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You've done a good job of thinking this through. What you are missing is General Relativity, which describes the universe on large scales.
The invariance of c is guaranteed only in inertial frames in much the same way as Newton's Laws are only guaranteed for inertial frames. Imagine turning around in a circle, making yourself a non inertial frame--- the distant galaxies in that frame travel around you at much greater than c, and that's OK!
In classical physics, inertial frames take up the whole universe; however, that is not true in GR. In GR, inertial frames are only local; they cannot contain the whole universe, or any significant part of it. They can only be as big as space-time curvature is ignorable.
But space-time curvature is so not-ignorable on scales of billions of light-years. So most of the universe is outside your local inertial frame, and the invariance of c can be broken. Indeed, the recession speeds of those galaxies you're talking about (if you consider speed to be proper distance over coordinate time) are much greater than c.
The cosmological curvature manifests as expansion. As light rays propagate towards you from those galaxies, the space between you and the light ray expands, so that it continually has farther to go. Or, alternatively, you can consider them to travel at less than c. Depends on your interpretation of the equations.
The invariance of c is guaranteed only in inertial frames in much the same way as Newton's Laws are only guaranteed for inertial frames. Imagine turning around in a circle, making yourself a non inertial frame--- the distant galaxies in that frame travel around you at much greater than c, and that's OK!
In classical physics, inertial frames take up the whole universe; however, that is not true in GR. In GR, inertial frames are only local; they cannot contain the whole universe, or any significant part of it. They can only be as big as space-time curvature is ignorable.
But space-time curvature is so not-ignorable on scales of billions of light-years. So most of the universe is outside your local inertial frame, and the invariance of c can be broken. Indeed, the recession speeds of those galaxies you're talking about (if you consider speed to be proper distance over coordinate time) are much greater than c.
The cosmological curvature manifests as expansion. As light rays propagate towards you from those galaxies, the space between you and the light ray expands, so that it continually has farther to go. Or, alternatively, you can consider them to travel at less than c. Depends on your interpretation of the equations.
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when you look at our sun you are seeing it from 6 minutes in the past (the time it takes the light to travel to earth)
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Your brain is not exploding, it's expanding. You're doing the same thing that thinkers have been doing since the dawn of time. You are however allowing that 13.6 figure to get in the way. When we observe something 13.6 b.l.y. away, it does not mean it's at the edge of the universe now. It may not even have been the edge of the of the universe 13.6 b.l.y. ago. It simply means that we cannot observe anything further at this time. There may be super giants further out there whose light has not yet reached us yet because they were born say 13.5 b.l.y. ago. Remember the universe is not only as strange as we can imagine - it's stranger then we have the ability to imagine. Bigger then we can possibly conceive certainly comes under that heading.