We assume that B accelerates very fast, reaching 4/5 light speed in, say, one second. Twin B has borrowed some inertial dampers from Star Trek so doesn't suffer undue discomfort as this happens.
As we've already seen, A's clock on the distant star moves forward extremely fast during this initial acceleration, but after that, all of A's clocks appear to run more slowly.
Now we have to consider another effect of relativity. As well as clocks doing strange things, a moving observer sees distances differently as well. In particular, distances in the direction of motion become shorter.
As B accelerates, the distance to the star becomes shorter and shorter. When at full speed, the star turns out to be only 3/5 of a light year away.
In the above diagram, B now feels stationary, with the star hurtling towards the spaceship at 4/5 light speed. It will take 3/5 divided 4/5, i.e. 3/4 year, to arrive.
B can use Einstein's formulas to figure out how A views all of this.
A's numbers are shown in red. The final coordinates for B are exactly the same as those calculated by A for both A's clock and B's clock. Both agree that B's clock (the blue time) shows a lower value.
The starting time on the star's clock is 4/5 year. This is how much it's clock advanced during B's one second of acceleration!
But what's happened to twin A during all of this?
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As we've already seen, A's clock on the distant star moves forward extremely fast during this initial acceleration, but after that, all of A's clocks appear to run more slowly.
Now we have to consider another effect of relativity. As well as clocks doing strange things, a moving observer sees distances differently as well. In particular, distances in the direction of motion become shorter.
As B accelerates, the distance to the star becomes shorter and shorter. When at full speed, the star turns out to be only 3/5 of a light year away.
In the above diagram, B now feels stationary, with the star hurtling towards the spaceship at 4/5 light speed. It will take 3/5 divided 4/5, i.e. 3/4 year, to arrive.
B can use Einstein's formulas to figure out how A views all of this.
A's numbers are shown in red. The final coordinates for B are exactly the same as those calculated by A for both A's clock and B's clock. Both agree that B's clock (the blue time) shows a lower value.
The starting time on the star's clock is 4/5 year. This is how much it's clock advanced during B's one second of acceleration!
But what's happened to twin A during all of this?
start
prev
next
