Post #528417

2026-03-05 00:47 UTC

@dougmerritt@mathstodon.xyz > On the timeline of a hypothetical observer far outside that gravity well, of course ?? not sure what you mean. This is about a completely flat spacetime, so being far away makes no difference in the distances/times that an inertial observer will measure. There is no actual gravity well here. When I said, > Gravity increases as you go downstairs, > but you'll live longer. I was referring to the experience of the passengers on the accelerating ships, the fake gravity that they feel; the passage of proper time is slower on the ships that are closer to the origin (and hence accelerating harder). And since it's proper time we're talking about, this is true no matter who's reference frame we're using. 1/2

Replies (1)

@wrog@mastodon.murkworks.net 2026-03-05 00:54

@dougmerritt@mathstodon.xyz We can even do a "twin paradox" scenario: I step off the ledge on the 100th floor (t,z)=(0,1) for those Moving People. √3/2 ≈ 0.866 years later the 50th floor ship catches up with me (√3/2,1) Assuming I somehow survive landing in that net (delta-v is a ruinous 0.866c; velocity angle 𝜑 ≈ 1.317, which represents a passage of time of 𝜑 years on the 100th floor and 𝜑/2=0.658 years on the 50th floor), I can then spend 5−𝜑 years on the 50th floor, then have them fire me upwards at 0.866c, just fast enough that after another 0.866 years in free fall, the 100th floor people can grab onto me, but for them a total of 10 years will have passed since I first stepped off. For me, total time passed will be 5−𝜑+√3 ≈ 5.415 years. 2/2

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