Something fishy in relativity? The gravity of the situation is clear!?

Question

According to Einstein and others, gravity results from the curvature of space-time. It has been tested and is found true. I don't argue it. I just do not understand the following.

How does this explain my strong attraction to earth?

How can I understand that curvature of space-time is causing falling objects to accelerate at ca. 9.8 m/s^2 toward earth -- unfailingly?

It seems that for objects on earth something else is at work?

Is it love? (sorry for my fuzzy humor)

Any ideas? Any good explanations?

I want to thank all of you for your fine answers. I am sorry I cannot choose all as the 'best answer.'

I am going to take the weekend to ponder your answers and see if I can understand what you are saying. My imagery of a four dimension space is a bit on the weak side.
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To Scythian: Our movement through the 4th dimension time cannot be at the speed of light since it would cause a black hole, or would it?

Thus we move through the fourth dimension otherwise no time (?) but how fast we move is another question.

Black holes that prevent light from escaping perhaps move that fast in the 4th dimension. That may be what prevents light from getting out -- dimensionally speaking. (?)

Just an opinion from a oh so peon.
Contact ok.
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2nd edit: Prof. Zikzak

I read your material carefully today. The spaceship explanation I have seen before.

Either I forgot it or didn't realize that it had anything to do with the curvature or space-time as you stated later.

I see you logic with my mind (in the 2nd last paragraph). I just don't see the mechanics of it in my mind.

I would like to see my mind animate this. In most most other cases it is possible to run the simulation by imagination, but this one evades me -- and that is too bad.

2nd edit: Prof. Zikzak

I read your material carefully today. The spaceship explanation I have seen before.

Either I forgot it or didn't realize that it had anything to do with the curvature of space-time as you stated later.

I see your logic with my mind (in the 2nd last paragraph). I just don't see the mechanics of it in my mind.

I would like to see my mind animate this. In most most other cases it is possible to run the simulation by imagination, but this one evades me -- and that is too bad.

Answer 1

The fact that all bodies fall at the same rate is the whole idea behind the re-conceptualization of gravity as curvature. In fact, a slightly more technical (but only slightly more) version of this statement is one of the three axioms of GR.

Throw an object. Any object you throw, so long as you throw it the with the same speed and direction, takes the same trajectory right?

In the 4-D spacetime of relativity, "speed and direction" becomes simply "direction" because speed is distance over time and time is just another direction. So any object you throw in a given spacetime direction follows exactly the same trajectory, regardless of its mass.

These trajectories are the *natural* unforced trajectories of the apple that you throw; your own trajectory through spacetime is not natural because you feel pressed against the floor: the floor is applying a force to you, accelerating you at 9.8 m/s^2: you can feel it! It's got to be a force! The apples feel weightless--- there's no force on them! The apples that you throw are NOT being accelerated! You observe a curved trajectory because it's YOU who is accelerated away from your natural, freely falling motion by the normal force of the floor. In other words, what you observe about the thrown apples is identical to what you would observe if you were on a spaceship in deep space accelerating at 9.8m/s^2. And in that case, there's no question that it's you that's doing the accelerating, and not the apples (which follow Newton's First Law and travel in straight lines at constant speed until they hit the floor of the spaceship)

Similarly, if you were on a spaceship freely falling in deep space, you would throw the apples and see them all obeying Newton's Laws... floating away from you in straight lines at constant speed, and you would feel "weightless" and not pressed against any walls of the spaceship. Which is EXACTLY what you observe if the floor is pulled out from under you, allowing you to fall freely at the same time you thrown the apples here on earth!

Now imagine that you throw apples in all possible 4-D directions and map all of their possible natural, freely falling, weightless trajectories through spacetime. These bodies are obeying Newton's Laws, travelling in straight lines at constant speeds, if only you were to observe them while you too were freely falling.... so if the trajectories curve on your map it must be because spacetime itself is curved.

Note again how this wouldn't work if objects fell at different rates: there wouldn't be just one and only one natural trajectory in each 4D direction to map out.

Answer 2

The best description I have heard is that for a portion of 4-D space that's been curved by gravity, 'down' has become the least energetically demanding route between now and later.
Or to look at it another way, you are moving forward along the time axis constantly. Therefore, if a spatial dimension is bent into that axis, you will find yourself compelled to move along it as well. It just happens that time and space are perceived differently by humans, which creates these intuitive problems.

Answer 3

The reason why people frequently find general relativity difficult to visualize is because they're still thinking in 3D space, not 4D. Thus, when we are "standing still", most people imagine that we are not moving anywhere. But in fact in 4D relativistic spacetime, we are hurling at the speed of light through time. Bend this 4D spacetime a little, and you'll find yourself hurling both through time and space, and that is the reason why we "fall down".

Answer 4

Spacetime is *so* distorted that the surface of the earth is actually accelerating upward at 9.8 m/s^2 relative to an inertial reference frame.