[Bored chemist]

Therefore, I wonder how it could be that our scientists claim that the expansion in space could increase the light from a far end galaxy.

Because they understand that "brightness" is different from "size".

More photons reaching the detector is a brighter image, not a bigger one.

Therefore, less photons get to our detector.

OK, ask a photographer what happens to the brightness of an image when you magnify the image by using a longer lens (of the same diameter) .

Brighter images mean smaller images.

So, you simply don't understand what is a really simple idea.

Get a piece of rubber sheeting, draw a picture of a galaxy on it.
Stretch the rubber sheet.
The picture gets bigger.

How do you not understand that?

[Kryptid]

It is very clear to me that you fully support the BBT and protect whatever our scientists claim.

The Big Bang theory seems to be the best thing we have at the moment. It may still have flaws (although not any that you've pointed out. Your arguments are all based on straw-men), and it's always possible that a better theory will be developed in the future.

Therefore, I wonder how it could be that our scientists claim that the expansion in space could increase the light from a far end galaxy.

Bored Chemist explained it. You have, once again, straw-manned the argument.

[Bored chemist]

It is very clear to me that you fully support the BBT and protect whatever our scientists claim.

There's nothing special about Kryptis or me.
It's not us supporting the BBT.
We couldn't do that.

The evidence, on the other hand, can, and does, support it.

You need to recognise that it isn't the people posting here that you disagree with.
You are picking an argument with reality.

There's only one way that ends.

[Dave Lev (OP)]

Get a piece of rubber sheeting, draw a picture of a galaxy on it.
Stretch the rubber sheet.
The picture gets bigger.

Thanks for your excellent example.
So, we have a picture of a galaxy on a rubber sheet (or universe).
We have already found that the size of the universe after the inflation was 10,000Ly
After 13 BY the observable universe had been expanded to 96 BLY.
Therefore, based on the idea a rubber sheet, a picture of the 10,000 Ly of the whole early universe had been stretched after 13BY to much bigger picture at a size of 96BLY.
Based on this key understanding, let's go back to the picture of a far end galaxy at a size of 10,000Ly which is located at a distance of 13BLY away.
Let's assume that there is a galaxy at the size of 10,000 Ly at a distance of 13 BLY.
Let's also assume that based on the size of our light detector on earth (without the expansion impact) we should detect 10,000 photons from this far end galaxy.
However, due to the expansion, it is clear that the picture of this galaxy (on a rubber universe) should stretch significantly.

Just to understand the impact of the expansion on the rubber sheet.
We start with a picture of a galaxy at a radius of 10,000Ly and we end after 13 BY at much bigger picture at a size of 96BLY
The ratio is : 10 to 96 * 10^6, or 1 : 9,600,000
If we want to make it easy we can assume that the ratio is:
1: 10,000,000
So, the picture of the far away galaxy gets bigger by 10,000,000 times due to the stretch of the expansion in space.

However, the size of our detector is fixed.
Therefore, as the picture of the galaxy gets bigger, less photons gets to our light detector.

Remember the following message:
Let's also assume that based on the size of our light detector on earth (without the expansion impact) we should detect 10,000 photons from this far end galaxy.
Now due to the expansion in the picture of the far end galaxy, we get in our detector only one photon instead of 10,000,000
Therefore, with this ration, we should get 0.001 photon from the far end galaxy (instead of 10,000 photons without the expansion)
Therefore, it is clearly that we can't detect this galaxy at all.

Conclusions -
As the picture of the far end galaxy gets bigger due to the expansion in space, less photons gets to our limited size detector in the Earth. Therefore, after a stretch of almost 10,000,000 times, we shouldn't detect any photon of light from a far end galaxy.
However, as we clearly see so many galaxies from the far end universe, it proves that there is no expansion in space!!!

[Kryptid]

Let's also assume that based on the size of our light detector on earth (without the expansion impact) we should detect 10,000 photons from this far end galaxy.

Very, very bad assumption. You really are hopeless.

[Bored chemist]

Remember the following message:
Let's also assume that based on the size of our light detector on earth (without the expansion impact) we should detect 10,000 photons from this far end galaxy.
Now due to the expansion in the picture of the far end galaxy, we get in our detector only one photon instead of 10,000,000
Therefore, with this ration, we should get 0.001 photon from the far end galaxy (instead of 10,000 photons without the expansion)
Therefore, it is clearly that we can't detect this galaxy at all.

You have just worked out why we need big telescopes and long exposures to take these pictures.
That's OK, we have big telescopes and take long exposures.

Why do you see this as a problem?

[Dave Lev (OP)]

You have just worked out why we need big telescopes and long exposures to take these pictures.
That's OK, we have big telescopes and take long exposures.
Why do you see this as a problem?

It isn't an issue of the size of the telescopes or the exposure time.
We can use any telescope that we wish.
However, the expansion in space should decrease the detected intensity of light from any far away galaxy.

The explanation is as follow:
https://www.answers.com/Q/Why_does_the_intensity_decrease_with_the_square_of_the_distance_from_a_point_source
Why does the intensity decrease with the square of the distance from a point source?
Intensity of light is defined as energy per unit area. As we move away from the light point source, the area over which the energy of light distributes is generally spherical or hemispherical. The area of a sphere or hemisphere increases proportional to the square of radius, where the radius in this case is the distance from the point source. Thus Intensity of light, which is inversely proportional to area, decreases with the square of distance.
Now, with regards to the expansion in space –
https://en.wikipedia.org/wiki/Expansion_of_the_universe
 "The expansion of the universe is the increase in distance between any two given gravitationally unbound parts of the observable universe with time"
Therefore, due to the expansion in space, it should take longer time for the light to get to our telescope or light detector.
That increasing time is equal to increasing distance or radius.
If we eliminate the impact of the expansion in space, it is clear that a galaxy that is located at a distance/radius of 1 BLY should take exactly 1By to get to our light detector.
However, due to the expansion it should take it significantly longer time.
Longer time (at the speed of light) means longer radius.
So, the expansion in space is actually increasing the radius over time due to the expansion process.
We already know that the intensity of light, which is inversely proportional to area, decreases with the square of distance/radius.
In other words, the expansion in space is increasing the radius over time and in the same token it is also decreasing the intensity of light from a far away galaxy.
Therefore, how could you both support a theory which fully contradicts clear science law???

[Bored chemist]

However, the expansion in space should decrease the detected intensity of light from any far away galaxy.

Nobody cares about the intensity.
That is not what defines the size of something.

Does your house get  smaller when it's only lit by the moon?

If the source isn't bright enough to see properly then, as I said, you can use a bigger telescope, or a longer exposure time.

[Dave Lev (OP)]

Nobody cares about the intensity.
That is not what defines the size of something.
Does your house get  smaller when it's only lit by the moon?
If the source isn't bright enough to see properly then, as I said, you can use a bigger telescope, or a longer exposure time.

The article actually confirms my understanding:
It is stated:
https://www.forbes.com/sites/startswithabang/2019/12/07/ask-ethan-do-ancient-galaxies-get-magnified-by-the-expanding-universe/#586dda7cb5fc
If we had an expanding Universe with nothing but matter in it, the angular scale would get progressively smaller in a quantitatively different fashion, but the farther away you looked, the same-sized object would always look smaller than a closer version of the same object."
So, they clearly claim that in an expanding Universe with nothing but matter in it, the same-sized object would always look smaller than a closer version of the same object."
In all my explanations I have only focused on a Universe with nothing but matter in it.
However, they also add the following:
But what we actually have is a Universe filled with dark energy, the angular scale does something very different. The farther away you look, the same-sized object looks smaller and smaller, but only to a point. Beyond that point, that object will actually start to look bigger again."
So, it is not the expansion in space activity that makes a further away galaxy to look as a bigger sized one, but it is due to the dark energy that is responsible for that activity.
I hope that we all agree with that!!!
If so, you all have to accept the idea that the expansion in space doesn't contribute any impact on the size of the far end galaxy
It is all about dark energy.
Now we need to understand how the dark energy works.
In this article they don't offer any indication how the dark energy increases the image of a far away galaxy.
Actually, the only relevant information about the dark energy is as follow:
"In the Universe we actually have — which is composed of 68% dark energy, 27% dark matter, 5% normal matter and about 0.01% radiation — you can determine that objects will appear smaller the farther away they get, but then the physics of the expanding Universe magnifies them once again the farther away you look."
However, they don't give any explanation how the dark matter really works in order to make a far end galaxy to looks bigger.
At the end they come back again to the expansion Universe:
"Even without gravitational lensing, the expanding Universe alone makes ultra-distant galaxies appear larger to our eyes."

Conclusions:
There is a severe contradiction in this article.
In one hand it is stated clearly that the expansion in space by itself in a Universe with only real matter won't be able to increase the image of a far end galaxy.
Then it is stated that only the dark matter can do it, while they don't offer any real explanation for that assumption.
At the end they come back to the idea of universe expansion.

Sorry - as they didn't offer any explanation about the impact of the dark energy, than this article is actually none relevant!!!

[Bored chemist]

So, it is not the expansion in space activity that makes a further away galaxy to look as a bigger sized one, but it is due to the dark energy that is responsible for that activity.
I hope that we all agree with that!!!

I don't know  if you agree with it.
Do you understand that what the dark energy does is make the rate of expansion variable?
(That wouldn't happen in a universe with just matter in it)
In doing so it creates a universe where more expansion (in early epochs makes) the apparent size of things dependent on distance.
Do you understand that?
More distant things are older, so the images of them have had more time for the space to be stretched. So they are stretched out more, so they look bigger.
Do you understand that?

What you have said is analogous to "it's not acceleration that makes a car go faster, it's the engine".
Well, yes and no. But it shows that you don't  understand how it works.

[Dave Lev (OP)]

Do you understand that what the dark energy does is make the rate of expansion variable?

Is there a possibility for expansion without dark energy?

However, what do you understand from the following statement?

https://www.forbes.com/sites/startswithabang/2019/12/07/ask-ethan-do-ancient-galaxies-get-magnified-by-the-expanding-universe/#586dda7cb5fc
If we had an expanding Universe with nothing but matter in it, the angular scale would get progressively smaller in a quantitatively different fashion, but the farther away you looked, the same-sized object would always look smaller than a closer version of the same object."

Do you agree that:

they clearly claim that in an expanding Universe with nothing but matter in it, the same-sized object would always look smaller than a closer version of the same object."

I really don't understand the logic.
If "what the dark energy does is make the rate of expansion variable" than why they claim that "in an expanding Universe with nothing but matter in it, the same-sized object would always look smaller than a closer version of the same object."

Does it mean that if the rate of expansion is not variable than the same-sized object would always look smaller than a closer version of the same object?
So, only if rate of expansion is variable we actually observe that the further galaxy looks bigger?
Can you explain/prove how this phenomenon works?

[Bored chemist]

Is there a possibility for expansion without dark energy?

Yes.
"Do you agree that:..."
Yes.

If "what the dark energy does is make the rate of expansion variable" than why they claim that "in an expanding Universe with nothing but matter in it, the same-sized object would always look smaller than a closer version of the same object."

Because a universe with only matter in it is different from a universe with matter and also dark energy.

Like a pizza with cheese and ham is different from a pizza with only cheese.

I really don't understand the logic.

You just told everyone that you are not clever enough to work in a fast food joint.
You previously implied you were an engineer.
I know which I believe.

[Dave Lev (OP)]

Quote from: Dave Lev on Yesterday at 19:11:45
Is there a possibility for expansion without dark energy?

Yes.

Thanks
So, with or without dark energy there will be expansion in space.

However, based on the following statement:
"If we had an expanding Universe with nothing but matter in it, the angular scale would get progressively smaller in a quantitatively different fashion, but the farther away you looked, the same-sized object would always look smaller than a closer version of the same object."

It is clear that in an expanding Universe with nothing but matter in it, the farther away you look, the same-sized object would always look smaller than a closer version of the same object."

Because a universe with only matter in it is different from a universe with matter and also dark energy.
Like a pizza with cheese and ham is different from a pizza with only cheese.

So please, try to explain this difference:
Why in a universe with dark energy it s expected that - the farther away you looked, the same-sized object would look bigger than a closer version of the same object", while in a universe with the same expansion in space but without dark Energy, the farther away you looked, the same-sized object would always look smaller than a closer version of the same object."

[Bored chemist]

Why in a universe with dark energy it s expected that - the farther away you looked, the same-sized object would look bigger than a closer version of the same object"

So please, try to explain this difference:

Again?
OK.

More distant things are older, so the images of them have had more time for the space to be stretched. So they are stretched out more, so they look bigger.
Do you understand that?

[Dave Lev (OP)]

Thanks Halc

You claim that:

All dark energy does is make those dotted worldlines curved.  They'd be straight without dark energy. You'll notice that the curvature of those lines make almost no difference. The dark energy causes an event horizon to form (not in this picture, but I have others) that would not exist with inertial expansion.

However, in the following article the dark energy is a key element as stated:

https://www.forbes.com/sites/startswithabang/2019/12/07/ask-ethan-do-ancient-galaxies-get-magnified-by-the-expanding-universe/#586dda7cb5fc
If we had an expanding Universe with nothing but matter in it, the angular scale would get progressively smaller in a quantitatively different fashion, but the farther away you looked, the same-sized object would always look smaller than a closer version of the same object."
So, they clearly claim that in an expanding Universe with nothing but matter in it, the same-sized object would always look smaller than a closer version of the same object."
In all my explanations I have only focused on a Universe with nothing but matter in it.
However, they also add the following:
But what we actually have is a Universe filled with dark energy; the angular scale does something very different. The farther away you look, the same-sized object looks smaller and smaller, but only to a point. Beyond that point, that object will actually start to look bigger again."
So, it is not the expansion in space activity that makes a further away galaxy to look as a bigger sized one, but it is due to the dark energy that is responsible for that activity.

So can you please explain the contradiction?
They clearly claim that without dark energy - "in an expanding Universe with nothing but matter in it, the same-sized object would always look smaller than a closer version of the same object."
Therefore, why they insist that the dark energy is mandatory requested in order to make a further away galaxy to look as a bigger sized one, while you claim that the impact of the dark energy is quite neglected and we should also get the same impact even without the dark energy.

So, do you claim that there is an error in this article?

[Halc]

So, they clearly claim that in an expanding Universe with nothing but matter in it, the same-sized object would always look smaller than a closer version of the same object.

I'm not claiming anything different. I notice you cut away the part where I stated that things look bigger because they were closer, and left the part about how dark energy causes those worldlines to curve differently (not 'straight' as originally posted) in Earth's frame.
Things that were nearby look bigger (wider angle) than similar size objects that were further away. If Ethan is claiming that this isn't true with dark energy present, then I might have issues, but I don't see your quoted bit saying that. I mean, an apple held 20 cm from my fact appears larger than one at arms length.  If Ethan claims that the latter apple should look larger because there is dark energy, then he's just wrong. I don't see him claiming this.

But what we actually have is a Universe filled with dark energy; the angular scale does something very different. The farther away you look, the same-sized object looks smaller and smaller, but only to a point. Beyond that point, that object will actually start to look bigger again."

My post said that if it appears bigger, we're seeing something when it was closer, not further away. I don't see Ethan claiming otherwise. I see him claiming that the further you look in time (not in space), there's a point after which older objects were actually closer and thus appear larger. This is entirely consistent with my post.

Therefore, why they insist that the dark energy is mandatory requested in order to make a further away galaxy to look as a bigger sized one

I see no such insistence in what you quoted. Ethan says something about a universe 'with nothing but matter in it', which, if you read, means without radiation and dark energy'. Without radiation, galaxies would not 'appear' as anything since there would be no light, so Ethan is technically wrong in how galaxies would 'appear' with nothing but matter.
Anyway, I see no statement that this effect would not be true without dark energy, although he says the dark energy case makes the scaling 'very different', so I agree the hint is there. This seems to be self inconsistency since in his pictures just above that statement, every case has the universe smaller in the far past and thus similar sized objects would occupy a larger field of view.  To quote him:
"the same sized object, billions of years ago, took up a greater proportion of the Universe's scale than the same object does at later times." which is true of each diagram, meaning that really distant things look larger in all four of his cases, not just the accelerating one.

What Ethan says (and means) is that things would scale in a 'quantitatively different manner', meaning we see something different than what we would expect without accelerated expansion, which is how we learned of the acceleration in the first place.  Dark energy is one explanation for this acceleration, and not the only one.

[Dave Lev (OP)]

Thanks Halc

Therefore, why they insist that the dark energy is mandatory requested in order to make a further away galaxy to look as a bigger sized one

I see no such insistence in what you quoted. Ethan says something about a universe 'with nothing but matter in it', which, if you read, means without radiation and dark energy'. Without radiation, galaxies would not 'appear' as anything since there would be no light, so Ethan is technically wrong in how galaxies would 'appear' with nothing but matter.
Anyway, I see no statement that this effect would not be true without dark energy, although he says the dark energy case makes the scaling 'very different', so I agree the hint is there. This seems to be self inconsistency since in his pictures just above that statement, every case has the universe smaller in the far past and thus similar sized objects would occupy a larger field of view.  To quote him:
"the same sized object, billions of years ago, took up a greater proportion of the Universe's scale than the same object does at later times." which is true of each diagram, meaning that really distant things look larger in all four of his cases, not just the accelerating one.

What Ethan says (and means) is that things would scale in a 'quantitatively different manner', meaning we see something different than what we would expect without accelerated expansion, which is how we learned of the acceleration in the first place.  Dark energy is one explanation for this acceleration, and not the only one.

Thanks for the explanation about the dark energy, although in the article they don't say anything about "radiation".

 In any case, I would like to focus on your following explanation:

My post said that if it appears bigger, we're seeing something when it was closer, not further away. I don't see Ethan claiming otherwise. I see him claiming that the further you look in time (not in space), there's a point after which older objects were actually closer and thus appear larger. This is entirely consistent with my post.

Well, I can agree that if a galaxy is closer, (not further away) than it should appear bigger.
However, I still don't understand why if it was closer 13BY ago, but due to the expansion its emitted photons of light had to cross very long distance (13BLY) than it also should appear bigger?
The science law is very clear
https://www.answers.com/Q/Why_does_the_intensity_decrease_with_the_square_of_the_distance_from_a_point_source
Why does the intensity decrease with the square of the distance from a point source?
Intensity of light is defined as energy per unit area. As we move away from the light point source, the area over which the energy of light distributes is generally spherical or hemispherical. The area of a sphere or hemisphere increases proportional to the square of radius, where the radius in this case is the distance from the point source. Thus Intensity of light, which is inversely proportional to area, decreases with the square of distance.

So, we must understand the total distance that the emitted photon of light from that galaxy had to cross over time.
We are focusing on a very further away galaxy in our visible Universe, therefore, the idea that 13BY ago this galaxy was closer won't helpץ

Don't you agree that if the photon of light from this galaxy that 13 BY ago was located next to us, had to cross a distance of 13 BLY than it should appear much smaller today?

In any case, if you wish to show that: "if it appears bigger, we're seeing something when it was closer, not further away.", than you have to show why the photons of light from that far away galaxy (let's assume at a distance of 13BLYaway) should cross shorter distance (let's assume from a galaxy at a distance of only 10BLY away) due to the expansion in space and dark energy.

With regards to the space - time diagram that you have offered:
This diagram represents only the observable universe of about 46BLY.
However, there is a chance that our real universe is bigger. It might even be infinite.
We have already discussed this issue in the past.
So, don't you agree that the space time diagram for a bigger universe (or even infinite Universe) should be quite different from this diagram?

Actually, I have set a simple calculation which can prove that our real universe should be much bigger that this 46BLY.
We clearly see today a minimal visible universe of 13 BLY.
So, we must be located at a sphere that represents a maximal radius of 46BLY-13BLY = 33BLY in this observable universe.
The chance to be in this 33BLY radius sphere is:
33^3 / 46^3 = 35937 / 97336 = 0.369 or about 1:3
Therefore, if our real universe was only 46BLY, the chance that we could see up to a minimal distance of 13BLY in any direction is 1:3.
That by itself proves that our real universe must be much bigger than this 46BLY
Therefore, the assumption based on that time space diagram might be wrong.

[Bored chemist]

The science law is very clear
https://www.answers.com/Q/Why_does_the_intensity_decrease_with_the_square_of_the_distance_from_a_point_source
Why does the intensity decrease with the square of the distance from a point source?
Intensity of light is defined as energy per unit area. As we move away from the light point source, the area over which the energy of light distributes is generally spherical or hemispherical. The area of a sphere or hemisphere increases proportional to the square of radius, where the radius in this case is the distance from the point source. Thus Intensity of light, which is inversely proportional to area, decreases with the square of distance.

Like many "laws" in physics, it isn't universally true.
For example, light travelling down a fibre optic cable does not follow the inverse square law.

Because we know the inverse square law doesn't always work, there's no way to use it to say that some other observation is impossible.

[Halc]

Thanks for the explanation about the dark energy, although in the article they don't say anything about "radiation".

The article talked about a universe consisting of only matter, different from the actual list:

But if your Universe is evolving in shape and size over time — which our expanding Universe consisting of radiation, matter, and dark energy most definitely is — you have to take that into account as well.

In any case, I would like to focus on your following explanation:

Then focus on it, instead of going off on a different track.

Well, I can agree that if a galaxy is closer, (not further away) than it should appear bigger.

Good.  That was the gist of my explanation.

However, I still don't understand why if it was closer 13BY ago, but due to the expansion its emitted photons of light had to cross very long distance (13BLY) than it also should appear bigger?

The distance the light travels is pretty meaningless without an exact specification of how that distance is measured.  Point is, that light was emitted from fairly close by, and the apparent size of the object can be directly computed from that without consideration of how much time it takes.  When I compute the apparent size (in arseconds) of the moon, I don't need to worry about how long light takes to make the trip or if the moon has moved somewhere else while the light was getting here.  It is simple trigonometry.

The science law is very clear
https://www.answers.com/Q/Why_does_the_intensity_decrease_with_the_square_of_the_distance_from_a_point_source
Why does the intensity decrease with the square of the distance from a point source?

Here you go completely off topic.  I said nothing about intensity, and as B-C points out, you quote a law that is not universally true.  It is in fact a Newtonian law that assumes locality and fixed (not receding) light sources. Neither condition is met in this instance, and general relativity must be invoked to do an intensity calculation for this scenario.

Intensity of light is defined as energy per unit area.

Oops. You don't even know what it is. Anyway, off topic, so it doesn't matter.

So, we must understand the total distance that the emitted photon of light from that galaxy had to cross over time.

It is very dependent on how that distance is measured, so there's no meaningful answer to this without that definition.  I defined the distance between here and where the light was emitted as proper distance in the comoving coordinate system (scaled for normal distance and time) as per my linked graph in post 396.  The distance is marked off at the bottom of the chart.  Where (or how long) the light traveled between here and there is irrelevant to the apparent size of the galaxy since the apparent size is not a function of either of those things, and where that galaxy is 'now' is also irrelevant since I'm not looking at light from where it is now, and yet it is on this that you choose to focus, having this naive intuition that we see things where they are now because that is a good approximation when you're looking at a tree.

Don't you agree that if the photon of light from this galaxy that 13 BY ago was located next to us, had to cross a distance of 13 BLY than it should appear much smaller today?

You ignore the logic that shows this to result in a contradiction.

With regards to the space - time diagram that you have offered:
This diagram represents only the observable universe of about 46BLY.

No. The red line represents everything that can currently be observed, but the 'observable universe' isn't defined as 'all events that we can currently see', but instead more like 'all events that are on comoving worldlines that include any events that can ever have had a causal effect on us today', and some events in that diagram are not part of that set, and a great deal that are in that set are not in the diagram.  The proper distance scale of that picture only goes out to 10 BLY, and the radius of the observable universe is about 4.6 times that distance.  The diagram does show the boundary of the observable universe on the lower left, labelled 'today's horizon', not to be confused with the event horizon which is not depicted in that picture.

So, don't you agree that the space time diagram for a bigger universe (or even infinite Universe) should be quite different from this diagram?

It can be extended to the sides as far as you like, which thus can include all the the observable universe and beyond. There's no edge to it.  I posted wider (extended upward as well) pictures in other threads, which include items like the event horizon not depicted in my recent post.

[Dave Lev (OP)]

So, we must understand the total distance that the emitted photon of light from that galaxy had to cross over time.

It is very dependent on how that distance is measured, so there's no meaningful answer to this without that definition.  I defined the distance between here and where the light was emitted as proper distance in the comoving coordinate system (scaled for normal distance and time) as per my linked graph in post 396.  The distance is marked off at the bottom of the chart.  Where (or how long) the light traveled between here and there is irrelevant to the apparent size of the galaxy since the apparent size is not a function of either of those things, and where that galaxy is 'now' is also irrelevant since I'm not looking at light from where it is now, and yet it is on this that you choose to focus, having this naive intuition that we see things where they are now because that is a good approximation when you're looking at a tree.

Let's take real example about the Farthest Known Galaxy in the Universe Discovered:
https://www.space.com/18502-farthest-galaxy-discovery-hubble-photos.html
"The new record holder is the galaxy MACS0647-JD, which is about 13.3 billion light-years away. The universe itself is only 13.7 billion years old, so this galaxy's light has been traveling toward us for almost the whole history of space and time."
The galaxy is about 13.3 billion light-years from Earth, the farthest galaxy yet known, and formed 420 million years after the Big Bang."

If we look to the other direction, we might see other galaxy at a similar distance.
So, in one side we see a galaxy (let's call it galaxy A) at a distance of 13.3 BLY, while on the other side there is other galaxy (galaxy B) at a similar distance from us.
Therefore, we can assume that the distance between galaxy A to galaxy B could be 26.6 BLY.
 
Now, let's verify if I understand correctly the BBT and the expansion process:
The Big Bang took place about 13.7 BY ago.
We all know that the size of the whole Universe after the inflation was only 10,000 LY.
We also know that it took almost 380 Million years for the atoms to be formed after the Big bang.
Somehow, 420 Millions after the BB (Or only 40 Millions years after the formation of the atoms in the universe), this far away galaxy had already been created.
At that time all the Matter/galaxies in the Universe were located next to each others.
Do we have any idea what was the size of the whole universe at that time?

Actually, at the end of the inflation process the size of the Universe was 10,000 Ly.
So, if we assume that in this time, the size had been increase by 10 times, than the size should be 100,000 MLY.

Let's assume that the Milky Way was there at a distance of 50,000LY away from galaxy A (420 Million years after the BB).
If I understand you correctly, that distance represents the proper distance.

I defined the distance between here and where the light was emitted as proper distance in the comoving coordinate system (scaled for normal distance and time) as per my linked graph in post 396.

We clearly know that the light travels at the speed of light. (With or without the impact of the expansion)
Due to the compact size of the early Universe (at the age of 420 MY) it is clear that the impact of the expansion rate at this compact early universe is quite neglected. (74 Km//s per 3MLY).
Therefore, the light from galaxy A  should cross a distance of 50,000LY in about 50,000 Year.
So, why it took the light from galaxy A so long time (13.3BY) to get to the Milky Way?
Can you please explain how the proper/commoving distance velocity could force the light to travel 13.3 BLY in order to cross a proper distance of only 50,000 Ly while the impact of expansion rate on the early universe is so low?

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Don't you agree that if the photon of light from this galaxy that 13 BY ago was located next to us, had to cross a distance of 13 BLY than it should appear much smaller today?

You ignore the logic that shows this to result in a contradiction.

I really don't understand the logic in your message.

However, I still don't understand why if it was closer 13BY ago, but due to the expansion its emitted photons of light had to cross very long distance (13BLY) than it also should appear bigger?

The distance the light travels is pretty meaningless without an exact specification of how that distance is measured.  Point is, that light was emitted from fairly close by, and the apparent size of the object can be directly computed from that without consideration of how much time it takes.  When I compute the apparent size (in arseconds) of the moon, I don't need to worry about how long light takes to make the trip or if the moon has moved somewhere else while the light was getting here.  It is simple trigonometry.

OK
Let's try to understand:

Point is, that light was emitted from fairly close by

So the light was emitted from a distance of 50,000LY (that was the distance between the Milky way to galaxy A when the universe was 420My old). Proper distance. This is very clear.

and the apparent size of the object can be directly computed from that without consideration of how much time it takes.

Why is it? This is totally unclear to me.
I still don't understand why the proper distance can set any sort of impact?
From our point of view we see a galaxy at a distance of 13.3 BLY that its light had traveled for 13.3 BY to get to our earth. With or without the expansion, the total distance is fixed and the total time is fixed.

When I compute the apparent size (in arseconds) of the moon, I don't need to worry about how long light takes to make the trip or if the moon has moved somewhere else while the light was getting here.  It is simple trigonometry.

Let me use your example about the moon:
It should take the moon light about 1.5 sec to get to earth.
Let's assume that somehow we can use the expansion process to move the moon away from us so fast that the next time that we get its light is after it gets to a distance of 1LY away and 1Y from now.
So, do you consider that at that moment that we see again the moon, we should see it at the same shape as we see it today?
There is no fiber optics in the open space.
If a light travels in space for 13.3 BY and cross 13.3 BLY, why it can't work according to the square law?