to take). So people that are standing on buildings/ground are moving upwards in a straight line when observed from a falling person who is an inertial observer falling along a geodesic hence not accelerating.

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Gravity is a force. But it belongs to the class of inertial forces, the type that acts on the whole volume of bodies, and not through a contact surface.

When we think of an experience to test the $2^nd$ Newton's law $F = ma$, it is like a spring pulling some object. The deflection of the spring shows that there is a force, and the acceleration of the mass can be measured. But there is a surface region of contact between the spring and the mass. We can not do it with a loosely bunch of bricks.

But inertial forces are different. If some luggage is left on the floor when a plane lands and decelerates, all of them accelerates forward for the people in the plane.

Any spring that moves together with the luggages will not deflect. On the other hand, if we hold one of them keeping it at rest using a spring, its deflection shows that there is a force present.

It is exactly what happens with gravity. Any loose object or bunch of objects will move down, but feeling no force while falling. On the other hand, a mass hanging from a spring shows that there is a downward force present.

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When you look at it, you'll find that gravity acts exactly like a low pressure system in the weather. Everything is sucked towards the centre of the low pressure system, and everything is sucked in towards the centre of the Earth. In the weather, the low pressure system is in the air. With gravity, the low pressure system is in time; i.e. time runs slower on Earth than in space, so things are sucked towards the low pressure of time.

There are a number of reasons why you can equate gravity with a low pressure system:

First, all objects fall with the same acceleration, exactly the same as objects will rise in the water (from high to low pressure) with the same acceleration.

Second, the wind circles around in a circle around a weather low, and Gravity Probe B showed us that gyroscopes in a satellite around Earth do not point straight down, but are tilted slightly, reflecting the speed of light as compared to the speed of wind.

Third if you look at two galaxies merging (or example the Antennae Galaxies) you will see that it looks exactly like two typhones merging (the Fujiwharea Effect).

I have seen videos that show that objects fall because time runs faster in the top of the object than at the bottom of the object. I believe this is an incorrect interpretation. Rather, it is because the time IN SPACE above the object runs faster than below the object. This is the same as water pressure as you go deeper in the ocean. A cork rises because the water pressure below the object is higher than the water pressure above the object.

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    $\begingroup$ A cork rises because of water displacement to weight ratio. A lead weight also has higher water pressure below than above. $\endgroup$ – Adrian Howard May 9 at 17:57
  • $\begingroup$ @AdrianHoward What you are looking at is the effect of the medium in which the object sits, whether it be a rock in water or a helium balloon in the air. But if we remove the medium, in a vacuum, then it no longer is a factor. A helium balloon falls on the moon, just as fast as a rock. Look here and you will see a bubble inside water in space. usgs.gov/special-topic/water-science-school/science/… Air still has less density than water, but the gravity effect is eliminated. $\endgroup$ – foolishmuse May 9 at 20:22

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