Wormholes, within the theory of General Relativity, are microscopic and short lived, but many serious physicists have speculated openly and hoped that perhaps with negative energy (as yet undiscovered) they could be enlarged and held open longer. Kip Thorne is one of the leading names proposing such ideas. https://en.wikipedia.org/wiki/Kip_Thorne
However, astrophysicists have observed space to be essentially a flat Euclidean geometry at large scales https://en.wikipedia.org/wiki/Wilkinson_Microwave_Anisotropy_Probe . Inflation cosmology has been invoked to explain this (as well as uniformity) https://en.wikipedia.org/wiki/Inflation_(cosmology).
My question is, if space is Euclidean flat, does or does not that imply wormhole paths between two points would be longer than paths through ordinary space? I want to rule out time dilation paths, because these are already known from special relativity and are very short for the traveler, but the traveler cannot get back to the time point she started from. (Thorne suggests we could even get back to earlier time points with wormholes but I don't want to go there in this thread as there is no end to it). I am looking for space-like paths only that would take less time at velocities below the speed of light than paths through flat Euclidean space. Please, also no arguments about whether flat space conclusion is correct. This question is restricted to "what if the flat space conclusion is correct, then do wormholes, if ever practical, have a practical use for space travel."
@Robert Low, thanks for your comments. I have seen similar pictures. I guess you are saying that space is Euclidean flat since it essentially is flat space in the ordinary sense rolled part way around a cylinder without changing the distances, is that right? I forgot about that. The observation of flatness can't rule that out. It would not bend light rays in any detectable way. We have no way of measuring that half roll then, right? Other than by poking wormholes in space to see where they come out? It might be even more rolled up, and perhaps in more dimensions that cannot be represented on a 3D in 2D image.
It seems to be restricted to travel to points accidentally nearby in the accidentally folded (but flat) space, though, or am I missing some degree of flexibility?
Hi Robert, you bring up a point that helps clarify my question. Really, it is a question about whether there are any meta constraints on space time? Are we sure it's not embedded in anything of higher dimension, and if not, there is still a question of possible constraints. Where would a wormhole go and why would we think it even goes back into space time at the other end? I'm sure I just do not know enough about the theory of wormholes, I mean the little small quantum ones. Is there an answer there? I'm aware of Thorne's idea of dragging one end of a wormhole around to create a time machine. But this ignores the question of what happens to the spatial length of the wormhole. Thorne sort of assumed when you drag the opening back near the other end, the distance through the wormhole is again short. But I see no reason to assume that. In fact if the wormhole remains sufficiently long, then there is no time machine at all, as the time to travel through the wormhole may cancel the induced time displacement of the openings?
I would like to share this document with you. Best regards, Mario
https://www.researchgate.net/publication/228295722_A_New_Multidimensional_Approach_for_Mathematics_and_Physics
Article A New Multidimensional Approach for Mathematics and Physics
I got as far as equation (1), written as infinity to the infinity power ∞∞ but described in two other ways, as an exponential e∞ and as a product ∞∞. The description you gave in terms of coordinates would be something like ∞n for n dimensions. Maybe that is what you meant by exponential.
George Cantor developed the idea some infinities were greater than others in the late 19th century. It's called cardinality, I believe. Some links below. If you use existing terminology your work will be easier to follow and accept. If you don't use existing terminology but seem to be describing a similar idea, then you will have to reference the similar idea and explain, derive or measure how yours is different, otherwise there is a presumption it is not novel.
http://io9.com/5873581/the-odd-genius-who-showed-that-one-infinity-was-greater-than-another
https://en.wikipedia.org/wiki/Infinity
https://en.wikipedia.org/wiki/Cardinality
Robert did do a good job explaining. One thing to remember, the throat doesn't go through normal space but hyper space and the distance is nil regardless of how far the mouths are separated in normal space. I love Stagate SG-1 but all that soaring around inside varies wormhole throats is pure rubbish.
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