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-I learned that if you look at a star 10 million lightyears away, the light that you are looking at is 10 million years old since the photons have been traveling at the speed of light for 10 million years to reach you.

-I also learned that all EM radiation travels at the speed of light.

-I know that there is not faster than light, but object that move slower than light redshift and blueshift on the visible spectrum depending on which direction they are moving with respect to the observer.

I'm asking this question because if I'm putting the pieces together correctly, then the stuff we observe "now", really all happened tens, hundreds, thousands, millions, and billions of years ago. Correct? Which, would that mean that gamma ray bursts, xrays, radio waves--all limited by the speed of light--are all events that happened in the past, and that their EM radiation takes time to reach us in every situation?

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Yes the speed of light is slow and everything you see happened in the past.

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Yes everything you look at happened in the past. The speed of light in a vacuum is 299,792,458 meters per second. It travels slightly slower in materials according to their refractive index. When you look at the moon, you see it as it was about 1.3 seconds ago, the Sun from about 8.3 minutes ago, even from your window to your front yard takes a few nanoseconds. Gravity also propagates at the speed of light, so if the Sun magically disappeared, we would still see it and go on in Earth's orbit around it for about another 8.3 minutes.

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