To put it another way, time travel machines are very much theoretically possible, and in fact are “only” an engineering problem (an extremely hard one, however). But, only forward travel is allowed: time travel machine could take you as far forward as its engineering would allow it, but there is no going back.
At 1G constant acceleration (both speeding up and slowing down) you can make it on a short vacation to the Andromeda galaxy and back in a lifetime (or 5 million years from the perspective or Earth).
Time elapsed (in starship's frame of reference, "Proper time")
T = (c/a) * ArcCosh[a*d/(c^2) + 1] (given acceleration and distance)
year = 365.25*24*3600; c = 3E8; a=9.8; d=1.25*1_000_000*(c * year)
from math import acosh
T = (c/a) * acosh(a*d/(c*c) + 1)
print(T/year)
=> 14.3 years each quarter
=> 57 years round trip
The speed at flip would be 99.99999999993978% c - good thing intergalactic space is mostly empty.
Oh, what a shame. I was about to install some rockets on my RV and head off to Andromeda. Guess I don't need to put my newspaper subscription on hold now.
since we are talking insane speeds and energies required to reach them why not just say you are in a bigger ship with more radiation shielding a dozen or so meters of water in the hull and a layer of lead a foot thick aught to stop most of it
FWIW, the Project Rho page I linked to also gives the derivation of the relativistic rocket equation. When I plugged in numbers, assuming an exhaust velocity of the speed of light (ie. impossibly high), I get a mass fraction of about 2,000,000 to reach top speed. Then another 2,000,000 to slow down.
Assuming the fully loaded RV weighs 5 tons, this means at max velocity the rest of the ship weighs 10 megatons, which is 10M cubic meters of water, or a cube 200m on each side.
That sounds like plenty of material, right?
The same Project Rho page links to https://arxiv.org/ftp/physics/papers/0610/0610030.pdf which calculates that at the relatively slow 0.995c "the penetration depth of protons of this energy will be ~40 m in water and ~10 m in titanium".
For 99.99999999993978% c, even 10M cubic meters isn't going to be enough.
They are only theoretically possible if you allow for negative mass and energy--not an engineering problem so much as a "need to find exotic matter"
Basically people ran the EFE "backwards" to see what matter distribution makes the wanted curvature. You get either negative mass-energy or the bubble doesn't travel ftl iirc.
Gp is talking about forward-only time travel though, you don't need anything exotic for that at all, just lots of energy and an efficient way to turn it into thrust.
> They are only theoretically possible if you allow for negative mass and energy--not an engineering problem so much as a "need to find exotic matter"
Basically people ran the EFE "backwards" to see what matter distribution makes the wanted curvature. You get either negative mass-energy or the bubble doesn't travel ftl iirc.
