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From this article,

Let’s say Alice is holding a light clock, and Bob is watching her run by, while holding it, with speed V. Alice is standing still (according to Alice), and the time,$ \tau$, between ticks is easy to figure out: it’s just $\tau = \frac{d}{C}$. From Bob’s perspective the photon in the clock doesn’t just travel up and down, it must also travel sideways, to keep up with Alice. The additional sideways motion means that the photon has to cover a greater distance, and since it travels at a fixed speed (EEP y’all!) it must take more time

My question is, why does photon need to travel sideways to hit the Alice light clock?

Michael Seifert
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PaulD
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1 Answers1

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Because in Bob's reference frame, the light clock has moved sideways a certain distance during the time of flight of the photon. So to hit the "top" mirror, the photon must have travelled some horizontal distance (depending on Alice's speed) as well as the vertical distance; the total displacement is a diagonal.

BTW, the diagrams on the page you linked to are (in my opinion) not all that elucidating. There are some better ones here.

Michael Seifert
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