While this question could fall under Space Exploration or Physics (I don't have the "best" reputation on THAT forum), I feel that it is very much related to how the universe itself functions, especially regarding Einstein. While looking to see if anyone has confirmed our universe having a 4th spatial dimension (or some non temporal or spatial dimension) due to the fact that space curves, for me curvature requires a higher dimension (paper bending or a stick bending, always +1 to its dimension), I was met with the explanation that this "curvature" was intrinsic and not extrinsic (requiring another dimension). That was fine and all until I realized that wormholes would be exclusively extrinsic, how could you make a wormhole if bending space is intrinsic? Obviously you can't. But Einstein put a lot of time into something that apparently wouldn't work, so personally I am siding with Einstein here. But that still leaves the question; Are wormholes possible thus making our universe a 3+1+1 dimensional universe (I wouldn't group it up with the 3 because that would say that matter could move like that, it can't) or are wormholes impossible and so our universe remains 3+1 dimensional?
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$\begingroup$ Why would a wormhole require extra spatial dimension(s)? And what experiment or observation could distinguish intrinsic curvature from extrinsic? I'm certainly no expert on the mathematics of GR, but I know that the spacetime curvature that it requires or permits doesn't need our 3+1 spacetime to be embedded in a manifold with more dimensions. And wormholes (if they exist) wouldn't change that $\endgroup$– PM 2RingAug 27, 2017 at 2:31
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$\begingroup$ My thinking is that if we look at space-time topologically, in this case for a wormhole, it is impossible to connect two points using topological rules without increasing dimensions as space, if intrinsic, would have to go through itself. $\endgroup$– TerranAug 27, 2017 at 17:01
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$\begingroup$ Caution should be taken when applying Euclidian topology to spacetime; spacetime is non-Euclidian, and coordinate time becomes part of distances in spacetime. $\endgroup$– Justin TOct 24, 2021 at 23:57
1 Answer
The idea of wormholes is completely abstract. We have no evidence they actually exist and they are a result of following the strict mathematics of general relativity to and beyond it's intended limits.
When you push a theory past it's "design limits" you can't expect the results to be valid. Sometimes they are, sometimes they aren't.
for me curvature requires a higher dimension (paper bending or a stick bending, always +1 to its dimension)
The problem here is that you're thinking in a common, everyday sense about something that fundamentally is not understandable using common everyday sense. One of the major problems people face learning even special relativity is that common sense ideas (like simultaneity) go out the window, and this is even more difficult in general relativity.
To understand how space-time is distorted in such extreme ways requires an understanding of the mathematics. The simple explanations that involve things like rubber-sheet analogies just don't give you the right idea at all.
A typical tool to explore space-time and how it distorts is a Carter-Penrose diagram. Another one is the Kruskal-Szekeres coordinates.
So really the problem here is you trying to use your common everyday sense in a situation that it does not work in. The reason physicists do all that complex mathematics in the first place is because that is what works.
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$\begingroup$ Shouldn't topological rules still have to apply to space-time regardless of the math (which would have to follow the same rules anyways). I have worked with Penrose diagrams before but they follow rules, set rules that could be understood in a topological perspective. For me wormholes break these topological rules associated with intrinsic spatial curvature. (cont) $\endgroup$– TerranAug 27, 2017 at 17:15
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$\begingroup$ (cont) Unless the topology of the wormhole ran across a temporal axis rather than a spatial one (since we have that extra +1 to our 3) it wouldn't work, and you would only be able to have time traveling wormholes rather than spatial ones (which wouldn't be very useful). Thus my extrinsic conclusion which would change everything we think about space. However I could already discount this as you pointed out that this is very abstract and has taken it to the limits (and beyond). So I would call that the answer, thank you for clarifying my misunderstanding. $\endgroup$– TerranAug 27, 2017 at 17:15
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$\begingroup$ "You can't get entangled without a wormhole: Physicist finds entanglement instantly gives rise to a wormhole" sciencedaily.com/releases/2013/12/131205142218.htm -Not disagreeing, just saying. $\endgroup$ Aug 28, 2017 at 14:05
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$\begingroup$ I've always disliked the possibility that entanglement is because of wormholes, just feels like a cheap answer to a very complicated problem. Although I have had time to think since my response above and I have started to reconsider my previous judgment on temporal wormholes. Perhaps the extrinsic element is time itself, a wormhole is a region of space moving through time in which it is connect through time (a kind of slide through time) where you observe the "wormhole" move from point A to B over time but lead to each other's corresponding partner in time. (cont) $\endgroup$– TerranSep 14, 2017 at 19:27
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$\begingroup$ (cont) An object entering this region of space would be observed throughout the entire process until it exits, but it would experience time differently while inside, perhaps slowed? But this is all just abstract conjecture and thought, I definitely don't have the background required to have any meaning in my words anyways... $\endgroup$– TerranSep 14, 2017 at 19:30