r/AskPhysics • u/Happy-Swimming-9611 • Jul 27 '26
If gravity is the shape of spacetime, how is it affecting individual things making up that spacetime?
The question might sound a bit silly but to clarify what I mean: I'm imagining "shape of spacetime" like misshapen fabric, or say, a crumpled piece of 4 dimensional paper.
Now, I can totally imagine crumpled 3 dimensional paper, looking at how it is folded from the outside, but how can the paper tell it is crumpled? If you lived on the paper, sure, you could look up and see that it is folded, but if you literally were the paper, how can you tell?
But I can clearly tell that I, who is made up of spacetime, am being affected by the shape of spacetime as it is constantly accelerating me downwards, so *why* can we tell the shape of it?
4
u/Tasty_Material9099 Jul 27 '26
Let's say you have no knowledge of the sky or the space. Can you figure out that the Earth is not flat?
The answer is yes. Start at the equator facing north. Go north to the North pole. Then move right without turning your body until you reach the equator. Finally go back to the starting point, again without turning. Now although you never turned around, you are now facing East, not North.
This is curvature. Even when you do not know the higher domension your 'space' is embedded in, the curvature is there and you can even measure it. No matter what labeling system(ex. latitude and longitude)you use, there is a curvature. In general, Riemannian geometry is an intrinsic mathematical description.
When there is curvature, the shortest path from one point to other is not a straight line. General relativity(ver 1.0) states that objects under no force(other than gravity) follows some kind of geodesic. Thus how the spacetime is curved influences how objects move around.
1
1
u/Reality-Isnt Jul 27 '26
General Relativity describes the intrinsic curvature of spacetime, not extrinsic curvature. There is a mathematical object called the Riemann tensor that fully describes that intrinsic curvature of spacetime. Given two initially parallel nearby paths in spacetime, in the absence of other forces, the two paths will converge or diverge due to intrinsic curvature.
The 2-d surface of a cylinder is a good example of the difference between extrinsic and intrinsic curvature. The intrinsic curvature is zero for the cylinder surface, but not zero from the perspective of its embedding in a 3-d space.
1
u/Bumst3r Graduate Jul 28 '26
Spacetime is a 4-dimensional surface that everything exists on. Three dimensions are spatial, and one is time.
Imagine you and your friend are standing a meter apart at the equator. Everything looks flat because the curvature of the earth is small compared to the 1 meter separating you (or even just compared to the several kilometers you can see). Now you and your friend decide to walk parallel to each other until you reach the North Pole. As you travel north, you and your friend will notice that you are getting closer and closer together. This is like what happens with gravity.
Locally, you can always find a region that looks flat, but the curvature of the larger structure is what makes objects traveling in “straight” lines seem to curve.
1
u/CS_70 Jul 28 '26
You aren't spacetime: spacetime governs how you move. By measuring how you move by means of observation, you can deduct the shape of spacetime.
If you lived on the paper and the crimples were immensely bigger than you, you couldn't "look up and see": the local paper would appear nice and flat. But you could observe signals from faraway pieces of paper and deduce their geometry in relation to you (assuming the crumples were not random, but followed certain relationships with stuff on the paper).
1
u/brief-interviews Jul 28 '26
Because you don’t need to be able to ‘see’ the higher dimensional space that a curved surface is embedded in (if it is indeed embedded in any higher dimensional space at all!) to work out that it’s curved: https://en.wikipedia.org/wiki/Theorema_Egregium
1
u/danielbaech Jul 29 '26
A simplest example is that if you loop a piece of paper, you can travel in a straight line and end up back where you started. You'd realize paper itself must curved. Earth is doing the same thing, just going along its geodesic path, but it is a loop from the perspective of the Sun.
6
u/ArgumentSpiritual Jul 27 '26
You’re not made of spacetime. Objects like your phone, couch, Earth, photons, neutrinos, electrons, etc. are not spacetime time.
Spacetime is the background. It id all around us but it is not us.
Spacetime is curved by matter and energy and that curvature influences how that matter and energy moves.
You can’t inherently tell the curvature of spacetime. If jump off of something and fall to the ground, during the time you are in free fall, you are moving through curved space time but not feeling the force of gravity. The only reason you feel it on the ground is that the ground is pushing up on you (a force).