Question about acceleration due to gravity

[Jpruyn]

Hi I am new to this and am edger to learn

 

This is a basic concept I am having a hard time understanding (please bear with me I know this a basic concept)

 

When a object falls of a high building, is the reason it accelerates towards the ground at 9.8m/s (ignoring wind resistance in this case) because:

 

: the object is following a geodesic in curved space towards the ground

 

: As the object gets closer to the ground gravity becomes stronger and time is realistically slower (gravitational time dilation)

 

:However the velocity of the object is conserved since no force is acting upon it (it is in free fall)

 

:However since the object is covering the same distance in less time (due to time dilation) it seems that the object has accelerated

 

Example with arbitrary numbers: It goes from taking 30 seconds a meter to 15 seconds a meter to 7.5 a meter (time decreasing because gravity is increasing)

 

I understand that there is coordinate acceleration and proper acceleration, and am wondering is this fits the criteria for one or the other

 

Also if this is true would this imply that gravitational time dilation causes acceleration, and that acceleration and curvature are somehow related

 

Is this correct or am I way off

 

Thanks for any help edger to learn

[mathematic]

Time dilation is not relevant for this example.

[Jpruyn]

So it has to do with geodesics and the geodesic equation than?

 

(In terms of math)

[ajb]

For these sort of situations you can safely describe things using Newtonian gravity. Over the distances of falling objects one can take the acceleration due to gravity as being constant. Any effects due to general relativity are going to be tiny.

 

Your real question is if geodesics and acceleration are related. Well, yes they are related.

 

The definition of the proper acceleration is the absolute derivative with respect to the proper time of the particles 4-velocity. You see that this is the geodesic equation. Thus in general relativity we see that geodesics are the paths taken by particles that are not acted up by any external forces. The only force is gravity, but we understand this not to be external, but due to the geometry of space-time.

[studiot]

 

: the object is following a geodesic in curved space towards the ground

 

No.

 

 

When a object falls of a high building, is the reason it accelerates towards the ground at 9.8m/s (ignoring wind resistance in this case) because:

 

 

This is a Newtonian statement, not a multidimensional spacetime one.

 

And it requires a Newtonian explanation.

 

Prior to falling off the building, high or low, the object is not moving.

 

So the first question is "Why did the apple fall at all"

 

Or in any system of mechanics what causes movement or under what conditions does movement occur?

Edited September 26, 2015 by studiot

[puppypower]

We model acceleration with GR, but this approach creates a middleman approach that has limits. Space-time is a dependent variable, since space-time does not just form wells all by itself in empty space void of matter and energy. The curving of space-time around the earth depends on earth's matter to curve it. The middleman approach of GR has a limitation, since middlemen, like space-time, don't have the final say.

 

If we look at the gravitational force, this is GR plus pressure. GR deals with space-time, while pressure deals with the interaction of matter to form various phases of matter and accompanied energy. Pressure and the phases of matter determine the final size and density distribution of matter, which then defines the shape and curvature of the space-time well.

 

Different materials can alter †he space-time well, due to different possible phases. It would not be easy to find gas planets with the same space-time well as our rocky earth planet. This has to do with matter phase differences and difference in mass density defining the parameters of space-time. Gravity can act on any form of matter.

 

 

That being said, acceleration is d/t/t or acceleration is one part distance and two parts time; It is space-time plus time. The extra time unit, beyond space-time reflects the impact of matter in shaping the space-time well defined for GR.

 

One way to explain this extra time unit is to consider the hypothetical situation of two space-time references, side by side. One reference is the standard and the other reference has time running slower. Say hypothetically, I could stand in the standard reference and then stick my arm into the slow reference. What I will do is dribble a basketball in the slow reference, while retaining my connection to the standard reference.

 

When I push the ball down to dribble it, because time is running slower, the ball does not respond properly relative to my reference The ball appears to lag. What I will need to do is push harder to compensation for the slowed time, so the ball appears to move the same as it should in the standard reference. When the ball rebounds the floor and hits my hand, it is moving properly, but it now has this extra inertia as though its mass has increased in my reference. It will require more force than normal to counteract the inertia of the mass, to get the expected ball reaction.

 

If you notice a simple time reference difference has created what appears to be changes in force, mass, acceleration and inertia relative to the standard. Mass is form of time potential.

[Strange]

We model acceleration with GR, but this approach creates a middleman approach that has limits. Space-time is a dependent variable, since space-time does not just form wells all by itself in empty space void of matter and energy. The curving of space-time around the earth depends on earth's matter to curve it. The middleman approach of GR has a limitation, since middlemen, like space-time, don't have the final say.

 

The curvature of space-time by mass-energy, and the effect of that curvature on mass is the strength of GR, not a limitation.

 

If we look at the gravitational force, this is GR plus pressure.

 

GR takes pressure into account.

 

Different materials can alter †he space-time well, due to different possible phases.

 

In what way does the phase affect space-time (other than a difference in density and, perhaps, pressure)?

 

It would not be easy to find gas planets with the same space-time well as our rocky earth planet. This has to do with matter phase differences and difference in mass density defining the parameters of space-time.

 

So what? And that has nothing to do with GR or space-time. Netonian gravity has to take density into account as well.

 

That being said, acceleration is d/t/t or acceleration is one part distance and two parts time; It is space-time plus time. The extra time unit, beyond space-time reflects the impact of matter in shaping the space-time well defined for GR.

 

That is nonsense.

 

One way to explain this extra time unit is to consider the hypothetical situation of two space-time references, side by side.

 

What is a "space-time reference"?

 

Mass is form of time potential.

 

Nonsense.

[swansont]

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Moderator Note

Please stick to mainstream physics in answering the question. Personal theories belong in speculations.