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It could be a compact[0] dimension, i. e. of finite length. In the simplest case you might imagine it as a circle attached to every point in our 3-dimensional E
by codethief 2y ago
It could be a compact[0] dimension, i. e. of finite length. In the simplest case you might imagine it as a circle attached to every point in our 3-dimensional Euclidean space. The aforementioned length scale would be the circumference of that circle.
[0]: https://en.m.wikipedia.org/wiki/Compact_space https://en.m.wikipedia.org/wiki/Compact_space
- taneq 2y agoTrying to wrap my head around this explanation and I’m picturing a looping gif. You have your normal x and y dimensions and then time through the gif. If the loop length is very short then distance between any two pixels will mostly only depend on x and y. Is that right?
- 317070 2y agoYes, that sounds right.
- codethief 2y agoIn the simplest case, yes. Though, once curvature (gravity) enters the picture, it could (in theory) become more complicated, as the additional dimension could get stretched or compressed.
- jiggawatts 2y agoThe classic example is a garden hose seen from afar looks like a line, but up close it is a cylinder that can be walked “around” by an ant.
- trhway 2y agoInteresting case if we are the “ants” and it is our 3 dims happen to be compact looping somewhere beyond our event horizon. Multitude of Universes in that garden hose in which gravity can be falling as cube or more while at small scale if our compact Universe we’ll see square, and only very precise measurements may notice a bit larger than square. Another possibility is if our brane has a lot of folds coming close/touching - that would make gravity there stronger like say that dark matter idea inducing rotation speed curve of the disk stars.
- MPSimmons 2y agoWould also be nice for possibly bridging gaps
- codethief 2y ago> Interesting case if we are the “ants” and it is our 3 dims happen to be compact looping somewhere beyond our event horizon. Multitude of Universes […] I think you're mixing up two different cases here: 1) Our established 3 dimensions are actually compact, i.e. loop around or hit a boundary somewhere. No multiverse here. 2) There are extra dimensions, meaning that for every point in that extra dimension there's another 3-dimensional universe as we know it.
- fc417fc802 2y ago> Our established 3 dimensions are actually compact, i.e. loop around Do they not loop? What other option is there? I assume you can't sail off the edge of the disk, so to speak.
- AnimalMuppet 2y agoOption 1: They loop. Option 2: They go on forever without looping. Option 3: They end - there is some kind of boundary to spacetime.
- trhway 2y agoThe expansion of the space is the feature which prevents any physical process inside to distinguish between those options. Kind of a hack - make compact Universe, add expansion and it would inside look and feel indistinguishable from non-compact.
- fc417fc802 2y agoHow does option 2 fit with the big bang? The obvious issue (at minimum) being accounting for the CMB.
- trhway 2y ago
- rcxdude 2y agoAnother visual that may be useful is imagine being stuck between two portals squeezed close together.
- moralestapia 2y agoAnd yet that circle has as many "points" as any other 1-dim independent axis, so ...
- codethief 2y agoThe "number" of points is irrelevant, topologically these are very different spaces (one is compact, one isn't).