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Relativistic Travel

Numerous misconceptions have been bred by lazy science fiction () authors anxious to circumvent the limitations imposed by the . Let's examine these limitations and ask whether in fact they restrict space-flight options as severely as fans have been led to believe.

The first and most familiar restriction is the familiar statement, "You can't ever go quite as fast as light." Why is this? Well, consider the behaviour of that ubiquitous scaling facter  $\gamma$  as  $u \to c$  (i.e., as $\beta \to 1$): as  $\beta$  gets closer and closer to unity,  $(1-\beta)$  gets closer and closer to zero, as does its square root, which means that  $\gamma$  "blows up" (becomes infinite) as  $u \to c$. TIME DILATION causes clocks aboard fast-moving spaceships to freeze completely and LORENTZ CONTRACTION causes the length of the ship (in the direction of its motion) to squash to nothing, if  $u \to c$. [As observed by Earth-bound telescopes, of course.] Worse yet, if we could achieve a velocity greater than  c,  time would not run backwards [or any of the other simplistic extrapolations tossed off in mediocre ]; rather the time-dilation / Lorentz-contraction factor  $\gamma$  becomes imaginary - in other words, there is no such physical solution to the LORENTZ TRANSFORMATION equations! At least not for objects with masses that are real in the mathematical sense. [I will deal with the hypothetical tachyons in a later section.] Another way of understanding why it is impossible to reach the speed of light will be evident when we begin to discuss RELATIVISTIC KINEMATICS in the next Chapter.

So there is no way to get from here to another star 10 light years distant in less than ten years - as time is measured on Earth! However, contrary to popular misconceptions, this does not eliminate the option of relativistic travel to distant stars, because the so-called "subjective time"23.11 aboard the spaceship is far shorter! This is because in the traveller's reference frame the stars are moving and the distances between them (in the direction of motion) shrink due to LORENTZ CONTRACTION.

It is quite interesting to examine these effects quantitatively for the most comfortable form of relativistic travel: constant acceleration at  1 g (9.81 m/s2) as measured in the spaceship's rest frame, allowing shipboard life to conform to the appearance of Earth-normal gravity. I will list two versions of the "range" of such a voyage (measured in the Earth's rest frame) for different "subjective" elapsed times (measured in the ship's rest frame) - one for arrival at rest [the only mode of travel that could be useful for "visiting" purposes], in which one must accelerate halfway and then decelerate the rest of the way, and one for a "flyby," in which you don't bother to stop for a look [this could only appeal to someone interested in setting a long-distance record].

Table: Distances covered (measured in Earth's rest frame) by a spaceship accelerating at a constant 1 g (9.81 m/s2) in its own rest frame.

Elapsed Time Distance Travelled (Light Years)
aboard ship (years) Arriving at Rest "Fly-by"
1 0.063 0.128
2 0.98 2.76
3 2.70 9.07
4 5.52 26.3
5 10.26 73.2
6 18.14 200.7
7 31.14 547.3
8 52.6 1,490
9 88 4,050
10 146 11,012
11 244 29,936
12 402 81,376
13 665 221,200
14 1,096 601,300
15 1,808 1,635,000
16 2,981 4,443,000
17 4,915 12,077,000
18 8,103 32,830,000
19 13,360 89,241,000
20 22,000 243,000,000
21 36,300 659,000,000
22 59,900 1,792,000,000
23 99,000 4,870,000,000
24 163,000 13,200,000,000
25 268,000 36,000,000,000
26 442,000 98,000,000,000
27 729,000 (present diam.
28 1,200,000 of universe
29   thought to be
30   less than about

The practical limit for an impulse drive converting mass carried along by ship into a collimated light beam with 100% efficiency is about 10-12 years. Longer acceleration times require use of a "ram scoop" or similar device using ambient matter.

Now, what does this say about the real possibilities for relativistic travel? Without postulating any "unPhysical" gimmicks -- e.g. "warp drives" or other inventions that contradict today's version of the "Laws" of Physics - we can easily compose stories in which humans (or others) can travel all through our own Galaxy without resorting to suspended animation23.12 or other hypothetical future technologies.23.13 There is only one catch: As Thomas Wolfe said, You can't go home again. Or, more precisely, you can go home but you won't recognize the old place, because all those years it took light to get to your destination and back (that you cleverly dodged by taking advantage of LORENTZ CONTRACTION) still passed normally for the folks back home, now thousands of years dead and gone.

So a wealthy misanthropic adventurer may decide to leave it all behind and go exploring, but no government will ever pay to build a reconnaisance vessel which will not return before the next election. This implies that there may well be visitors from other stars, but they would be special sorts of characters with powerful curiosities and not much interest in socializing. And we can forget about "scouts" from aggressive races bent on colonization, unless they take a very long view!

next up previous
Next: Natural Units Up: The Special Theory of Relativity Previous: The Polevault Paradox
Jess H. Brewer - Last modified: Mon Nov 23 11:01:21 PST 2015