How Does Time Dilation Impact Space Travel Durations?

[matheinste]

Taken from Seminar Poincare, Einstein 1905-2005 page 106.

The section from which it is taken is called "A comfortable trip for the Langevin traveler", comfortable because the acelerations for the inward and outward journey are just plus and minus g, equivalent to Earth's gravity, and the forces involved at the (instantaneous) turnaround are said to be easily handled by human beings. The article points out that considerable, prohibitive amounts of fuel, comparable to planetary masses, would be required for the longer journeys and the gravitational effects of such large fuel masses are ignored in the calculation. It also assumes that the journey takes place in flat Minkowski spacetime.

<br /> \begin{tabular}{| c | c | c |}<br /> \hline Traveller&#039;s proper time &amp; Earth&#039; proper time\\<br /> \hline 1 year &amp; 1 year 4 days\\<br /> \hline 2years &amp; 2years and 1month \\<br /> \hline 4 years &amp; 4.7 years \\<br /> \hline 8 years &amp; 14.5 years \\<br /> \hline 16 years &amp; 104 years \\<br /> \hline 20 years &amp; 297 years \\<br /> \hline 28 years &amp; 2,200 years\\<br /> \hline 32 years &amp; 5,960 years \\<br /> \hline 40 years &amp; 44,000 years \\<br /> \hline 48 years &amp; 326,000 years \\<br /> \hline 60 years &amp; 5.54x$10^6$ years \\<br /> \hline 72 years &amp; 131x$10^6$ years \\<br /> \hline 84 years &amp; 2.64x$10^9$ years \\<br /> \hline 86 years &amp; 5 billion years \\<br /> \hline<br /> <br /> \end{tabular}<br /> <br /> [/itex]<br /> <br /> Matheinste.

 

[matheinste]

A more detailed explanation and clarification of the method proposed in an almost word for word transcription of the same source:-

------The standard presentation of the “twin paradox” (or “Langevin traveller), which amounts to a direct trip with return between a point of the Earth and some far distant space station, with large uniform velocity v, in both directions, is remarkable by its beautiful pedagogical simplicity. In fact, we can see that it illustrates the Minkowskian triangular inequality. However, since it appeared in the literature, various objections have been eaised whose point was generally to conclude that this was a school example which was probably physically incorrect or at best unrealistic. This type of opinion has also been often endorsed by vulgarizers of special relativity, as a reassuring thought with respect to what looks like a scandal for the common sense.

The main objection was about the instantaneous passage from velocity v to –v when reaching the term of the travel. Such passage had to be produced by a shock, or even if smoothened out by some decelerating device, it seemed to involve so large accelerations that certainly the biological organisms and maybe clocks themselves could not stand such constraints. Now in view of Minkowski’s study of uniformly accelerated motions, one can actually show the possibility of organizing a more comfortable trip in which the traveller would be submitted to a constant acceleration, or deceleration. We even impose, for making the accelerations biologically normal, that its value be precisely equal to the value of the gravity acceleration g on the earth. Of course, we admit that the whole travel will take place in the vacuum, far from any gravitational source, in such a way that the flat Minkowski sapcetime remains a reasonably good approximation to the real spacetime.

Choice of the motion.

The trajectory is along a straight line joining the Earth denoted by A and a space station B considered as at rest with respect to the earth. The travel which is proposed is composed of

A uniformly accelerated motion with acceleration g from A to the middle M of AB.

A uniformly accelerated motion with acceleration –g from M to B (namely a phase of deceleration).

The acceleration –g is maintained and produces the first half of the returning trip from B to M.

The acceleration is shifted from –g to g for producing a uniformly decelerated motion from M to A.

It is clear that the discontinuity of the acceleration from g to –g produced at M is bearable by the physical and biological systems in the spaceship: of the direction of the normal gravity g on earth.it is just felt as a sudden inversion.-----

Matheinste.