Schrödinger's Cormorant

(A2-10) ① 1 light minute = distance travelled by light in a vacuum in 1 minute.

Speed of light = 3.00 x 108 ms-1;

so 1 light minute = 60 x 3.00 x 108 = 1.80 x 1010m.

Distance to Mars = 9.0 x 1010m ⇔ 9.0 x 1010 / 1.8 x 1010m = 5.0 light minutes.

② Nefertiti is stationary in her own frame, so her position, xN(N) remains at zero throughout. Mars is also stationary in Nefertiti’s reference frame, at a distance of 5.0 light minutes.

Cormorant maintains a velocity of 0.5c (measured in Nefertiti's frame of reference) until he reaches Mars, then bounces back with a velocity of -0.5c.

We are only concerned with Nefertiti’s frame of reference here - so no relativistic effects to worry about: we can just apply the classical formula:

time = distance / speed = 5.0 / 0.5 = 10.0 minutes for the outward leg. The same will be true for the return journey, so total journey time = 20.0 minutes.

③ Nefertiti is a moving observer of Cormorant (moving at a velocity of -0.5c relative to him, on the first leg of the mission, and at +0.5c on the second leg), so she will observe that his time is dilated. Rearranging the time dilation expression and using the journey time as measured by Nefertiti:

So in total, Cormorant’s journey time will be 2 x 8.66 = 17.32 minutes.

If you're feeling slightly nervous about the factor that Cormorant changes his rest frame of reference at the halfway point and we have just ignored that in these calculations, don't worry: we'll do it again in later (in Question A2-13), with explicit consideration of the change of reference frame and (spoiler alert) we'll get the same answer.

These calculations confirm that, from Nefertiti’s perspective, she should expect to age more than Cormorant does, while he is away on his Mars mission.

Table so far:

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