Are you good with Lorentz' tranformations ?(adsbygoogle = window.adsbygoogle || []).push({});

I tought I was, until I tried to do this exercice (it is really classical):

Two planets, A and B, are at rest with respect to each other, a distance L apart, with synchronized clocks. A spaceship flies at speed v past planet A toward planet B and synchronizes its clock with A’s right when it passes A (they both set their clocks to zero). The spaceship eventually flies past planet B and compares its clock with B’s. We know, from working in the planets’ frame, that when the spaceship reaches B, B’s clock reads L/v. And the spaceship’s clock reads L/γv, because it runs slow by a factor of γ when viewed in the planets’ frame.

How would someone on the spaceship quantitatively explain to you why B’s clock reads L/v (which is more than its own L/γv), considering that the spaceship sees B’s clock running slow?

The answer is :

The person on the spaceship says is: “My clock advances by L/γ v during the whole trip. I see B’s clock running slow by a factor γ , so I see B’s clock advance by only (L/γv)/γ = L/γ^2v. However,B’s clock started not at zero but at Lv/c2. Therefore, the final reading on B’s clock when I get there is Lv/c2 + L/γ^2v = L/v( v^2/c^2 + 1/γ^2) = L/v( v^2/c^2 + (1 − v^2/c^2)) = L/v

My question is why is B's clock in advance, shouldn't it suppose to be A (rear clock ahead) ?

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# I Explaining time dilation

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