I’ve always seen gravity demonstrated as a sheet of stretchy fabric being pushed down, thus creating a cone from which things moving toward it can’t escape.
I understand the principle, but how does this reflect 3D space? Should space be really imagined as a sheet, or is this experiment only meant to show the effect of gravity, not how the fabric of space behaves?
In: Physics
So humans are really really bad at visualizing things in higher dimensions. The visualization of stretchy fabric imagines a 2D space, but the actual visualization requires us to see it in 3D.
To actually visualize gravity, we cannot really do so intuitively in 3D (hence why everyone uses the stretchy fabric). If we could see 4D objects, then we probably could have a better idea, but we can’t.
The best way that i can think of is to look at an image of the orbits of planets. To us, in 3D they all look like they are going in circles. However, that is the distortion of gravity. In reality, the planets are moving in straight lines, and it is the way gravity distorts space that makes us observe the planets moving in a circle.
Is it a picture of gravitational potential, or of spacetime?
Gravitational potential:
The graph is the graph of the strength of gravitational potential over 2D space. The height is the potential, and the other 2 dimensions are space.
For spherically symmetry gravitational field, this is sufficient, because the only thing you need to know is potential vs radius anyway. In fact, a 2 dimensional graph potential over radius is sufficient, and this is what you often seen in a physics book. But people also draw 3 dimensional graph because it looks cool.
For axially symmetry gravitational field, you really do need to look at 2 dimensions of space, which would lead to 3-dimensional graph.
Spacetime:
If it’s spacetime, then the height has no meaning!!! The horizontal components are still 2 dimensions of space, and there are no time components, the entire picture is just 1 slice of time. The reason why we need the height dimension is to illustrate the curvature, because we can’t visualize a curved surface without having it being distorted in 3D space.
I watched [this on YT](https://www.youtube.com/watch?v=wrwgIjBUYVc) a while ago – the channel owner claims it’s designed to make best use of video as a medium.
I don’t know how accurate it is, but it’s an alternative to the rubber sheet thing, which I always disliked because it’s trying to explain Earth’s gravity, with a pretend Earth in the middle of the sheet, and the sheet stretches and the ball rolls in a deflected path because of the *actual real Earth’*s gravity.
In the sheet example, we are pretending like space is only 2D, and we are visualizing the force of gravity as if it were the 3rd dimension. The reason for this is that we don’t have a 4th spatial dimension to work with so we can’t easily make a representation with 3 spatial dimensions and a 4th magnitude of force dimension. This gets even harder if you try to then turn this representation into a 2d image format.
Here’s the best I can come up with. Imagine a foam ball, the kind you squish and then release and it returns to form when you let it go. Now imagine there is a super tiny little straw that someone has pierced through the foam ball. Also imagine there are tiny little microscopic explorers that want to walk down the length of the straw from one end to the other. Now take the ball and squish it and then twist it. The straw on the inside would also get twisted since the space around the straw is changing position. Now the microscopic explorers just walk in what feels like a straight line, but the straw (i.e. their path through space) is distorted by the warpage.
[removed]
Gravity bunches space (and time) up.
Picture a big, empty bit of space.
Now imagine overlaying that with a 3d grid, dividing it up into lots of little cubes. Something [like this](https://blenderartists.org/t/how-to-create-a-3d-grid-floor/578784) but in space, where the lines are equal distances apart.
Now if we put some massive object in the middle, it will squish and stretch those lines, pulling them in towards it from all directions. The lines will be more bunched up around the object, more spread apart further away.
So from the outside (a long way away) it looks like there is the same amount of space. But if you were in there you would find there was more space than you’d expect. So what would look like a 10,000km path by might actually be ~15,000km if you tried to travel it.
Gravity in 3D is really a 4D thing. Mass curves spacetime. If we perceive space as consistent, mass bends time. Specifically, the closer you get to a massive object the slower time ticks.
If we perceive time as having a fixed rate then space will contract the closer you get to a mass. Things in orbit are really traveling at a constant speed in a straight line, but if space is more contracted around a mass that straight line will bend toward the mass.
That’s just a representation, you are used to 3 dimensions, there’s 4 if you include time but you’re not really used to seeing the 4 at the same time, you can represent it, I’m sure you’ve seen plenty of graphs where time is a dimension, for example you can represent how high an object is if you throw it in the air and as time passes by, you could make a 3D model of me in a 3d graph, and you could for example make a graph of my height as time passes by, but how would you make both a 3d model of me and how my dimensions have changed over time?
That’s really hard to do, so what is usually done is that you take our 3d space we’re used to seeing, discard one of the dimensions and replace it with time, hence the fabric. You’ve never seen something in 4 dimension so you have no frame of reference to how it should look.
Have you seen the movie interstellar? It’s a great movie and you should see it and I’m about to spoil the hell out of it.
>! At the end of the move when Cooper is inside the black hole the higher dimension beings had to build a space for him to be able to see time because otherwise he wouldn’t be able to understand it, every bookshelf was a different moment in time so that Coop could interact with it!<
The best we can actually visualize is 3D space, 4D space is almost impossible to visualize without some heavy psychedelics ☮😋☮
If you want to give it a shot imagining it though: you know how you can take a flat piece of paper in a ‘t’ shape and fold it into a cube? If all faces are pointing “up,” when they are flat on a table, then when you fold them into the cube they will all be pointing “inward.”
Now imagine doing the same thing, but instead of going from 2D cross to 3D cube, try imagining going from a 3D cross to a [4D hypercube](https://upload.wikimedia.org/wikipedia/commons/d/d7/8-cell.gif). That’s basically how gravity works. It’s a fucking trip trying to imagine it, but it’s about the best we got.
Latest Answers