Understanding Gravity: Mass, Size & Curvature

[IYIaster]

I was watching this video:
https://www.youtube.com/watch?v=KcXxHZssCh4

At 17:36 Michio Kaku says "There is no such thing as gravitational pull. Space is pushing me into this chair." So, is it the size of the object in space that determines the gravity or the mass? A neutron star has a small size and contains a large mass and it's gravity is enormous, Jupiter on the other hand has a small mass but a large size. I'm trying to picture the curvature that causes gravity. I picture Earth sitting on top of a sheet and I see the curvature but, in space there is no up, down, left or right so the curvature would completely surround the earth. What I don't understand is how could mass cause more curvature and in turn more gravity?

 

[phinds]

(1) NEVER listed to Kaku. He occasionally says something that is true, but only by accident. I do not mean this as a joke.

(2) You'll have to learn General Relativity to answer your question (but we've got some smart folks here who will undoubtedly put it in layman's terms for you)

 

[Crazymechanic]

i think it's important to realize that it;'s not so much the overall mass as mass per given area that causes the curvature to skyrocket , like in a black hole.
It's like putting 1kg on a pencil tip on a sheet of paper or putting that 1kg on that same sheet just on a dish , guess in which case there is a bigger posibillity to go through the sheet ?

ofcourse a mass that is large enough to form a black hole will do so sooner or later, it will collapse and squeeze the matter into a point small enough for that given mass to become a black hole and as the size will decrease but the mass will stay the same the curvature will get bigger and bigger.

as an example if Earth was much more dense which means more mass per the same area then the surface gravity would also be much higher.

 

[A.T.]

I'm trying to picture the curvature that causes gravity.

Curvature of space-time is related to tidal effects (gravity gradient), not to gravity in the sense of attraction.

So, is it the size of the object in space that determines the gravity or the mass?

Size determines the tidal effects, not the attraction.

I picture Earth sitting on top of a sheet...

That is a misleading analogy. See here:
https://www.physicsforums.com/showthread.php?p=4597121&postcount=18

What I don't understand is how could mass cause more curvature and in turn more gravity?

Curvature is not really needed to explain gravity. Locally curvature effects (tidal forces) are negligible, but you still have gravity (apples fall from trees). See this post for more on this:
https://www.physicsforums.com/showthread.php?p=4618558&postcount=3

 

[captcorajus]

Hello everyone. My first post on the forum! I'm going to attempt to put this in simple, layman terms, using everyday experience.

"Force of Gravity" is an anachronism from classical, Newtonian physics. An apple falls from the tree, and it hits the ground with a certain force based on the distance it fell. The way we all experience this makes gravity seem like an invisible force that pulls us downwards.

Einstein visualized this differently. All mass distorts space-time. In our every day macro world, the only mass that really matters to us, is the Earth's mass, as it tends to override everything else.

The reality, versus our perception is that the space around us is distorted due to the mass of the Earth. Gravity is not really a 'force', but the effect that we experience due to the fact we live in this curved space. It 'feels' like we are being 'pulled' to the Earth's center, when in fact we are actually being 'pushed down' by the space around us.

 

[A.T.]

It 'feels' like we are being 'pulled' to the Earth's center, when in fact we are actually being 'pushed down' by the space around us.

Free falling stuff is being not pushed down by anything. Not falling stuff is being pushed/pulled up, by whatever prevents it from free fall.

https://www.youtube.com/watch?v=DdC0QN6f3G4

 

[Freddy86]

Try not to picture Earth on the top of a sheet as this is merely a 2-D analogy of a 4-D phenomenon and can serve to create confusion. I tend to agree with phinds on Kaku, he often imposes his very abstract thinking on his audience, most of which stems from his extreme interpretations of string theory (which has no real place in physics yet). I don't agree with the notion of curved spacetime 'pushing' on something. I haven't done much general relativity but from what I have done I would envision curved spacetime as a complex vector space. Vectors are just a type of tensor which have a certain direction. In a very simple way, you can think of things falling towards the Earth due to fact that most of the vectors from curved spacetime are pointing this way.

 

[A.T.]

Try not to picture Earth on the top of a sheet as this is merely a 2-D analogy of a 4-D phenomenon and can serve to create confusion.

It valid to reduce the dimensionality, so that you can visualize the curvature. The problem of the usual ball-on-rubber-sheet is that it reduces the dimensionality by omitting the time dimension, which is crucial to explain the main effect of gravity. See comments here:
https://www.physicsforums.com/showthread.php?p=4597121&postcount=18
But you are right, the Earth should not be shown above the sheet in that analogy. Instead there should be a 2D-slice of the Earth within the sheet.

The above video and this applet also use a 2D sheet to represent a slice of 4D space-time. But unlike the usual ball-on-rubber-sheet they include the time dimensions.