[meteorite-list] Speed-of-light question

From: Rob Matson <mojave_meteorites_at_meteoritecentral.com>
Date: Wed, 26 Aug 2009 00:27:46 -0700
Message-ID: <GOEDJOCBMMEHLEFDHGMMGEFADOAA.mojave_meteorites_at_cox.net>

Hi All,

Doug was first with the correct answer: 1/sqrt(2) * speed of light
or a little more than 70% of the speed of light. I figured it
might come down to a race between Doug and Sterling. ;-)

Here's an alternative way of looking at the problem which will
give you the correct answer almost immediately. The trick is to
assume that *ALL* objects travel at the same "velocity" in
4-dimensional space-time, and for convenience we'll call this
velocity "c". For simplicity, assume linear motion along just
one spatial axis -- let's just call it the X-axis and make it
horizontal. Now add a perpendicular axis (traditionally the
Y-axis) but instead we're going to call it the T-axis (the
velocity component in the time-axis direction):

  ^
  |
  |
T |
  |
  +--------->
       X

A vector representing the velocity of any object will have a
length of c. Any object traveling at the speed of light (e.g.
a photon) is represented by the vector of length c parallel
to the X-axis; in other words, time stands still for this
object. And any object at rest gets represented by a vector
of length c parallel to the T-axis; all the "motion" is in
the direction of time.

For our problem, we're looking for the vector that has equal
velocity components in both the X-axis and T-axis (X=T).
Obviously this is a 45-degree angle clockwise from +T (or
counterclockwise from +X). So the component of the 4-D velocity
that is in the spatial direction is C*COS(45), while the
component of the 4-D velocity that is in the time direction
is C*SIN(45). Voila!

When you accelerate from a stand-still, your 4D velocity vector
rotates away from vertical and toward horizontal (by a
miniscule amount). Using the simple system above, you can easily
figure out the required velocity in order to cover 2 light-years
distance in one year, 4 light-years in one year, etc.

--Rob
Received on Wed 26 Aug 2009 03:27:46 AM PDT