<p><hr><hr><p> <center><table cellpadding=6 border=10 bgcolor=lightgreen><tr> <td><img src="rocket-launch-02.jpg"></td> <td><h3><center>High-Speed Space Travel and Special Relativity</center><p> There is a well-known upper limit to the speed to which a massive object can be accelerated. Objects with mass cannot be accelerated to the speed of light, <i>c</i> = 300,000 kilometers per second without an investment of an infinite amount of energy. Because of this limit on the ultimate speed of travel, there remains an upper limit of 100,000 years or so to explore our Galaxy thus not allowing <i><font color=magenta> LAWKI</font></i> to perform a single generation (or few generational) trip to cover our Galaxy. Or does it? </td></tr></table></center> <p> <table cellpadding=4 border=6><tr> <td><img src="dilation.gif"></td> <td><h3>There is an interesting feature of Einstein's <font color=magenta> Special Theory of Relativity</font> which affects this issue. For a brief discussion of <font color=magenta>Special Relativity</font> go to <a href="http://pages.uoregon.edu/~imamura/FPS/fps.time.html">this link</a>. Because of the property of spacetime that it is <i>malleable</i>, not rigid (<i><font color=red>which also includes the time part</font></i>) time does not have to flow at the same rate for all observers. In fact, it has been amply demonstrated by experiment that <font color=magenta> moving clocks run more slowly than stationary clocks!</font> The rate at which a moving clock runs is given by the formula to the right. For the rider on the rocket (see left panel), let's say his watch reads that <font color=magenta><i>t</i> = 10 hours</font> have elapsed. If the rocket is traveling at speed v = 0.9 c, then, amazingly, it turns out that the watcher (on the ground) would find that his clock would read that roughly <font color=magenta> <i>t'</i> = 23 hours elapsed</font> over the <i>same</i> time interval.</td> <td><img src="TimeDilation.gif"></td></tr></table> <p> <table cellpadding=6 border=5><tr> <td><img src="http://pages.uoregon.edu/~imamura/FPS/images/twinparadox.jpg"> </td> <td><h3><center>Twin Paradox</center><p> There is an interesting consequence of <i><font color=magenta>time dilation </font></i>. Imagine two twins, one stays on the Earth while the second travels to Proxima Centauri (on a ship traveling at 90 % of the speed of light). After reaching Proxima Centauri, the traveling twin immediately turns around and returns to the Earth. Because Proxima Centauri is 4.3 light years from the Earth, the stay-at-home twin sees the trip take 9.6 years. Interestingly, the traveling twin finds that the trip, according to his watch takes only 4.0 years. The closer the traveler gets to the speed of light, the less he will have aged. </tr></table> <p> But wait, according to Einstein, <font color=magenta>time dilation </font> says that, according to a stationary observer, a moving clock runs more slowly than the stationary clock. This fits nicely so far as it suggests that the traveling twin's clock does indeed tick more slowly than the stay-at-home twin. The paradox arises because all that is really needed is that two observers are in <font color=magenta> relative motion</font> for <font color=magenta>time dilation</font> to occur. So, if we were to consider the situation from the point of view of the traveling twin, we would come to a different conclusion. The traveling twin sees the stay-at-home twin running away from him as he speeds toward Proxima Centauri, that is, he believes that the stay-at-home twin is the one who was in motion. Consequently, he believes that the stay-at-home twin's clock is the one that ran more slowly and he is surprised when they re-unite and the stay-at-home twin has actually aged more. This is the <font color=magenta>Twin Paradox</font>. For an explanation of the paradox see <a href="http://pages.uoregon.edu/~imamura/FPS/week-3/week-3.html"> here</a>. <p><hr><p>