Problem in understanding how upwards acceleration works (General Relativity)

[Mike_bb]

Hello, PF!

As is known, if body stays on the ground then body is accelerated upwards by the ground.
For example, free-falling observer see that body on the ground move to him with acceleration $9.81m/s^2$

I have a problem in understanding how it is possible.

If the body is being accelerated by the ground then this is only to prevent body to fall down. But how is it possible that body accelerates (and move) relative to free-falling observer?

Thanks.

 

[Dale]

But how is it possible that body accelerates (and move) relative to free-falling observer?

Can you explain your confusion here? What would make you think it is not possible?

You can drop an object and visually see that relative to the object the ground is moving.

 

[Mike_bb]

Can you explain your confusion here? What would make you think it is not possible?

Free-falling motion assumes that falling observer is at rest or moving inertially. But body on the ground doesn't lose contact with the support. Nevertheless, body on the ground moves with upward acceleration. I can't understand how.

 

[Roberto Pavani]

body on the ground moves with upward acceleration.

You have to specify the reference frame to define motion, that's the key.

Here perhaps a too simple explanation:

Three stones: A and B rest on the ground, C falls.
A: "B is at rest relative to me, we both feel an acceleration ($F/m = g$), and C falls toward us."
C: "I feel nothing ($F/m = 0$), and I see A and B accelerate toward me."

 

[A.T.]

But how is it possible that body accelerates (and move) relative to free-falling observer?

This isn't specific to General Relativity, but also applies to Newtonian mechanics, which you should properly understand first, before tackling Relativity.

 

[Mike_bb]

This isn't specific to General Relativity, but also applies to Newtonian mechanics, which you should properly understand first, before tackling Relativity.

Why? I can't provide link but I saw that this is example from GR.

 

[Halc]

But how is it possible that body accelerates (and move) relative to free-falling observer?

This isn't specific to General Relativity, but also applies to Newtonian mechanics, which you should properly understand first, before tackling Relativity.

There are important differences between the two, but A.T. is correct in pointing out that the concept of reference frames (inertial or not) and of acceleration are common between Newton and GR.

It is possible that a body accelerates relative to a free falling observer simply by that body having a force applied to it. So the free falling observer can light a bottle rocket and off it goes (good trick in vacuum, but I didn't say vacuum).

Differences: Under Newtonian mechanics, gravity is exerting a continuous force on everything near Earth. So a house is stationary because the downward force of gravity is perfectly cancelled by an equal and opposite force applied upward by the ground. The guy jumping off the cliff accelerates due to gravity since nothing counters the force (at first).

Under GR, there is no gravitational force, so the guy jumping off the cliff has no forces applied to him (again, at first), so he's in free fall. No acceleration and no proper acceleration. The house on the other hand has an unbalanced force applied upward to it, so it (and the observer on the ground) all accelerate upwards. They have positive proper acceleration, as can be measured by any accelerometer.

As for reference frames, those two guys each using reference frames where they are stationary and the other guy is moving. Under Newton, the free falling guy is using an accelerating reference frame and the guy in the house is in using an inertial one. Under GR it's the other way around, with the freefalling guy being inertial and the guy on the ground using an accelerating frame.

The bold part answers your question in post 3

 

[Mike_bb]

You have to specify the reference frame to define motion, that's the key.

Here perhaps a too simple explanation:

Three stones: A and B rest on the ground, C falls.
A: "B is at rest relative to me, we both feel an acceleration ($F/m = g$), and C falls toward us."
C: "I feel nothing ($F/m = 0$), and I see A and B accelerate toward me."

Good. Is this explanation work if C is at rest on the height?