The Photon Clock Challenge

In summary, the question is whether a clock moving towards you at 50% the speed of light will appear to tick faster, slower, or at the same rate when it is moving away from you. After discussing the concept of the speed of light being absolute and the distance and time changes, it is concluded that the clock will appear to tick faster due to the relativistic Doppler shift formula. This can be compared to the concept of red and blue shifting of distant spectral lines. The analogy of an acoustic analogue is also mentioned.
  • #1
Iconoclast
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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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  • #2
Draw a spacetime diagram...

Is there an acoustic analogue?
 
  • #3
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.
 
  • #4
Iconoclast said:
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 ...
 
  • #5
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.
 
  • #6
That doesn't answer the question. Sure, the clock will look bluer, but what will it read?
 
  • #7
Iconoclast said:
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?
 
  • #8
Vanadium 50 said:
clue-shifted

I meant blue shifted...but I think I like "clue shifted" better.,
 
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  • #9
Iconoclast said:
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.
 

1. What is "The Photon Clock Challenge"?

"The Photon Clock Challenge" is a theoretical scenario that explores how time is measured and perceived at different speeds and in different reference frames according to Einstein's theory of relativity.

2. What is the main concept behind "The Photon Clock Challenge"?

The main concept behind "The Photon Clock Challenge" is that the passage of time is relative and can be influenced by factors such as speed and gravity.

3. How does "The Photon Clock Challenge" demonstrate the effects of time dilation?

In "The Photon Clock Challenge", a photon is sent back and forth between two mirrors at different speeds. This demonstrates time dilation, as the photon experiences time at a different rate depending on its speed, compared to an observer outside the system.

4. What are some real-life applications of "The Photon Clock Challenge"?

Understanding the concept of time dilation explored in "The Photon Clock Challenge" is crucial for GPS systems, as they need to account for the different rates of time experienced by satellites in orbit compared to receivers on Earth. This also has implications for space travel and high-speed transportation.

5. What are some potential implications of "The Photon Clock Challenge" for our understanding of the universe?

"The Photon Clock Challenge" highlights the fundamental nature of time and its relationship to space and motion. It challenges our traditional understanding of time as a constant and opens up possibilities for further research and discoveries in the field of physics and cosmology.

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