ACCELERATION PHASE of Relativistic Trip to Alpha Centauri Acceration due to rocket engine is constantly 528.2 m/sec^2 This entire trip will take 218 weeks, a little over four years, as recorded by BOTH the Traveler and by the Earth observer! There IS no "Twins Paradox" at all! General Relativity applies due to the acceleration of this phase of the trip and therefore Time Compression appears to occur. The Earth observer watches for only about one week and sees the Traveler age by 108 weeks, more than two years! This is due to the logically necessary Time Compression due to General Relativity. The Traveler does not experience anything unusual, except for when looking back to Earth to see everything occur and age SLIGHTLY faster than he is experiencing. After he has traveled for those 108 weeks, he sees his twin brother on Earth as being about a week older than himself, having aged 109 weeks. They BOTH see the other as aging FASTER than himself during this phase of the trip! The brother on Earth sees a pronounced effect while the Traveler sees a minimal effect. This difference is due to the acceleration of only one of them. The Traveler sees himself as constantly accelerating to virtually the speed of light during this phase of the trip, and he sees himself as having traveled roughly HALF of the distance to Alpha Centauri, 2.05 light-years of distance, during the two-plus years that he has experienced. Nothing seems bizarre about that to him. The Earth observer sees the Traveler as barely having started the trip, during this acceleration, regarding distance, around 0.018 light-years of distance, although he sees that the traveler has AGED 108 weeks during the one week of watching him! TRAVELER's Expererience Earth Viewed _________________ ______ ________________________ Chronometer Traveler Earth-seen Time Time Speed Total Total Time Years Factor km/sec Distance Distance Passed (l.y.) (l.y.) Year Week 0.00 1.00 0. 0. 0.0 0.0 0.0 0.04 2.35 271,554. 0.0242 0.016 0.01629 0.84714 0.08 4.38 292,059. 0.0605 0.018 0.01752 0.91111 0.11 6.47 296,392. 0.0981 0.018 0.01778 0.92463 0.15 8.58 297,954. 0.1360 0.018 0.01788 0.92950 0.19 10.70 298,686. 0.1741 0.018 0.01792 0.93178 0.23 12.82 299,086. 0.2123 0.018 0.01794 0.93303 0.27 14.94 299,327. 0.2505 0.018 0.01796 0.93379 0.31 17.07 299,485. 0.2887 0.018 0.01797 0.93428 0.34 19.19 299,593. 0.3269 0.018 0.01797 0.93461 0.38 21.32 299,670. 0.3652 0.018 0.01798 0.93485 0.42 23.45 299,727. 0.4035 0.018 0.01798 0.93503 0.46 25.58 299,771. 0.4418 0.018 0.01798 0.93517 0.50 27.70 299,805. 0.4801 0.018 0.01799 0.93527 0.54 29.83 299,831. 0.5183 0.018 0.01799 0.93536 0.57 31.96 299,853. 0.5566 0.018 0.01799 0.93543 0.61 34.09 299,871. 0.5949 0.018 0.01799 0.93548 0.65 36.22 299,886. 0.6332 0.018 0.01799 0.93553 0.69 38.35 299,898. 0.6716 0.018 0.01799 0.93557 0.73 40.48 299,908. 0.7099 0.018 0.01799 0.93560 0.77 42.61 299,917. 0.7482 0.018 0.01799 0.93563 0.80 44.74 299,925. 0.7865 0.018 0.01799 0.93565 0.84 46.86 299,932. 0.8248 0.018 0.01799 0.93567 0.88 48.99 299,938. 0.8631 0.018 0.01799 0.93569 0.92 51.12 299,943. 0.9014 0.018 0.01799 0.93571 0.96 53.25 299,947. 0.9397 0.018 0.01799 0.93572 1.00 55.38 299,951. 0.9781 0.018 0.01799 0.93573 1.03 57.51 299,955. 1.0164 0.018 0.01800 0.93574 1.07 59.64 299,958. 1.0547 0.018 0.01800 0.93575 1.11 61.77 299,961. 1.0930 0.018 0.01800 0.93576 1.15 63.90 299,963. 1.1313 0.018 0.01800 0.93577 1.19 66.03 299,966. 1.1697 0.018 0.01800 0.93578 1.23 68.16 299,968. 1.2080 0.018 0.01800 0.93578 1.26 70.29 299,970. 1.2463 0.018 0.01800 0.93579 1.30 72.42 299,971. 1.2846 0.018 0.01800 0.93580 1.34 74.55 299,973. 1.3230 0.018 0.01800 0.93580 1.38 76.67 299,975. 1.3613 0.018 0.01800 0.93580 1.42 78.80 299,976. 1.3996 0.018 0.01800 0.93581 1.46 80.93 299,977. 1.4379 0.018 0.01800 0.93581 1.49 83.06 299,978. 1.4763 0.018 0.01800 0.93582 1.53 85.19 299,979. 1.5146 0.018 0.01800 0.93582 1.57 87.32 299,980. 1.5529 0.018 0.01800 0.93582 1.61 89.45 299,981. 1.5912 0.018 0.01800 0.93583 1.65 91.58 299,982. 1.6296 0.018 0.01800 0.93583 1.69 93.71 299,983. 1.6679 0.018 0.01800 0.93583 1.72 95.84 299,984. 1.7062 0.018 0.01800 0.93583 1.76 97.97 299,984. 1.7445 0.018 0.01800 0.93584 1.80 100.10 299,985. 1.7829 0.018 0.01800 0.93584 1.84 102.23 299,986. 1.8212 0.018 0.01800 0.93584 1.88 104.36 299,986. 1.8595 0.018 0.01800 0.93584 1.92 106.49 299,987. 1.8978 0.018 0.01800 0.93584 1.95 108.61 299,987. 1.9362 0.018 0.01800 0.93584 1.99 110.74 299,988. 1.9745 0.018 0.01800 0.93585 2.03 112.87 299,988. 2.0128 0.018 0.01800 0.93585 2.07 115.00 299,989. 2.0512 0.018 0.01800 0.93585 CRUISING PHASE of Relativistic Trip to Alpha Centauri THIS is the part of the trip that everyone is familiar with! Acceration due to rocket engine is constantly 0.0 m/sec^2 as the rocket engine has been shut off, but only for what he sees as a two week period. After this two week interval of cruising, he will turn the rocket around and begin the following two years of Deceleration (below). Special Relativity applies and therefore does Time Dilation. The time factor is now opposite, where the Earth observer watches for more than four years in seeing the traveler seem to age very slowly, just two week of aging during those four years of watching him, per standard Special Relativity and Time Dilation. Interestingly, if the Traveler now watches for those two weeks (or 0.04 years, from yeardate 2.07 to yeardate 2.11 on his chronometer) of this phase of the trip and sees the Earth and his identical brother as moving and aging very SLOWLY, only 1/115 as fast as he is experiencing. Instead of seeing the Earth as aging by two weeks, he sees it age only 1/115 of that, or about an HOUR AND A HALF. BOTH brothers see the other one as aging more SLOWLY than himself during this phase of the trip. The Traveler sees a very pronounced effect while viewing Earth, but only for a brief time. The Earth observer also sees a pronounced effect, over the entire four-plus years of watching that phase of the trip. The Earth observer believes that nearly the entire trip occurred during this Cruising phase of coasting without power, while the Traveler sees (more correctly) that the Cruising phase was only a brief interval (two weeks) while nearly the entire trip occurred during acceleration and deceleration. But they will each see that a total of 218 weeks of traveling occurs between leaving the Earth and arriving at a planet around Alpha Centauri. They just PERCEIVE the trip rather differently! TRAVELER's Expererience Earth Viewed _________________ ____________________________ Chronometer Traveler Earth-seen Time Time Speed Total Total Time Years Factor km/sec Distance Distance Passed (l.y.) (l.y.) Year Week 2.07 115. 299,989. 2.0512 0.018 0.018 0.93585 2.11 115. 299,989. 2.0942 4.122 4.162 (meaningless) DECELERATION PHASE of Relativistic Trip to Alpha Centauri Deceration due to rocket engine is constantly -528.2 m/sec^2 TRAVELER's Expererience Earth Viewed _________________ ____________________________ Chronometer Traveler Earth-seen Time Time Speed Total Total Time Years Factor km/sec Distance Distance Passed (l.y.) (l.y.) Years 2.11 115.00 299,989. 2.0942 4.122 4.162 The detailed analysis of the deceleration phase is much like the acceleration phase presented above. The numbers will be left out here except for the starting and ending situations. 4.18 1.00 0.0 4.14 4.14 4.18 The Traveler has experienced a trip of 108 + 2 + 108 weeks. The Earth observer has SEEN a trip of 1 + 216 + 1 weeks. The Traveler has SEEN the Earth age 109 + 0.006 + 109 weeks. The Earth has experienced 1 + 216 + 1 week while watching the trip. 4.18 years is 218 weeks, so each of these totals 218 weeks, which both brothers see as the time required for the entire trip, both for himself AND of what he observed of his brother!