🚀 go-pugleaf

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