Re: [math-fun] Physics: Longest possible solid object?
Brent Meeker <meekerdb@verizon.net> wrote:
Why do you think the CMB defines a different rest frame at different points in the universe?
Because of the expansion of the universe. The Hubble constant is usually given in units of kilometers per second per megaparsec. (A megaparsec is about 3 million light years, or about 3E+22 meters.) In those units its current value (it's not really a constant) is about 70. In other words, if every civilization in the universe were to erect a survey marker in their neighborhood at rest relative to the CMB, two such markers a megaparsec apart would be receding from each other at 70 kilometers per second. Earth's motion relative to the CMB is given as 371 kilometers per second. (Presumably that's averaged over the year, as Earth's orbital speed is about 30 kilometers per second.) So with today's technology it can apparently be measured to a precision of 1 kilometer per second. That means the CMB rest frame ought to be detectably different if we measure it from about 50,000 light years from here. Obviously not practical. But if the CWB rest frame can be measured to a precision 8 orders of magnitude better -- and I can't see any reason why that should be impossible -- it will become possible to notice the differences from opposite ends of the solar system. More interesting is whether the expansion of the universe exerts a force, and if so whether it could be detected and measured with anything close to today's technology. The most distant man-made object, Voyager 1, is about 2E+13 meters away, moving at about 17 kilometers per second relative to the sun. If the cosmic expansion is pushing it via "linear frame dragging," it ought to have added a speed of 4E-5 meters per second to it. That would obviously be lost in the noise, given that the mass of the solar system is not known to a sufficient precision that its deceleration of Voyager can be subtracted out. On the other hand, the total additional distance to Voyager due to that hypothetical acceleration would be 24 kilometers. And the distance to Voyager can presumably be measured to within about 1 meter by timing the return signal. So if the experiment were to be repeated in deep space, it would be perfectly feasible. Another way to think about it is that there's a distance from the sun at which Hubble's constant times the distance to the sun is equal to solar escape velocity at that location. Would an object placed there at rest relative to the sun just hang there? I wrote a lot more here, but it was very confused and muddled, so I've deleted it. I may get back to it, especially if others are interested. Better yet, a real GR expert will speak up. Getting back to the enormously long loop of steel cable, it occurs to me that the CMB itself would exert pressure on it. If it's at rest relative to the CMB, that pressure would balance out (assuming the minor anisotropies in the CMB are negligible on that scale). But if the loop is large enough, not all of it can be at rest relative to the CMB. The CMB would induce an outward pressure on the loop, placing it under tension. This is a purely classical effect, no GR needed. Unlike gravitational and other GR forces, the cable thickness doesn't cancel out for this, since a cable of twice the diameter has eight times the strength, but only twice the CMB-intercepting surface area.
On 4/15/2018 8:37 PM, Keith F. Lynch wrote:
Brent Meeker <meekerdb@verizon.net> wrote:
Why do you think the CMB defines a different rest frame at different points in the universe? Because of the expansion of the universe.
The Hubble constant is usually given in units of kilometers per second per megaparsec. (A megaparsec is about 3 million light years, or about 3E+22 meters.) In those units its current value (it's not really a constant) is about 70. In other words, if every civilization in the universe were to erect a survey marker in their neighborhood at rest relative to the CMB, two such markers a megaparsec apart would be receding from each other at 70 kilometers per second.
Earth's motion relative to the CMB is given as 371 kilometers per second. (Presumably that's averaged over the year, as Earth's orbital speed is about 30 kilometers per second.) So with today's technology it can apparently be measured to a precision of 1 kilometer per second. That means the CMB rest frame ought to be detectably different if we measure it from about 50,000 light years from here.
I don't follow that? Are you calculating that, because of the expansion rate, a place 5e4lyr (0.015megaparsec) away will be moving away from us at about 1km/sec /and therefore the CMB won't look isotropic from there?/ That last is just false. The expansion is uniform and so looks the same from any point. Otherwise you could imagine a point 14e9lyr away at which the CMB was stationary relative to you in one direction. Brent
Obviously not practical. But if the CWB rest frame can be measured to a precision 8 orders of magnitude better -- and I can't see any reason why that should be impossible -- it will become possible to notice the differences from opposite ends of the solar system.
More interesting is whether the expansion of the universe exerts a force, and if so whether it could be detected and measured with anything close to today's technology.
The most distant man-made object, Voyager 1, is about 2E+13 meters away, moving at about 17 kilometers per second relative to the sun. If the cosmic expansion is pushing it via "linear frame dragging," it ought to have added a speed of 4E-5 meters per second to it. That would obviously be lost in the noise, given that the mass of the solar system is not known to a sufficient precision that its deceleration of Voyager can be subtracted out.
On the other hand, the total additional distance to Voyager due to that hypothetical acceleration would be 24 kilometers. And the distance to Voyager can presumably be measured to within about 1 meter by timing the return signal. So if the experiment were to be repeated in deep space, it would be perfectly feasible.
Another way to think about it is that there's a distance from the sun at which Hubble's constant times the distance to the sun is equal to solar escape velocity at that location. Would an object placed there at rest relative to the sun just hang there?
I wrote a lot more here, but it was very confused and muddled, so I've deleted it. I may get back to it, especially if others are interested. Better yet, a real GR expert will speak up.
Getting back to the enormously long loop of steel cable, it occurs to me that the CMB itself would exert pressure on it. If it's at rest relative to the CMB, that pressure would balance out (assuming the minor anisotropies in the CMB are negligible on that scale). But if the loop is large enough, not all of it can be at rest relative to the CMB. The CMB would induce an outward pressure on the loop, placing it under tension. This is a purely classical effect, no GR needed. Unlike gravitational and other GR forces, the cable thickness doesn't cancel out for this, since a cable of twice the diameter has eight times the strength, but only twice the CMB-intercepting surface area.
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participants (2)
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Brent Meeker -
Keith F. Lynch