What am I missing here? (aging more slowly when moving near the speed of light)

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It states that we will age slower if we were travelling at the speed of light compared to being on Earth. Would we not age the same but just be further away hypothetically?

Next it states that if we travel away from a clock at the speed of light at 12:00, we would always see 12:00.

Surely the initial 12:00 would instantly become a fading memory and you would only see black, as no more photons would reach the eye as you would be moving at the same speed as the photons.
 
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Ibix
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It states that we will age slower if we were travelling at the speed of light compared to being on Earth. Would we not age the same but just be further away hypothetically?
You can't travel at the speed of light - it's impossible and trying to reason about what happens if you do travel at the speed of light inevitably involves self-contradiction and nonsense.

If you travel somewhere near the speed of light relative to the Earth and return (the returning part is important) then yes, you will experience less time than someone who stays on Earth. That's strictly true even at low speeds, but you need high quality atomic clocks to detect the difference even at airline speeds. The experiment is usually called the "twin paradox", and is easily googleable (and there are a billion threads on it here). It was first actually tested by Hafele and Keating.
Surely the initial 12:00 would instantly become a fading memory and you would only see black, as no more photons would reach the eye as you would be moving at the same speed as the photons.
Again, you can't travel at the speed of light and trying to discuss it leads to nonsense. You can travel at a very high speed relative to the clock, though, and you are correct that you will barely be able to see the clock because light will be extremely redshifted. This is simply a relativistic version of the Doppler effect, familiar from the change in pitch of a siren as an emergency vehicle passes by. The relativistic version has a few interesting features that aren't relevant here, so is qualitatively similar to the non-relativistic version.
 
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You need to read up on the twin paradox where one twin is placed on a spaceship and travels away at a high rate of speed say 1/2 speed of light while the other waits anxiously on Earth. When the spacefaring twin returns he/she will have aged less than the twin on Earth. This is a tested fact using atomic clocks on jets.

https://en.wikipedia.org/wiki/Twin_paradox

Its also called a paradox because students who study it think the spacefaring twin could just view the other twin on Earth as speeding away at 1/2 speed of light so that time is relative and neither really age.

The flaw in the reasoning is that the spacefaring twin must slow down, turn around and return. In that slowing down ie he/she changes to a new inertial frame of reference and thus the ages are forever changed with the Earth bound twin aging more quickly than the spacefaring twin. It can be shown via spacetime diagrams and light pulses that this is so.

 
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