like I am I mean really this is kind of a running joke to poke around with the fun shit associated with relativity and its discontents. I can give you a real one to show you how noped out I am: Presume a motor of unlimited, massless fuel such as the archetypal Bussard ramjet. Presume a steady acceleration of 1g to midpoint, at which point you will switch to 1g of steady deceleration. Presume all special relativity holds. How much experienced time will have elapsed for non-passengers to the goal, Alpha Centauri? How much experienced time will have elapsed for passengers? I'm pretty sure that's a barely quadratic problem yet my consultant on that script said "c'mon you have an engineering degree, I'm not helping you any more until you run the calcs" and I was all "yeah but I'm not writing screenplays because I enjoy story problems."
I need to correct myself and point out that the values I got were wrong. Formulae: t' = (c / g) * asinh(gt/c) - time measured by ship's crew Numerical values: g = 9.81 m/s² x = 4.3 ly = 4.07E16 m Time from the perspective of people on Earth (t): 1.63E8 seconds = 5.18 years. Time from the perspective of people on the ship (t'): 7.27E7 seconds = 2.31 years. Derivation was OK, had four other people check it for me and can show the work. It's not a new result anyway. Regardless, sorry for the mistake. am_Unition, ButterflyEffect, nil - you also shared that post, so I'm shouting out just in case it has any relevance for you guys. t = sqrt(x²/c² + 2x/g) - time measured on Earth c = 3.00E8 m/s
I’m in the kleinbl00 bucket of “studied engineering but fuck that”. I sometimes, kind of work as an engineer but it’s mostly stats and more simplistic math based. No derivations here woo-hoo. Am always interested in what the smart folks like you and am_Unition get to saying about math, though!
Pedantry above and beyond the call. The fact that this was worrying in the back of your head like a loose tooth says a lot about your character. The fact that you decided to drag your friends down with you says a lot about the people you hang out with.
Did you do it like: d(t' = t/𝛾), with 𝛾(t), after substituting v=9.8*t into 𝛾(v), and then integrate both sides, solving for the upper limit of the t' integral? Unprimed is Earth's frame, for posterity. Also, "approaching shitfaced at 1 g": not sure if claiming to be drunk or ugly... :| Edit: no but if you really hate yourself, do d(𝛾*t' = t), with 𝛾(t), and then do algebra for days. It reminds me of some homework shit once with deriving a particularly simplistic expression algebraically for a Rankine-Hugoniot shock jump condition expression.
Drunk. Probably still are. Definitely had too much, but flatmate finally got his M.Eng after years of bullshit, so at least it seemed like a good occasion. I have a math major and loved courses like real analysis, so obviously started drinking and deriving from Lorentz transform. For kb's case I got: t' = (c/g) asinh(gt/c) x - distance from stationary frame's perspective. Mea maxima culpa if I fucked it up along the way, but it looks reasonable to me.but if you really hate yourself, do d(𝛾*t' = t), with 𝛾(t), and then do algebra for days.
t = sqrt(x²/c² + 2x/g)
Looks good to me. I might come back with pictures of my chickenscratch, but yeah, I can see how some geometric substitution in the integral leads to a sinh function. Perhaps somewhat ironic is that the asinh function is sometimes pronounced "a cinch", a.k.a. American slang for something considered easy. But some would say "arc shine". As for "inverse hyperbolic tangent", it's just that no one wants to take the time to say an 8 syllable thing. The fact that pronunciation runs the gamut is proof that we've needed to standardize communication since science got off the ground. It's just dumb luck that I'm born into the English-speaking contingent of the world. But meanwhile, you know at least two languages thoroughly, and your brain is all the more ductile for it. Long term benefit! But yeah, I do genuinely feel kinda guilty for just having been born in the U.S., for what seems like an ever-increasing number of reasons, when I consider it. For now, at the very least, enjoy that booze. Kill off the weak brain cells. You'll make more, no worries.
FutureNeg: bebe, U pretty on the surface (Earth's), but at the 2 g's we gotta get to Titan at, that's just U 2 shitfaced 4 me, srry~