VLSI@DEC-MARLBORO@sri-unix (08/10/82)
From: John Redford <VLSI at DEC-MARLBORO>
- - - - - - - Begin message from: John Redford <dm.jlr at BBN-RSM>
Mail-from: ARPANET host BBN-RSM rcvd at 9-Aug-82 2157-EDT
Date: 9 Aug 1982 21:12:02 EDT (Monday)
From: John Redford <dm.jlr at BBN-RSM>
Subject: we know how to go FTL
To: spacspace at mit-ai
Cc: vlsi at dec-marlboro
Interstellar travel is not difficult because of special relativity; it's
difficult because space is big. In fact, special relativity makes
things easier, not harder. Although the ground observer never sees
the spaceship go faster than c, time dilation makes the person on board
think he's going much faster than light. An Earth-perceived velocity of
.99c is seen on-ship as going seven light-years/year.
Now, the real critierion for space travel is how much energy you
have to put in to go a certain speed. By Newtonian mechanics that's
En = (1/2)mv^2
In SR the kinetic energy goes into the difference between the moving mass
and the rest mass.
Ee = (c^2)(Mmoving - Mrest) = (c^2)(Mrest)((1/[(1 - (v^2/c^2))^0.5]) - 1)
= (c^2)(Mrest)([(1 + (V^2/c^2))^0.5] - 1)
where v = the Earth measured velocity
and V = the spaceship's perceived velocity
(I know this is nearly unreadable without subscripts and superscripts).
If you work out how energy each takes to accelerate a unit mass you get:
V/c | .1 | .3 | 1 | 3 | 10 | 30 | 100 |
-------+-----+-----+-----+-----+-----+-----+-----+
Ee/En | .99 | .97 | .82 | .46 | .18 | .06 | .02 |
So the faster you go the more the time dilation helps you. You only need
a fiftieth of the energy to go a 100c in SR than you do in ordinary mechanics.
Of course the folks at home are getting old and gray while you're out
cruising the galaxy, but that shouldn't stop true pioneers. America was
settled by people who never expected to see their homeland again.
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