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/sci/ - Science & Math

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3354218 No.3354218 [Reply] [Original]

Can anyone here explain to me how it is that space can be infinite?

Would be much appreciated.

>> No.3354228

never ending

>> No.3354226

You can go left and never stop going left.

That's all there is to it.

There won't always be landmarks to the left. Eventually there will be no matter or energy at all.

Of course it's possible that the curvature of space makes it while it's "infinite", it's "bounded". Think the surface of a sphere, you can run along it infinitely, but there's not infinite distance you are traveling, only a finite loop.

>> No.3354231

Infinite and bound, or
Finite and unbound

>> No.3354250

>>3354226
>There won't always be landmarks to the left. Eventually there will be no matter or energy at all.

The fuck? Then how is the universe flat on large scales? If the universe is truly infinite and not just multiply connected, then the amount of matter in the universe must also be infinite in order to satisfy the flatness condition.

>> No.3354251

>Of course it's possible that the curvature of space makes it while it's "infinite", it's "bounded". Think the surface of a sphere, you can run along it infinitely, but there's not infinite distance you are traveling, only a finite loop.

>infinite
>bounded
>infinite
>finite loop
Do people even read what they post

>> No.3354293

>>3354226

But to travel on the surface of a sphere, you would only travel in two-dimensions.

It's infinite, three-dimensional movement that I just can't fathom.

>> No.3354303

>>3354231

Well that *would* make sense - to be finite and bound -, but then that raises the question of how or to what are we bound, and what is it that contains what we're bound to?

>> No.3354306

>>3354293
The surface of a 4 dimensional sphere would work, but it would be a poor description of our universe since it would break some of the topological restraints we have if the universe is finite.

>> No.3354310

>>3354293

You are implying that space is three-dimensional. We have actually found it to be four-dimensional; try fathoming that. Some scientists even believe there are more dimensions to our universe. You should maybe read some Kuku (hyperspace) or Hawkinggggg (a brief history of time).

>> No.3354334

finite objects, such as planets and stars etc cannot exist in an infinite space.

>> No.3354342

>>3354310
Don't be a dick, he's obviously talking about spatial dimensions.

>>3354306
The FRLW metric, which is often used in cosmology as the large-scale metric of the universe, uses the 3-surface of a 4-sphere for the spatial part. What topological constraints are you talking about?

>> No.3354354

>>3354342
The surface of a 4 sphere would be non-Euclidean.

>> No.3354358

>>3354310

well, can anyone explain a four-dimensional object to me?

>> No.3354367
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3354367

>>3354358

>> No.3354377

>>3354354

Why do you think spacetime has to be Euclidean?

Even without going to general relativity, the spacetime described by special relativity (Minkowski) is already non-Euclidean.

>> No.3354383

>>3354358

Such objects cannot be visualized physically in their entirety. Pictures of "four-dimensional boxes" are at best projections. They are good visual representations, however. It is a mind boggling concept many physicists have a hard time wrapping their heads around. It is best explained mathematically.

>> No.3354389

>>3354367
holy dicks

>> No.3354390

>>3354377
The time dimension can be ignored for the sake of spatial geometry. Since the Minkowski metric only has one dimension different from the others, the spatial dimensions remain Euclidean when we consider geometry. So, if we look at spatial geometry [on large scales since gravitational distortions break it locally], it is observed to be Euclidean making the relative density ~1.

>> No.3354404

>>3354390

Surely that can't be assumed a priori? Because then your argument is circular

>> No.3354411

>>3354404
The Euclidean condition has been observed on fairly large scales, IIRC, and the relative density has been calculated independently [many, many times]. If one is true, the other must be true [the relative density is 1 if and only if the spatial dimensions are Euclidean].

>> No.3354424
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3354424

>>3354226
>You can go left and never stop going left.
Thats easy for you to say.

>> No.3354434

>>3354293
>It's infinite, three-dimensional movement that I just can't fathom.

Don't bother trying to imagine such a universe from the "outside," since there is no outside from which to view it anyway. You can, however, imagine what it would be like to be inside.

Being on the surface of a 4 sphere, for example, would seem roughly Euclidean on small scales, but traveling long enough in a straight line in any direction would just bring you back to where you started. Much like walking traveling in a straight line on Earth will eventually bring you back to where you started.

>> No.3354435

>>3354411

Doesn't the dark energy problem break this? Since a cosmological constant is equivalent to a "background" curvature, a non-zero CC (which clearly exists) implies non-euclidean geometry

>> No.3354446

>>3354435
1.) Dark energy is not necessarily a cosmological constant, though it is most often inserted into models as such.
2.) The calculations for the relative density have been done including the dark energy term and it still comes out to be really close to 1 [the error bars are bigger though].

>> No.3354470

>>3354446

1) But it's equivalent. Whatever it is, if you look at the Friedmann evolution equations, it's obvious that dark energy must add an extra curvature term (on top of the Ricci tensor) to the field equations, in the same way a cosmological constant does.

2) Close to 1 with large uncertainty is not 1. Sure, euclidean geometry is consistent with observations, but so is some amount of background curvature.

>> No.3354480

>>3354470
When last I had looked, the uncertainty wasn't that large. But, it is rather clear that you have more information on this than I do, so I am done arguing about it.