# The Photon Clock Challenge

#### Iconoclast

A Youtube channel has just uploaded a video proposing a challenge. The question is pretty simple. It can be summed up to: A clock is moving towards you at 50% the speed of light, and eventually it passes you and continues its travel. When the clock is moving towards you, will it appear to tick faster, slower, or at the same rate than when it is moving away from you?

Watch from 0:47 or so.

Attempt at a solution
It seems to me that yes, the clock will be ticking at the same rate. Afterall, the velocity is the same and the speed of light is absolute (that means, when the clock is approaching you, it won't make light travel faster towards your eyes).

So, can you help? It's worth a t-shirt.

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#### robphy

Homework Helper
Gold Member
Draw a spacetime diagram....

Is there an acoustic analogue?

#### Janus

Staff Emeritus
Gold Member
The speed of light approaching doesn't change, but the distance between you and the clock does and so does the time it takes for the light to travel from it to you.

#### phinds

Gold Member
It seems to me that yes, the clock will be ticking at the same rate..
But that's not the question. The question is will it APPEAR to ...

Staff Emeritus
Why is this hard? Even if you didn't know the equation for the relativistic doppler effect, all you would need to know is that distant spectral lines (i.e. clock ticks) are red-shifted if they are moving away from us and clue-shifted if moving toward us.

#### Iconoclast

That doesn't answer the question. Sure, the clock will look bluer, but what will it read?

#### Nugatory

Mentor
That doesn't answer the question. Sure, the clock will look bluer, but what will it read?
It comes about as close to answering the question as anyone can without just blurting out the answer - which is generally discouraged here.

If the clock looks bluer, then the successive wave peaks are closer together. How are the wave peaks related to the ticks of the clock and how are the ticks of the clocks related to what it reads?

Staff Emeritus
clue-shifted
I meant blue shifted...but I think I like "clue shifted" better.,

#### Janus

Staff Emeritus
Gold Member
That doesn't answer the question. Sure, the clock will look bluer, but what will it read?
The reading on the clock and blue shift are relate. Imagine the clock starts tick 1 when it 1 light sec away and is moving towards you at 0.6c You will see tick one 1sec later.
Now one second later(according to the clock) it starts tick 2. According to you, this tick occurred 1.25 sec after the first (time dilation), by which time the clock has moved a distance of 0.75 light sec closer to you. The light from this tick reaches you 0.25 sec later. The time between tick 1 and when you see tick 1 is 1 sec and the time between tick 1 and when you see tick 2 is 1.5 (1.25 +0.25) sec. so the time difference between seeing tick 1 and tick 2 is only 0.5 sec, so you see the clock tick twice as fast.
using the relativistic Doppler shift formula gives a blue-shift factor of 2 for something approaching at 0.6c, So you see the clock tick fast by the same factor as you see the frequency of its light increased.

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