Gravity question: Why do things fall?

[staballoy]

I understand that mass warps spacetime, and am well familiar with the bowling ball/rubber sheet analogy, but that to me is a depiction without explanation of the process. It doesn't explain for me what actually causes an object, Newton's apple for example, to accelerate toward another mass, in this case the Earth. I recall seeing an explanation on a PBS show years ago called Einstein's Universe, that involved gravitational time dilation causing acceleration, IIRC, but can't remember the details. I am an interested non-mathematical layperson, so any explanation is appreciated.

 

[mgb_phys]

It doesn't explain for me what actually causes an object, Newton's apple for example, to accelerate toward another mass, in this case the Earth.

Basically we don't know.
Newton's laws say objects attract each other because of their mass, Einstein's theory says mass curves space - but these are just ways of saying 'because it does'.

 

[A.T.]

I understand that mass warps spacetime, and am well familiar with the bowling ball/rubber sheet analogy, but that to me is a depiction without explanation of the process. It doesn't explain for me what actually causes an object, Newton's apple for example, to accelerate toward another mass, in this case the Earth.

The ball/rubber sheet analogy doesn't explain Newtons gravity. This is explained in this post (check also the links there):
https://www.physicsforums.com/showpost.php?p=2046692&postcount=4

I recall seeing an explanation on a PBS show years ago called Einstein's Universe, that involved gravitational time dilation causing acceleration, IIRC, but can't remember the details. I am an interested non-mathematical layperson, so any explanation is appreciated.

Gravitational time dilation and mass attraction are both effects of a distorted time dimension:
http://www.physics.ucla.edu/demoweb...alence_and_general_relativity/curved_time.gif

 

[JesseM]

Are you asking why mass curves spacetime in the first place, or are you asking why, given that mass curves spacetime in this way and that objects follow geodesics in curved spacetime, it so happens that geodesic paths near a massive object will have the property that the smaller objects seem to accelerate towards the larger one from the perspective of an observer on the surface?

 

[staballoy]

Are you asking why mass curves spacetime in the first place, or are you asking why, given that mass curves spacetime in this way and that objects follow geodesics in curved spacetime, it so happens that geodesic paths near a massive object will have the property that the smaller objects seem to accelerate towards the larger one from the perspective of an observer on the surface?

I'll take answers to both. The diagram from the link offered above (http://www.physics.ucla.edu/demoweb...alence_and_general_relativity/curved_time.gif) helps a bit. If I understand correctly, the passage through time slows the closer an object is to a another mass, but passage through space accelerates, like approaching the speed of light, where the faster an object moves through space, the slower it moves through time.

 

[JesseM]

I'll take answers to both. The diagram from the link offered above (http://www.physics.ucla.edu/demoweb...alence_and_general_relativity/curved_time.gif) helps a bit. If I understand correctly, the passage through time slows the closer an object is to a another mass, but passage through space accelerates, like approaching the speed of light, where the faster an object moves through space, the slower it moves through time.

Well, there isn't really an answer to why mass curves spacetime, every theory of physics just has some basic ground assumptions which aren't derived from anything else, and which are justified solely in terms of the accuracy of the resulting theory. I think you can show that curved spacetime is a necessity if you start out with some other basic assumptions like the equivalence principle, though, but those other assumptions have to be taken as given.

As for the second question, if you found the diagram A.T. posted useful, I remember A.T. posted a bunch more diagrams based on the "curved time" visualization in post #4 of this thread, so you may want to take a look at those links.

 

[A.T.]

The diagram from the link offered above (http://www.physics.ucla.edu/demoweb...alence_and_general_relativity/curved_time.gif) helps a bit. If I understand correctly, the passage through time slows the closer an object is to a another mass, but passage through space accelerates, like approaching the speed of light, where the faster an object moves through space, the slower it moves through time.

Yes but this are two different time dilation effects: 1) advancing more along the space dimensions and less along time dimension. 2) having longer distances along the time dimension to go. You can examine both in closeup here:
http://www.adamtoons.de/physics/relativity.swf

On the http://www.physics.ucla.edu/demoweb/demomanual/modern_physics/principal_of_equivalence_and_general_relativity/curved_time.gif":
The object is initially at rest in space (at the ceiling) and advances initially only along the time dimension. It advances on a straight world line because it is free falling (force free). The distances along the time dimension are bigger at the floor level, so the entire diagram is distorted. This makes the object start to advances along the spatial dimension (falling to the floor).

Imagine how a standard rectangular Newtonian space-time diagram would look like. The path of the free falling object would be a parable. Now you stretch this diagram so that the path of every free falling object becomes a straight line, and you get a diagram of curved space time.

 

[staballoy]

Your explanations have given me my "Eureka!" moment. Thanks to all for the patient and kind explication.