Space wtf is it?

(1/?)

Pictures like this or "trampoline analogies" are just very simplified metaphors for the real physical model, which goes something like this:

a) Spacetime is a 4 dimensional (1 time + 3 spatial) manifold, that is some mathematical object whose surface on small scales looks like 4 dimensional euclidean space.

b) This mathematical object can be put into terms of a "metric", or more accurately a "metric tensor". This is basically a mathematical tool that lets you define lengths on the surface of the manifold. In flat 3D space you measure lengths with the Pythagorean theorem: d^2 = x^2 + y^2 +z^2. If you know the coordinates of two points, you know the distances between the points in each dimension (x,y,z) and can in such a way find out the overall distance d. Now, this seems very natural to us, but you could also say "okay, now our distances are determined by the Pythagorean theorem, but now the third coordinate is valued twice as much: d^2 = x^2 + y^2 + 2* z^2." This would define you a way to measure lengths differently in your space (whether that is a sensible definition is another question). In fact, in special relativity we introduce the idea of contracting and elongating lengths and times. We see that our conventional way of measuring lengths and times is obsolete (since those depend on the choice of frame of reference and are not universal), and we must introduce a new way of defining lengths: We must introduce a new metric tensor.

(2/?)
And in fact, in Special Relativity the way we calculate lengths (that is measurable properties that are invariant of our choice of frame of reference) like this: d^2 = t^2 - x^2 - y^2 - z^2, where t is the difference between two points on the space time (measured in a certain frame of reference). In General Relativity we take this concept even further: The way we measure lengths is not only depend on how fast we go in relation to a different frame of reference, but also on the distribution of mass and energy in the system. This means the massive things (anything that has mass) change the metric tensor and in this way change the way we measure lengths. This then leads us to the idea of curvature:

c) We can assign to the manifold the concept of curvature. We can conceptualize this curvature in different ways, one way is to think of curvature defining the shortest (or longest) paths between two points (e.g in zero curvature this is just a "straight line", however on a sphere the "straightest lines" are segments of circles (think of planes flying from New York to Sydney)). We call the "straightest" lines on an arbitrary manifold "geodesics".
The other popular way is to think about what happens when we move a vector (in slightly simplified terms an arrow with a certain direction) across the manifold and back to the origin, and especially what happens when we make an infinitesimally small closed path that goes back to the starting point.

(3/3)

On a flat manifold, if you point your finger at some direction and then move along a path and back to origin, the direction your finger pointed in doesn't change. However, imagine you're standing on the north pole pointing "south" towards London. Then you walk down to London (keeping your finger pointing south). In London you walk West to New York (still keeping your finger pointing south) and in New York you walk back up to the North Pole. Now, suddenly, you're not pointing at London anymore, but at New York. The direction of your vector has changed, due to the curvature of the sphere.
Of course, curvature is also directly linked to the metric tensor. We can associate on each point of the manifold surface the metric that generates the curvature (or vice versa).

d) Now, the fundamental equations of General Relativity, the Einstein equations link up the way we measure lengths and the curvature of the manifold with the distribution of energy and mass in space. Given a certain distribution of energy and mass, this distribution will alter the metric tensor (and by this the curvature) according to the Einstein Field Equations. Once you have the metric and curvature of your system, you can figure out what the "straightest lines" are, and then any object that is free of other forces (i.e electromagnetic or strong or weak interaction) will travel along theses "straightest lines".

>gravity and space
Two sides of the same coin
youtu.be/IcxptIJS7kQ?t=33m

I didn't understand any of this except that when you calculate distance sometimes it doesn't come out right so the conclusion is that it must be curved.

gravity doesn't exist in outer space. what makes you think that moon orbits earth because of gravity

are you retarded?

The "dent" is slightly misleading - the picture would work just as well if Earth were sitting at the peak of an equally-sized bump. The *curvature* is what matters, not the embedding of that curved surface into space. You know from Galileo that objects on a flat surface, subject to no other forces, will move in straight lines. Well, objects on a curved surface, subject to no other forces, will move in curved paths - specifically, curved paths called geodesics, that are the equivalent of straight lines generalized to curved surfaces.

The idea of gravity in general relativity is that, like centrifugal force, or the extra weight you feel in an elevator moving upwards, gravity isn't a "real force." Instead, objects in freefall are really just moving in straight lines like Galileo says they should in the absence of outside forces, but matter bends all four dimensions - both space and time - around it such that the geodesic "straight-line" paths trace out free-fall trajectories.

This isn't even a uniquely Einsteinian concept - it's entirely possible to write down Newtonian gravity in the curved-spacetime form. However, it happens to work extremely well as a way of writing down gravity in a way that works with special relativity instead of Newtonian mechanics.

I could give a more complete explanation, but I don't want to type it all out if you don't want to hear it. Would you like me to try?

Alright go on.

Alright, so.

First of all, time is a dimension. This is kind of a meaningless statement in Newtonian physics, where time is totally separate from space, but in special and general relativity this actually means something.

(Quick clarification: Special relativity is basically Newtonian mechanics - energy, momentum, elastic and inelastic collisions, all that jazz - but tweaked to work in 4D space-time instead of space and time. It's where you get stuff like the constant unreachable speed of light, time slowing down for stuff moving quickly, [math] E = mc^2 [/math], all that jazz. But it can only handle the special case of constant velocity - hence "special" relativity. It's actually very simple and easy to understand.

General relativity, the general form that can handle accelerations, is where you get into gravity and bending spacetime. The equations here are pretty hairy - doing stuff in curved coordinate systems that change curvature depending on the arrangement of stuff in them makes things pretty complicated - and it's not nearly as easy to explain.)

... look, I'll be honest, I wasn't expecting you to reply. I need to eat breakfast and shower and get dressed, I can't just sit in my room and type all this out on my phone. I'm going to have to bail on this one; I'll try and get back to you later. I'm honestly, genuinely sorry.

OK well that wasn't very helpful but thanks.

Those graphs are bullshit, but documentaries insist on using them.

Consider them graphs of the apparent gravitational force between the bodies at distance between the bodies.

Getting this baited

People often say that space is nothing but the existence of dimensions is hardly 'nothing'. Space is an unique type of stuff despite what Veeky Forums tells me.

What's hard to understand? Matter/Energy curves space-time. In the curved space-time, a body without a force acting on it travels along geodesics (which happen to be ellipses in this case) in the same way it would travel along straight lines in usual space-time.

t. non-brainlet who knows next to nothing about GR

Just so that you know. IF you really want to understand gravity as it is seen by today sphysics....
You need to read ART and understand it....
its a long way.

>curves
In which direction?

what the fuck am i reading

Don't let them fool you. Space and time are abstractions (without physical existence) we use as descriptors in our models. As soon as you ascribe properties to space you are talking about the primal medium, historically called ether (not to be confused with the material aether). www-groups.dcs.st-and.ac.uk/history/Extras/Einstein_ether.html

Yep. Definitely due to electromagnetism

>haha guys space and time are relative
>just kidding spacetime has properties and bends around matter and energy

Which is it?

This is stupid /popsci/ intepration that doesnt explain shit. Learn true GR.

Basically:

1) Object in motion stays in motion

2) Space is no longer "flat" or "curveless"

So in the picture, this little orange ball's little tail is actually straight by (1) above. Objects move only in straight lines.

However, the mass of the big ball in the center there has distorted space enough to the point that the ball's straight path ends up ending where it starts.

The trampoline sorta thing is a bit of a joke. Gravity in this context is not a force, since it's distorting the shape of space.

Remember. The ball going in the "circle" believes it's going straight. Kind of like how you can believe the earth is flat because the local curvature is so small.

Shut up and solve the Einstein Field Equations.

Just like “Time is nature's way of keeping everything from happening at once.”
space is nature's way of keeping everything from existing at the same place.

Talking about science in Veeky Forums. I know right.

Well, I liked it. Thanks.

this:
relativity.li/en/epstein2/read/h0_en/h5_en/

In a sense, the results of general relativity are that energy and momentum cause local definitions of direction and distance to change, and this effects the dynamics of nearby energy and momentum.

I think the major problem we have with teaching the public about GR is that we keep falling back on these ridiculous illustrations and animations of curved surfaces and bowling balls.

The problem is that you end up teaching the analogy and not the physics. GR relies on differential geometry, in particular Riemannian geometry. Everyone knows that the important characteristic of Einstein's theory is curvature, but they also become misguided by these pictures by thinking that it has to be curved INTO something else. This is called an embedding (or an immersion) and it's completely unnecessary to do such a thing in Riemannian geometry. We don;'t have to think of the "inside" or "outside" of a sphere to abstract about the sphere itself.

So people get confused because they are introduced to the results of GR as if they were observing from a higher dimensional space, instead of observing it like a human being in the Universe actually would. Two dimensions is fine, but how are we supposed to imagine a 4-dimensional space curving? What is it curving into? These questions are misguiding, because it doesn't have to curve into anything else.

Curvature is not what it's made out to be. Unfortunately, we (probably) can't teach the public about differential forms or connections, so the only tools they have to inform themselves on GR are these shitty, inaccurate (GR doesn't work in two dimensions, at least not the basic model) misguiding figures.

I like your post.

There is however a remarkable difference between the curvature of space-time and that of space: The spatial curvature only affects objects that are moving through space, it has no influence on objects at rest! In particular, the curvature of space cannot cause an object to begin falling. But if it falls then it affects its trajectory. That the apple begins to fall is attributable to the curvature of space-time alone.

do all objects have infinite 'gravity distance'?
if there was two grains of sand seperated by billions of light years in an empty universe they would attract each other and eventually collide correct?
this means, at the end of the universe there will be only two particles left (two black holes for example) they would eventually collide, correct?
every particle in the universe would be in one place at the same time, there would be no movement through space relative to other objects so time would pass instantly and the entire hawking radiation from that black hole would be released immediately (big bang 2).
is this an already established theory? if not, where do i accept my nobel prize?

Addendum:
I like your post but...
>The idea of gravity in general relativity is that, like centrifugal force, or the extra weight you feel in an elevator moving upwards, gravity isn't a "real force."

The thing about labeling forces as "real" or "fictitious" as intro textbooks always do is that it's a complete load of horse shit.

Often it's introduced by demonstrating that in rotating coordinate systems, things like the Coriolis force appear, that are "better" explained as regular motion in a non-rotating coordinate system. All fine and well, but then we come to GR, where gravity itself can be discarded by picking a coordinate system defined by your geodesics.
But forces in particle physics are understood as the same underlying concept: local curvature of yang-mills fields. Sure we're no longer talking about spacetime coordinates, but to the geometrist there is no difference.

A particular coordinate system or section of your bundle induces a connection form with non-zero curvature. Ta da, physics!

I think it detracts from the awe of the theory by selecting some as real and others as not real. Coordinates are unnecessary to understand physics, as are the particular gauge transformations of field theory. So let's not act so surprised when we pick bad ones and find that the equations get messier.

tl;dr
The Coriolis force is just as real as the forces that bind atoms together.

How about a "fabric" that is real, has properties, mass, energy. You dont have the awareness of its existence such as the feeling of water, the feeling of gravity, of hard rock, of being electrically shocked, etc.

Like the Emperor's new clothes?

>this means, at the end of the universe there will be only two particles left (two black holes for example) they would eventually collide, correct?
No, because the expansion of spacetime can make objects move away from each other faster than the speed of light, so that they cannot attract each other.

speaking of space, a question to all, in this scene in the movie Passengers Jlaw gets swallowed up in a giant blob of water in zero G, would she be able to swim out of it?

youtu.be/7BWWWQzTpNU?t=2m16s

Yes you could. You can even swim in regular air in zero gravity.

>trying to understand GR
>without invoking tensors, metrics, and geodesics
>hurr just gimme a good analogy
lol

This illustration is shit.

It's just a typical image of the rubber-sheet model, there's nothing particularly bad about it.

Are you saying the rubber sheet model is shit?

Brainlet.

That is why I put scare quotes around "'real force'", yes. Normally, I'm using the analogy the other way around, to protest against centripetal/centrifugal pedantry.

BTW, is there any good simplified formulation of GR? Like, for special relativity there's the (1+1)-dimensional setting, where you can just draw worldline diagrams on paper and you still get a decent understanding of the mechanics, especially by comparing the similar but opposite properties of the familiar two-dimensional Euclidean geometry.

Is there a (1+1)-dimensional slice of GR that works similarly? That way, you could just draw curved coordinate grids and make use of a much simpler kind of curvature (since 2D curvature can be handled with a scalar).

Maybe (2+1)D would be better, since that would allow you to show things like orbits. Unless the form of the theory is such that you can't have inverse-square gravity without explicitly working in 3D space?

I confess, I'm not really proficient with the math behind GR (which means I must not really understand the theory either), so I don't know how to derive this myself. Since I haven't seen these anywhere, but have seen 1+1D SR, there is probably some reason this doesn't really work.

>same wouldapply to classical newton aswell
>hurr its good model

Yes. It leads to a lot of confusion. The actual message - that stuff moves differently on curved surfaces - is always confused with the fact that stuff will roll into dimples in an actual rubber sheet in a classroom because of Earth's gravity.

Without the background to set it up, it is an incredibly poor teaching tool.

>I think that there's something wrong with either how we view space or how we view gravity.

What if the gravitational constant is "off"?
What if they calculated it wrong?
What if the experiment they derived the mass of earth from has NEVER been repeated since?
What if they just solved for "Big G" by estimating the mass of earth because they 'knew' the volume?
You'd eventually "run out" of mass when calculating the universe and have to make something up like dark matter....
REALLY.
MAKES.
YOU.
THINK.

>Is there space above earth then?

Yes, of course. What you're visualizing is a curvature in 2D space, which visually needs 3D to represent. If you wanted to actually model the 3D curvature, you need 4D visually, which you don't have.

>If you wanted to actually model the 3D curvature, you need 4D visually, which you don't have.

But then we'd see the true nature of this universe and we've have bigger problems on our hands than what spacetime looks like on a 2d plane.

Plane...
plane...t....
hmmm

I'm not aware of a simplified version. The field equations are obtained by minimizing the Hilbert action with respect to variations in the metric.In the Einstein GR, this involves minimizing the integral of the Ricci scalar over spacetime. It's the simplest action one can create. Perhaps there's a more complicated action that can be defined from the relevant quantities that doesn't produce a vanishing field in 2 dimensions, but there's no guarantee the dynamics of that theory will resemble our own universe at all. Like maybe in that GR, the Kepler potential doesn't exist and you can't even form stable orbits. Know what I mean?

I'm not completely against this approach to science as long as they don't use shit terminology. Curvature suggests direction. If this isn't an applicable consequence in GR why the fuck use the term?

A long time ago I saw a History Channel documentary "10 Ways to Destroy the Earth" one of them was "turn off gravity" I do not know how or why.
Can this be done? In the documentary said that could change the values of gravity and that could send us to shit, but does not say how it would happen or why.

Bad modes of thinking, i.e. Archons.

OP here, I'm back. I have a few more questions:

Can the object fall through space?
How strong is space and how much can it be stretched before it rips?
Can it even rip?
Does space have any mass?
How much does the space weigh?
How can an object travel through space without eventually stopping?
What is space made of?

>still thinking of spacetime as a physical analogue
0/10

Yeah but it is though. It's some kind of materia that the objects can travel on and it can even curve apparently. If it can curve then how is it not physical?

>taking a crappy analogy for the layretards seriously: the post

>still thinking people will take the bait
fucking KEK

Maybe you should stop being a troll and actually answer the questions. If you know how to that is, but you probably don't so you resort to KEKing.

>hurr durr answer muh questions
>someone already has
>but hurr durr muh fuggin analogies. space is made of somefing rite?
kek
end yourself you stupid nigger

Sertiously, why do trolls like you even try?

it's time to go back

Cool image Lucy. NOT

You understand there is a genocide happening right now in Syria brah?

>appeal to emotion

yeah just keep shrinking the mass of earth until theres nothing left of it

There's an interesting theory about gravity just being an emergent property, and that it just passed a first wave of tests. Thoughts, guys?

dailymail.co.uk/sciencetech/article-4047500/Was-Einstein-WRONG-gravity-Controversial-new-theory-rewrite-physics-passes-test.html
futurism.com/a-new-theory-of-gravity-just-passed-its-first-test-heres-what-this-means-for-physics/

inquisitr.com/3807495/new-theory-of-gravity-passes-first-test-could-explain-dark-matter/

I'm just posting three links for redundancy. You'll get the gist of it regardless of how awful the authors are.

I think its pretty interesting. Except the whole "EINSTEIN WRONG" thing. He's not wrong. And he would be happy to be wrong.

People just don't get the whole philosophy behind science and what scientists think, I guess.

Oh. And the relevancy to the thread is that we really don't know what the hell is going on. We have a pretty good idea, but there's so much more to learn. Something in the future could change "pretty good idea" to "we don't know shit". Or, you could say we're there now. Depending on what perspective you want to have.

The best and most functional description of the universe seems to be that we are in a frequency. Everything is waves.

>we really don't know what's going on
user, please.
Jumping straight to that mindset says more about you than it does the rest of us. It's unbecoming

Lol this is peak you're all typing out paragraphs and serious answers to a baitpost

So what exactly is space?

No. The post is fine but all keep posting bait answers and stupid shit they don't even understand.

Yes, the answers were underwhelming.

wow the very nature of your comment and the intent behind it prove that you are a dim-witted, low-life idiot. grow the fuck up, you adolescent imbecile

popsci btfo

I cannot contain all these baitposts kek

First,the space and time are one single concept.
The spacetime is like a rug,it can be have a curvature
If you put a body over the spacetime their mass will produce an attraction,because is the centre of mass. It will atract energy and matter

Just like the sun is the heavist here,that's why we all are around it

>I get gravity and I get space. Space works. Look at the picture. So when the Earth sinks into the space and makes a dent that's what gravity is. There is space above earth. Also the distance in the picture is up to scale, that moon is actually like half a football length away from the Earth. The moon does get attracted by the earth's dent when it's so far. I've read about it from many different sources it just makes sense to me and I can imagine it.

I'm saying both, at the same time! I figure you would catch on to that. You are a bright person, aren't you? Let's hope so.

It's starting a discussion, why does it matter? But also it could be legit.. I don't know why it's hard for you to believe someone would go to Veeky Forums and type up what OP typed up.

he is right you know

>pic related
just to prove that he's not samefagging

>saying both at the same time in the hopes you can be perceived as some middle ground
yeah, no user.
You said what you said, and what you said was stupid. Lets hope you aren't as stupid as what you said

The water would never be floating around like that, there's too much surface tension for it to escape a surface and form those shapes.

Brainlet; space is 3D, not 2D like this picture shows.

Its a sloppy but helpful analogy of how large concentrations of matter effect space/time around it.

Yeah, doing further research, apparently in (1+1)-dimensional GR enough stuff cancels out to force space to be completely empty, and in (2+1)D you're allowed to have matter but space is flat everywhere that doesn't contain matter, so matter can't interact gravitationally.

Only in 3+1D do you actually get masses gravitating. Disappointing. Well, I suppose you can just use only coplanar / collinear masses and just show the relevant lower-dimensional slices of the coordinate system, even if the math itself is no simpler.

Think of time as a flat circle.

>I don't get gravity and I don't get space.

What's to get?

They both exist.

>Think of time as a flat circle.

how about no?

arxiv.org/abs/1611.02269
this paper might interest you then it's not pop-sci from my understanding but it goes way over my head

So how much space is there?

While this illustration is good for imagining how gravity works, I don't think it's great for conceptualizing it in a 3D sense.

The way I usually think of it is that objects have a tendency to fall towards each other.

>daily mail
>futurism
>inquisitr

Next time try Nature.

Oh and no single theory can simultaneously explain all of the observed effects that can be explained by dark matter. The evidence for it is incredibly convincing. It even appears in the baryon acoustic oscillations of the CMB, which is an imprint of early universe physics.

i bet your stupid ass still believe that electrons orbit around nuclei like moon around earth