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Is the following analogy correct, if not- what changes are necessary to correct it?

Let's consider a guy riding on a photon with a clock, and every time his clock ticks he paints a dot. Let's also assume we launch him to ride a set trip and that we have a clock too.

  1. Time does not flow any differently for the photon-guy from his perspective, whether space-time is warped or not. It simply proceeds as normal and the clock will tick as normal and in 5 of his seconds he will paint 5 dots, the curvature of space-time does not change this for him from his perspective at all.

  2. From our perspective, looking at what happens to him, the change in gravity (warp in space-time) does change the flow of time (similar to how change of speed would change his flow of time, but let's put that aside for now). Looking at photon-guy, his clock will appear to speed up (or slow down) relative to ours when his space-time is warped, and he will seem to be painting those dots at a faster or slower rate.

  3. Nevertheless, time does not flow any differently for us from our perspective either. It simply proceeds as normal and the photon-guy's trip will appear to take the same amount of time relative to our clock, and furthermore he will have always covered the same distance whether his gravity has changed or or not. His trips will always take the same amount of time according to our clock.

  4. Therefore, since his clock may have gone faster or slower relative to ours - when he arrives at the destination, he will have painted more or less dots during the trip depending on how his flow of time was affected by changes in gravity (e.g. a gravitational wave).

  5. Hence, if we launch multiple photon-guys, and some are hit by gravitational waves and others aren't, they all look a bit different to us. Specifically, we can calculate how many dots photon-guy would have painted according to the initial relative time and distance if he was not hit by a gravitational wave, and note the exact strength of the gravitational wave (change in relative time) based on that.

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You cannot consider a guy riding on a photon because the rest frame of a photon is undefined. Any analogy based on this concept is meaningless.

The time dilation caused by gravity is calculated from the metric tensor. Although this sounds complicated in many cases it is suprisingly simple to do. See for example my answer to Are time and gravity affected when at rest compared to free fall? (though admittedly my definition of simple may differ from yours :-).

The red/blue shift of light can be used to measure the relative time dilation between two observers simply because the frequency of the light changes proportionally to the time dilation.

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