How can we see universe further out than its age? Especially if universe is expanding the distance is getting bigger and bigger right?

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I will explain what I mean.

Assumptions to help simplify: Point A is stationary, point b is moving away from it. And the expanding universe is moving point b away 1 light year in a year at point “a’.

Year 0 we see nothing

Year 1 we see point “b” 1 ly away

In year 1 point “b” is already 2 years away because universe expanded.

So it will take 2 years for the light from point “b” to hit observers eye in point “a” (year 3)

In that 2 years point “b” would have moved 2 more light years away.

In year 3 point “b” is observed as being 2 ly away but is 4 ly away.

In year 7 point “b” would be observed as being 4 years away. But in Year 7, the point “b” would actually be 8 ly away.

Based on this, how do we know age of universe is 13B+ light years and observable universe radius is 46B+ light years?

Since we are only at 13B years old, how does the light reach us from 46B light years away?

Also, since we haven’t been observing the process from beginning how do we know if a star was moving away from us at x light years per year or w/e? Things can change directions in those billions of years as galaxies merge or w/e, right?

In: Physics
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The light doesn’t reach us from 46B light years away. What we are seeing is the light from close to year 0 in your example which was emitted ~13B years ago, but we know that the objects which emitted that light are currently 46B light years away so we can say that the observable universe is 46B light years across

It’s precisely because the universe is expanding, and it’s expanding faster than light. Everyone knows that nothing can travel faster than light, and it’s a common but incorrect assumption that this applies to space as well, but it doesn’t. Things in space can’t move faster than light, but space itself can and in fact is expanding faster than the speed of light. We can see this because the farther an object is from us, the faster it is receding, and at a point we call the Hubble radius, things are receding from us faster than light because space itself is expanding faster than light.

In a static universe, if light emitted 13.8 billion years ago just reached us now, that would mean that object emitted that light when it was 13.8 billion light years away and it is still 13.8 billion light years away. But we know the the universe is not static, and is in fact expanding faster the farther away from us you go. That means the object that was 13.8 billion light years away when it emitted that light is now much farther away than that. If we plot the distance vs velocity of these objects, we see that the most distant possible object that could emit light that we are now seeing is roughly 46.6 billion light years away, which is the radius of the observable universe. In other words, the sphere in light emitted from objects has had enough time to reach us.

So the distance we measure isn’t actually the distance right now between the star and us. It’s the distance the light took to reach us. That’s what we can measure.

So I’ll take the Galaxy GN-z11 as an example. If we measure our distance to that galaxy we get 13.4 billion ly. But the proper distance right now between us and GN-z11 is 32 billion light year. Now the following number are made up, it’s just to explain to you what is happening, but calculating the real numbers is way above my pay grade.

Let say that when the galaxy GN-z11 formed it was 3 billion light year away from where are right now. It started to blast light all around it and some of that light was going straight toward where we are right now. The distance the light HAD to travel to reach us was 3 billion light year. But as the light travelled toward us, space itself expanded and so by the time the light reach us, it actualy had to travel 13.4 billion light year.

At the same time the Galaxy didn’t stay in place. Even if when the light we see today was emitted when the Galaxy was 3 billion light year away from us, it was dragged away from us even more with the expansion of space and so the actual distance between GN-z11 and us is 34 billion light year.

So when the light we see was emitted GN-z11 was mayby 3 billion light years away from us (made up number).

The light had to travel 13.4 billlion light year to reach us (real number). How we know that? Well there is different methods, but one category of method is standard candle. There is even in the universe that emit electromagnetic radiation at specific wavelenght, we call them standard candle. Since space is expanding we know how much redshift happen to radiation. So if we see a shifted spectrum of a standard candle, we can measuer the amount of redshift in the spectrum and with that we can calculate how much distance the light had to travel through the expanding space to get that exact redshift. The goal is to use as much different method to get a convergence of answer and higher certainty in the distance we measured.

And today the distance between us and GN-z11 is 34 billion light year (real number). How we know that? Well we still know how much space expand, it’s a constant rate. We know the expansion right, we know the red shifting and we know the amount of time the galaxy was travelling. Complicated math, but we can estimate where the galaxy should be today.

No no no. You see, we see the oldest light is 13,8 billion years old. The CMB. How far its coming form is a different question since space have expended since the formation of the CMB we can calculate how far it is. Thats the 46 billion light years. The light can reach us no problem but we see the past when we look super far. See a galaxy 36 billion light years away, the light you see was emailed when it was a lot closer. So you see how the galaxy looked like but since space expanded we know that it’s in fact 36 billion light years away.