0 Members and 1 Guest are viewing this topic.
Here is the graph for D = 0.5 and 1.0, and the data from the program.
Trying again to get full size Scan 2023-7-9 13.37.06.jpg (518.85 kB . 1700x2338 - viewed 525 times).
Quote from: Halc on 01/07/2023 22:59:05Note that all the [ships with greater initial separation] actually, which accelerating forward at first, move backwards initially.No they don't. You are apparently not following my description of how the curves are to be determined. Try again.
Note that all the [ships with greater initial separation] actually, which accelerating forward at first, move backwards initially.
at least that's what my computer program says, and I haven't been able to find any errors in it, so far.
The more accurate smooth curves are consistent with your straight-line approximations.
I need to look back at that analysis, and try to see where it goes wrong.
At least, the latest results still DO say that the thread doesn't break!
I'll try to print out my program:
#include <stdio.h>#include <math.h>#define DD 0.5#define MF 1 // 1 to print Mike's number, 0 to print mine.int main(){ double ctime; // Coordinate time of inertial frame double ptime; // Proper time of ship double md1; // Computed distance per Mike double srd1; // Computed distance per SR double vm, vsr; // Speed per Mike and SR double gim, giSR; // Gamma factor inverted, per Mike & SR int mf = MF; printf("ctim%s d1 d2 v gamma\n", mf ? "" : " ptime "); for (ctime = 0.1; ctime <= 3.05; ctime += 0.1) { ptime = asinh(ctime); // proper time // Compute speeds as a function of time vm = tanh(ctime); vsr = tanh(ptime); // Compute gamma as a function of those speeds gim = sqrt(1 - vm * vm); giSR = sqrt(1 - vsr * vsr); // Compute distance traveled by lower ship md1 = log(cosh(ctime)); srd1 = cosh(ptime) - 1.; // I think we're good. Print results if (mf) printf("%.1f %.5f %.5f %.6f %7.4f\n", ctime, md1, md1 + gim*DD, vm, 1./gim); else printf("%.1f %.5f %.5f %.5f %.6f %8.4f\n", ctime, ptime, srd1, srd1 + DD, vsr, 1./giSR); }}
In my code d2 is just d1 + D.
But you're already positing going FTL, [...]
But I'm not sure that actually violates any rules.
how would YOU apply the length contraction equation in this case?
I.e., what is your alternative solution?
If I'm right about that, how do you square that chart with the length contraction equation
which says the inertial observer MUST conclude that the separation of the two rockets must get smaller by the factor gamma?
For that to be true, it means that the people on the rockets would say that the separation of the two rockets was INCREASING with time