I If gravity is not a force, what is holding us down?

[paradisePhysicist]

How can you offer any meaningfull explanation if you don't even know and understand this subject on a technical level? What for? It's a waste of time - primarily yours. You could use this time to try to learn technical details.

I am going to look into reading Dave's theory on the matter, then watch all of the Flatland movies, then maybe read one of the chapters of the books mentioned, after that if I still don't get it I plan on maybe giving up on this for a few weeks.

 

[PeterDonis]

when it collides with the Earth most of the object is still moving or at least trying to move, except for the parts of the object touching Earth.

During the collision, yes, the object will in general not be rigid; its shape will deform. If the collision is hard enough, the object's shape when it comes to rest on the Earth will still be deformed, but once it has come to rest its motion in the new shape will again be rigid; it won't deform any further once it has reached its new equilibrium shape resting on the Earth's surface.

Also, "move" as you are using the term here means "move through space", and "space" is not an invariant; what "space" is depends on how you split up spacetime into "space" and "time". You are implicitly doing that in the way that is most natural for an observer at rest relative to the Earth (which is the way we usually do it intuitively in our everyday lives), but that is not the only possible way to do it.

A curve is produced when a function uses x input to change the y output. Are you saying that some dimension of space, let's say z, changes the t output of time?

Yes; the closer you are to the center of a large massive body like the Earth, the slower time flows for you. Or, to be more precise, the slower your proper time (the time according to the clock you carry with you) "ticks" as compared with the proper time of someone very, very far away from Earth. (I am assuming here that both observers are at rest relative to the Earth.)

Don't be confused by the fact that your worldline, sitting on the surface of the Earth, doesn't "look curved". It is not curved in space (in space, as we are defining "space" here--see my comments above on that--your worldline is just a point, not even a curve); it is curved in spacetime. It "looks straight" in a particular kind of coordinates because those coordinates are representing a curved geometry.

when a plane chooses not to follow a geodesic, the plane doesn't automatically experience a force compelling it to follow the most geodesic trajectory

Neither does an object in spacetime. Gravity is not a force in GR.

Try the analogy this way: suppose you have a plane that has no global navigation system; all it knows how to do is pick out the path that is locally straight (say by shining a laser beam pointing straight ahead from the nose--we'll ignore wind and all the other complications of actual flight and assume that the plane always moves in the direction the nose points if its controls are set at neutral). If the plane just flies directly along that locally straight path, leaving the controls in neutral all the time, it will end up following a geodesic (great circle) around the Earth. This is the analogue of an object freely falling in spacetime; in spacetime, falling freely (feeling no weight) is how you pick out the locally straight path; in a plane, flying "straight and level" (controls in neutral, no inputs) is how you do that.

Now suppose the pilot of the plane decides to turn, say by banking to the left (left rudder and left ailerons). How will he know he is turning? Because the plane doesn't move in the direction the laser beam points. It moves to the left of that direction. (The direction of the laser beam itself will change as the plane turns, but it will lag behind the actual direction of flight. Just as, if you are in a rocket whose engines are firing, the direction in spacetime that you would go if the rockets suddenly shut off changes, but it lags behind the actual direction of flight of the rocket.) There is no force compelling the plane to "try" to move in the direction the laser beam points. But if the pilot puts the controls back to neutral--stops the turn--the plane will again start moving in whatever direction the laser beam is pointing. Just as, if you are in a rocket whose engines are firing, and they stop firing, the rocket starts moving in whatever direction in spacetime is the geodesic (free-fall) direction.

So it's not right to think of geodesic motion as something objects have to be "forced" back to. Geodesic motion is just the "natural" motion that all objects undergo if nothing is pushing them (no rocket engine in spacetime; no control inputs in the plane).

 

[PeterDonis]

I was not trying to contradict the Einstein theory but offer an explanation of why it works

You should not try to do this with a theory you don't understand. Before you even try to explain why a theory works, you first need to understand how it works.

 

[stevendaryl]

I watched this video again, the animation seems to show gravity causing gravity, like the Earth is using free energy and pulling the fabric of space inwards.

The idea isn't that gravity causes the "fabric of space" (once again, it's spaceTIME, not space, that is curved) to bend by pulling on it. According to General Relativity, gravity simply IS curved spacetime. It's not that gravity causes spacetime to bend, any more than high temperature is what causes something to be hot.

And there is absolutely nothing anywhere in the video that mentions "free energy". I don't know where that idea came from.

 

[PeterDonis]

this video

Unfortunately I don't think this video's final representation, the one it claims is new and improved, is useful; rather, it is misleading. The best representation the video actually gives is in the middle, the one with the grid all around the Earth and clocks at each point of the grid. It does not, however, show the clocks closer to the Earth ticking slower than the clocks further away, which is the crucial point of looking at things that way. All you would need to add to that is a rule that the worldlines of objects in free fall bend towards the region where the clocks tick slower.

The later animations that seem to show the grid being "sucked" into the Earth are misleading because they wrongly imply that the grid is somehow dynamic; but it isn't. The "grid" around a massive object like the Earth is static; it doesn't change with time. This video misleadingly suggests that it does.

 

[mitochan]

Still, even in that case - geodesic is a curve in spacetime, not space, and everything is "moving" only one way along it.

Say a ball falls and bounce back from the floor to make a reverse motion. Falling ball is along a geodesic and the going up ball is along another geodesic because momentum is given from the floor and free motion is interrupted then. This shows that reverse motion is not going backward along the geodesic, from future to past, but transfer to another geodesic starting with reversed velocity.

 

[A.T.]

I particularly like the following video:

It's good that they point out the issues with the rubber sheet analogy. But I have issues with this video too:

- The animation at 7:00 makes it look like the spatial geometry is changing with time, which is wrong.

- The video concentrates too much on spatial geometry, which is not really that important for gravity (except for fast objects like light)

- The way the spatial geometry is presented, is also misleading, as I explained once when similar pictures were posted:

You cannot correctly show the curved 3D space around a mass with a distorted 3D-grid that is embedded in non-curved 3D space (the illustration). The shown distorted 3D-grid still encompasses the same total volume as would a non-distorted 3D-grid with the same outer boundary. But in actual curved 3D-space around a mass there is more spatial volume enclosed than in flat space of the same outer boundary.

So basically the 2D sheet with a dent or hill is actually a better representation of the spatial geometry than those distorted grids, because it has more surface area than a flat sheet would have. But spatial geometry doesn't explain gravity.

 

[jbriggs444]

Oh. So far I have watched Flatland, but the movie Sphereland seems elusive, website is down. I see a physical copy of it for $24.95 on Amazon but maybe there is someway to rent it.

Movies... *pffft*. Kids these days.

 

[stevendaryl]

It's good that they point out the issues with the rubber sheet analogy. But I have issues with this video too:

- The animation at 7:00 makes it look like the spatial geometry is changing with time, which is wrong.

Yeah, the animation shows a distorted 2D grid, but I don't have any idea what that grid is supposed to mean.

The video seems way overly complicated. To get across the main point, that an apple falls to the Earth because of curved spacetime, it seems to me that you could just suppress one spatial dimension to make the problem 3D, with a time axis and 2D spacelike slices. The surface of Earth would be represented approximately as a cylinder centered on the time axis. The geodesics of a small object (with a nonzero angular momentum) would be represented as a helix around the time axis. The apple crashes into the surface of the Earth when the helix representing the apple intersects the cylinder representing the surface of the Earth.

 

[paradisePhysicist]

Movies... *pffft*. Kids these days.

On a more serious note though, I think the movie will be easier to visualize since its already visual. On the other hand, the book may be so well written that it is easy to visualize also.

 

[jbriggs444]

On a more serious note though, I think the movie will be easier to visualize since its already visual. On the other hand, the book may be so well written that it is easy to visualize also.

Understanding is the goal. A visual understanding is not.

 

[MikeeMiracle]

As someone not familiar with the math's I find Vsauce's youtube video below very informational for those trying to get a grasp on why no forces are involved. I would recommend you watch it all though for a quick snippet check out timeframe 16:15 - 17:25, this demonstrates how straight paths come together on a curved surface. Possibly continue watch through to 20:40.