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

[ioannisakousoulakos]

A debate has started where the accelerometers

when stacic on the ground produce real acceleration towards the surface or propper acceleration (α) / free falling ( Geodesic ) . Lets figure out what the GR says about all this .

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.

Sir I 100% agree with you and maybe I sould differentiate the term proper from the very beggining , so there is no real acceleration towards the sky and the value taken is because the ground exerts a mechanical normal force that prevents the device from entering free fall as its path deviates from a geodesic.

 

[Ibix]

I sould differentiate the term proper from the very beggining ,

Yes, you should have done.

there is no real acceleration towards the sky

You haven't defined what you mean by "real acceleration". If you mean "coordinate acceleration in the frame in which the ground and sky are at rest", which appears to be what you mean, then your statement is simply a tautology - the ground does not move in a coordinate system where it is at rest. If you mean something else, then you should define your term.

the ground exerts a mechanical normal force that prevents the device from entering free fall as its path deviates from a geodesic.

Yes, this is the proper acceleration, and it is directed upwards. It is the only acceleration defined without reference to something external that you arbitrarily define to be "not accelerating".

 

[Dale]

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

Both the time field and the coordinates are a matter of convention, not a fact of nature.

 

[Nugatory]

A debate has started where the accelerometers when stacic on the ground produce real acceleration towards the surface or propper acceleration (α) / free falling ( Geodesic ) .

There is no such thing as "real acceleration", at least until you provide a definition of this non-standard term. There is proper acceleration, which is invariant, independent of coordinate choice, what an accelerometer (calibrated to read zero in free fall, as opposed to zero at rest on the surface of the earth) reads; and there is coordinate acceleration, which is merely the second derivative of the position coordinates with respect to the time coordinate. Whether the latter is zero or not tells us nothing except that the coordinate system has been chosen to produce that value.

 

[Dale]

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

To understand why this is false in a curved space, it is important to understand how acceleration is represented. Newton's first law says that a free body moves along a straight line at constant speed. In spacetime this is simply a straight line. So, an inertial body moves along a geodesic, which is indicated physically by an attached accelerometer that reads 0. Conversely, an accelerating body is represented by a worldline that is not a geodesic but has a curve.

Now, in flat spacetime, a worldline with constant curvature to the right forms a hyperbola that opens to the right, and a worldline with constant curvature to the left forms a hyperbola that opens to the left. The distance between the two increases as you go along the time direction.

Consider a curved spacetime in the shape of a sphere, with space being the north-south direction and time being the east-west direction. The equator is a great circle, so it is a geodesic and does not curve either left or right. Now, consider the latitude lines at 5 degrees north and south of the equator. These are not great circles, so they are curving. Specifically the 5 degree north latitude line curves north and the 5 degree south latitude line curves south. The curvature is constant and always in the north-south direction. These are the worldlines of two bodies that are constantly accelerating away from each other.

However, note that as you go east-west (time) the distance (north-south) between these two lines remains constant. So in curved spacetime continuous proper acceleration away from another worldline does not imply that the distance between the worldlines will increase. It is therefore simply false that upward acceleration implies spatial expansion.

 

[A.T.]

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

Yes, you can. Note that even in Newtonian physics, acceleration is not motion. And in GR you can have ongoing upward (outward) proper acceleration without continuous spatial expansion.

See post #9 and #10. And chapter 10 of this book for an introduction:
https://archive.org/details/L.EpsteinRelativityVisualizedelemTxt1994Insight/page/n157/mode/2up

Do you imply axiomatically that the misreading and misinterpretation of an accelerometer should be taken as a literal, physical value?

Yes, that is the key difference of the General Relativity interpretation compared to the Newtonian interpretation: In GR taking the accelerometer reading literally is not a "misinterpretation", but what actually defines inertial frames vs accelerated frames.