Really what is gravity, I don't understand.
Einstein says that gravity is a fictitious force; it is an effect of the warping of 4-dimensional space-time continuum by massive objects. Objects in warped space-time will to follow the shortest path - not a straight line, but a geodesic curve.
The usual 2D analogy is that of a bowling ball and a marble resting on a rubber sheet. The bowling ball makes a big dent in the sheet, the marble makes a neglible dent. If the marble is set rolling in the vicinity of the bowling ball, the marble's path will deviate toward the bowling ball and may even "go into orbit" around it.
A common but very misleading analogy. It omits the time dimension of space-time, which is crucial to explain gravity. Imagine the marble initially at rest. Explain why it starts moving towards the bigger mass on the rubber sheet. But without using gravity to explain gravity!
I recommend to forget about the rubber sheet, and follow the links I gave in this post:
Easy - have 4 persons each grab one corner of the rubber sheet in free space and accelerate all 4 corners in the same direction - the fabric will be indented by the F = ma reactance of the mass to the acceleration
This is not the marble-rolling-on-a-rubber-sheet-analogy I criticized. But I doubt it is much better. A layman will ask: If the space accelerates in all directions, how come the radius of the earth stays constant.
OP; If none of this has made things any clearer, let me just say that the "rubber sheet" analogy is only a way of describing that gravity is not so much a force travelling out from a source object (like light or heat), but more like a condition of spacetime around that object.
Actually, the FIRST thing a layman will say is: "rubber sheet? Ohhhhhhh! That makes more sense than what I had on my head up till now..."
Frankly, if they then understand the rubber sheet model so well that they can ask a question like you posed, I would consider that a very positive sign that they're learning fast!
Thank you Lurch. I hear people complain about the rubber sheet analogy being flawed all the time. Of course it is! Analogies are flawed by definition!
But you've hit on the reason the analogy does work. Many laypeople start with the preconception that gravity is either rays extending outward or sucking inward or such.
The rubber sheet gives them a much better model.
In fact, I have no problem with the rubber sheet, but with the marbles rolling into dimples created by bowling balls.
The rubber sheet with a big dimple can be used as an analogy for curved space. But curved space does not make apples fall from trees. Thats why it is misleading. It confuses those really interested in the topic. They stop thinking about it, assuming that they are not smart enough to grasp it. But in fact it's very easy and can be explained in a way that is both: correct and visual. See here!
It's almost a hundred pages! We were looking for something "in a nutshell".
Curvature of space affects only objects, which are already moving trough space. The apple is initially at rest in space, and therefore not affected by curved space at all. You need curved space-time to explain why it starts moving trough space. But space-time is not a rubber sheet with a dimple.
Why should it roll down? Because of gravity? This is explaining gravity with gravity.
Then just take Figure 2.9 and some explanation. Chapter 2 is everything "in a nutshell" (8 pages, mostly pictures).
I've read this and read this and I can't make heads or tails of any of the sentences in it.
"Curvature of space affects only objects..." as opposed to?
"...which are already moving trough space." who said they have to be moving?
"The apple is initially at rest in space, and therefore not affected by curved space at all." What? Why not?
"You need curved space-time to explain why it starts moving trough space."Isn't that the point?
"But space-time is not a rubber sheet with a dimple." If you're using this as logic to show that space-time is not a rubber sheet with a dimple, then this statement is pretty circular logic...
Phew. I understand spacetime and gravity pretty well, but I'm gonig to need to concentrate to read through the whole paper to understand what they're getting at. You can't simply read one section (eg.: what's a "staff"?)
I'd say this is likely a good "intermediate" lesson in GR, but it's not a "beginner" course in GR.
I don't know what's gfoing with PF today, but editing seems to have gone splah.
"I'd say this is likely a good "intermediate" lesson in GR, but it's not a "beginner" course in GR."
No, it is a beginner's lesson, it just takes longer than 30 seconds to get.
Your questions suggest that you are not differentiating between "curved space" and "curved space-time".
Isn't this obvious? Intrinsic curvature of a manifold merely implies certain distances between coordinates. But distances are pretty irrelevant, if you are not moving on the manifold.
Objects at rest in space, are still moving in time. That's why they are affected by gravity which is curvature of space-time. The rubber sheet with a dimple caused by a spherical mass represents two dimensions of space. But without the time dimension it cannot show the curvature of space-time. So it cannot explain even the simplest phenomena of gravity, like apples falling from trees.
But not longer than 30min. I believe that laymen asking questions about gravity in this forum a those who really want to understand the topic. They often already know the marbles-on-a-rubber-sheet-analogy and cannot make sense of it (for good reason).
Basically the answer is this:
In a world without any massive objects (flat spacetime) any body in motion continues in a straight line. One way to tell if an object moves in a straight line from point A to point B is for it to carry a watch and measure how much time it takes. When the object follows the straightest path it will measure the most time. Now when ST is warped bodies still follow the path that they measure to take the most time (called a geodesic). This path is one that causes the body to move toward a massive object near it (the one that's causing ST to be warped).
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