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I heard someone explain that if you were falling in space (i.e, a rooftop) you wouldn't sense gravity as a force acting upon you. But it would accelerate (≈ 9.8 m/s^2) , which to me suggest that a gravitation field exist.

How is a +charge moving in a uniform +electric field different? It would experience some acceleration in some direction. Just like a piece of mass would in falling. I can't see any difference

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  • $\begingroup$ All masses experience the same acceleration when falling in uniform gravity (in absence of other forces). Massive charged particles/objects accelerated by a uniform electric field (in absence of other forces) experience different accelerations depending on their mass. $\endgroup$ Commented Jun 1, 2023 at 13:49
  • $\begingroup$ Other answers are good, but for additional reading, look into the difference between body forces and surface forces. $\endgroup$
    – Ryan_L
    Commented Jun 2, 2023 at 3:41

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If you've ever been in an airplane taking off or a car taking a corner fast you'll know that you can feel the acceleration. This is commonly referred to as the g-force.

In general relativity this feeling of acceleration has a precise definition. It is called the proper acceleration. The definition is quite complicated but there is a simple way of understanding it. Drop an object then watch it to see if it accelerates away from you, and if it does then your proper acceleration is equal and opposite to the acceleration of the dropped object.

For example you may have seen video of astronauts on the International Space Station releasing objects and the object just floats next to them. This means their proper acceleration is zero, which we often describe as being weightless. Conversely if you drop an object it accelerates downwards at $9.81~\textrm{m/s}^2$ so your proper acceleration is 1$g$ - yes you are accelerating at 1$g$ even though you are not moving.

Anyhow, the point of all this is that when you are being accelerated by a gravitational field your proper acceleration is zero. This is unique to gravity. If I give you an electric charge and accelerate you with an electric field your proper acceleration will not be zero and you'll be able to feel the g-force. Likewise if I accelerate you using an airplane, car or even just an elevator. It is only when you are being accelerated by gravity that you feel weightless.

You may have heard it said that gravity is not a force, and statements like this are referring to the unique quality of gravitational acceleration i.e. that its proper acceleration is zero. In general relativity gravity is a geometrical property of spacetime not an external force being applied to you.

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    $\begingroup$ Don't you think it would be a good idea to rename gravity: Newton force, as in Archimede force, centrifugal force, Coriolis force? $\endgroup$
    – dan
    Commented Jun 1, 2023 at 6:07
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    $\begingroup$ @dan Good luck with that :-) I suspect we're stuck with the historical terminology now! $\endgroup$ Commented Jun 1, 2023 at 6:33
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    $\begingroup$ I don't think this is specific to gravity. If you are uniformly electrically charged and placed into a homogeneous electric field, you would not be able to feel anything: all parts of you are accelerating equally. In an elevator you can feel the compression from the floor due to acceleration that is transmitted through your body, but not the acceleration itself. $\endgroup$ Commented Jun 2, 2023 at 11:25
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    $\begingroup$ @Martin'Kvík'Baláž charges are discrete so there no such thing as a uniform charge. The best you could do is an approximately uniform charge. Even in this case there would be internal forces unless your object also had a uniform density. That's because the acceleration is proportional to q/m so higher density regions would accelerate more slowly than lower density regions. $\endgroup$ Commented Jun 2, 2023 at 12:31
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    $\begingroup$ @Martin'Kvík'Baláž The discrete nature of matter makes no difference to gravity because the gravitational mass is equal to the inertial mass. This means there is never any internal stress on any object of any shape and any density distribution in a uniform magnetic field. This is a feature shared by no other force. $\endgroup$ Commented Jun 2, 2023 at 14:07
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Observing your acceleration relative to external objects isn't what the person meant when they talked about sensing gravity as a force. When you are standing on the floor, you can literally feel the floor pressing against your feet. If you are falling freely, it feels to your body just as if you are in a space station far from any galaxy. This is meant to be an informal way of stating the Equivalence Principle, which says basically that you can't detect a gravitational field doing only local experiments.

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I heard it explained like gravity doesn't really accelerate you, you are just following your path through curved spacetime. The gravity you "feel" on Earth is because a bunch of rocks and stuff are in the way and applying a force to you and preventing you from following that natural path through curved space-time.

That is the 'force' that you feel. When standing, the rocks are applying a force to your feet to 'accelerate' you away from your natural path. This force is transferred throughout your body and skeleton. It takes energy to raise your arm not because gravity is pulling it down, but because the rocks are accelerating the rest of your body upwards.

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Since relativity introduces time as being a fourth dimension rather than simply being a parameter, we have to establish two kinds of acceleration: three-acceleration, and four-acceleration. The former is only with respect to spatial coordinates, while the latter is with respect to your time coordinate as well.

As falling bodies follow paths through spacetime called geodesics, they don't experience any four-acceleration. Four-accelerations are caused by things that cause you to not follow a geodesic, like electromagnetic interactions. That being said, we know that gravity "feels" like an acceleration, which is why the equivalence principle is so important.

In other words, since gravity doesn't impart a four-acceleration, it's not a force. Rather, it's what we call a pseudo-force.

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