Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!ames!lll-winken!uunet!mitel!sce!cognos!geovision!gd From: gd@geovision.uucp (Gord Deinstadt) Newsgroups: sci.space Subject: Re: Approaching c Message-ID: <546@geovision.UUCP> Date: 1 Feb 89 23:45:45 GMT References: <894@nih-csl.UUCP> Reply-To: gd@geovision.UUCP (Gord Deinstadt) Organization: GeoVision Corp, Ottawa, Canada Lines: 60 In article <894@nih-csl.UUCP> jim@nih-csl.UUCP (jim sullivan) writes: > ...Also, relativity > means that all things are relative to an observer. An observer > on a ship traveling at near c can accelerate and surpass c > from his point of view. He will however notice that his > destination is now further away than he thought so to get > say 5 light-years away, it will still take 5 years even though > he continues to accelerate. Actually, it's the other way around. The observer on the ship finds, as he keeps throwing exhaust out the back, that his speed doesn't seem to be increasing much, but instead the distance to his destination keeps decreasing. From his frame of reference, the whole galaxy becomes shorter and shorter in the direction of flight, so naturally it takes less time for him to cross it. From the galaxy's frame of reference, HE is getting squished-up, but from his frame of reference, THE GALAXY is the one getting ever flatter. And they both see the other guy's clocks running slower. Bizarre, but that's relativity. Incidentally, I had assumed that it all balanced out, so that if you put a particular amount of energy into accelerating the ship, you arrived in the same *subjective* length of time, as you would if Newton ruled the universe. However, I plugged in a few numbers, and this is what I got: Vr 0.10000000 Vn 0.100377 ke 0.00504 gamma 0.994987 Tr/Tn 0.998743 Vr 0.20000000 Vn 0.203080 ke 0.02062 gamma 0.979796 Tr/Tn 0.994884 Vr 0.30000000 Vn 0.310757 ke 0.04829 gamma 0.953939 Tr/Tn 0.988143 Vr 0.40000000 Vn 0.426824 ke 0.09109 gamma 0.916515 Tr/Tn 0.977977 Vr 0.50000000 Vn 0.556238 ke 0.15470 gamma 0.866025 Tr/Tn 0.963433 Vr 0.60000000 Vn 0.707107 ke 0.25000 gamma 0.800000 Tr/Tn 0.942809 Vr 0.70000000 Vn 0.894740 ke 0.40028 gamma 0.714143 Tr/Tn 0.912818 Vr 0.80000000 Vn 1.154701 ke 0.66667 gamma 0.600000 Tr/Tn 0.866025 Vr 0.90000000 Vn 1.608824 ke 1.29416 gamma 0.435890 Tr/Tn 0.779189 Vr 0.99000000 Vn 3.489645 ke 6.08881 gamma 0.141067 Tr/Tn 0.497248 Vr 0.99900000 Vn 6.537013 ke 21.36627 gamma 0.044710 Tr/Tn 0.292564 Vr 0.99990000 Vn 11.807832 ke 69.71245 gamma 0.014142 Tr/Tn 0.167000 Vr 0.99999000 Vn 21.100112 ke 222.60736 gamma 0.004472 Tr/Tn 0.094363 Vr 0.99999900 Vn 37.579435 ke 706.10696 gamma 0.001414 Tr/Tn 0.053145 Vr 0.99999990 Vn 66.859076 ke 2235.06803 gamma 0.000447 Tr/Tn 0.029900 Vr 0.99999999 Vn 118.912302 ke 7070.06781 gamma 0.000141 Tr/Tn 0.016817 where Vr is the real (relativistic) speed as a fraction of C, gamma is the resulting Lorentz contraction factor, ke is the kinetic energy of a unit mass travelling at that speed (measured in mass units), and Vn is the speed that would require the same kinetic enery in the absence of relativity. The remarkable thing is the ratio of Tr/Tn, that is, the subjective time to go a given distance, with relativity and without. You actually get there FASTER, in your frame of reference, than you would without relativity. Or, conversely, you can get someplace in the same length of time at a lower cost in hard-earned energy. Of course, everybody else, staying at home, still sees you taking 100,000 years or so to cross the galaxy, but who cares about them? Just be sure to empty the refrigerator before you leave for your weekend jaunt. 8^) Disclaimer: Shucks, ma'm, 'tweren't nothin' -- Gord Deinstat gd@geovision.uucp