Timeline for How far can you travel until you can't get back to where you started?
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16 events
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| Oct 18, 2020 at 18:18 | comment | added | Andrew McKnight | According to your math, the "accessible universe" is only ~0.4% the volume of the observable universe. (4/3)π(7.2)^3 / (4/3)π(45.7)^3 | |
| Jan 5, 2018 at 17:16 | comment | added | Terran | @OON I just realized this when responding to an answer below, while the limit may be true for all velocities less than the speed of light, theoretically wouldn't traveling at the speed of light have no limits? If all distances equate to a travel time when traveling at c, and the travel time becomes infinite, if you indeed were traveling at the speed of light, your perceived time rate (dilation) should also be infinite, since you feel no time pass, could you then go past this limit if you waited forever? Since forever is how long it would then take? | |
| Jan 4, 2018 at 21:06 | comment | added | Terran | @OON thanks! I just keep seeing hyperbolic equations in almost every part of spacetime equations and probability equations, makes me a little paranoid wondering if euclidean space is just a truncated section of a hyperbolic anti-de Sitter spacetime :/ Probably not... universe is weird... | |
| Jan 2, 2018 at 20:32 | comment | added | OON | @Terran I've added a simple derivation not relying on $H=\mathrm{const}$ and it probably even make it more clear | |
| Jan 2, 2018 at 20:31 | history | edited | OON | CC BY-SA 3.0 |
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| Jan 2, 2018 at 19:13 | comment | added | OON | @Terran If there's any meaningful interpretation in terms of the hyperbolic geometry you should rewrite this formula in terms of the embedding coordinates of de Sitter as hyperboloid in the 5d Minkowski spacetime, see e.g. de Sitter space -> flat slicing in wikipedia | |
| Jan 2, 2018 at 19:07 | comment | added | OON | @Terran Look, right now the point of no return is 7.2 Gly from Earth. But when the light signal reaches it it will be 14.4 Gly from Earth which is a horizon distance. From there you will reach Earth in asymptotic future (as SF. correctly noted) Any point closer - return trip in finite time. Any point farther - return is impossible. Concerning the equation, it's just an integral of exponent=) I can't see right now any meaning in its reinterpretation in terms of sinh and cosh, though perhaps there's some | |
| Jan 2, 2018 at 17:16 | comment | added | Terran | ^ And a final clarification: the e^ - e^ equation when halved is based on the hyperbolic sin but diverges with a same signed exponent because of the two time variables or due to some other reason? I recognized the equation from hyperbolic geometry and thought I would ask :) | |
| Jan 2, 2018 at 16:59 | comment | added | Terran | @OON Just clarifying, so the non-returnable distance is 7.2 Gly or half that distance? As in, if i went 7.2 giga-light-years away, can i come back, or would I have to go half that distance in order to travel the other half back? | |
| Jan 2, 2018 at 16:55 | vote | accept | Terran | ||
| Jan 2, 2018 at 15:56 | history | edited | OON | CC BY-SA 3.0 |
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| Jan 2, 2018 at 15:49 | comment | added | OON | @S.F. I'm afraid you underestimate the size of the observable universe. It's much larger than 13.8 Gly again thanks to the expansion of the universe. | |
| Jan 2, 2018 at 15:43 | history | edited | OON | CC BY-SA 3.0 |
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| Jan 2, 2018 at 15:26 | comment | added | SF. | @uhoh: A little more than half the size of the observable universe. Actually, once you reach that point you'll be the Hubble Radius (14GLy) away from Earth; a bit more than the Observable Universe radius - thanks to space expansion providing about half of the distance covered (plain old movement through space being the other half). - the point that NOW is 7.2GLy away will be at Hubble Radius then. Then, to return, you must begin the arduous climb against the slippage of space expansion to return eventually, in an infinitely distant future. 7.2GLy there, $\infty$ GLy back. | |
| Jan 2, 2018 at 15:07 | comment | added | uhoh | Can you put 7.2 Gly in perspective somehow? How does that compare to the present age of the universe for example, or the present "size" of the universe? This isn't a distance unit most people work with on a daily basis! :-) | |
| Jan 2, 2018 at 14:58 | history | answered | OON | CC BY-SA 3.0 |