A finite universe

[substitutematerials]

If space is finite, you can define a distance from yourself to the edge of the universe. If space is finite but expanding, this distance will grow larger over time.

 

Spatial expansion is a scaling factor, not a speed. But if space is finite, a speed can be defined at which the edge is receding.

 

Are these correct assumptions for a finite universe?

 

 

 

 

[uncool]

No.

 

The universe could be finite, but not have an edge. Think, for example, of a 2-D "universe" that exists on the surface of a sphere. There is no edge - and so no distance-to-edge.

[Lord Antares]

I thought of these but everyone seems to say what uncool is saying.

I don't get what people mean when they say that there is no edge on the surface of a sphere.

 

I guess the only thing they could mean is that if you were to attempt to go to the edge, you would be diverted along the edge, so you could juist ''cruise'' along the edge and never reach it.

It still doesn't make sense to me that you would say that there is no distance to the edge.

Edited February 14, 2017 by Lord Antares

[Delta1212]

I thought of these but everyone seems to say what uncool is saying.

I don't get what people mean when they say that there is no edge on the surface of a sphere.

 

I guess the only thing they could mean is that if you were to attempt to go to the edge, you would be diverted along the edge, so you could juist ''cruise'' along the edge and never reach it.

It still doesn't make sense to me that you would say that there is no distance to the edge.

The volume of a sphere obviously has an edge, which is the surface. The surface of a sphere does not have an edge, however. There is no "edge of the Earth." Pick a direction to travel, go in a straight line along the surface and eventually you'll just wind up back where you started.

 

It is easier to conceptualize the way a 2D surface could curve back around on itself because we can picture it bending around in three dimensions to form a sphere or a torus. It is possible for a 3D volume/universe to curve back around on itself as well, but this is much harder, or may even impossible, to properly visualize because the geometry is a bit more complex than we're use to dealing with.

 

Just think of it as the ability to travel in a straight line and wind up back where you started, and that should help you grasp it a bit better.

[Lord Antares]

The volume of a sphere obviously has an edge, which is the surface. The surface of a sphere does not have an edge, however. There is no "edge of the Earth." Pick a direction to travel, go in a straight line along the surface and eventually you'll just wind up back where you started.

 

 

I don't think that analogy is correct because you traverse the outer edge of the earth, whereas you are traversing the inside volume of the universe.

It would be more like if we all inhabited the inside of the earth beneath the crust. Then the earth would clearly have an edge.

[Strange]

But the 2D surface is an analogy for our existence in a 3D universe. In the analogy there is no inside the sphere, there is only the surface.

[substitutematerials]

We are talking about 2 potential finite scenarios- finite and bounded versus finite and unbounded (Earth surface analogy) right? As I understand it, both are possible.

 

But both cases should be measurable though, or they don't qualify as finite. Distance to edge, or distance back to where you started from.

[Strange]

Indeed. You can measure the (unbounded) surface area of he Earth. For example by measuring the curvature (and assuming it is the same everywhere). Current measurements of the overall curvature of the universe show it to be pretty flat. Which either means that the universe is very, very large. Or it is infinite.

 

I don't think there is any current cosmological model where the universe has any sort of edge or boundary.

[substitutematerials]

Since we are safely ensconced in the speculations forum, anybody got non-standard cosmologies that feature an edge?

 

Could you argue that any singularity is an edge? It seems to me that a horizon where both space and time end alleviates the problem of describing what lies beyond, since it is not possible to travel beyond it.

[substitutematerials]

Also back to my original conjecture: in both a bounded or unbounded finite universe, we have to be able to take a measurement of the total extent-like a simple radius or a higher dimensional circumference. And that measurement should be increasing in an expanding universe, and therefore an aggregate speed of spatial expansion should be definable in the case of a finite universe.

[Strange]

Also back to my original conjecture: in both a bounded or unbounded finite universe, we have to be able to take a measurement of the total extent-like a simple radius or a higher dimensional circumference. And that measurement should be increasing in an expanding universe, and therefore an aggregate speed of spatial expansion should be definable in the case of a finite universe.

 

 

As the universe is many times larger than the observable universe then it would never be possible to make any such measurement (the nearest you can do is measure things like the (local) curvature.

 

The rate of spatial expansion (which we can measure) has nothing to do with whether the universe is finite or infinite, bounded or unbounded.

[StringJunky]

I thought of these but everyone seems to say what uncool is saying.

I don't get what people mean when they say that there is no edge on the surface of a sphere.

 

I guess the only thing they could mean is that if you were to attempt to go to the edge, you would be diverted along the edge, so you could juist ''cruise'' along the edge and never reach it.

It still doesn't make sense to me that you would say that there is no distance to the edge.

Picture yourself as a 2d object (flat), with no altitude, on a spherical plane. Does that help? The idea is simply to show what an unbounded but finite space can look like.

[substitutematerials]

 

 

As the universe is many times larger than the observable universe then it would never be possible to make any such measurement (the nearest you can do is measure things like the (local) curvature.

 

The rate of spatial expansion (which we can measure) has nothing to do with whether the universe is finite or infinite, bounded or unbounded.

 

 

 

I disagree Strange. The Earth is also larger than my tape measure, but Eratostene could measure its curvature and then infer the Earth's circumference. We should be able to calculate a circumference of a finite and unbounded universe if we know it's global curvature, provided it is not perfectly flat or open. Furthermore, this curvature should be becoming flatter over time, as the universe becomes larger.

[Strange]

I disagree Strange. The Earth is also larger than my tape measure, but Eratostene could measure its curvature and then infer the Earth's circumference. We should be able to calculate a circumference of a finite and unbounded universe if we know it's global curvature, provided it is not perfectly flat or open. Furthermore, this curvature should be becoming flatter over time, as the universe becomes larger.

 

 

That is exactly what I said in post 8: we can measure the curvature. (We cannot measure something like the radius, as you suggested before.) As far as we can tell it is flat. This suggests that universe is very large and possibly infinite.

 

 

From: http://scienceblogs.com/startswithabang/2012/07/18/how-big-is-the-entire-universe/

 

 

 

And what they teach us is that not only is the Universe consistent with being flat, it’s really, really, REALLY flat! If the Universe does curve back and close on itself, its radius of curvature is at least 150 times as large as the part that’s observable to us! Meaning that — even without speculative physics like cosmic inflation — we know that the entire Universe extends for at least 14 trillion light years in diameter, including the part that’s unobservable to us today.

[uncool]

That is exactly what I said in post 8: we can measure the curvature. (We cannot measure something like the radius, as you suggested before.) As far as we can tell it is flat. This suggests that universe is very large and possibly infinite.

 

 

From: http://scienceblogs.com/startswithabang/2012/07/18/how-big-is-the-entire-universe/

Flat things can still be finite, though. For example, a 2-torus can be made flat (though not in 3-dimensional space).

[Strange]

Flat things can still be finite, though. For example, a 2-torus can be made flat (though not in 3-dimensional space).

 

 

A torus is flat. That is one of the examples in the article.

 

I agree, flatness by itself doesn't tell us whether the universe is finite or infinite. We also need to know the topology. I suspect that this will always be an unanswerable question (because the information to answer it lies outside the observable universe). But it may be that a future replacement for GR (perhaps by incorporating quantum theory) will tell us more....

[substitutematerials]

Flat things can still be finite, though. For example, a 2-torus can be made flat (though not in 3-dimensional space).

 

 

Ah this is good guys thanks. I had thought that perfect flatness necessitated an infinite space, without realizing the the cylinder and 2 torus are geometries that are flat and finite.

 

Imagine that we obtain a really fantastic measurement of curvature, and it is curved right at the threshold of what we can't observe right now- so implying a diameter of 14 trillion light years or 4292419 megaparsecs as per the article mentioned. Why couldn't I multiply that diameter by the present rate of spatial expansion, 72 km/s/megaparsecs, and state that the diameter of the universe is increasing by 309,054,168 km/s?

 

 

I have to let some crankiness rip here though: the precise observations of apparent flatness make FLRW space look endangered to me. Sure, flatness is a possibility in FLRW space, but we have no explanation for how mass-energy should be so precisely balanced to achieve this. Include the acceleration of expansion, and you've got a universe made of 95% undetectable mystery sauce balanced on the head of a pin.

 

I'm also curious what you think of my suggestion in post #9, that a singularity is a spatial edge, akin to a needle punching a hole in a sheet.

[Strange]

I'm also curious what you think of my suggestion in post #9, that a singularity is a spatial edge, akin to a needle punching a hole in a sheet.

 

 

I guess you can think of it like that. Two things though:

 

1. They have zero size so, in a sense, this edge doesn't exist.

 

2. There is no reason to think that singularities have any physical meaning (existence); they are the result of trying to use a theory where it no longer applies (like a "divide by zero" error).

[hoola]

yes substitute, I see this universe as having an edge. That is the spherical boundary where space is expanding into the void, dragging matter behind it. I see that expansion as the dark energy, matter and space as finite, only the void is "infinite".

Edited February 16, 2017 by hoola

[Strange]

yes substitute, I see this universe as having an edge. That is the spherical boundary where space is expanding into the void, dragging matter behind it. I see that expansion as the dark energy, matter and space as finite, only the void is "infinite".

 

 

There is no edge and no "void".

[substitutematerials]

 

 

I guess you can think of it like that. Two things though:

 

1. They have zero size so, in a sense, this edge doesn't exist.

 

2. There is no reason to think that singularities have any physical meaning (existence); they are the result of trying to use a theory where it no longer applies (like a "divide by zero" error).

Those are both good points Strange, especially the uncertainty about the physical existence of singularities.

[substitutematerials]

Many laypeople have trouble imagining a finite universe; I'm a layperson who struggles more with an infinite one. It seems to me that infinity is purely a useful mathematical abstraction. Just as reality is not infinitely subdividable, i.e. it is quantized, I can't imagine it being infinite in extent. Especially if we adhere to the Copernican principle and assume we are in a representative section of the universe, an infinite universe seems absurd to comprehend. We couldn't do calculus without the abstraction of infinite subdivision, but there is math that requires the square root of -1 as well. These abstractions are useful but non-real.

[hoola]

right, the informational context of the realm of mathematics and may contain "infinites" ( or more precisely, heading to infinite) and geometric reality, constrained even further to the grounding of finite concepts. I see the concept of infinite as not infinite, but as the end product of the fastest possible theoretical calculation begun at the start or a particular universe, that is limited to a finite expression by the lifespan of the particular universe the said calculation takes place in.

Edited February 17, 2017 by hoola

[Strange]

Just as reality is not infinitely subdividable, i.e. it is quantized,

 

 

We don't know that.

 

 

 

Especially if we adhere to the Copernican principle and assume we are in a representative section of the universe, an infinite universe seems absurd to comprehend.

 

Reality isn't determined by whether we can comprehend it or not.

[substitutematerials]

We don't know that.

You're right, we don't know that reality itself isn't infinitely subdividable. But everything we do know about it points to quantization, that's particle physics. We know that if a spectrum of blackbody radiation were infinitely sub-dividable, it would contain infinite energy as per the ultraviolet catastrophe. Zeno's paradox also argues against infinite subdivision.

 

 

Reality isn't determined by whether we can comprehend it or not.

 

I think you are allowing a broad fallacy of 20th century science in your second point. I think it stymies critical thinking and the pursuit of new models if we accept an incomprehensible reality. "Making sense" is an important part of our tool box. If a scientific model isn't comprehensible, I assume it is provisional, no matter how well it generates results. "Shut up and calculate", as quantum physicists sometimes say, is a bad attitude.