Why does Space-Time curve and more importantly, why and how does Space and Time come together to form a “fabric”?
In: Physics
Gravity causes changes in time in relation to space, expressions like curvature and fabric are really more in the order of explaining what is happening – https://youtu.be/dEintInq0YU
The fabric of space is a concept to describe the field in which light travels in a given distance and time from one reference plane. Since the speed of light must be the same for all planes of reference, the fabric of space must distort in order to keep the speed of light at a constant value.
From an observer floating in space looking miles from a large mass that can bend light in their reference frame, the fabric of space that they witness will need bend to insure that light traveling around the radius of the bend does not allow the light to accelerate past the speed of light nor increase in velocity. An observer on the large mass will observe another different phenomenon of the same light with their plane of reference making another fabric of space to keep the speed of light the same value for both observers.
[We don’t know.](https://xkcd.com/1867/) It just… seems to do that when heavy things are around. Maybe, when you grow up, you can figure it out.
That’s not a satisfying answer? Ok, then. Erm… well, technically Space-Time isn’t a real thing. [It’s just something Einstein made up.](https://xkcd.com/895/) A story, if you will. We tell ourselves stories about how the universe works, like “a person lets go of an apple, and it falls to the ground”, and then we look at the universe and, if we see those stories in the universe, we remember them for later. This is a story with a lot of maths in it, which makes some people think it’s real, but it’s actually just a story. We’ve already noticed places where the story doesn’t tell us what actually happens, and we’re trying to find a better story. This story’s good enough for most of the things we need it for, though, so we’re keeping it in the meantime.
We used to have a story written by Isaac Newton, that told us that things just fell down, but we got rid of the story when we noticed that the story said that the planets move in a certain way, but they were actually moving in a different way. It’s really interesting, actually. You know that the planet is a big ball, right? Well, when things fall “down”, they’re falling towards Earth. So if you’re in [country on the “bottom” of the globe] and you throw an apple into the air, it’ll still fall down to Earth, even though “down” is _that_ way instead of _that_ way. So, Newton’s story goes that if you put a cannon on top of a mountain and fire it sideways, the cannonball would cuuurve and hit the ground. Like this. But if you fire it further, it’ll curve around like this… and hit the ground, but it’s sort of curved around the Earth because “down” is always towards Earth, no matter where you are. But if you fire it hard enough… it’s just going round and round! Because it’s going so fast that it’s rushing past and, even though it’s being pulled towards Earth, it’s still curving. In fact, if you fire it fast enough, like this, it’ll shoot off into space and _never_ fall down again!
And Newton’s story is accurate enough for almost everything you’ll ever need. But it’s not quite right. It says that things move sliiightly differently to the way they actually move. So Einstein came up with a slightly better theory – one that’s a lot more complicated, though still quite simple if you’re really good at maths – (I’m not good enough at maths to understand it) – and Einstein’s theory predicted that, among other things, light was bent around the sun. We knew that light was bent around the sun before that, because we saw it, but because it had a lot of maths Einstein’s theory predicted _exactly how much_ the light was bent around the sun. (Actually his first theory was wrong about this, but he made a second theory that was better, and predicted it right.) Now, the only light that we can see that could’ve been bent around the sun was light from stars, which would make the stars look like they’d moved _very_ slightly when they were near the sun, but you’ll probably have spotted the problem with trying to spot stars moving near the sun.
Yes, you can’t see the stars in daytime. So they had to wait until a solar eclipse, and Eddington and his friends got a telescope with a special filter to stop them from going blind and took photographs of the stars near the sun, and found that the prediction made by Einstein’s second theory was right and Newton’s theory’s prediction was wrong.
We’ve got two main stories about the universe at the moment. One of them is Einstein’s theory, called “General Relativity”, which is the one about gravity, and the other one is called the “Standard Model”, and talks about really tiny things. These two stories predict different things, and we’ve measured that the Standard Model is wrong about gravity, and that General Relativity predicts contradictory things to the Standard Model. But that doesn’t make these stories useless. In fact, Newtonian Physics is still useful, and it’s what you’ll get taught in school until you’re an adult, and most adults don’t even use General Relativity when they’re working things out.
You do need General Relativity if you need to be really exact, or need to deal with clocks moving at different speeds to you, because Relativity says that time passes at different speeds depending on how fast you’re travelling. (Yes, it seems confusing, but that’s because your brain is designed for Newtonian Physics with time that passes at the same speed everywhere, and that’s just a story.) For example, [the GPS satellites that orbit Earth](https://physics.stackexchange.com/q/1061/105169) (like Newton’s cannonball) have clocks on them, and those clocks need to have the right time on them, so they need to use relativity to make their clock go at a different speed so it still matches up with the clocks on Earth.
General Relativity is an incredibly useful story. But it’s just a story. We don’t really understand the universe; we’re not even close.
Not yet.
Just to clarify the point, space-time curves around gravity, but is otherwise flat. Why? Cosmological estimates. See “How can the Universe be Flat” on Youtube for a more concise explanation.
There’s a youtube video out there about some reporter asking Feynman “why” a magnet works, or something like that. His answer was basically “it just does”. You can keep asking “why” or “how” something happens until the answer is finally “it just does”. We might have a good model to predict “what” is going to happen, but the “why” and the “how” have much more nebulous answers.
Short answer? SpaceTime curves in the presence of mass. How does it form a “fabric?’ The fabric is a loose analogy.
The concrete example is of a piece of paper. The paper is “2D”, but you could curve it into 3D. It would be a curved surface in 3D. The distance squared on the paper would be spatial x^2 + y^2. If you followed your pencil in a straight line on the flat paper, then curved it, you would notice the straight line has a different trajectory.
In General Relativity, the piece of paper is space time. Curvature is defined in the presence of mass which consequentially causes gravity. On this surface we travel in straight lines along the curvature in the absence of forces.
The distance squared on this surface includes what we think of as time (time is just a special spatial dimension). The distance squared, s^2 = x^2 + y^2 + z^2 – c^2 t^2. Notice the minus sign. c is the speed of light and speed times time is distance, so it works out.
Objects in free fall on curved surfaces follow straight lines. For a flat piece of paper this is a straight line. For the surface of a sphere, this is a great circle (a circle whose center is at the center of the sphere).
Light has mass. Mass is effected by gravity. So light bends because it has mass? Gravity effects time. The stronger the gravity the faster time? Weaker gravity slower time?
God I’m a dense individual. I wish I could grasp this!!
If this interests you, you might enjoy [warped passages](https://www.amazon.com/Warped-Passages-Unraveling-Mysteries-Dimensions/dp/0060531096) by Lisa Randall. It’s a few years old now, so I’d bet the science has evolved, but she does a great job of explaining these kinds of concepts in lay-terms.
I’m going to have to go with “it really doesn’t”, but that is about the best analogy we can come up with so we understand it. It is a mental model, not really what it is, just something we do understand that is sort of close to it.
All multi-dimensional systems have a structure of sorts, but all we humans have to use for imagining such things is how this 3-d world looks to us. So we think about other dimensions and other systems as if they were something that looks like what we actually can relate to. This does not make them like we imagine, it makes it so we can imagine something that at least starts to approach what the unknown thing actually is like.
Oh, that’s all.
The notion of a fabric and curvature are mostly just tools to help us wrap our heads around it. These physical theories are basically just mathematical models of how things actually work. In the case of general relativity (GR) the models predict pretty accurately.
The concept of curvature comes from an extrapolation of something we can understand well. If you take a piece of fabric and pretend it’s infinitely thin, it becomes a 2 dimensional surface embedded in a 3 dimensional space. You can bend and deform it. But if you were a 2 dimensional creature on that surface, it would just appear to be a flat plane, because you have no way to observe a 3rd dimension. An object moving along that fabric would twist and turn in ways you couldn’t understand. But to us 3 dimensional creatures looking at the fabric we can see the bends and deformations. To us it’s obvious why the object is moving in the way it is.
Gravity works similarly. Objects in space bend in the presence of a gravitational object – the moon orbiting the earth. But how does it do that? There’s nothing ‘pulling’ the moon to the earth – no particle we can see, no string, etc. Well, if we consider that our 3 dimensional space may be bending and deforming in 4 dimensional frame, in ways we can’t see and understand, we can visualize how that might work – that just like putting a weight in our 2d fabric distorts it and therefore distorts the path of objects traveling on it, without any obvious interaction of particles, string tying them together, etc. Massive objects do the same to 3d space. The earth distorts 3d space causing the moon to orbit it.
Is it an actual distortion? Don’t know. Doesn’t really matter, either. What matters is that the model works well enough that we can predict things we previously couldn’t. Further, and this is a sign this is a good model, it predicts things we’ve never seen. When we discover one of those things, it serves as good evidence that the model is valid. Distortion of light around the sun, gravitational lensing, time dilation in a gravitational field, etc. are all things the theory predicted that weren’t observed until later.
So, mainly it’s a way of conceptualizing a physical effect in a way that allows us to understand the interaction between these objects without seeing an exchange of information between them (particles, etc)
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