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How far are we?


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I'm trying to do research for my own extra-dimensional manifold physics for engineering purposes, but I don't know exactly how to accomplish certain tasks. Have we even made a real life Klein bottle yet? And if so how? Or how close are we? Is there anything that can help with constructing objects in real life that have apparent dimensions higher than 3? I was looking into using high-energy laser beams to bend the fabric of space into different 4-dimensional shapes, possibly into mobius strips, does anyone know of any research that's already been done like that that they can direct me to? I know DeGrasses Tyson wanted to build some kind of accelerator that bent space enough in a way to do what he thought would be accelerating particles faster than light. I know it's not actually possible, he's more of an astronomer than a physicist and probably at the time didn't know that the lorentz transformation would cause more and more length contraction as particles approached the speed of light in whatever relative direction they were instantaneously moving in, but that's pretty much just a 4 dimensional well, a pretty simple shape, basically what objects do already.

Edited by SamBridge
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