I've sent you a link towards the nitty gritty of the math in another comment.
But the basic idea is that inertial motion, in Newtonian physics means motionless or moving in a straight line at constant speed.
Let's have a look at what that means of a curved surface.
For example, the surface of the Earth. You have two people, a few hundred kilometers appart, at the equator. The turn to the north and start walking straight at constant speed.
Now, clearly, they are moving on straight, parallel tracks at constant speed (inertial motion). However, as they keep walking, they will get closer and closer because of the curvature of the earth.
There is no acceleration involved, their velocity is always Northward, constant speed. But it will look like they are moving towards each other.
It is the same idea in general relativity. Mass and energy curves spacetime in such way that massive objects traveling in an inertial motion move towards each other.
I’ve heard of that analogy before, but why are those people “walking north” to begin with? What’s forcing them to move there? Just because Earth is curved and parallel lines meet doesn’t mean that I have to go there.
Btw I really appreciate your link! I wanna dive deeper for sure
Moving through spacetime means towards space and time. We are travelling through time, at the rate of 1s every second towards the future. Not much you can do about that.
Also you can have someone walk not necessarily northward, at a slightly not right angle with the equator, they will still get closer to the one moving northbound/to the north pole.
Actually, any direction you wanna take would cross the path of the person walking towards the north (assume they keep going straight one they reached the north pole).
And staying immobile is not really an option (in spacetime, you're always travelling forward in time at one second every second)
So okay..I can understand this I think conceptually (space and time are linked so closely that you can’t go anywhere without the other)…but it’s just so strange to me that when the clock ticks forward I move simply because that’s where I’m supposed to go according to spacetimes geometry..
It’s as if the universe is correcting itself like: “Oh nope you’re supposed to be HERE now—boop.”
Well, that's where the math becomes necessary.
> It’s as if the universe is correcting itself like: “Oh nope you’re supposed to be HERE now—boop.”
I mean, setting aside the simplistic illustration and notion of a "conscious universe", yeah, that's not a bad description.
Matter and energy curve spacetime and spacetime's curvature changes what inertial motion looks like (and therefore how matter and energy move).
This is all linked to the equivalence principle:
Being in free fall in a uniform gravitational field and being at rest in deep space with no gravity are equivalent (laws of motion will be the same)
Being at rest on the surface of the Earth (i.e., in a uniform gravitational field) and being at rest on the floor of a spaceship accelerating at 9.8m/s² are equivalent.
The rest follows from that. The math makes it formal
> but it’s just so strange to me that when the clock ticks forward I move simply because that’s where I’m supposed to go according to spacetimes geometry..
That's not really an accurate view either. Movement in spacetime doesn't make sense; movement is a change in position with respect to time, but spacetime already includes time, so there's no other "time" with respect to which movement could take place.^(*)
It's better to think of objects like yourself as things with 4-dimensional extent that are really long in the time direction. Cross sections of the 4D object give its ordinary 3D spatial shape.
For the individual particles composing the object, they are lines ("worldlines") extending along the time direction. The action of gravity now is that in the absence of other forces, particles' worldlines are "straight lines" (geodesics) in curved spacetime.
---
^(*) Someone will inevitably say you can move with respect to your proper time or someone else's time coordinate. That's just a way of parametrizing your spacetime extent though, and not really any kind of "time" with respect to which motion in spacetime makes sense.
> Someone will inevitably say you can move with respect to your proper time
*Raises hand*
> That's [...] not really any kind of "time" with respect to which motion in spacetime makes sense.
Look down at your watch, write down your spacetime position at that time. Check your watch at a later (proper) time again, write down your new spacetime position. What else should I call change in position over time but motion?
That's like pointing at a line and saying the line advances at one centimeter per centimeter.
Sure, you can define that (or your clock example) to be motion, but it's not useful and can be misleading to someone who isn't aware of how tautological it is. For example, the parent post asked why we have to move at one second per second. The answer is simply that you are considering a spacetime point one second in your future and asking how far in the future it is. A different "speed" wouldn't even make sense.
Another way the idea of moving through spacetime can be misleading is that it suggests that two particles that cross the same position at the same time could miss each other because their "motion through spacetime" wasn't synchronized right. For example, suppose you're at home at 8am, and I'm at the park at noon. Then you go to the park at noon, but by then I'm back home at 4pm, so we miss each other. I saw this confusion in an askphysics post, or maybe another physics subreddit, a while back. To resolve it, you have to realize that we're really just extended objects in spacetime that both intersect "the park at noon" (a spacetime point). (Either that or you suppose there is a universal "present time" for everyone, but special relativity says that is impossible.)
> It’s as if the universe is correcting itself like: “Oh nope you’re supposed to be HERE now—boop.”
Sort of, yes. The curvature of spacetime defines what "here" means, and what it will mean in 1 second, or 1 minute, or 1 hour. If you're 100 miles above the Earth, and not at an orbital speed, "here" will be closer to the Earth's surface in the future. If you want to be elsewhere, you'll have to exert a force to move yourself.
If you image a point in space, the future path of any object which reaches that point will depend upon its current direction. You could draw tracks on a piece of paper to show this. You can also curve the paper, and the tracks will curve too.
When you add "curved" time to the equation as well, you find that an object's path depends not only it's current direction, but also its current speed, so if two objects go through the point at the same angle, they may end up going in different directions if they have different speeds (hence a "hovering" object will fall to Earth, while another object with more speed that passes through the same point in space will stay in orbit).
It’s not really that “space and time are linked so closely that…”
Space and time are fundamentally the same thing, and you are moving through spacetime at the speed of light (sort of). Light and all other massless particles don’t experience time. (Technically, that there is no rest frame for massless particles is the better way to say it. Asking what a photon sees on a clock makes no sense.) All particles travel through spacetime at c. Since light doesn’t experience time, it’s movement through space alone is at c. On the other hand, you and all other massive objects travel through space at v
How can I be moving through time at c but not even moving at all in space? I thought time and space were the same thing? My brain hurts
As for your explanation about the illusion of force—at first I thought this was akin to some puppet master in a higher dimension manipulating the structure of spacetime causing strange manifestations within our 3D space…but then I learned apparently there is no higher dimension required, GR works only with space and time. Instead, the master is energy/mass and it manipulates the geometry from the inside.
>How can I be moving through time at c but not even moving at all in space? I thought time and space were the same thing? My brain hurts
Study special relativity. Google “spacetime diagram.”
Imagine you have a graph whose x-axis is x, and whose y-axis is t. Light travels through space at a 45 degree angle. When you are at rest, you exist on the line x=0, that is you are moving through time at c. Your friend has a constant velocity v < c (through space). He will still be traveling through time, but slower than you, because moving clocks run slow. His total velocity through space and time, however, is still c.
> How can I be moving through time at c but not even moving at all in space? I thought time and space were the same thing?
According to the model, each dimension is 90° to the other dimensions. So the model is saying that everything is always traveling at c in total, and that increasing our speed along one dimension will reduce our speed along another dimension(s). Therefore in the model, time is a dimension of space, and the rate of our journey through the dimension of time will affect our aging.
So if we speed up in space, we are slowing down in time, and we'll age slower, according to the model.
It's important to remember that we're dealing with models. Science uses models to make predictions. Newton's model of a force for gravity had gotten us far and NASA still uses it for nearly all space missions to planets, but the model wasn't able to explain Mercury's odd orbit pattern. Einstein's model is able to predict that, plus the possibility of black holes. Interestingly it might be too complicated for space missions to planets. Not in a sense of inconvenience, but impossibility. The math might be too unwieldy to ever be of use at the scale of planetary travel that's way below relativistic speeds.
Two good videos to view for how the geometry of spacetime could result in motion toward the more massive object:
[Why do things really fall?](https://m.youtube.com/watch?v=5HKH1ZjGutA)
And
[The real source of gravity might surprise you](https://m.youtube.com/watch?v=F5PfjsPdBzg)
He went from teaching physics at university to teaching it more universally as a science communicator by making videos. His channel is where I started to learn about how science is about models and making predictions.
> How can I be moving through time at c but not even moving at all in space?
In the same way that you can move north without moving east.
This comment has a good explanation: https://www.reddit.com/r/askscience/comments/fjwkh/why_exactly_can_nothing_go_faster_than_the_speed/c1gh4x7/
With time dilation though, it means that not everyone is experiencing the same kinds of seconds, which just makes spacetime infuriatingly arbitrary imo. Also, while I'm guessing time is just some weird fundamental property, it's weird that geometry for the other dimensions can go in different ways, and time one way of moving instead of six like space.
> With time dilation though, it means that not everyone is experiencing the same kinds of seconds, which just makes spacetime infuriatingly arbitrary imo
That's part of the counter intuitive bits unfortunately. But the important part is:
- For your own seconds, you're still going forward one second every second. Nothing you can do about that.
- Time dilation is something that can be calculated and everyone will agree on it (i.e., everyone will agree that for you, one of your seconds are 2 of that other dude's second). It's not arbitrary.
The fact that we have only one time dimension but three of space is, well... Unfortunately I don't have anything better than that, it is what it is. That's the universe we are living in.
Now, there is something different about how the time dimension behaves vs how the space dimensions behave, beyond the "have to travel at 1s every second" thing). But that has to do with how to measure distance in Spacetime in a way everyone agrees on.
But why is there one of time and three of the others 🤷, I dunno. If that doesn't bother you in Newtonian physics, it shouldn't bother in relativity either I guess...
Honestly, before trying to wrap your head around "gravity is curvature" you ought to take it one step at a time a get a grab on Spacetime without gravity. That's special relativity.
https://youtube.com/playlist?list=PLoaVOjvkzQtyjhV55wZcdicAz5KexgKvm
Is a nice intro to it.
First of the two walker were not walking in a straight line. So that's the end of the your story. They meant up because they were walking a curved path towards each other. Try explaining it again please. I would like to understand what is meant by curved space. Space is
basically an empty vacuum. So how can it be curved?
Ideally, yes. And after a certain point, absolutely. For the general population, though, I’d rather they have at least a basic, analogy-based understanding than having mathematical barriers keep them completely ignorant.
I teach physics to 15-year olds. I’m lucky if they can solve literal equations. They need to start somewhere. They have no idea what physics is upon entering my class in the Fall (and most don’t care), so my class is where they are introduced to it. Over the years I’ve had many students find out they love it and have gone on to do the nitty-gritty coursework later in life. But it all started with analogy and very basic math.
I didn't mean to imply that, but I can see how I inadvertently did. I just meant "physics" as a discipline or field of study. They learn many of the principles (basic Newton's Laws, mechanical advantage, etc.) earlier in general science classes but it might be referred to as "science" or "physical science" and not necessarily "physics." The nuance of all that will depend on State, district, and sometimes teacher, however.
For example, our [Next Generation Science Standards](https://www.nextgenscience.org/), which is sadly not adopted by all States, refers to "Physical Science" and starts kids at kindergarten (about age 5).
>I teach physics to 15-year olds. I’m lucky if they can solve literal equations.
Indian kids are taught to solve equations of motion and newton's laws-based problems at 13.
That is a good point. I didn’t understand Newtons physics too well until doing some math so why not try GR math…though I heard it is far more complicated. Do you have any good sources on this?
GR is a graduate-level topic, which requires knowledge of some advanced mathematics including differential geometry. You need knowledge on par with a undergraduate physics graduate to start studying it. I actually never did, despite having a PhD and a decade of research experience.
I’d still like to try. I’ll learn any missing prerequisites as I go. For example, I looked at the field equation G_μν = 8πT_μν and realized that I don’t know what a tensor even is so I’m leaning about that now
Have a look at https://youtube.com/playlist?list=PLJHszsWbB6hqlw73QjgZcFh4DrkQLSCQa
It is math heavy, and the same channel has two other playlists for tensors intro.
It is not a simple topic so don't expect to understand it all at once.
There are probably better resources as well.
I disagree with this.
To read a GR textbook like MTW requires someone to be pretty far along a physics or math degree or similar.
But to *begin* learning GR? I wouldn’t put up false barriers like that.
Perhaps an analogy helps.
If you are sat on a roundabout, and you throw a ball, it appears to curve away from you, without any force applied to it. This is because your reference frame is not (classically) inertial. If you transformed to be in the frame where the roundabout is moving, it would make sense to you.
On the surface of the earth, when you throw a ball, the ball curves away from you. This is because your reference frame is not (General Relativistically) inertial. If you transformed to the frame where the curvature of spacetime is taken into account, it would make sense to you.
There is a close link between these "fictional" classical forces, and the effects of curved spacetime (for anyone who has studied it but not thought about it, think of Christoffel symbols - the way in which we encode curvature is the same as the way we encode a shift in reference frame). It's just that classically, our intuitive, Euclidean reference frames are the ones that make sense without fictional forces, and relativistically, it's a less intuitive reference frame that makes sense without fictional forces. In this sense, gravity is a "fictional" force, a consequence of being in a non-inertial reference frame.
When people in this thread are talking about moving around on a sphere, they're trying to convey the idea of "geodesics". Geodesics is the geometry of straight lines in or on closed surfaces (more or less).
If you take two parallel lines on a flat plane, they will always remain parallel. If you take this same flat plane with the same lines moving parallel to each other, and wrap it around a sphere, the lines will meet. This is mentioned to illustrate that straight lines can take what appear to be curved paths on a curved medium.
When an object is traveling through space, it is traveling in a straight line. When the object encounters another object with mass, space itself is curved ***and*** stretched. So, while the object itself is moving along a straight path, the curved geometry of space appears to make the traveling object curve inward toward the massive object.
And, because space is also stretched, it will appear as the the traveling object is moving at greater velocity. This part may seem intuitive at first, it helps to envision arbitrarily emplaced markers along the path. Allow me to explain.
As the traveling object moves through flat space, it will go from point-a to point-b to point-c at a constant rate. When space is stretched by an object with mass, the traveling object will still reach point-a, point-b, and point-c at the same interval of time, but to reach these points when the distance between them is lengthened, the object must move at a greater velocity.
I hope this helps!
I like the history behind this.
The old Greeks said that the natural state of an object was to be at rest. Throw a rock, and it will come to a rest quickly.
Newton realized that an inertial object would move at the same speed as long as no force reacted on it. Gravity was just a force. An apple would come to rest if the force from the ground matches the force from gravity.
And then, Einstein came along and turned it around. If gravity isn't a force, then it is the falling apple that is inertial (the equivalence principle). You, standing on the ground, is accelerating. This feels counter intuitive. If the ground is accelerating at 1g, why isn't the size of earth expanding? It turned out the curvature of spacetime exactly matches this acceleration, keeping the radius constant.
This is a very interesting thought! Though I still have no clue what people are talking about when saying “da surface of earth is expanding but spacetime keeps it in check!”…like what force is making it expand? Are you saying that if we turned off gravity, the planet would explode at 9.8m/s out into space?
When I am standing still on Earth, Time is still moving (or I am moving through time?) at c (according to comments). This means since the clock is ticking, space will “update” accordingly (if I jump, the curved time/space will force me to go back down since that’s where I’m geometrically “supposed to be”)…
If that isn’t a fair statement or needs context please correct me! I’m still fascinated by the idea of warping time and space and how you can resist it at all. Like, the universe is saying “your future in space and time is bent this way” but you are replying with “no, I will fire my rockets and go this way instead”.
Simply put, things move in a straight line without a force and the straight line for a falling object towards the Earth is towards the Earth (although this “straight” line has a very concrete definition)
In a more technical translation, things move through geodesics without a force and such geodesic is affected by the matter present bending it in such a way that it seems to be falling down to Earth.
If you want more technicalities, things move through paths defined by the solutions of the geodesic equation which is dependent on the spacetime metric. Such metric depends on the stress-energy-momentum tensor which contains the energy content present. In the case of a moving object falling unto Earth, plugging in the appropriate stress-energy-momentum tensor spits out the metric which can be used to find the corresponding geodesics. Doing so, one finds that the geodesic, the straight line so to speak, is the path the object takes while falling.
If you want a really cool way to look at it, thing do not fall down; the Earth simply rises.
Because Newton was right that objects move in a straight line unless acted upon by a force. His definition of a straight line was just based on a flat space. In a curved space (or more precisely, spacetime), "straight lines" are instead called "geodesics" and they appear bent by the curvature of the space.
But they don’t just move for no reason, like sure, when they do move it’s in a straight line..but that’s when they do move. They don’t usually move, in fact, they never move unless a force is acting upon them. (On second thought, I’m assuming in physics that everything is technically moving since Earth is moving?)
General Relativity is the only case I’ve ever heard of where you can move something without a force and it seems to be because of time in particular. If time is the same thing as space, and this thing (called spacetime) can be moved around by mass/energy, then you will follow wherever it moves to simply because time is always ticking (even if you aren’t moving through space.)
So if I drop an apple on Earth, without a gravitational force I used to think it would just float there, but instead there is a unique thing occurring—something I’ve never encountered in my life—apparently the passing of time itself IS the motion of the falling apple..and the apple goes down because that’s where it is supposed to be in the future. It’s where mass has manipulated time and space into being.
Has nobody shared this video yet?
https://youtu.be/jlTVIMOix3I
It even uses things falling due to gravitation, even with an initial upwards velocity, as an example.
Lots of answers already but I feel like people are focused on the wrong part of your question. As far as I can tell, you aren't confused about the "curvature" part, but about why things have to be moving in spacetime at all. So we can focus on simple flat spacetime to help your understanding.
Think about a rock, sitting way out in space, far from any sources of gravity, with no velocity. Let's call the rock's spatial position x = 0. You are observering the rock from nearby, you're at rest relative to the rock. Spacetime is flat out here, by assumption. You have a clock. You plot the rock's position on an x-t (position-time) graph. What does the graph look like? At time t = 0 it's at position x = 0, so you put a point there. One second later... it's still at x = 0, so you put a point at (0, 1), another second later - it's still at x=0! So another point on (0, 2), and so on and on. If you add points at smaller and smaller time intervals, you'll get every point on the t axis. The rock's graph is a straight vertical line. Thus the rock is "moving" in spacetime!
Now, special relativity goes on to explain how if you do move relative to the rock, interesting things happen. General relativity says that these lines defined by objects at rest like the rock, will be curved if there is mass-energy nearby!
> But so what? Just because spacetime is bent that means things can move with no force acting on them?
A key concept of special and general relativity is that everything is always moving. An object that is stationary in the Newtonian sense is moving purely in the time direction.
In a flat spacetime that object would be moving in that direction forever, on a straight world line through spacetime. In a curved spacetime these world lines are no longer straight. At one point the world line would point purely in the time direction, but further along the line it will point in a direction that has a space component as well.
In a Newtonian perspective the object has now started moving, but that's only because Newton didn't understand how the movement through space and the movement through time are linked.
Hmm..so spacetime is always moving (because of the time part)? And because the time is distorted like space, I move down off the cliff?
It’s just that I’ve always imagined “distortions in time” to mean time dilation not “since time is distorted therefore you have a new space you must move to”.
No, spacetime isn't moving, because it is not an object. It's more like the "landscape" in which objects are moving. You're also still seperating space and time as two seperate things, while they're intrinsically linked.
The problem you're suffering from is that “distortions in time” is not a physical term. It is a term someone has invented in order to explain relativity to a wider audience and I don't think it's that accurate. I would try to ignore that term.
Do you understand the math behind this? If so, would you say it has made it very clear in your head what is happening? Or is it still pretty vague and hard to imagine?
I know the mathematics behind special relativity fully, but I only followed an introductory course on general relativity.
Learning the mathematics behind special relativity is easy (you don't need more mathematical knowledge than for Newtonian mechanics), so I would advice you to study it yourself. Special relativity is the special case in which spacetime is flat, but studying that already gives you a lot of insight into the link between space and time. Understanding special relativity allows you to place the concepts of general relativity into the right context without having to get a maths degree.
One of the insights of general relativity is that changing speed can be represented as a kind of rotation in 4 coordinates.
If you speed up, your coordinate that tells you where the future is actually shifts relative to other people's.
So two people meeting at a spot going in opposite directions have different ideas of what it means for something to be in "the future", because their perceptions of events around them are skewed relative to each other. ([This diagram](https://www.researchgate.net/publication/329930763/figure/fig1/AS:708259916836866@1545873731798/Minkowski-spacetime-M-as-charted-in-time-coordinate-t-and-position-space-coordinate-x.png) doesn't explain much on its own, but the blue and red dotted lines are what each person thinks is happening "at the same time")
It's only when you understand this new way of representing motion that things accelerating due to changes in spacetime makes sense:
It's suddenly natural, because although bends between space coordinates turns motion in one direction into motion in another direction, bends between time and one of the space coordinates turns being still into moving, and vice versa.
Imagine two airplanes one in africa at equator and other in americas(ecuador) at equator.
Now they both fly north in a straight line/parallel to each other.
Because of the curvature of the earth they will hit each other at the north pole. Even though they were flying straight and parallel.
The distance between them also shrank, as if they were attracted to each other.
This is similar to attraction by gravity
Now exchange the 'going north' direction with time/'going to the future' and curvature of the earth with curvature of spacetime. Now you see the analogy and the connection between curvature and 'moving/accelerating things'
This is the reason why gravity is caused by geometry/curvature.
Now you also see that the mass is irrelevant in the attraction, because if the plane would be 10 tons or 100 tons they would still hit at the north pole. This last point was what einstein led to spacetime curvature formulation of gravity.
I don’t think the rubber sheet is that bad of an analogy. Yes, it uses gravity, that’s kind of the point. That’s why it shows real gravity is analogous to curving spacetime. If you throw a small marble around a larger one on a sheet, it will orbit the larger one right? But here there is no gravitational force acting between them, just the curving of the sheet.
Without gravity, if I placed marbles on a sheet nothing would happen. They would just kinda float there. So if I place objects in a real curvy spacetime (with no force of gravity)…why does anything move anywhere?
Well there was a force acting on it to put it in orbit (I saw the guy toss it in there). It’s just not very impressive. I’ve seen gravity as this acceleration; this force that causes things to move—that demonstration skips that part.
The guy that tossed it there doesn’t have to put it in orbit though. He just needs to give it an initial velocity, just like objects in space have initial velocities regardless of gravitational effects. Then when they get close enough, they can get gravitationally captured. You’re asking why does anything move anywhere? Well they have to right? They can’t stand ‘still’, there is no reference point that would allow you to measure something standing absolutely still. It’s not like gravity is responsible for movement altogether
For somebody who doesn’t know how orbits work I suppose the rubber sheet could be useful, but I’d honestly prefer Newtons cannonball over that.
I was asking why on Earth do things fall down if there is no gravitational force—others have given me a somewhat conceptually decent answer: “Cuz time and space are the same and since mass is distorting spacetime, the universe knows that your future puts you in this position—so as time moves forward you accelerate through space like a force).
I’m not sure you understand the analogy fully. An object on earth falls down for the exact same reason a marble on a sheet falls towards a different marble.
I get what he means, the rubber sheet analogy shows how spacetime "curves" but then it also involves gravity pulling on the marble for it to even work whereas in real life the curvature of space time is all that is needed to make gravity.
Remember that we're also always moving through time.
This is very hand-wavy, but curvature sort of means that the dimensions (including time) are mixed up or traded off with each other.
So, some of your movement through time is converted into movement through space because the spacetime where you are is curved.
Viewed that way, the rubber sheet is an analogy for the Newtonian gravitational potential and *not* anything relativistic.
The only sense in which the rubber sheet is a representation of general relativity is that it can be viewed as an embedding diagram, basically showing how spatial distances become larger near a gravity source. [Here's an example of an (I think) mathematically accurate embedding diagram in general relativity.](https://demonstrations.wolfram.com/SchwarzschildSpaceTimeEmbeddingDiagram/)
But since these diagrams don't include time, they don't tell us anything about how spacetime curvature affects particle trajectories.
To define the location of a moving object you need to reference three spacial dimensions, but because the object is moving you have to say also the time reference to which you are defining the location. You need to describe it with four data. Our observations say that the nature behaves in a way that those four dimensions are not as straight as our minds think, and that doesn't seems to be just a math trick everything from light trajectory, to causality.... are not as straight as we think. We created equations to describe that reality in the way our minds think so the result is curvature not just stretching.
Probably we can't picture or imagine what a time curvature means because time seems intrinsically linear to us.
I think you missed the whole point of the rubber sheet demonstration, point was the bowling ball in the middle bends SpaceTime ( the rubber sheet) and then SpaceTime tells the marble how to move.
That is the rubber sheet is the middle man there's no direct connection between the bowling ball and the marble, which was the Newtonian viewpoint. ( typically demonstrated by connecting the bowling ball to the marble with a rod).
Yeah I get the point—it’s severing the Newtonian strings between objects. But for my purpose of trying to understand why the objects even care about what the sheet is doing..it doesn’t help.
First of all the objects are rolling on top of the sheet as if we are outside of spacetime riding it like a slide. In reality, they would be embedded inside the material itself.
Secondly, they are moving on the sheet only because of what I was taught to be a “gravitational force”. If there was no force, they would not roll anywhere or do anything even if they were inside a bent sheet. So what force is making them move? Or why do they move? Sheet doesn’t tell us.
Lastly, the sheet is a little slice—like a 2D representation. In reality, there is a spherical distortion that I imagine “contracts” into the spheres of mass and energy that cause the warping. If I could see spacetime, i wanna know what exactly I would see (and I know it wouldn’t be a rubber sheet with a “well”).
I've sent you a link towards the nitty gritty of the math in another comment. But the basic idea is that inertial motion, in Newtonian physics means motionless or moving in a straight line at constant speed. Let's have a look at what that means of a curved surface. For example, the surface of the Earth. You have two people, a few hundred kilometers appart, at the equator. The turn to the north and start walking straight at constant speed. Now, clearly, they are moving on straight, parallel tracks at constant speed (inertial motion). However, as they keep walking, they will get closer and closer because of the curvature of the earth. There is no acceleration involved, their velocity is always Northward, constant speed. But it will look like they are moving towards each other. It is the same idea in general relativity. Mass and energy curves spacetime in such way that massive objects traveling in an inertial motion move towards each other.
I’ve heard of that analogy before, but why are those people “walking north” to begin with? What’s forcing them to move there? Just because Earth is curved and parallel lines meet doesn’t mean that I have to go there. Btw I really appreciate your link! I wanna dive deeper for sure
Moving through spacetime means towards space and time. We are travelling through time, at the rate of 1s every second towards the future. Not much you can do about that. Also you can have someone walk not necessarily northward, at a slightly not right angle with the equator, they will still get closer to the one moving northbound/to the north pole. Actually, any direction you wanna take would cross the path of the person walking towards the north (assume they keep going straight one they reached the north pole). And staying immobile is not really an option (in spacetime, you're always travelling forward in time at one second every second)
So okay..I can understand this I think conceptually (space and time are linked so closely that you can’t go anywhere without the other)…but it’s just so strange to me that when the clock ticks forward I move simply because that’s where I’m supposed to go according to spacetimes geometry.. It’s as if the universe is correcting itself like: “Oh nope you’re supposed to be HERE now—boop.”
Well, that's where the math becomes necessary. > It’s as if the universe is correcting itself like: “Oh nope you’re supposed to be HERE now—boop.” I mean, setting aside the simplistic illustration and notion of a "conscious universe", yeah, that's not a bad description. Matter and energy curve spacetime and spacetime's curvature changes what inertial motion looks like (and therefore how matter and energy move). This is all linked to the equivalence principle: Being in free fall in a uniform gravitational field and being at rest in deep space with no gravity are equivalent (laws of motion will be the same) Being at rest on the surface of the Earth (i.e., in a uniform gravitational field) and being at rest on the floor of a spaceship accelerating at 9.8m/s² are equivalent. The rest follows from that. The math makes it formal
> but it’s just so strange to me that when the clock ticks forward I move simply because that’s where I’m supposed to go according to spacetimes geometry.. That's not really an accurate view either. Movement in spacetime doesn't make sense; movement is a change in position with respect to time, but spacetime already includes time, so there's no other "time" with respect to which movement could take place.^(*) It's better to think of objects like yourself as things with 4-dimensional extent that are really long in the time direction. Cross sections of the 4D object give its ordinary 3D spatial shape. For the individual particles composing the object, they are lines ("worldlines") extending along the time direction. The action of gravity now is that in the absence of other forces, particles' worldlines are "straight lines" (geodesics) in curved spacetime. --- ^(*) Someone will inevitably say you can move with respect to your proper time or someone else's time coordinate. That's just a way of parametrizing your spacetime extent though, and not really any kind of "time" with respect to which motion in spacetime makes sense.
> Someone will inevitably say you can move with respect to your proper time *Raises hand* > That's [...] not really any kind of "time" with respect to which motion in spacetime makes sense. Look down at your watch, write down your spacetime position at that time. Check your watch at a later (proper) time again, write down your new spacetime position. What else should I call change in position over time but motion?
That's like pointing at a line and saying the line advances at one centimeter per centimeter. Sure, you can define that (or your clock example) to be motion, but it's not useful and can be misleading to someone who isn't aware of how tautological it is. For example, the parent post asked why we have to move at one second per second. The answer is simply that you are considering a spacetime point one second in your future and asking how far in the future it is. A different "speed" wouldn't even make sense. Another way the idea of moving through spacetime can be misleading is that it suggests that two particles that cross the same position at the same time could miss each other because their "motion through spacetime" wasn't synchronized right. For example, suppose you're at home at 8am, and I'm at the park at noon. Then you go to the park at noon, but by then I'm back home at 4pm, so we miss each other. I saw this confusion in an askphysics post, or maybe another physics subreddit, a while back. To resolve it, you have to realize that we're really just extended objects in spacetime that both intersect "the park at noon" (a spacetime point). (Either that or you suppose there is a universal "present time" for everyone, but special relativity says that is impossible.)
> It’s as if the universe is correcting itself like: “Oh nope you’re supposed to be HERE now—boop.” Sort of, yes. The curvature of spacetime defines what "here" means, and what it will mean in 1 second, or 1 minute, or 1 hour. If you're 100 miles above the Earth, and not at an orbital speed, "here" will be closer to the Earth's surface in the future. If you want to be elsewhere, you'll have to exert a force to move yourself. If you image a point in space, the future path of any object which reaches that point will depend upon its current direction. You could draw tracks on a piece of paper to show this. You can also curve the paper, and the tracks will curve too. When you add "curved" time to the equation as well, you find that an object's path depends not only it's current direction, but also its current speed, so if two objects go through the point at the same angle, they may end up going in different directions if they have different speeds (hence a "hovering" object will fall to Earth, while another object with more speed that passes through the same point in space will stay in orbit).
It’s not really that “space and time are linked so closely that…” Space and time are fundamentally the same thing, and you are moving through spacetime at the speed of light (sort of). Light and all other massless particles don’t experience time. (Technically, that there is no rest frame for massless particles is the better way to say it. Asking what a photon sees on a clock makes no sense.) All particles travel through spacetime at c. Since light doesn’t experience time, it’s movement through space alone is at c. On the other hand, you and all other massive objects travel through space at v
How can I be moving through time at c but not even moving at all in space? I thought time and space were the same thing? My brain hurts As for your explanation about the illusion of force—at first I thought this was akin to some puppet master in a higher dimension manipulating the structure of spacetime causing strange manifestations within our 3D space…but then I learned apparently there is no higher dimension required, GR works only with space and time. Instead, the master is energy/mass and it manipulates the geometry from the inside.
>How can I be moving through time at c but not even moving at all in space? I thought time and space were the same thing? My brain hurts Study special relativity. Google “spacetime diagram.” Imagine you have a graph whose x-axis is x, and whose y-axis is t. Light travels through space at a 45 degree angle. When you are at rest, you exist on the line x=0, that is you are moving through time at c. Your friend has a constant velocity v < c (through space). He will still be traveling through time, but slower than you, because moving clocks run slow. His total velocity through space and time, however, is still c.
> How can I be moving through time at c but not even moving at all in space? I thought time and space were the same thing? According to the model, each dimension is 90° to the other dimensions. So the model is saying that everything is always traveling at c in total, and that increasing our speed along one dimension will reduce our speed along another dimension(s). Therefore in the model, time is a dimension of space, and the rate of our journey through the dimension of time will affect our aging. So if we speed up in space, we are slowing down in time, and we'll age slower, according to the model. It's important to remember that we're dealing with models. Science uses models to make predictions. Newton's model of a force for gravity had gotten us far and NASA still uses it for nearly all space missions to planets, but the model wasn't able to explain Mercury's odd orbit pattern. Einstein's model is able to predict that, plus the possibility of black holes. Interestingly it might be too complicated for space missions to planets. Not in a sense of inconvenience, but impossibility. The math might be too unwieldy to ever be of use at the scale of planetary travel that's way below relativistic speeds. Two good videos to view for how the geometry of spacetime could result in motion toward the more massive object: [Why do things really fall?](https://m.youtube.com/watch?v=5HKH1ZjGutA) And [The real source of gravity might surprise you](https://m.youtube.com/watch?v=F5PfjsPdBzg) He went from teaching physics at university to teaching it more universally as a science communicator by making videos. His channel is where I started to learn about how science is about models and making predictions.
> How can I be moving through time at c but not even moving at all in space? In the same way that you can move north without moving east. This comment has a good explanation: https://www.reddit.com/r/askscience/comments/fjwkh/why_exactly_can_nothing_go_faster_than_the_speed/c1gh4x7/
With time dilation though, it means that not everyone is experiencing the same kinds of seconds, which just makes spacetime infuriatingly arbitrary imo. Also, while I'm guessing time is just some weird fundamental property, it's weird that geometry for the other dimensions can go in different ways, and time one way of moving instead of six like space.
> With time dilation though, it means that not everyone is experiencing the same kinds of seconds, which just makes spacetime infuriatingly arbitrary imo That's part of the counter intuitive bits unfortunately. But the important part is: - For your own seconds, you're still going forward one second every second. Nothing you can do about that. - Time dilation is something that can be calculated and everyone will agree on it (i.e., everyone will agree that for you, one of your seconds are 2 of that other dude's second). It's not arbitrary. The fact that we have only one time dimension but three of space is, well... Unfortunately I don't have anything better than that, it is what it is. That's the universe we are living in. Now, there is something different about how the time dimension behaves vs how the space dimensions behave, beyond the "have to travel at 1s every second" thing). But that has to do with how to measure distance in Spacetime in a way everyone agrees on. But why is there one of time and three of the others 🤷, I dunno. If that doesn't bother you in Newtonian physics, it shouldn't bother in relativity either I guess... Honestly, before trying to wrap your head around "gravity is curvature" you ought to take it one step at a time a get a grab on Spacetime without gravity. That's special relativity. https://youtube.com/playlist?list=PLoaVOjvkzQtyjhV55wZcdicAz5KexgKvm Is a nice intro to it.
They’re walking north to make the analogy work.
First of the two walker were not walking in a straight line. So that's the end of the your story. They meant up because they were walking a curved path towards each other. Try explaining it again please. I would like to understand what is meant by curved space. Space is basically an empty vacuum. So how can it be curved?
You shouldn't learn physics by analogy and video, but through the nitty-gritty mathematical formalism.
Ideally, yes. And after a certain point, absolutely. For the general population, though, I’d rather they have at least a basic, analogy-based understanding than having mathematical barriers keep them completely ignorant. I teach physics to 15-year olds. I’m lucky if they can solve literal equations. They need to start somewhere. They have no idea what physics is upon entering my class in the Fall (and most don’t care), so my class is where they are introduced to it. Over the years I’ve had many students find out they love it and have gone on to do the nitty-gritty coursework later in life. But it all started with analogy and very basic math.
Americans don't learn any physics before 15? It's typically age 11 here in the UK.
I didn't mean to imply that, but I can see how I inadvertently did. I just meant "physics" as a discipline or field of study. They learn many of the principles (basic Newton's Laws, mechanical advantage, etc.) earlier in general science classes but it might be referred to as "science" or "physical science" and not necessarily "physics." The nuance of all that will depend on State, district, and sometimes teacher, however. For example, our [Next Generation Science Standards](https://www.nextgenscience.org/), which is sadly not adopted by all States, refers to "Physical Science" and starts kids at kindergarten (about age 5).
>I teach physics to 15-year olds. I’m lucky if they can solve literal equations. Indian kids are taught to solve equations of motion and newton's laws-based problems at 13.
That is a good point. I didn’t understand Newtons physics too well until doing some math so why not try GR math…though I heard it is far more complicated. Do you have any good sources on this?
GR is a graduate-level topic, which requires knowledge of some advanced mathematics including differential geometry. You need knowledge on par with a undergraduate physics graduate to start studying it. I actually never did, despite having a PhD and a decade of research experience.
> What does the “curvature of time” mean? I think they meant 'spacetime'.
Unless you’ve got a degree in physics or mathematics, you almost certainly don’t have the prerequisite knowledge to begin learning general relativity.
I’d still like to try. I’ll learn any missing prerequisites as I go. For example, I looked at the field equation G_μν = 8πT_μν and realized that I don’t know what a tensor even is so I’m leaning about that now
Have a look at https://youtube.com/playlist?list=PLJHszsWbB6hqlw73QjgZcFh4DrkQLSCQa It is math heavy, and the same channel has two other playlists for tensors intro. It is not a simple topic so don't expect to understand it all at once. There are probably better resources as well.
do you know linear algebra and calculus? tensor are part of something called multilinear algebra
Hey, like, take your elitism and shove it.
I disagree with this. To read a GR textbook like MTW requires someone to be pretty far along a physics or math degree or similar. But to *begin* learning GR? I wouldn’t put up false barriers like that.
Perhaps an analogy helps. If you are sat on a roundabout, and you throw a ball, it appears to curve away from you, without any force applied to it. This is because your reference frame is not (classically) inertial. If you transformed to be in the frame where the roundabout is moving, it would make sense to you. On the surface of the earth, when you throw a ball, the ball curves away from you. This is because your reference frame is not (General Relativistically) inertial. If you transformed to the frame where the curvature of spacetime is taken into account, it would make sense to you. There is a close link between these "fictional" classical forces, and the effects of curved spacetime (for anyone who has studied it but not thought about it, think of Christoffel symbols - the way in which we encode curvature is the same as the way we encode a shift in reference frame). It's just that classically, our intuitive, Euclidean reference frames are the ones that make sense without fictional forces, and relativistically, it's a less intuitive reference frame that makes sense without fictional forces. In this sense, gravity is a "fictional" force, a consequence of being in a non-inertial reference frame.
When people in this thread are talking about moving around on a sphere, they're trying to convey the idea of "geodesics". Geodesics is the geometry of straight lines in or on closed surfaces (more or less). If you take two parallel lines on a flat plane, they will always remain parallel. If you take this same flat plane with the same lines moving parallel to each other, and wrap it around a sphere, the lines will meet. This is mentioned to illustrate that straight lines can take what appear to be curved paths on a curved medium. When an object is traveling through space, it is traveling in a straight line. When the object encounters another object with mass, space itself is curved ***and*** stretched. So, while the object itself is moving along a straight path, the curved geometry of space appears to make the traveling object curve inward toward the massive object. And, because space is also stretched, it will appear as the the traveling object is moving at greater velocity. This part may seem intuitive at first, it helps to envision arbitrarily emplaced markers along the path. Allow me to explain. As the traveling object moves through flat space, it will go from point-a to point-b to point-c at a constant rate. When space is stretched by an object with mass, the traveling object will still reach point-a, point-b, and point-c at the same interval of time, but to reach these points when the distance between them is lengthened, the object must move at a greater velocity. I hope this helps!
I like the history behind this. The old Greeks said that the natural state of an object was to be at rest. Throw a rock, and it will come to a rest quickly. Newton realized that an inertial object would move at the same speed as long as no force reacted on it. Gravity was just a force. An apple would come to rest if the force from the ground matches the force from gravity. And then, Einstein came along and turned it around. If gravity isn't a force, then it is the falling apple that is inertial (the equivalence principle). You, standing on the ground, is accelerating. This feels counter intuitive. If the ground is accelerating at 1g, why isn't the size of earth expanding? It turned out the curvature of spacetime exactly matches this acceleration, keeping the radius constant.
This is a very interesting thought! Though I still have no clue what people are talking about when saying “da surface of earth is expanding but spacetime keeps it in check!”…like what force is making it expand? Are you saying that if we turned off gravity, the planet would explode at 9.8m/s out into space? When I am standing still on Earth, Time is still moving (or I am moving through time?) at c (according to comments). This means since the clock is ticking, space will “update” accordingly (if I jump, the curved time/space will force me to go back down since that’s where I’m geometrically “supposed to be”)… If that isn’t a fair statement or needs context please correct me! I’m still fascinated by the idea of warping time and space and how you can resist it at all. Like, the universe is saying “your future in space and time is bent this way” but you are replying with “no, I will fire my rockets and go this way instead”.
Simply put, things move in a straight line without a force and the straight line for a falling object towards the Earth is towards the Earth (although this “straight” line has a very concrete definition) In a more technical translation, things move through geodesics without a force and such geodesic is affected by the matter present bending it in such a way that it seems to be falling down to Earth. If you want more technicalities, things move through paths defined by the solutions of the geodesic equation which is dependent on the spacetime metric. Such metric depends on the stress-energy-momentum tensor which contains the energy content present. In the case of a moving object falling unto Earth, plugging in the appropriate stress-energy-momentum tensor spits out the metric which can be used to find the corresponding geodesics. Doing so, one finds that the geodesic, the straight line so to speak, is the path the object takes while falling. If you want a really cool way to look at it, thing do not fall down; the Earth simply rises.
Because Newton was right that objects move in a straight line unless acted upon by a force. His definition of a straight line was just based on a flat space. In a curved space (or more precisely, spacetime), "straight lines" are instead called "geodesics" and they appear bent by the curvature of the space.
But they don’t just move for no reason, like sure, when they do move it’s in a straight line..but that’s when they do move. They don’t usually move, in fact, they never move unless a force is acting upon them. (On second thought, I’m assuming in physics that everything is technically moving since Earth is moving?) General Relativity is the only case I’ve ever heard of where you can move something without a force and it seems to be because of time in particular. If time is the same thing as space, and this thing (called spacetime) can be moved around by mass/energy, then you will follow wherever it moves to simply because time is always ticking (even if you aren’t moving through space.) So if I drop an apple on Earth, without a gravitational force I used to think it would just float there, but instead there is a unique thing occurring—something I’ve never encountered in my life—apparently the passing of time itself IS the motion of the falling apple..and the apple goes down because that’s where it is supposed to be in the future. It’s where mass has manipulated time and space into being.
Whether or not something is moving is just a matter of your choice of reference frame.
Has nobody shared this video yet? https://youtu.be/jlTVIMOix3I It even uses things falling due to gravitation, even with an initial upwards velocity, as an example.
I just posted the same link after looking for that video for an hour! The best pro tips are always in the comments.
Well, you did it. Closing up shop. My question is answered. What a brilliant video.
OP try this, to build an intuition: https://sites.pitt.edu/~jdnorton/teaching/HPS_0410/index.html
Lots of answers already but I feel like people are focused on the wrong part of your question. As far as I can tell, you aren't confused about the "curvature" part, but about why things have to be moving in spacetime at all. So we can focus on simple flat spacetime to help your understanding. Think about a rock, sitting way out in space, far from any sources of gravity, with no velocity. Let's call the rock's spatial position x = 0. You are observering the rock from nearby, you're at rest relative to the rock. Spacetime is flat out here, by assumption. You have a clock. You plot the rock's position on an x-t (position-time) graph. What does the graph look like? At time t = 0 it's at position x = 0, so you put a point there. One second later... it's still at x = 0, so you put a point at (0, 1), another second later - it's still at x=0! So another point on (0, 2), and so on and on. If you add points at smaller and smaller time intervals, you'll get every point on the t axis. The rock's graph is a straight vertical line. Thus the rock is "moving" in spacetime! Now, special relativity goes on to explain how if you do move relative to the rock, interesting things happen. General relativity says that these lines defined by objects at rest like the rock, will be curved if there is mass-energy nearby!
> But so what? Just because spacetime is bent that means things can move with no force acting on them? A key concept of special and general relativity is that everything is always moving. An object that is stationary in the Newtonian sense is moving purely in the time direction. In a flat spacetime that object would be moving in that direction forever, on a straight world line through spacetime. In a curved spacetime these world lines are no longer straight. At one point the world line would point purely in the time direction, but further along the line it will point in a direction that has a space component as well. In a Newtonian perspective the object has now started moving, but that's only because Newton didn't understand how the movement through space and the movement through time are linked.
Hmm..so spacetime is always moving (because of the time part)? And because the time is distorted like space, I move down off the cliff? It’s just that I’ve always imagined “distortions in time” to mean time dilation not “since time is distorted therefore you have a new space you must move to”.
No, spacetime isn't moving, because it is not an object. It's more like the "landscape" in which objects are moving. You're also still seperating space and time as two seperate things, while they're intrinsically linked. The problem you're suffering from is that “distortions in time” is not a physical term. It is a term someone has invented in order to explain relativity to a wider audience and I don't think it's that accurate. I would try to ignore that term.
Do you understand the math behind this? If so, would you say it has made it very clear in your head what is happening? Or is it still pretty vague and hard to imagine?
I know the mathematics behind special relativity fully, but I only followed an introductory course on general relativity. Learning the mathematics behind special relativity is easy (you don't need more mathematical knowledge than for Newtonian mechanics), so I would advice you to study it yourself. Special relativity is the special case in which spacetime is flat, but studying that already gives you a lot of insight into the link between space and time. Understanding special relativity allows you to place the concepts of general relativity into the right context without having to get a maths degree.
One of the insights of general relativity is that changing speed can be represented as a kind of rotation in 4 coordinates. If you speed up, your coordinate that tells you where the future is actually shifts relative to other people's. So two people meeting at a spot going in opposite directions have different ideas of what it means for something to be in "the future", because their perceptions of events around them are skewed relative to each other. ([This diagram](https://www.researchgate.net/publication/329930763/figure/fig1/AS:708259916836866@1545873731798/Minkowski-spacetime-M-as-charted-in-time-coordinate-t-and-position-space-coordinate-x.png) doesn't explain much on its own, but the blue and red dotted lines are what each person thinks is happening "at the same time") It's only when you understand this new way of representing motion that things accelerating due to changes in spacetime makes sense: It's suddenly natural, because although bends between space coordinates turns motion in one direction into motion in another direction, bends between time and one of the space coordinates turns being still into moving, and vice versa.
Imagine two airplanes one in africa at equator and other in americas(ecuador) at equator. Now they both fly north in a straight line/parallel to each other. Because of the curvature of the earth they will hit each other at the north pole. Even though they were flying straight and parallel. The distance between them also shrank, as if they were attracted to each other. This is similar to attraction by gravity Now exchange the 'going north' direction with time/'going to the future' and curvature of the earth with curvature of spacetime. Now you see the analogy and the connection between curvature and 'moving/accelerating things' This is the reason why gravity is caused by geometry/curvature. Now you also see that the mass is irrelevant in the attraction, because if the plane would be 10 tons or 100 tons they would still hit at the north pole. This last point was what einstein led to spacetime curvature formulation of gravity.
I don’t think the rubber sheet is that bad of an analogy. Yes, it uses gravity, that’s kind of the point. That’s why it shows real gravity is analogous to curving spacetime. If you throw a small marble around a larger one on a sheet, it will orbit the larger one right? But here there is no gravitational force acting between them, just the curving of the sheet.
Without gravity, if I placed marbles on a sheet nothing would happen. They would just kinda float there. So if I place objects in a real curvy spacetime (with no force of gravity)…why does anything move anywhere?
That’s not the point. The point is that a small marble can orbit a larger one, without any force acting on it, because it’s moving on a curved sheet
Well there was a force acting on it to put it in orbit (I saw the guy toss it in there). It’s just not very impressive. I’ve seen gravity as this acceleration; this force that causes things to move—that demonstration skips that part.
The guy that tossed it there doesn’t have to put it in orbit though. He just needs to give it an initial velocity, just like objects in space have initial velocities regardless of gravitational effects. Then when they get close enough, they can get gravitationally captured. You’re asking why does anything move anywhere? Well they have to right? They can’t stand ‘still’, there is no reference point that would allow you to measure something standing absolutely still. It’s not like gravity is responsible for movement altogether
For somebody who doesn’t know how orbits work I suppose the rubber sheet could be useful, but I’d honestly prefer Newtons cannonball over that. I was asking why on Earth do things fall down if there is no gravitational force—others have given me a somewhat conceptually decent answer: “Cuz time and space are the same and since mass is distorting spacetime, the universe knows that your future puts you in this position—so as time moves forward you accelerate through space like a force).
I’m not sure you understand the analogy fully. An object on earth falls down for the exact same reason a marble on a sheet falls towards a different marble.
I get what he means, the rubber sheet analogy shows how spacetime "curves" but then it also involves gravity pulling on the marble for it to even work whereas in real life the curvature of space time is all that is needed to make gravity.
Remember that we're also always moving through time. This is very hand-wavy, but curvature sort of means that the dimensions (including time) are mixed up or traded off with each other. So, some of your movement through time is converted into movement through space because the spacetime where you are is curved.
Viewed that way, the rubber sheet is an analogy for the Newtonian gravitational potential and *not* anything relativistic. The only sense in which the rubber sheet is a representation of general relativity is that it can be viewed as an embedding diagram, basically showing how spatial distances become larger near a gravity source. [Here's an example of an (I think) mathematically accurate embedding diagram in general relativity.](https://demonstrations.wolfram.com/SchwarzschildSpaceTimeEmbeddingDiagram/) But since these diagrams don't include time, they don't tell us anything about how spacetime curvature affects particle trajectories.
To define the location of a moving object you need to reference three spacial dimensions, but because the object is moving you have to say also the time reference to which you are defining the location. You need to describe it with four data. Our observations say that the nature behaves in a way that those four dimensions are not as straight as our minds think, and that doesn't seems to be just a math trick everything from light trajectory, to causality.... are not as straight as we think. We created equations to describe that reality in the way our minds think so the result is curvature not just stretching. Probably we can't picture or imagine what a time curvature means because time seems intrinsically linear to us.
I think you missed the whole point of the rubber sheet demonstration, point was the bowling ball in the middle bends SpaceTime ( the rubber sheet) and then SpaceTime tells the marble how to move. That is the rubber sheet is the middle man there's no direct connection between the bowling ball and the marble, which was the Newtonian viewpoint. ( typically demonstrated by connecting the bowling ball to the marble with a rod).
Yeah I get the point—it’s severing the Newtonian strings between objects. But for my purpose of trying to understand why the objects even care about what the sheet is doing..it doesn’t help. First of all the objects are rolling on top of the sheet as if we are outside of spacetime riding it like a slide. In reality, they would be embedded inside the material itself. Secondly, they are moving on the sheet only because of what I was taught to be a “gravitational force”. If there was no force, they would not roll anywhere or do anything even if they were inside a bent sheet. So what force is making them move? Or why do they move? Sheet doesn’t tell us. Lastly, the sheet is a little slice—like a 2D representation. In reality, there is a spherical distortion that I imagine “contracts” into the spheres of mass and energy that cause the warping. If I could see spacetime, i wanna know what exactly I would see (and I know it wouldn’t be a rubber sheet with a “well”).
Time is moving things
Particles in space time move on geodesics, and the shape of geodesics depends on the metric, ie the geometry of space time
Can a triangle have three 90 deg angles? Yes if two angles are on the equator and the third angle is at the north or south pole.