OK. I understand the principle of equivalence between acceleration and gravity's effect on an object, I understand the notion that space and time are both curved near massive bodies. I understand that Newton's idea of the attraction of bodies works fine except for motions near the speed of light, but it is in fact a false understanding of gravity.

I find the cartoons of the "rubber sheet" projection and the moving marble irritating and confusing because it is using the understanding of Newtonian gravity to explain why spacetime curvature causes moving objects to move in curved paths. Not helpful to me, at least, in understanding why spacetime curvature causes the effect we experience as gravity.

Here is what I cannot visualize. Explain in Einsteinian terms the simple falling of an apple. Suppose one settles on one time and one (or perhaps two) spatial coordinates, which is visualizable. What makes the apple attracted to the earth and what is going on as it falls through the different clock rates (because of the curvature of time as one moves away from the surface of the earth)?? :confused:

I have read literally dozens of articles, including Feinman's lectures (which gets me close!) but I still cannot internalize this concept.

You have reached the absolute limit of what you are capable of understanding and should not expect to know anything more than you do already.

Nonsense. Einstein did very beautiful thought experiments that clarified his thinking before he ever wrote down an equation. These thought experiments are totally understandable by an educated lay person. It's understandable if I can get the attention of the right mentor. Obviously, not you.

keep in mind here that I am using logic and perception and some of the physics based stuff I know from chemistry to answer this and do NOT have a backround in physics.


1. As to why the apple falls this is a question of what is the nature of gravity, why does it exist, and in general where it comes from. No one seems to know. In my opinion, gravity is just another trend, much like how a electromagnetic wave moves. Don't know why it so happens to move in that way, it just does.

2. From what I have read of Einstein's equations his physics apply to everything, not just objects moving close to the speed of light (relatively of course), its just that the change in answer resulting from taking into account new variables is negligible when talking about small things, like the apple falling. Therefore, I'm sure that the apple is affected by the curvature of time and space as well as said clock rate things, but einsteinian physics being what they are the effects are negligible. It seems to me that there's a good reason you can't visualize this stuff happening; for all intents and purposes it isn't!

Some years ago I saw a special program on Einstein, and they had an animated cartoon explaining the falling apple, first from Newton's perspective, and then the Einstein concept. It had something to do with the apple being drawn through the different clock-rate zones. Clocks at the base of a tree are running an infinitesimal amount slower than a clock at the top of the tree (i.e. time coordinates are warped by the mass of the earth). The spatial coordinates are likewise curved more the closer to the earth you get. Einstein also said something about a law that objects will always follow the shortest path, and if the spatial coordinates are curved then this might explain why they will appear to be attracted to the largest mass.

Anyway, thanks for the reply. I'm still waiting for the cosmologist/physics guy who can show me how this works, maybe in a 2D example.

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Originally Posted by Hiro

keep in mind here that I am using logic and perception and some of the physics based stuff I know from chemistry to answer this and do NOT have a backround in physics.


1. As to why the apple falls this is a question of what is the nature of gravity, why does it exist, and in general where it comes from. Noone seems to know. In my opinion, gravity is just another trend, much like how a electromagnetic wave moves. Dunno why it so happens to move in that way, it just does.

2. From what I have read of Einstein's equations his physics apply to everything, not just objects moving close to the speed of light (relatively of course), its just that the change in answer resulting from taking into account new variables is negligable when talking about small things, like the apple falling. Therefore, I'm sure that the apple is affected by the curvature of time and space as well as said clock rate things, but einsteinian physics being what they are the effects are negligable. It seems to me that there's a good reason you can't visualize this stuff happening; for all intents and purposes it isn't!

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Originally Posted by wizardchef

Nonsense. Einstein did very beautiful thought experiments that clarified his thinking before he ever wrote down an equation. These thought experiments are totally understandable by an educated lay person. It's understandable if I can get the attention of the right mentor. Obviously, not you.

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Kip Thorne and John Wheeler wrote a book in the 1970s entitled "Gravity." It is directly on point. I've read it. You never heard of it until now. Get it from the library or buy a used one from Amazon, read it, and maybe then you'll know enough to ask a meaningful question.

OK. I am getting the visualization of what I was looking for. In reading some of the posts on other physics sites on this issue, it seems the key for me is the concept of 'worldline' and matter moving along geodesics in spacetime. In space far away from large objects that interact with spacetime, the geodesics are straight lines and matter moves along without experiencing acceleration (due to any nearby mass). But, near a large mass, because the geodesics of spacetime are now curved, matter will move in freefall and experience an acceleration toward the mass causing the curvature. Hence, the connection to the equivalence principle. So, we on the planet earth are all in 'free fall' all the time, since we exist in a curve spacetime continuum that has the effect of accelerating us toward the surface of the earth, our experience of the curvature of spacetime.

It is still difficult to visualize this manifold, and I have to think about that some more. It seems the biggest effect in gravity is the warping of time, but space is also warped, so of course 4D spacetime is warped as well.

In some simple-minded but technically incorrect way, I can imagine to am on a time coordinate that is bent toward the earth, hence, I feel drawn toward the surface of the earth since I reside in this warped coordinate system. I'm sure this is not technically correct, but it is the visualization I'm looking for. I'll keep thinking about it.

The apple falls because as it is untethered from the tree it experiences the acceleration of gravity due to the curved spacetime coordinates that it exists/moves in.

Best I can do for now.

Read "Gravity from the Ground Up" - all is explained