Freefall and gravity

[Ranku]

An object in freefall does not experience gravity, while an object on the ground does. Because the object in freefall does not experience gravity, it is considered to be in a locally inertial frame of reference, whereby the principle of equivalence is applicable, and which enables the extension of the postulate of relativity, and gravity can therefore be described by general relativity. Because an object on the ground experiences gravitational acceleration, that would imply that it is not in a locally inertial frame of reference, and therefore the principle of equivalence would not apply, and therefore the postulate of relativity cannot be extended. So how would gravity upon an object on the ground then be described by general relativity?

 

[Sagittarius A-Star]

Because an object on the ground experiences gravitational acceleration, that would imply that it is not in a locally inertial frame of reference, and therefore the principle of equivalence would not apply

The principle of equivalence applies. The object is locally at rest with reference to an upward accelerated frame. This situation is equivalent to an object in an accelerated rocket in flat spacetime.

 

[Ibix]

The equivalence principle just says that you can't tell the difference between accelerating in deep space and standing on a planet, at least not by local measurements. When you express it mathematically it turns out just to mean that you can always pick coordinates so the first derivatives of the metric vanish at an event, and there exist "small" regions around that event where the second derivatives are negligible.

If you want to use local inertial frames to describe an object sitting on a planet you can do so - it's accelerating so isn't at rest more than instantaneously, but that isn't a problem. The difference between this and Newtonian gravity is that Newtonian gravity posits a global inertial frame and an object on the surface of a planet is at rest because the gravitational and contact force from the ground are equal and opposite, where general relativity says that there is only one force, the contact force from the ground, and this is accelerating the object. That acceleration is the source of the feeling of weight.

 

[Nugatory]

An object in freefall does not experience gravity, while an object on the ground does. Because the object in freefall does not experience gravity, it is considered to be in a locally inertial frame of reference, whereby the principle of equivalence is applicable, and which enables the extension of the postulate of relativity, and gravity can therefore be described by general relativity. Because an object on the ground experiences gravitational acceleration, that would imply that it is not in a locally inertial frame of reference, and therefore the principle of equivalence would not apply, and therefore the postulate of relativity cannot be extended. So how would gravity upon an object on the ground then be described by general relativity?

Objects "experiencing gravity", whether in freefall or not, is not part of the theory of general relativity; it's a misunderstanding that you will have to unlearn before you can start learning how GR works. The concept that replaces it is "proper acceleration".
You should also learn why it makes no sense to talk of objects "being in a frame of reference", whether inertial or not, local or not. All objects are always in all reference frames all the time; for any reference frame the question is whether it is inertial and whether the object is at rest in that frame.

So the premise of your question is flawed. An accurate description would say that an object on the ground is experiencing proper acceleration from the force of the ground on the object, and this statement will be true no matter what reference frame we choose when we're analyzing the situation - nothing requires that we use the non-inertial frame in which the object and the surface of the earth are at rest. Similarly, an object in freefall experiences zero proper acceleration, and again this statement is true no matter what reference frame we choose.

 

[Ranku]

So the premise of your question is flawed. An accurate description would say that an object on the ground is experiencing proper acceleration from the force of the ground on the object, and this statement will be true npo matter what reference frame we choose when we're analyzing the situation - nothing requires to use the non-inertial frame in which the object and the surface of the earth are at rest. Similarly, an object in freefall experiences zero proper acceleration, and again this statement is true no matter what reference frame we choose.

What determines a freefalling object experiencing zero proper acceleration and an object on the ground experiencing proper acceleration?

 

[Ibix]

What determines a freefalling object experiencing zero proper acceleration and an object on the ground experiencing proper acceleration?

You can measure proper acceleration locally. Put a mass on a spring balance held at rest with respect to you. Does it register weight? If so, you're accelerating. If not, you're inertial.

 

[PeroK]

What determines a freefalling object experiencing zero proper acceleration and an object on the ground experiencing proper acceleration?

The ground applies an upward force on an object. That stops it falling any further. If there is a hole in the ground the objects falls down the hole until an upward force stops it.

 

[Nugatory]

What determines a freefalling object experiencing zero proper acceleration and an object on the ground experiencing proper acceleration?

Proper acceleration is measured with an accelerometer. Imagine a cubical box with six springs inside; one end of each spring is attached to one of the six sides of the box and the other end is attached to a mass suspended in the center of the box by the six springs.

In freefall (zero proper acceleration) the mass will be held in the center of the box by the balanced force of all six springs. Any movement of the mass away from the center indicates that the box is experiencing proper acceleration. In the elevator and on the surface of the earth the mass will move towards the bottom of the box as the upper spring is stretched and the lower spring relaxes. We interpret this as the box experiencing proper acceleration upwards from the force of the ground/floor pushing the box up; the upper spring is stretched as it pulls the mass along.

 

[Dale]

What determines a freefalling object experiencing zero proper acceleration and an object on the ground experiencing proper acceleration?

That can be determined with an accelerometer.

Edit: I see I am late to respond

 

[robphy]

Get an app like https://phyphox.org/
which lets you get the raw accelerometer data.

While holding my phone at rest with my phone facing upwards, the accelerometer reads a_z=9.8\ \rm{m/s^2}.
After about half-a-second, I dropped my phone over the middle of a bed.
Note that, in freefall, the accelerometer read a_z=0.0\ \rm{m/s^2}.
It bounced and tumbled a little bit before coming to rest face up on the bed, when it reads a_z=9.8\ \rm{m/s^2} again.

 

[A.T.]

Because an object on the ground experiences gravitational acceleration,

This is a highly misleading statement, that confuses different types of acceleration, which also have opposite directions. The correct statement is:

An object on the ground experiences upwards proper acceleration due to the contact force with the ground, which has the same magnitude as the local gravitational downwards coordinate acceleration relative to the ground.