Hypothetical video feed of time dilation

Question

As a thought experiment, I'm imagining an observer on Earth video conferencing with an observer traveling at a high velocity away from Earth, or in a very large gravitational field relative to Earth.

What would a live video feed look like to each observer? Would the video of the observer on Earth appear in slow motion proportional to the intensity of the gravitational field where the other camera is located?

Would the observation of either observer change if the signal carrying information to build the video was traveling at the speed of light? I don't intuitively understand how the time dilation could be observed if the information was being received by either observer at the speed of light.

Answer 1

Time dilation is based on the same fact that the entire special relativity is based on i.e, light's speed is $c$ which is constant and nothing can travel faster than light in a vacuum. So let's consider this thought experiment of yours. A spaceship is moving with a speed $v$, for your conceptual clarity you can take $v$ to be equal to $c$. Light can only travel $c$ metres in 1 second of time. When the distance starts to increase above c, the signal starts getting delayed because the signal being an EM wave travels with $c$ and now it has to travel a larger distance to reach you. Alright, this being clear, let's talk about what video you see. You will see everything what the person is broadcasting but with a time delay. This is how the time dilates for you.It is the exact same for the observer in the spaceship as he sees you moving away with the same speed $v$. The faster he travels, the longer is the delay when the signal reaches you because of the $\gamma$ factor. The time dilation as you know can be given by $$\tau=\frac{t}{\gamma}.$$ Time dilation arises simply due to the fact that one observer is travelling relative to another observer. It's just who is looking at whom, i.e, reference frame change. Tip. You can think of a reference frame as a huge framework of clocks and light sensors at every co-ordinate. Hope it helps.