Why is g = 9.8 and from where/what triggers the upward acceleration?

[Abi1007]

We know that we are being accelerated upward at 9.8 m/s^2 which prevents us falling toward the core of earth through our geodesic. But, from where and what triggers the upward acceleration? Google AI mode says that it is electrostatic repulsion but I suspect that. And as the earth itself is following a geodesic due to gravity created by sun through spacetime curvature, does that contribute anywhere to this upward acceleration? How is it 9.8?

 

[Roberto Pavani]

The upward proper acceleration is provided by the electromagnetic contact forces exerted by the ground. Its magnitude is about $9.8 m/s^2$ because the Earth's gravitational field at the surface is $g = \frac{G M_\oplus}{R_\oplus^2}$ which follows directly from Gauss' law (or equivalently Newton's shell theorem).
A freely falling observer follows a geodesic; a person standing on the ground does not.

 

[A.T.]

But, from where and what triggers the upward acceleration?

From whatever prevents free fall and holds you at constant height.

And as the earth itself is following a geodesic due to gravity

Only the center of the Earth is in free fall and thus follows a geodesic.

 

[Abi1007]

The upward proper acceleration is provided by the electromagnetic contact forces exerted by the ground. Its magnitude is about $9.8 m/s^2$ because the Earth's gravitational field at the surface is $g = \frac{G M_\oplus}{R_\oplus^2}$ which follows directly from Gauss' law (or equivalently Newton's shell theorem).
A freely falling observer follows a geodesic; a person standing on the ground does not.

If the ground is constantly accelerating upward, why doesn't the earth expand?

 

[loop quantum gravity]

If the ground is constantly accelerating upward, why doesn't the earth expand?

There are two forces acting on Earth's surface:
Gravity pushing us downwards and that which reacts to it is the force exerted by the pressure our bodies exerting on the surface, which according to Newton's third law is the normal force contrary to gravity.
Or you might say that the core of Earth's is the one that exerts the opposite force to gravity. Those two forces balance each other (approximately).
In the stars there's the fusion energy that react to gravity's pull.
At least that's what I can recall from Intro to Astrophysics way way back; I need to reread those materials.

 

[Ibix]

If the ground is constantly accelerating upward, why doesn't the earth expand?

Because this is curved spacetime, and the freefall paths of particles at the surface of the Earth always point downwards, not horizontally. So if they didn't accelerate upwards they'd fall towards the center of the Earth.

 

[Ibix]

There are two forces acting on Earth's surface

The OP seems to be asking in the context of general relativity, where there is only the reaction force. Gravity is not a force in this model.

 

[Ibix]

If the ground is constantly accelerating upward, why doesn't the earth expand?

This animation by @A.T. is a good illustration:

 

[A.T.]

This animation by @A.T. is a good illustration:

The below image shows how the local geometry in the above animation above fits into the global picture. The two green apples still hanging on the branches have both proper acceleration pointing outwards, without moving apart.

 

[A.T.]

If the ground is constantly accelerating upward, why doesn't the earth expand?

Even in Newtonian mechanics accelrating towards eachother doesn't imply getting any closer together. Think about the opposite sides of a spinning object.

In General Relativity accelrating away from eachother doesn't imply getting further apart. The above video and graphics might help.

Also see the links in this post:
https://www.physicsforums.com/threa...of-spacetime-1s-1t-in-3d.996487/#post-6421761

 

[Sagittarius A-Star]

If the ground is constantly accelerating upward, why doesn't the earth expand?

That's because the related coordinate-acceleration of the ground is relative to a local free falling coordinate-system. Such an inertial coordinate-system could be for example at rest in a free-falling elevator-cabin.

 

[Roberto Pavani]

I think the phrase "we are accelerated upward" can be misleading if taken too literally.
We are not moving upward relative to the Earth. Rather, we have an upward proper acceleration relative to a local freely-falling frame.

 

[Dale]

If the ground is constantly accelerating upward, why doesn't the earth expand?

Because spacetime is curved.

 

[Dale]

Rather, we have an upward proper acceleration relative to a local freely-falling frame.

Proper acceleration is not relative. We have an upward proper acceleration. Full stop.

Relative to a local freely-falling frame we also have an upward coordinate acceleration.

 

[PeroK]

If the ground is constantly accelerating upward, why doesn't the earth expand?

Acceleration and velocity are not the same thing. An object moving in a circle at constant speed has constant centripetal acceleration towards the centre of the circle. But, it's not moving towards the centre of the circle.

 

[Roberto Pavani]

Fair enough, I missed a comma.

“We have an upward proper acceleration, with ‘upward’ defined relative to a local freely-falling frame.”

 

[Sagittarius A-Star]

The proper acceleration is equal to the (momentary) coordinate-acceleration with reference to a momentarily co-moving inertial coordinate-system.

Details:

Undergrad Post in thread 'SR textbooks covering accelerated reference frames without GR'

Nov 6, 2023

such as the fact that at any point along the worldline of an accelerating observer, certain local space-time information in the frame of the observer can be carried over from the instantaneous inertial rest frame

That can be done to understand Rindler-coordinates.

Source:​

https://www.geogebra.org/m/dYyg5ZB8#material/NnrRvA46​

The diagram shows two instantaneous co-moving inertial reference-frames $S$ and $S'$.
A worldline of constant spacetime-distance from the origin of a Minkowski diagram is the following hyperbola:
$$x(t)^2 - c^2t^2 =...

• Sagittarius A-Star

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[ioannisakousoulakos]

No , according to GR and at the extent I am able to understand , there is no upward acceleration from the ground . The moment you contact the ground you are part of its gravitational system therefor your Geodesic is absorbed from the grounds Geodesic and replaced by it .If you jump up with enough force ( maybe as Lebron James .. ) your Geodesic will be recreated at upwards vertical v=0 the curvature of spacetime reinitiates and the procces will be repeated

 

[Dale]

according to GR and at the extent I am able to understand , there is no upward acceleration from the ground

This is incorrect. There is an upwards proper acceleration for objects on the ground. It can be measured with an accelerometer.

 

[ioannisakousoulakos]

This is incorrect. There is an upwards proper acceleration for objects on the ground. It can be measured with an accelerometer.

I Think you might confusing the reading of a device (proper acceleration) with actual physical motion through space (coordinate acceleration). When the accerelometer stands on the ground is a subject of the grounds Geodesic so all it does is to show inverted the G force .
An accelerometer on the ground reads +9.8 m/s² upward because the spacetime curvature is pulling its internal test mass downward, forcing the device's internal springs to compress upward to support it . The device is literally measuring the inverted resistance to a downward gravitational pull.

 

[A.T.]

The moment you contact the ground you are part of its gravitational system

This makes zero sense. Nothing changes about gravity itself by the contact.

therefor your Geodesic is absorbed from the grounds Geodesic

This is just wrong. The ground doesn't have a geodesic worldline, because just like the things resting on the ground, it experiences proper acceleration upwards.

 

[A.T.]

I Think you might confusing the reading of a device (proper acceleration) with actual physical motion through space (coordinate acceleration).

The accelerometer reading (proper acceleration) is the actual physical measure. Coordinate acceleration is just a matter of coordinate choice.

 

[ioannisakousoulakos]

This makes zero sense. Nothing changes about gravity itself by the contact.

This is just wrong. The ground doesn't have a geodesic worldline, because just like the things resting on the ground, it experiences proper acceleration upwards.

When you say 'the ground doesn't have a geodesic because it experiences proper acceleration,' you are playing a semantics game. Spacetime curvature around a static mass is stationary. The Earth’s surface is not expanding, it is not moving, and its coordinate acceleration through space is exactly zero. And as for the zero sense on contact , when I say the ground absorbs your geodesic, it means that the moment you make solid contact, your independent free-fall trajectory is arrested. You become a static, unified part of the Earth’s bound molecular matrix. Your worldline is now physically locked to the Earth's worldline.

 

[ioannisakousoulakos]

The accelerometer reading (proper acceleration) is the actual physical measure. Coordinate acceleration is just a matter of coordinate choice.

Now we are not being very logical, are we? Do you imply axiomatically that the misreading and misinterpretation of an accelerometer should be taken as a literal, physical value?
If so, where is the expansion of the Earth? Because unless I am mistaken, the entire geological and scientific bibliography confirms that the Earth has maintained the exact same diameter for the last billion years.
You cannot have real, ongoing upward physical acceleration without continuous spatial expansion. Therefore, the 1g reading is not a measurement of upward motion; it is a measurement of mechanical resistance against a stationary downward effect.
For the last time =To argue that the ground is literally 'accelerating upwards' to explain why we stay pinned down—without any change in physical spatial coordinates—is treating a geometric mathematical description as a real mechanical rocket propulsion. An accelerometer on the ground reads 1g for one reason only: it is measuring the continuous inverted electrostatic resistance of the molecular lattice keeping its internal test mass from collapsing downward.

 

[Mike_bb]

Spacetime curvature around a static mass is stationary. The Earth’s surface is not expanding, it is not moving, and its coordinate acceleration through space is exactly zero.

No. If you are staying at rest on the ground you are moving through the time in spacetime.

 

[Sagittarius A-Star]

You cannot have real, ongoing upward physical acceleration without continuous spatial expansion.

You can. The following experiment proved, that the surface of Earth has a proper upwards acceleration of $9.81 \ m/s^2)$.

The Pound–Rebka experiment monitored frequency shifts in gamma rays as they rose and fell in the gravitational field of the Earth.

https://en.wikipedia.org/wiki/Pound–Rebka_experiment

Reason:

High School Post in thread 'Physicists .... help me understand free fall & acceleration'

Sep 18, 2026

Similarly, if every atom of an accelerometer was simultaneously accelerated by gravity, it would read 0G, no?

Yes, but then it would not be an acceleratometer.

You can also construct an accelerometer with a lamp and a light sensor, mounted at constant distance.
A proper acceleration leads to a Doppler frequency-shift, because after the finite time, a light pulse needs from the lamp to the sensor, the sensor is already moving faster than the lamp, when it sent out the light pluse.

If such an accelerometer is at rest relative to the surface of Earth, then the measured...

• Sagittarius A-Star

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[Dale]

I Think you might confusing the reading of a device (proper acceleration) with actual physical motion through space (coordinate acceleration)

I think you are confusing coordinate artifacts for physical motion. Coordinates can be changed on a whim, so coordinate dependent things are not “actual physical”, including coordinate acceleration.

The proper acceleration is the actual physical acceleration. It is measured by actual physical accelerometers, requires actual physical forces, and can have actual physical effects.

The coordinate acceleration is only math and can be changed arbitrarily with no physical effects. Coordinates cannot be detected, only assigned.

The device is literally measuring the inverted resistance to a downward gravitational pull.

It certainly does not. Remove the ground and the measurement drops to zero despite the gravitational pull remaining. Remove gravity and push the accelerometer with a real force and the reading is non-zero despite having zero gravity.

Accelerometers do not detect the gravitational force, nor other fictitious forces. They only detect real physical forces.

You cannot have real, ongoing upward physical acceleration without continuous spatial expansion.

Sure you can. That is what spacetime curvature does.

 

[ioannisakousoulakos]

No. If you are staying at rest on the ground you are moving through the time in spacetime.

Of course so you dont move in space in spacetime

 

[ioannisakousoulakos]

I think you are confusing coordinate artifacts for physical motion. Coordinates can be changed on a whim, so coordinate dependent things are not “actual physical”, including coordinate acceleration.

The proper acceleration is the actual physical acceleration. It is measured by actual physical accelerometers, requires actual physical forces, and can have actual physical effects.

The coordinate acceleration is only math and can be changed arbitrarily with no physical effects. Coordinates cannot be detected, only assigned.


It certainly does not. Remove the ground and the measurement drops to zero despite the gravitational pull remaining. Remove gravity and push the accelerometer with a real force and the reading is non-zero despite having zero gravity.

Accelerometers do not detect the gravitational force, nor other fictitious forces. They only detect real physical forces.


Sure you can. That is what spacetime curvature does.

It is movement on spacetime that reffers to the Time field , the geocoordinates remain the same

 

[Ibix]

It is movement on spacetime that reffers to the Time field , the geocoordinates remain the same

To repeat what everyone else has said, it is the proper acceleration that is the direct observable. This is the lesson you are supposed to have taken from Einstein's lift thought experiment. If you are in a closed box (such as a lift) there is no local way to distinguish between the cases that the lift is at rest on the surface of a planet or in a rocket in deep space under thrust. In both cases you can measure identical weight from a given mass. Nor is there any way to distinguish between free falling above an (airless) planet and floating inertially in deep space. And in any of these cases you may consider yourself to be at rest or undergoing coordinate acceleration.

The only physically meaningful quantity here is the proper acceleration.