A question concerning gravity... and the animations thereof

partinobodycular said:

This question has puzzled me for quite some time. The following image is meant to be an illustration of how gravity can be modelled as a warp in spacetime, but isn't it completely backwards? In other words, it shows space being warped AWAY from the center of gravity, but shouldn't it actually show space being warped TOWARD the center of gravity?

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While we wait for the physicists to arrive. I don't see the toward or away part in picture. I believe it is important that it is a quasi 3D representation of gravity on a 2D-space, as in differences in the Z-direction are only there as a visual representation of how the gravitational forces changes. That the heavier object is in a "actual" well is a consequence of the visualization aid. It is the elongation of the squares towards the objects that is as important.

Someone will come along and clear it up for us I think.

partinobodycular said:

...shouldn't it actually show space being warped TOWARD the center of gravity?

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Isn't that what we're seeing? Anything passing near the large ball will tend to fall in towards it along the 'distorted' space.

partinobodycular said:

That's not really what we're seeing. We're seeing the plane (the grid) being bent downward under the ball. For a plane that dissects the center of the ball it should remain perfectly flat, only being warped along the plane toward the center of gravity, but not downward. If however it were a plane that ran above the ball, then yes, it should bend downward toward the center of gravity. And if it were a plane running under the ball then it should bend upward toward the center of gravity. But any plane dissecting the center of the ball should bend neither up nor down, but toward the center of gravity.

At least that's how my 9th grade education sees it. I'm just waiting for Hans or Sj to come set me straight.

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Space in that visualization is the 2D-plane, not the 3D perspective (which is there to allow us to see the space bending), IMO.

At least I push the thread to the top of list. I realise that I have already started to mix my thought models talking both about gravitational forces and bending space.

partinobodycular said:

That's not really what we're seeing. We're seeing the plane (the grid) being bent downward under the ball. For a plane that dissects the center of the ball it should remain perfectly flat, only being warped along the plane toward the center of gravity, but not downward. If however it were a plane that ran above the ball, then yes, it should bend downward toward the center of gravity. And if it were a plane running under the ball then it should bend upward toward the center of gravity. But any plane dissecting the center of the ball should bend neither up nor down, but toward the center of gravity.

At least that's how my 9th grade education sees it. I'm just waiting for Hans or Sj to come set me straight.

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I think it's deformed downwards just to show what would happen to a ball entering that gravity well. It falls in towards the centre of gravity. It's almost as if it's a 2 1/2 D representation. 2D wouldn't show anything being captured by gravity and I'm struggling to imagine what on earth (no pun) it would look like in 3D.

partinobodycular said:

That's my theory as well. But if you think about it, it wouldn't work with a 3D model either, you have to have a 4D model in order to accurately represent a warp in 3D space. Unless, we're not just dealing with a warp in space, but a warp in time as well. In which case I'm totally lost, and I'm just going to continue to wait for somebody much smarter than me to explain it.

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I think we are seeing it the same way. But it still works in 3D (or even higher) -space, it is just not readily visualizable.

partinobodycular said:

That's not really what we're seeing. We're seeing the plane (the grid) being bent downward under the ball. For a plane that dissects the center of the ball it should remain perfectly flat, only being warped along the plane toward the center of gravity, but not downward. If however it were a plane that ran above the ball, then yes, it should bend downward toward the center of gravity. And if it were a plane running under the ball then it should bend upward toward the center of gravity. But any plane dissecting the center of the ball should bend neither up nor down, but toward the center of gravity.

At least that's how my 9th grade education sees it. I'm just waiting for Hans or Sj to come set me straight.

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But the “grid” isn’t in just the shown plane, it is in all planes and all possible planes.

partinobodycular said:

Exactly, but in that case you're using gravity to explain what causes gravity. A little circular don't you think. Which is why it never made sense to me.

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I don't think it's mean to explain gravity. It's just giving us a simplistic visual representation of passing objects being caught in a gravity field. I've seen this done with a rubber sheet stretched across a frame and a steel ball placed in the middle as per that diagram. Which is not actually correct because the centre of gravity is then at the bottom of the ball and not the centre.

To be honest, I don't think our minds are built to be able to visualise it accurately.

partinobodycular said:

You're certainly correct when you say that it's hard to visualize. But me being me, I'm going to try anyway. We can still use that 2D plane to visualize a warp in 3D space. If that 2D plane bisects the ball then it shouldn't bend up or down. Any bending that does take place has to happen along that plane.

So, just using that 2D grid, can you show how it bends, without bending it up or down?

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Mathematically yes (at least I think so, through the curvature tensor), curvature is a property of the space itself, not a property emerging when it can be seen curving in a higher dimension. There need not be an "outside" to curve into.

I haven't touched this kind of math in 25 years, it is all provisional, I have almost certainly forgot some precondition.

partinobodycular said:

Yeah, AI has been attempting to explain non-Euclidean Geometry to me, but methinks that I'm a bit of a lost cause.

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That is true for everybody. When we stray too far away from everyday experience, math becomes the tool to best describe going further (so far).

It's been nice speculating a bit

partinobodycular said:

This question has puzzled me for quite some time. The following image is meant to be an illustration of how gravity can be modelled as a warp in spacetime, but isn't it completely backwards? In other words, it shows space being warped AWAY from the center of gravity, but shouldn't it actually show space being warped TOWARD the center of gravity?

Click to expand...

Here a relatively (pardon the the pun) mathematically friendly explanation.

The diagram is not an accurate depiction of how gravity works or how space-time curves due to gravity (it does not).

(1) The diagram shows a 2D plane and balls embedded in 3D space.
(2) It incorrectly depicts gravity as a real force as the small ball is “falling” towards the large ball.
(3) The diagram does not show the orbital plane can rotate which is known as precession.

In GR (General Relativity) gravity is depicted as a fictitious not a real force.
Gravity is only real in GR when defined as a tidal force such as when moon is too close to a planet and breaks up, or an object undergoes spaghettification when too close to a black hole.
We feel fictitious forces when we drive a car, when the car accelerates, we are pushed into the seat, or when decelerating we are pushed out of the seat.
Einstein visualized this using an elevator, a person inside an elevator cannot tell if the elevator is stationary in the Earth’s gravitational field or is being accelerated in space at g in the opposite direction to dropping a ball inside the elevator.
This is known as the equivalence principle and was a precursor to GR as a theory for gravity.

The geometry of space-time is determined by a metric ds² which is an interval when summed (∫ds) over all the intervals defines the straightest possible path between two points.
If an object follows this trajectory it is known to be on a geodesic.
In 3D flat space the metric is ds² = dx² + dy² + dz² which is Pythagoras’s theorem in 3D.

For a planetary orbit in 4D spacetime is the Schwarzschild metric for a massive central body of mass M around which space-time curves in a spherical symmetry. G is the gravitational constant, c the speed of light while r, θ and φ are parameters describing spherical space.

ds² = (1-2MG/c²r)c²dt² - dr² /(1-2MG/c²r) - r²(dθ² + sin²θdφ²)

A planet or satellite moving on this geodesic will be in an orbit and also in free fall as an accelerometer will read zero as there is no proper gravitational force acting on it, while the plane of the orbit can undergo precession which the metric predicts and Newtonian gravity cannot fully explain.

partinobodycular said:

This question has puzzled me for quite some time. The following image is meant to be an illustration of how gravity can be modelled as a warp in spacetime, but isn't it completely backwards? In other words, it shows space being warped AWAY from the center of gravity, but shouldn't it actually show space being warped TOWARD the center of gravity?

Click to expand...

2D is inaccurate and misleading. It should be 3D. I have been trying to get AI to produce that image but not successfully, so far.