posted on Aug, 18 2007 @ 06:40 PM
Near Light Speed Travel is possible. nlspropulsion.net...
If we suppose that we eventually have the ability to harness enormous resources, but do not uncover new laws of physics, then it will always take
individual humans years to travel between the stars. The problem is that we can't accelerate faster than our bodies can survive. So, if we assume
that the passengers want to experience the journey at an acceleration of 1 g, then how much travel time do they experience on an interstellar
The difficulty that we have to work through is that the traveler isn't in an inertial frame of reference. That is, v keeps changing. The traveler
starts at rest and undergoes a constant rate of acceleration g (in the traveler's frame of reference). What is the traveler's velocity (relative to
the original frame of reference) at any time?
Let's define some coordinates. The position of the traveler in the original frame of reference is (x, t). (Here I'm using "position" to refer to
both space and time.) The velocity of the traveler as measured in the original frame of reference is v. (The traveler sees the same velocity, but has
a different distance scale...) The cumulative elapsed time that the traveler has experienced is τ. We want to define the relationship between these
coordinates. To do so, we define two additional sets of coordinates: The coordinates in the traveler's inertial frame of reference are (x1, t1). The
traveler doesn't really have an inertial frame of reference, since he/she is accelerating constantly, but this is the inertial frame that the
traveler would be in if the acceleration were turned off briefly. The traveler is at position x1 = 0. When we envision turning off the acceleration
briefly, we will take that moment to correspond to t1 = 0. At that moment, we will also want to consider another set of coordinates (x0, t0) in the
Earth's inertial frame of reference. These coordinates are defined by the Lorentz transformation:
This is very close to the formula that we want. We want to know the value of τ when the traveler has made it halfway to the destination, because then
the deceleration starts. If the total distance is X, then the total travel time T is given by
(8) X / 2 = (c2 / g) [cosh (0.5 g T / c) – 1]
T = (2 c / g) cosh–1 (1 + 0.5 g X / c2)
If X = 4.3 light-years, then T = 3.6 years. Dozens of stars could be reached in five to six years. In fact, a traveler could even go the Andromeda
galaxy in under 29 years if a constant acceleration could be maintained.