I need help with an analogy here because I simply don’t know/can’t visualise the true physics here.
Many people use an analogy for gravity acting on space-time as a sheet of material stretched across a plane and a heavy object in its center acting as a celestial body.
This is great for envisioning orbits, the curvature of spacetime and so on.
Now this is a “2D” sheet/plane that deforms “downward” in the 3rd dimension, I get it… But how does it translate to the actual universe? The universe is always 3D in all directions, isn’t it?
I’m stuck here guys, science help me!
In: 81
“Gravity tells spacetime how to bend, spacetime tells mass how to move.” That ‘heavy object on a bedsheet’ analogy is a 2-D representation of something we can’t really easily visualize in 3-D, which is the actual shape of space itself being warped by gravity. Mass moving through that space moves differently because of the geometric shape of space has warped.
Another way to envision gravity is to imagine spacetime as a fluid being sucked into a gravity well. If that gravity well is deep enough, it will flow quickly towards it, causing everything in it to be caught in the ‘current’. If it is very deep, it will flow faster than the speed of light – now you have a black hole, where spacetime is rushing into the center faster than the speed of light and nothing, not even light, can escape.
Same as magnetism, more or less. Just imagine all objects as both metallic and magnetic in 3D.
saw this from an older post with a similar question. the vid is far from the formal definition/explanation but I think it makes the concept a little easier to understand.
So a counterintuitive fact is that a curved, two dimensional surface is still only two dimensional. When we see a sphere, we understand it as a three dimensional shape with volume, but the *surface* of the sphere is still only two dimensions. That is, we can represent every point in the surface of a sphere just using two measurements (such as latitude and longitude, which we use to define points on Earth’s surface).
From the perspective of a hypothetical, two-dimensional being on the surface of a sphere, they would only be able to move in two dimensions: east-west and north-south. They would have no concept of depth or the volume of their sphere. But they would be able to tell that their world was curved, based on how their geometry works. If they went in one direction in a straight line, they would eventually end up where they started, for example. The angles of a triangle drawn on the surface of their sphere would total more than 180 degrees, and two straight lines would converge or diverge rather than remain parallel.
General relativity posits the same is true for us, but in three dimensions. Space is still three dimensional — we can only move through it along forward-backwards, left-right, and up-down axes. But it is possible for there to be a curvature such that straight lines don’t remain parallel around massive objects.
Try this PBS Spacetime episode for why time dilation can lead to the observed effect of gravity.
And if you want to know even more, here’s one about how gravity causes time dilation. I think this is even the episode that says how inadequate an analogy the bowling ball on a sheet is.
Our perception of the universe is always 3D, but that doesn’t mean the universe only exists in those 3 dimensions.
I suppose one way to help visualize the difference is to imagine what the 2-dimensional perspective the ball will have as it moves in the sheet example. As far as the ball cares, its momentum and movement is trying to carry it through a straight line in its 2D space and plane of existence. If limited to only 2 dimensions, it can’t visually observe the 3rd-dimensional feature that’s affecting its movement (the indention in the sheet), its possible to measure and record the effects, it can even write laws and predict on how it will move around that point in its 2nd-dimensional space. It can do plenty of things, even when limited to 2 dimensions. But, as long as you are confining it to a 2D existence, it will never be able to observe the 3D feature that is affecting its 2D motion in its 2D existence.
That’s what’s going on here with gravity and spacetime. Our observations are limited to the scope of our dimensions. Spacetime in itself is a dimension we can only experience and measure in only singular points at a time. When we say something is bending spacetime, what we are really saying is “at this specific point in space, at this specific time of existence, this particular point in our dimension is bent.”
Once a single moment passes, that point in space is a different point in the dimension that is spacetime. If there happens to be a large mass near your point of spacetime, that mass can distort your spacetime in the form of gravity. In fact, if there’s enough mass and enough gravity, your sense of space and time can be distorted. You can’t observe the distortion of spacetime affecting your 3rd-dimensional existence, but it is possible to measure and record how you are affected. We even write laws and can predict how your 3rd-dimensional movement through spacetime will be affected by such distortion. We can do plenty of things, even when limited to 3 dimensions. But, as long as we are confined it to a 3D existence, we will never be able to *observe* observe the 4D feature that is affecting your 3D motion in your 3D existence.
One way not yet mentioned: A point (gravity “source”) and a line (moving particle, photon…) will always create a 2D plane. That’s for your standard effects of gravity on motion as you mentioned. Circular motion (planets, asteroids,…) around a gravity well still only require 2 dimensions. A “3D” result such as gravitational lensing (x, y for the image, z for the distance) can still be broken down to a series of 2D problems creating the desired effect by tracing each photon path individually.
Expanding this: If you have multiple bodies in actual 3D space influencing a point of interest, you can use the same approach, using 2D for each body-PoI combination and then adding the individual vectors in 3D space. Keep in mind that those are static calculations, especially once the individual bodies influence each other significantly, you’ll end up with a three-body-problem or worse. That means we’re currently limited to numerical simulations to approximate the result.
Otherwise maybe try to imagine a point cloud with each point representing the current space-time curvature at its location similar to a 3D vector field? Hard to look through the closer “layers” of points/vectors (this is a visualization problem), you can’t easily show the inside of a body with it looking normal so check visualizing 4D shapes maybe? That’s basically what you’d need to do (x,y,z for spacetime and curvature as a 4th dimension) and why it’s usually not done that way.
**TL;DR** – Pinching, ants, and beachballs.
The go to analogy to explain gravity is the ball on a rubber sheet analogy which, while helpful at illustrating that the fabric of spacetime is “bendy”, is dogshit in pretty much every other way. It explains gravity using gravity and it doesn’t give people an intuitive sense about why time plays a role in gravity. All they see is a marble rolling down a slope like a marble in a bowl because of… gravity.
The reality is that spacetime **curves** which you can think of like “pinching” when being represented in 2D space. The Super Mcduper important part is to pay attention to what happens when we “pinch”.
Imagine a series of gridlines which run along the sheet and when you set something heavy on the sheet (or more aptly *into* the sheet) instead of the sheet “bending down” it instead begins pinching the gridlines together (which you don’t need “up” or “down” to do). You’ll notice that two lines – which were formerly straight and parallel to one another when the grid was “flat” – now bend towards each other once we introduce curvature. Another analogy would be to stretch a rubber band between your fingers so that the bands are parallel to one another. Pinch the center together and you’ll see that they converge so that the bands now intersect. It’s that effect of two straight parallel lines eventually intersecting that’s the defining feature of the type of curvature we see in spacetime. We call that **curvature** gravity.
If you’re struggling to make sense of this no worries. Think of it like this:
Imagine two ants at the equator of a beachball, parallel to one another but spaced several inches apart. At the same exact moment both ants begin marching towards the North Pole at the exact same time – always putting one foot in front of the other and so always moving “straight ahead” – never turning. As they walk up the ball we’d notice that they begin moving closer and closer together, until they eventually intersect with one another at the North Pole.
How is it that the ants started parallel to one another, both only moved straight ahead so never turned, and yet still managed to run into each other? Was it some magical force that pulled them together? No, it was just the curvature of the beach ball and the effect that curvature has on straight parallel lines. If the ants made the same journey on a flat piece of paper their paths would never intersect, because the straight lines would remain parallel with one another forever. But because of the curved geometry of the ball their straight line paths curve towards one another until eventually they do intersect. The ants move closer and closer together – as if seemingly pulled towards one another.
The big leap in this analogy is understanding that when we talk about curvature in spacetime we’re talking about curvature in space **and time**. So if you ask yourself the ants come together if they were never moving along the line in the first place remember that they’re always moving along the line because *they’re always moving in time from their past to their future*. Away from their yesterday and towards their tomorrow. In this analogy “past” is where they started on the equator and “future” is where they ended on the North Pole. They move along their straight line axis of time, and it’s the geometry, the curvature, that brings them closer and closer together towards one another. Curved spacetime. Replace one ant with the Earth and another ant with an apple and you can visualize how the apple “falls” to the ground.
Now keep in mind that this shit is legit Einstein levels of complex and so any ELI5 analogy we use is going to be imprecise to what is really going on, but if you don’t know jack shit about general relativity then this should hopefully give you a better intuition about the role that geometry and time play which I think the rubber sheet isn’t very good at.
It’s really tricky to get your head around. Even physicists have a hard time with this unless they are looking at the maths.
How I try to get my head around it is instead of a flat sheet of rubber, think of a giant sponge. You are in the center of the sponge and pull the sponge material toward you to make a dense little point from all directions. The point you make is the center of mass of the object you are trying to represent. That point can be very dense (an object with a lot of mass) but as you look at the sponge, the further away from that point the less dense the sponge is. And it will describe a sphere in the sponge that is getting less and less dense the further you get away from the center.
Now if try to move through the sponge your path will curve depending on how close you are to the “center of mass”
It’s not perfect, but it can help visualize it in 3D.
The way I picture it is you have the sheet on a 2D plane, now imagine that same sheet rotated around the body infinitely at every possible angle all pulling equally.
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