If space is infinite, then gravity waves at the edge of the infinity approach 0. At 0 gravity wavelength...

What resistance is there to gravity waves? Is there multiple universes? I'm not aware what's going on here.

No u

I'm pretty sure this just means the scope of gravity waves/light waves becomes more narrower relative to the observer.

Multiple universes are theoretical and gravitational waves are not.

Gravitational wave strain goes as 1/r, not r^-2. Light intensity we measure in wave energy, which is proportional to the square of the wave amplitude. The light wave amplitude, however, drops off as 1/r. GW strain also drops off as 1/r.
The detectors we use to see EM radiation are sensitive to the energy EM waves carry, so they drop off as r^-2. However, for gravitational waves our detectors measure the wave amplitude directly (aka strain) and hence drop off as 1/r.

0 Doesn't exist because nothing can't exist.

Care to detail the structure of your reality in mathematical terms?
I'm pretty sure saying something can't exist is a highly structured argument you're getting into.
So extrapolate.

>extrapolate

First, i am not saying "something" can't exist but "nothing" can't exist.

Second, in physics, when your result is 0 or ∞, there is something wrong or that indicates that we don't fully understand the object.

>the edge of the infinity
No such thing.

>then gravity waves... approach 0
Why? The universe is homogeneous and isotropic. Whatever gravity we observe in our local universe is how gravity is everywhere else. Yes, this implies infinite matter. There is matter everywhere, and gravity everywhere.

Object.0 exists.

Nothing can exist. Not(something) implies something. E.g. (I'd like you to do give examples more often) the speed of causation.

>Nothing can exist

Seriously, you don't understand what "nothing " is.

I believe nothing is very persistent.

Object.0 orients to some purpose. It has an identity.

I'm sure it implies infinite matter, except where there is matter in empty space?

>where there is matter in empty space?
There isn't matter in empty space. Every part of space is essentially like our part of space. Each part has a finite amount of matter, but there are infinite parts and therefore infinite matter in total.

Everywhere there is matter, there is a finite amount of it. But everywhere extends forever so there must be infinite matter? No, the actual quantity of matter remains finite.

That object.0 is a qualitative nothing. (e.g. perfect/imperfect duality in geometry)

something implies nothing

wanna go on a date?

>No, the actual quantity of matter remains finite.
Why? If the distribution of matter is isotropic, and the space this matter is distributed over is infinite, then it is necessary that there is infinite matter. A finite amount of matter uniformly distributed over an infinite amount of space would result in 0 matter in any finite amount of space. But we observe matter in our part of space, so there cannot be a finite amount of matter in total.

Hey guys lets get real here, we all know space doesn't exsist, it's just a part of the Liberal Marxist Nazi Athiest agenda to trick us into believing there is one

There's too much shitposting in this thread so I'm ignoring every post, but I'll at least try to answer OP's questions.

>If space is infinite
No one believes that

>At 0 gravity wavelength, we have 0 space and time. This is absolute 0 of space-time values
Gravitational waves are not all there is to spacetime. We write the metric as
[math]g_{\mu\nu} = \eta_{\mu\nu} + h_{\mu\nu},[/math]
where [math] \eta_{\mu\nu} [/math] is the Minkowski metric (flat spacetime, a "background") and [math] h_{\mu\nu} [/math] is a small perturbation in the metric such that [math] |h_{\mu\nu}|\ll 1 [/math] (allows us to make linear approximations and find actual solutions). We find that one solution to the EFEs using this metric (flat + small perturbation) gives [math]\Box \bar{h}_{\mu\nu} = -16\pi G T_{\mu\nu}[/math] (units of [math]c = 1[/math]), where [math]\Box[/math] is the d'Alembert operator in the mostly positive signature, [math]T_{\mu\nu}[/math] is the usual stress-energy tensor, and [math]\bar{h}_{\mu\nu} = h_{\mu\nu} - \dfrac{1}{2}\eta_{\mu\nu}\eta^{\rho\sigma}h_{\rho\sigma}[/math] is the small perturbation reassembled in the transverse traceless gauge.

As we can see, the behavior of gravitational waves result entirely from [math]h_{\mu\nu}[/math], a perturbation on top of flat spacetime. If the waves die away, then we simply have [math]g_{\mu\nu} = \eta_{\mu\nu}[/math].

Derivation of this solution^^ (have had this for awhile)

>No one believes that
So what does a spacial boundary look like?

I'm not this guy .

But the only "physical" models around (that I am aware of) which explicitly describes our spacetime as being bounded are brane-world theories in String Theory. In these models our spacetime would be the volume swept out by some D-brane. D-branes are actual physical objects, so our spacetime would be bounded by one of them.

To add on a bit: Manifolds, by definition, do not have boundaries. So sticking to purely general relativistic descriptions, spacetime would be have to be unbounded (but not necessarily infinite).

>metaphysics
Fuck off faggots. /x/ is that way-->

does that mean that space is like sphere or a torus

It is possible, but I'm pretty sure that in Cosmology people generally believe spacetime to be flat on a universal scale.

But we know from empirical analysis of the CMBR that the universe is flat well within 5 sigma. So that does in fact imply that space is infinite. I find it odd that seems to know his cosmology yet claims "no one" believes space is infinite.

Why do you think flat implies infinite?

Flat and no boundaries implies infinite.

[math]\left( {0,1} \right) \subseteq \mathbb{R}[/math]

>what is flat torus
>what is klein bottle
schuttelte mein kopf

What does that have to do with what I said?

You're right, but I also assume space is simply-connected.

>You're right, but I also assume space is simply-connected.

By definition, manifolds do not have boundaries. So what you are saying, is every flat, (simply-connected apparently), manifold is infinite.

This is obviously not true. is a trivial counterexample.

i've never taken any higher level physics so i don't know, but why is that a valid assumption?
what does physics say about the shape of space?

How is (0,1) unbounded?

You seem to be confusing topological definitions of boundary and the definition used for manifolds.

The only one who brought up manifolds was you. I'm talking about the topology of space. (0,1) is not analogous to a boundless space.

We are talking about spacetime. Spacetime is a manifold.

i'm not that guy, but what exactly is the difference between regular topological boundary and manifold boundary?
i always thought "the boundary of a manifold" was just its topological boundary

No, we're just talking about space. How is boundless space analogous to (0,1)? It's clear that a boundless, simply-connected flat space must be infinite.

Though inflationary relativity implies that space is infinite, we know that the math only applies within certain parameters. It does not apply to quantum scales, and it probably does not describe the system as a whole either.

The answer is we don't know, and that both a finite and infinite universe are very much possible. From what I've heard there are things that suggest both, so we're limited in our evidence here.

Bait?

Ok first of all, there is no concept of "flatness" on arbitrary topological spaces.
To define what it means for something to be flat, you need to have a notion of curvature. To have a notion of curvature, you need to have a manifold.

Manifolds are completely independent of any ambient space. So the usual topological definition of boundary has no meaning for them.

Manifolds themselves do not have boundaries. To define a notion of boundary for a manifold you actually have to look at a slightly different kind of object.

A Manifold With Boundary (manifold-w-b) follows the usual definition, but is locally homeomorphic to a half-space instead of all of euclidean space. So a n-dim. manifold-w-b is the union of a n-dim. manifold M and a (n-1)-dim. manifold ∂M.
So when talking about manifolds, the idea of a boundary is actually that of another manifold of 1 dimension less that acts as sort of an edge to the main manifold.

here
thanks, i get it now

You're not answering the question. How is (0,1) a manifold without boundary? a 1 dimensional manifold can only be a circle or a line, not a line segment.

A manifold is defined as a second countable Hausdorff space locally homeomorphic to euclidean space.

(0,1) obviously satisfies that definition.

To make sure I am being as specific as possible, let me correct myself:
"locally homeomorphic to open subsets of euclidean space"

Again, I'm talking about topological boundary. The reason why physicists avoid bounded space is because there is no physically coherent theory of a spacial boundary. If space was like (0,1) it would necessitate a topological boundary. Saying that (0,1) is a manifold and has no manifold boundary is a non-sequitur.

If the earth is round, and rain falls down, then how does it rain in Australia?

But you should not be talking about a topological boundary. This discussion started as whether spacetime was infinite.

Spacetime is the "fabric" of our universe and there is absolutely no evidence that there exists any bigger "space" into which our universe is embedded. This is exactly why spacetime is modeled as a manifold.

Going back to the trivial example of (0,1):
The topological boundary of (0,1) are the points 0 and 1. But by saying that you are assuming these points 0 and 1 exist. i.e. There exists something "outside" of our manifold (0,1). So by trying to use a similar concept for spacetime, you are implicitly assuming there exists something "outside" of our universe.

>But you should not be talking about a topological boundary.
I started the discussion by asking what a spacial boundary would look like. This is a topological boundary. And no, it has nothing to do with saying that this boundary "exists" because there is no coherent idea of such a boundary in the first place. If this was a 1-dimensional universe which could be modeled as the interior of a line segment, what happens when you get to the boundary of that line segment, or approach it? The fact that this boundary is "only" a topological boundary or doesn't "exist" in the manifold does not elucidate one bit this question. It has no physical meaning at all.

But there can not exist a topological boundary unless the topological space is defined as a subspace of some bigger space.

(0,1) has the boundary {0,1} when we view it as a subspace of R.

But when it is viewed as a manifold, it necessarily has no topological boundary because it taken as its own independent topological space. Independent of any ambient space.

So if you want to talk about what a possible boundary of spacetime would look like, it only makes sense for the term boundary to be defined in the manifold sense. Because its topological boundary would necessarily be empty due to definition.

If you want an answer to the question: "What would a topological boundary of our universe possibly look like?"
The answer it would always be empty unless at some point we discover that our universe is actually embedded into some multiverse.

A manifold boundary however could be any 3-manifold ∂M such that Spacetime U ∂M is a well-defined 4 manifold-w-b.

I was thinking that the topological space is simply the Euclidean space with the proper number of dimensions, but again this does not really interest me as I don't yet see the physical relevance in the distinction between manifold and topological boundary, or boundary existing or not existing in the manifold. So what do you see as you approach the end of a manifold "without boundary"?

What is the space between atoms?

full of force-carrying particles?

This is wrong. Gravity is a scalar field that propagates throughout the entirety of the universe. Although the force of gravity falls off with the inverse square law, it is infinite, but non zero.

So (0,1) is unbounded in itself in the topology sense and manifold sense.

But there is a 1-ball that all the points are contained in. Is this like a metric space only definition?

It is space, that's the point. Space is not nothing, it's space.

>Although the force of gravity falls off with the inverse square law, it is infinite, but non zero.

>approaches 0

Well that is why it only approaches to zero. Meaning that it will never reach that. However, since it actually does loose energy and underlying physics seems to be quantized, I don't believe it can be infinite. At some point it is so small that it is smaller than smallest possible energy.

Is space like the inside of a ball with galaxys hanging around?

Is all the black in space caused by black holes?

I mean the light and energy will eventually end up gathering in one of the black holes causing the universe to slowly cool and dry up?

infinity implies no ending
Edge implies ending

Do you not see what is wrong with this logic