Why do you think the CMB defines a different rest frame at different points in the universe? Brent On 4/14/2018 10:23 AM, Keith F. Lynch wrote:
What's the longest a solid object can be in our universe, i.e. the greatest possible distance between its parts?
If you had a lot of stuff in one place, solid or otherwise, it would collapse into a black hole. But what about an I-beam in deep space? How long could it be before it collapsed due to its own gravity? You could partially counteract the gravity by slowly spinning it end over end, but the forces wouldn't balance everywhere.
Then I realized that in a ring the forces would balance. I'm envisioning a narrow steel cable (or carbon nanotube if you prefer) in a circular loop, slowly rotating around the loop's axis. Gravity would point toward the center, and centrifugal force would point away from the center. The forces should balance everywhere so long as it's in very deep space where tidal stresses are negligible.
If it's steel, you have the advantage that most metals, including steel, get stronger as they get colder, and in deep space it would be very cold. (The reason why the insulation on the Space Shuttle's main tank was on the outside, despite all the trouble that caused, was so that the tank's aluminum fuselage would be very cold, hence could be thinner and lighter for the required strength.)
You'd give it a slight surplus of spin so that it's under slight tension everywhere, as steel is stronger under tension than under compression. Especially if it's a cable rather than a beam.
I think the size would only be limited by stresses from the expansion of the universe. But that raises a bunch of questions. If you build it with all the parts at rest relative to each other (other than the slow rotation) rather than at rest relative to the cosmological microwave background (whose rest frame is different in different places) would the cosmic expansion have any effect? I think it would have to, since distant parts of the universe are receding from us faster than light. (The speed limit of c is strictly local.) The radius of the ring obviously couldn't exceed the cosmic horizon distance.
Even if I'm wrong on that, there's also the *acceleration* of the expansion of the universe to account for. And nobody knows how that varies with time. One dire conjecture is that eventually we'll all be literally torn limb from limb by it. Dyson found a possible way to live forever in an expanding universe, and Tipler found a possible way to live a subjective forever in a collapsing universe, but as far as I know nobody has yet found a way to survive a "Big Rip" universe.
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