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I understand that this question has recently been asked, and yet not answered to the greatest and most understandable extent, but I was wondering whether travelling at the speed of light is really the most EFFICIENT speed at which to travel when going from any given point (A) to another point (B) in space.

Example: I want to travel from one planet (point A) to another (point B) in space as quickly as possible, thus taking the least time. Now, according to Einstein's theory of special relativity, if I were to travel, say, 270,000 kms-1 (km/s), my relativistic change factor would be 2.3, meaning every year I spend on the ship, while travelling at this speed, would be 2.3 years for a bystander on the planet that I am travelling to (point B). While I am travelling VERY fast at this speed, the time it takes me to reach point B will be perceived by the bystander on that planet as longer than I perceive, as time for me whilst on the ship has slowed down. Now if I were to travel at a slower speed, say 230,000 kms-1, my relativistic change factor would be only 1.3, substantially less.

In conclusion, I am curious as to whether travelling FASTER will benefit when someone wants to travel from point A to B, meeting a bystander at Point B.

Now so that no one is confused, the time the space shuttle leaves point A, and then arrives at Point B to meet the bystander, is how long the trip takes, meaning that is is in the bystanders perception of the length of time taken and not the person in the shuttle.

Is there a way of calculating, i.e a formula of some sort, this theory.

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    $\begingroup$ If you want to minimise the bystander's perception of the length of time, the person in the shuttle should travel as fast as possible. Even though time will be running much more quickly for the bystander than the person in the shuttle, the journey will take much less time for the person in the shuttle than if she were moving more slowly. The net result is that the total time elapsed for the bystander is still less if the shuttle moves more quickly, which is what you would guess intuitively. $\endgroup$ – gj255 Jan 29 '16 at 13:10
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    $\begingroup$ I love this question, sounds like you are making arrangements to arrive on time to a space appointment (this is a true concern from a physicist's point of view). Anyways, in order to find the answer all you need to do is to draw a spacetime diagram. A diagram in which the arrival point is spatially still works best, as the elapsed time at that point is shown directly as one of the coordinates of the diagram. You will see that, independently of time dilation, the trajectory through which the arrival time is minimized is still that which approaches the speed of light. $\endgroup$ – Giorgio Comitini Jan 29 '16 at 13:17
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    $\begingroup$ On the other hand, when approaching the speed of light, the elapsed time from the traveler's point of view approaches zero. Thus the same trajectory minimizes the time of travel too. $\endgroup$ – Giorgio Comitini Jan 29 '16 at 13:22
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The time taken to travel to the planet, as seen by the bystander at point B, is the distance from A to B, is simply the distance divided by your speed. The time experienced by you doing the travelling is the time seen by B divided by your relativistic factor. It's just like moving from A to B in non-relativistic physics. So the faster you go, the shorter the time measured by B is.

To be pedantic, this is all glossing over the issue of simultaneity at different locations. So I'm assuming we have a situation where B can infer the time at which the traveller left A, such as B signals A with a light beam, knows the distance to A, and therefore knows the appropriate time at B at which to start the clock (namely after (distance/speed of light) seconds have passed).

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