[Bored chemist]

There is no fiber optics in the open space.

Why did you say that?
It's not as if anyone had said that there was.

[Halc]

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

Get with the program Dave. That's 8 year old news.  GN-z11 is further than that one.

"The new record holder is the galaxy MACS0647-JD, which is about 13.3 billion light-years away."

Cute. They're measuring distance using 'light travel distance' which is a practically useless value for any purpose except perhaps obfuscation, which is of course why you're selected this article. Funny how the visible universe is said to be about 90 BLY in diameter despite this being about the furthest object. Well, it turns out the 90 BLY distance is a statement of current proper distance, not light travel distance.
Here's a link concerning why light-travel distance shouldn't be used:
http://www.astro.ucla.edu/~wright/Dltt_is_Dumb.html

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.

Using light travel distance, yes.
 

We all know that the size of the whole Universe after the inflation was only 10,000 LY.

Reference please. I'm not buying that one.

We also know that it took almost 380 Million years for the atoms to be formed after the Big bang.

Off by 3 orders of magnitude. Get your facts straight.

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 made no mention of galaxy A, but divide the two figures and you get gA increasing its proper distance from us at a pace of 0.00012c. Galaxy A, holding that pace (which it wouldn't due to the mutual attraction between us and them), would be closer than Andromeda today, and due to attraction, would in fact have resulted in the merger of us and them by now.

We clearly know that the light travels at the speed of light. (With or without the impact of the expansion)

Clearly not.  It gets to the moon and is reflected back in less time than the distance traveled divided by c.  Light moves locally at the speed of light. The moon is not local.
Again, as B-C points out, don't use laws that are not universally true in situations where that law does not apply.

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.

Galaxy A is so close by that the difference in the way it is measured is the same to 4 digits, so that's almost true.

So, why it took the light from galaxy A so long time (13.3BY) to get to the Milky Way?

It didn't.  Galaxy A is already part of 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

It doesn't.  It took close to 50000 years, assuming it is meaningful for two things to be 50 KLY apart when at least one of them is (currently) twice that size.

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?

Error: Equivocation of light travel distance with proper distance.

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.

Your numbers, not mine.  Assuming these are point objects, the light would have arrived at the Milky Way at year ~420,050,001, which is long ago, which is why we can't see that emitted light today.
Perhaps your example could be real one like MACS0647-JD which was much further away than 50,000 LY at age 420 MY.  More like 3 billion LY away, according to the limited resolution of my picture. That event is on our current light cone. Your Galaxy A is not.

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.

Again, simple geometry. Consider several such round objects arranged in a ring so their edges touch, and at that distance, and compute the angle that they would appear from the center of that ring. That angle cannot change over time. Expansion of space does not add new degrees to the 360 that make up a circle.
Think about it instead of just dismissing it because you already know a different answer.
Suppose there are 19 circular objects of size about 1 BLY diameter, each 3 BLY distant, with edges touching.  How large would they appear (in degrees?).  It's not hard.

I still don't understand why the proper distance can set any sort of impact?

And yet you go on making assertions about things about which you admit your understanding is lacking.

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.

The apparent size of something is in no way a function of its light travel distance. I told you the figure was meaningless for anything useful.

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.

You make it sound like the moon blinks off, and then on again when it's completely somewhere else.
Your numbers are unreasonable.  If expansion is that severe, the universe would be 1.5 seconds old, and there would be nothing to see at all.

[Dave Lev (OP)]

Here's a link concerning why light-travel distance shouldn't be used:
http://www.astro.ucla.edu/~wright/Dltt_is_Dumb.html

In this article it is stated:
" This has one simple property: the distance in light years is never greater than the age of the Universe in years, avoiding at least one appearance of speeds greater than the speed of light."
However, you have just confirmed that the distance between two galaxies based on light travel distance is 26.6 BLY:

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.

Using light travel distance, yes.

In one hand our scientists claim:
"The redshift z is usually the only number in the whole story that is unambiguous and likely to be correct."
So, if there is something that is correct by 100% - it is the redshift.
They even add that we can easily calculate the distance from a shift in a sound:
"If an SR-71 blackbird flies over at Mach 3 and you hear the sound 30 seconds later, then answer to the question "How far away is it?" is clearly not 30 "sound seconds" or 10 km."
They also add
"he Universe is homogeneous and isotropic, so it has no edge. Thus there cannot be a maximum distance."
Therefore, without an edge and in order to meet the requirement to homogeneous and isotropic it actually must be infinite or at least very, very big. Much bigger than that 92BLY.
At that big size it is clear that galaxies could move away from each other faster than the speed of light.
They actually confirm it by the following:
"Distances greater than speed of light times the age of the Universe are commonplace."
However, they add the following: "But a uniform grid in the Universe shown at left below is very non-uniform when plotted using the light travel time distance, as shown at right below"
So, their main problem is how they fit all of it in a Universe with a limited age of only 13.8 BY.
Why is it so impossible mission for our scientists to assume that the universe could be older than 13.8BLY?
How could they ignore the real meaning of redshift while they clearly claim that: "The redshift z is usually the only number in the whole story that is unambiguous and likely to be correct."
If they claim that redshift is the only number that is really correct, than this Number should be used for Travel Time Distance!!!
If there is a contradiction between the BBT to the redshift, than the redshift must win.
The BBT must explain the redshift and not the other way.
If based on the redshift "the distance in light years is greater than the age of the Universe in years" than something must be wrong with the BBT.
Our scientists don't have to fix the redshift. They have to fix the BBT!!!
In the article it is even stated that by using the redshift for light travel time distance we get disagrees with the Hubble law:
"The Hubble law is satisfied exactly for "distance now", or metric radial distance. In fact the Hubble law with time variable Hubble parameter is satisfied exactly at all times by the metric radial distance D(t) which is the spatial separation at the common time t, so
"velocity" = dD/dt = H(t)D(t).
This is not true for the light travel time distance. The rate of change of the light travel time distance with observation time is always
dDltt/dt = cz/(1+z)
which generally disagrees with the Hubble law as shown below:
Hence, if it generally disagrees with the Hubble law than they have to understand that there is a problem with Hubble law (not with the redshift!!!)
As the redshift is 100% correct, than we have to offer a valid theory that fully meets our clear observation about the redshift.

As we discuss about a redsfit, I also see other sever contradiction between the redshift and the BBT:
Based on this article we can calculate the light travel time based on the redshift
http://www.astro.ucla.edu/~wright/CosmoCalc.html
So, if the redshift is 6 than:
The age at redshift z was 0.942 Gyr.
The light travel time was 12.779 Gyr.
If the redshift is 12
The age at redshift z was 0.372 Gyr.
The light travel time was 13.349 Gyr.
So, we can claim that we see the light from two galaxies at the early Universe.
One at the age of 0.942 Gyr while the other at the age of 0.372 Gyr.
Based on the BBT, at that time the universe was quite compact and small.
Therefore, those galaxies were located quite nearby.
However, the difference in their redshift is 12-6 =6.
So, two nearby galaxies in the early universe have already so severe difference in their redshift.
However, based on this calculation we know that the meaning of redshift 6 is:
The light travel time was 12.779 Gyr.
Therefore, if about 13BLY we could stand in one galaxy and monitor the redshift from the other nearby galaxy, we could find that we get a redshift of 6 which equivalent to light travel time of 12.779 Gyr.
So, how could it be that in a maximal early universe age of only one billion years, we could have a light travel time of 12.779 Gyr between two nearby galaxies?

We all know that the size of the whole Universe after the inflation was only 10,000 LY.

Reference please. I'm not buying that one.

https://www.physicsforums.com/threads/comparable-size-of-the-observable-universe-immediately-after-inflation.731775/
"It is very difficult to quantify the size of the observable universe after inflation ended. We do not know how 'big' it was when inflation started, how rapidly it doubled in size ['inflated'], or how long the inflationary period persisted. Estimates of size after inflation vary wildly. Alan Guth guestimated it was around the size of a marble. Lineweaver estimates the universe grew by a factor of ~10E30 during inflation - re: http://arxiv.org/abs/astro-ph/0305179v1. By that standard, if you assume the observable universe was a planck length prior to inflation, you end up with a size of about 1.6E-05 meters after inflation. If you assume it was the size of a proton, you get a universe of about 1.6E15 meters, or around 1/10 the size of our galaxy. "
So, 1/10 of the milky way is about 10,000LY

Perhaps your example could be real one like MACS0647-JD which was much further away than 50,000 LY at age 420 MY.  More like 3 billion LY away, according to the limited resolution of my picture. That event is on our current light cone.

You claim that the size of the universe at age 420MY should be 3BLY.
How the expansion process (based on the expansion rate of 74Km/s per 3MLY) could increase the size of the Universe from 10KLY into 3BLY in only 420MY?
Actually, if we increase the early universe at the speed of light, it should get to about 420MLY.
Therefore, in total we need to increase its size at 10 times the speed of light in order to get a 3BLY universe after 420MY.
Is it real?
What about the momentum?
If due to the expansion/inflation we get that kind of size increasing (10 times the speed of light), why it suddenly slow down?
What kind of force slows down that ultra high expansion/inflation rate? Why the Momentum law couldn't keep that rate?
Theoretically, if something is moving away from us faster than the speed of light, while the momentum law is very clear, than how can we ever see again its light?
Actually, if due to the expansion+ inflation any matter/star/galaxy is moving away from us faster that the speed of light, than we shouldn't see it again - never and ever.
So, how could it be that we see those far away galaxies at a distance of 13.3BLY while we surly know that in order to get to this distance, somehow they must move away from us (during the process of the Inflation/expansion) faster than the speed of light.
 

You make it sound like the moon blinks off, and then on again when it's completely somewhere else.
Your numbers are unreasonable.  If expansion is that severe, the universe would be 1.5 seconds old, and there would be nothing to see at all.

Yes, I fully agree with you.
When I consider the expansion/inflation process, it sounds like the far end galaxy blinks off (420MY after the BB), and then on again when it's completely somewhere else (at 13.3 BLY away).
This numbers are unreasonable.  "If expansion is that severe, the universe would be 1.5 seconds old, and there would be nothing to see at all."
Yes, that exactly what I think about the unreasonable inflation expansion of the early universe.
So, if the story of the early inflation + expansion was correct, we shouldn't see almost no galaxy in the whole universe.

The other issue is the formation of Atoms/Stars/galaxies.
How can we get any sort of star while the expansion rate is so high at the early universe?
How the gravity could work under those ultra high forces.
Do you agree that when the Universe was very compact and very dense, its internal gravity was maximal?
Why the gravity at that time couldn't prevent the expansion + inflation process?
How could it be that the expansion/inflation could overcome the ultra high gravity forces in the early universe?
I see it as we take the sun (for example) and expand its size by one billion times.
By doing so, there will be less matter in a cube and less density.
That by itself reduces dramatically internal gravity forces.
If we do so, how the gravity could work in the Universe after that kind of size increasing due to the inflation+ expansion?

I the expansion + inflation was so strong to overcome the early ultra gravity force, how suddenly when the density had been reduced so dramatically and therefore, the gravity forces had been reduced, that low gravity forces could suddenly take control and do the requested job of forming new stars and new galaxies?

Think about it instead of just dismissing it because you already know a different answer.

I really try to understand how the BBT works. I'm ready to accept any answer.
However, I still see several contradictions in this theory

Don't you think that as "The redshift z is usually the only number in the whole story that is unambiguous and likely to be correct" than we should fix our theories to meet this redshift instead of the other way?

[Dave Lev (OP)]

They also add
http://www.astro.ucla.edu/~wright/Dltt_is_Dumb.html
"The Universe is homogeneous and isotropic, so it has no edge. Thus there cannot be a maximum distance."
Therefore, without an edge and in order to meet the requirement to homogeneous and isotropic it actually must be infinite or at least very, very big. Much bigger than that 92BLY.

I never said otherwise.

Thanks
So you confirm that as our universe has no edge and in order to meet the requirement to homogeneous and isotropic our current Universe must be infinite or at least very, very big. Much bigger than that 92BLY.
That was also correct 13.8 B years ago.
Therefore, even at the early time of our universe it has no edge. Hence in order to meet the requirement of homogeneous and isotropic it has to be infinite or almost infinite at that time.
So, how can you believe in a compact universe in the early time?
How can you set an infinite or almost infinite Universe from a size of 10,000Ly or even 3MLY in only 13.8BLY under the limitation of the expansion rate of 74KM/s per 3MLY???
Do you also agree that if the universe was compact and all the matter/galaxies were located nearby than the early Universe must had an edge and it couldn't considered as homogeneous and isotropic?
"The Friedmann equations are a set of equations in physical cosmology that govern the expansion of space in homogeneous and isotropic models of the universe within the context of general relativity."
https://en.wikipedia.org/wiki/Friedmann_equations

However, if the Universe was compact it couldn't be homogeneous and isotropic at its early life time, therefore those equations are none relevant for our universe.
Without Friedmann_equations, don't you agree that the expansion/ BBT are none relevant any more?

and the apparent size of the object can be directly computed from that without consideration of how much time it takes.
Again, simple geometry. Consider several such round objects arranged in a ring so their edges touch, and at that distance, and compute the angle that they would appear from the center of that ring. That angle cannot change over time. Expansion of space does not add new degrees to the 360 that make up a circle.
Think about it instead of just dismissing it because you already know a different answer.
Suppose there are 19 circular objects of size about 1 BLY diameter, each 3 BLY distant, with edges touching.  How large would they appear (in degrees?).  It's not hard.

If each of those 19 circular objects is at a size of about 1 BLY diameter, and each one is located at a 3 BLY distant, than how can you claim that their edges are touching?
Do you agree that the solar system or the Milky Way isn't located at the center of the Universe?
Therefore, how could you position us at the center of the ring? Actually, we should be considered as just one spot of light in those rings.
I have no problem with your following statement: "Expansion of space does not add new degrees to the 360 that make up a circle."
However, This is correct if we are located exactly at the center of the Universe and the distance to the rings is fixed.
This is clearly not the case.
We aren't located at the center of the Universe, and we clearly monitor the light travel time from the far end galaxies.
That time is very critical.
Somehow, our scientists have decided that light travel time can't represent a distance travel time.
So, based on your example - if we are located at the center of a ring and there is a galaxy at a distance of 1BLY, do you claim that due to the expansion it should take its light 13 BLY to get to our eyes while we should see it as it is at a distance of only 1BLY?
Sorry, based on your 19 Cycles you didn't confirm that idea.
In any case, you also need to show how the image of a galaxy with light travel time of 13 B years could be bigger than the image of a similar galaxy with light travel time of only 10 B years.

[Dave Lev (OP)]

I never said otherwise.

Quote from: Dave Lev on Today at 16:15:32
So you confirm that as our universe has no edge

I never said that either.  I only said we have no evidence of one.

Sorry you/our scientists can't just hold the stick in both sides.
You must take a decision: what is the real size of the UNIVERSE???
Is it 13BLY, 92BLY, 500BLY,  10^10BLY or just infinite???
If you can't tell the size of the universe, than how can you expect us to believe your story?
How can you believe in your own theory?
Before starting any sort of theory - it is our obligation to set the size of the Universe!!!
I'm ready to accept any size, however once you set a size and surprisingly -your theory contradicts this size, than you should set this theory in the garbage.
Any theory should give a clear explanation for the whole real universe.
If our real universe is bigger than the observable Universe, while the BBT can only cover the observable universe, than this theory is none relevant.

We all know that Freidmann formulas are vital for the expansion and for the BBT.
However, those formulas are based on homogenous and isotropic universe.
Therefore, it is stated:
http://www.astro.ucla.edu/~wright/Dltt_is_Dumb.html
"The Universe is homogeneous and isotropic, so it has no edge. Thus there cannot be a maximum distance."
What is the meaning of: "it has no edge"?
What is the meaning of "there cannot be a maximum distance"?
If you like it or not, a Universe without "maximum distance" means - infinite Universe.
Therefore, the ONLY meaning is that the universe MUST be INFINITE. (Almost infinite is actually infinite).
If you think that this is incorrect,  than please explain how a finite Universe that clearly contradicts the meaning of – " so it has no edge. Thus there cannot be a maximum distance",  could still be considered as homogeneous and isotropic universe while its size is increasing during the last 13.8 BY from almost zero to 92BLY, and as we know that our real universe is much bigger than this 92BLY that we call observable Universe.
Do you agree that if the Universe isn't homogeneous and isotropic, than friedmann equation are none relevant and therefore the BBT is none relevant?

Regardless of how long it takes the light to get to us, how big (in radians or degrees) is that 1BLY circular object going to appear?

Sorry.
The light travel time is very critical.
There is no fiber optics in space.
Therefore,  longer moment in space, should negatively effect the image.
Hence, a similar galaxy with longer travel light time should appear smaller.

[Dave Lev (OP)]

I said 3BLY proper distance when the universe was around 0.4 BY old.

So, do you claim that when the universe age was 0.4BY, the size of the Universe was already 3BLY?
That proves that at the early time, when the matter of the whole real universe was located at a compact area (same space time), the expansion should be much faster than the speed of light in order to set a size of 3BLY from virtually zero in only 0.4BY.
That actually contradicts the law of physics that in the same space time nothing could move faster than the speed of light.
So, how can you expand the early universe from almost zero to 3BLY in only 0.4 BY?

[Bored chemist]

There is no fiber optics in space.

And again, nobody ever said there was.
Why waste bandwidth on it?

[Dave Lev (OP)]

Redshift

http://www.astro.ucla.edu/~wright/Dltt_is_Dumb.html
"The redshift z is usually the only number in the whole story that is unambiguous and likely to be correct."

Yes, this is the one empirical observation. Hard to contest it.

As we agree that the redshift is correct, let's try to understand the real meaning of that redshift:
http://astro.wku.edu/astr106/Hubble_intro.html
"Redshift is a term used to describe situations when an astronomical object is observed to being moving away from the observer, such that emission or absorption features in the object's spectum are observed to have shifted toward longer (red) wavelengths."
In this articale they also add the following example:
Absorption lines of hydrogen, normally measured to be at 4861Å and 6563Å, are measured in the spectrum of a particular galaxy to be at 4923Å and 6647Å.
The speed of light, c, has a constant value of 300,000 km/sec.
Therefore this galaxy has a redshift of
z = [(4923 - 4861) / 4861] and z = [(6647 - 6563) / 6563]
z = [62 / 4861] and z = [84 / 6563]
z = 0.01275
and the is moving away from us with a velocity, v = c * z = 300,000 km/sec * 0.01275 = 3826 km/sec

So, based on Redshift our scientists can easily calculate the velocity of any galaxy based on the simple formula that:
v = c * z = 300,000 km/sec * z
Therefore, based on this formula:
When z=1 the galaxy is moving away from us at the speed of light
When z=8 the galaxy is moving away from us at 8 times the speed of light
When z=10 the galaxy is moving away from us at 10 times the speed of light.
However, somehow our scientists have decided that if the redshift is equal or bigger than one, this formula is not relevant.
Why is it?
Why if we see a galaxy with a redshift of 10 we can't just understand that this galaxy is moving away at 10 times the speed of light?

[Bored chemist]

Why if we see a galaxy with a redshift of 10 we can't just understand that this galaxy is moving away at 10 times the speed of light?

Because, no matter how often you ignore the issue, things don't travel faster than light.

[Dave Lev (OP)]

Quote from: Dave Lev on 07/06/2020 17:48:18
So, based on Redshift our scientists can easily calculate the velocity of any galaxy based on the simple formula that:
v = c * z = 300,000 km/sec * z

This formula is based on Newtonian physics, meaning it is a good approximation for an object that is 1) local and 2) not receding at relativistic speed.

Let's look at the following image with regards to  v = cz:
https://en.wikipedia.org/wiki/Hubble%27s_law#/media/File:Velocity-redshift.JPG
"A variety of possible recessional velocity vs. redshift functions including the simple linear relation v = cz; a variety of possible shapes from theories related to general relativity; and a curve that does not permit speeds faster than light in accordance with special relativity. All curves are linear at low redshifts. See Davis and Lineweaver."
We have three possibilities:
1. Linear
2.general relativity
3. Special relativity

With regards to linear:
The relativity principle is called Galilean relativity. It is obeyed by Newtonian mechanics.
https://en.wikipedia.org/wiki/Velocity-addition_formula
The cosmos of Galileo consists of absolute space and time and the addition of velocities corresponds to composition of Galilean transformations. The relativity principle is called Galilean relativity. It is obeyed by Newtonian mechanics.

With regards to special relativity:

Quote from: Dave Lev on 07/06/2020 17:48:18
Why if we see a galaxy with a redshift of 10 we can't just understand that this galaxy is moving away at 10 times the speed of light?

Because, no matter how often you ignore the issue, things don't travel faster than light.

So, you base this assumption on special relativity:
http://www.math.ucr.edu/home/baez/physics/Relativity/SR/velocity.html
Suppose an object A is moving with a velocity v relative to an object B, and B is moving with a velocity u (in the same direction) relative to an object C.  What is the velocity of A relative to C?
In non-relativistic mechanics the velocities are simply added and the answer is that A is moving with a velocity w = u+v relative to C. 

But in special relativity the velocities must be combined using the formula
               u + v
         w =  ---------
              1 + uv/c2
If u and v are both small compared to the speed of light c, then the answer is approximately the same as the non-relativistic theory.  In the limit where u is equal to c (because C is a massless particle moving to the left at the speed of light), the sum gives c.  This confirms that anything going at the speed of light does so in all inertial reference frames.

Let's try to get better understanding on special relativity:
https://en.wikipedia.org/wiki/Velocity-addition_formula
Special relativity
According to the theory of special relativity, the frame of the ship has a different clock rate and distance measure, and the notion of simultaneity in the direction of motion is altered, so the addition law for velocities is changed. This change is not noticeable at low velocities but as the velocity increases towards the speed of light it becomes important. The addition law is also called a composition law for velocities. For collinear motions, the speed of the object (e.g. a cannonball fired horizontally out to sea) as measured from the ship would be measured by someone standing on the shore and watching the whole scene through a telescope as:

                  u + v
         w =  ---------
                1 + uv/c2


So, they specifically discuss on an a velocity which is relative to observer:
""The speed of the object (e.g. a cannonball fired horizontally out to sea) as measured from the ship would be measured by someone standing on the shore and watching the whole scene through a telescope."

Now, let's try to understand the real meaning of Hubble discovery:
https://en.wikipedia.org/wiki/Hubble%27s_law#/media/File:Hubble_constant.JPG
We see almost perfect fit between redshift velocities to distance (Hubble's law).
Hubble assumed that this fit only works locally for low distances (or low velocities) (Z should be lower than 0.1)
So, let's look at the following example:
We are located at point A and observe all the way to the furthest galaxy with redshift 11.
Let's set a direct line between our location and this galaxy (let's call it galaxy M)
However, in this line, next to us, we might find in this line a galaxy (let's call it galaxy B) with a redshift of 0.1.
That galaxy must move away from us at a velocity of:
Vab=cz = c*0.1
However, due to homogenous and isotropic Universe, Hubble law works locally everywhere.
Therefore, if we will stand at B and look at the direction of M we should see other local galaxy (C) that is moving away from us at redshift 0.1
So the relative velocity between B to C is also
V(bc) = c*0.1 = 0.1c
We can continue with this line all the way and see more and more galaxies
V(cd) = 0.1c
V(de) = 0.1c
V(ef) = 0.1c
at each segment the velocity should be increased by c*0.1
Therefore, if we set 20 galaxies in this line, while each one observe the nearby galaxy at a redshift of only 0.1 than the total velocity with regards to our location should be:
V(a- 20th) = 0.1c + 0.1c +.... +0.1c = 20 * 0.1c = 2c
Therefore, a redshift of 2 clearly represents a velocity of 2c.

However, due to special relativity (and many thanks to Einstein) we actually can still observe a galaxy which is moving away twice the speed of light from us.


                  u + v
         w =  ---------
                1 + uv/c2

Wac = (0.1c + 0.1c) / (1+ 0.01/c^2) = 0.2c/(1+ 0.01/c^2)
therefore, due to relativity, Wac should be smaller than just 0.1c +0.1c = 0.2c

We can continue with this calculation till the 20th galaxy and find that the relative velocity between us and that galaxy
is lower than the speed of light although we clearly proved that each local two galaxies must move away from each other at 0.1c.

Therefore, that proves that while the 20th galaxy is moving away from us at twice the speed of light, due to special relativity we can still observe/see this galaxy.

Conclusion:
There is no error in the Redshift
The special relativity or the expansion can't change the redshift of any galaxy.
This redshift tells us the real velocity of that galaxy.
If the redshift of a galaxy is higher than one, it proves that it is moving away faster than the speed of light.
However, due to special relativity we can still see it.

The galaxy I mentioned with redshift of 11 is increasing its present proper distance from us at a rate of a bit more than twice light speed.

Sorry
A redshift of 11 represents a real velocity of 11 times the speed of light.
However, due to special relativity we can still see that galaxy.

[Bored chemist]

A redshift of 11 represents a real velocity of 11 times the speed of light.

no matter how often you ignore the issue, things don't travel faster than light.

[Dave Lev (OP)]

no matter how often you ignore the issue, things don't travel faster than light

No matter how often you ignore the issue, you just can't hold the stick in both sides.

So, please let me know where is the error:

1. Do you confirm the following Hubble Law for redshift velocity/distance ratio?
https://en.wikipedia.org/wiki/Hubble%27s_law#/media/File:Hubble_constant.JPG
If so, please look at the blue line. Do You confirm that at a distance of 15 MPC the redshift velocity is 1,000Km/s?
Let's call this location galaxy B.
2. Do you confirm that our Universe is homogenous and isotropic?
If so, do you confirm that Hubble law must work exactly at the same way from any galaxy in the Universe?
3. Therefore, if we can jump all the way to Galaxy B, and look forward in the same line, at a distance of 15MPC from B we should find galaxy C with a redshift velocity of 1,000Km/s. Hence, do you confirm that galaxy C is moving away from the earth at 2,000Km/s while it is located at a distance of 30MPC?
4. If we will continue to jump in this line again and again, do you confirm that at any neaby galaxies we should find that at a distance of 15MPC we should see a galaxy that is moving away at a redshift velocity of 1000 Km/s?
5. So, do do agree that after 10 Jumps we should get to the 10th galaxy at a distance of 10* 15MPC = 150MPC that should move away from Earth at 10*1000Km/s = 10,000Km/s?
6. Therefore, do you agree that if we jump to the 300th galaxy, that galaxy should be located at a distance of 300* 15MPC = 4500MPC and should move away from Earth at 300*1000Km/s = 300,000Km/s (about the speed of light)?
7. Hence, every segment of 4500MPC represents a redshift that is equal to the speed of light.
4500 MPC = 14677037085.28995 LY = 14.677 BLY
therefore, a galaxy at a distance of 14.677BLY should move away from us at the speed of light. (z=1)
So, any galaxy with a redshift that is higher than 1 must be located at a distance which is higher than the maximal distance of only 13.8 BLY?
7. Do you confirm that a galaxy with a redshift of 10 should be located at a distance of:
10 *  14.677BLY = 146.77 BLY ?

If you don't agree with that, than please explain where is the error, while you still hold Hubble law and homogenous and isotropic universe.

[Bored chemist]

If you don't agree with that, than please explain where is the error,

What?
Again?
OK.
The error is in "3"

a galaxy at a distance of 13 BLY is actually moving away from us almost the speed of light. Due to the idea that the Universe is isotropic and homogenous, a galaxy at 26 BLY should move away at 2c

That's still wrong.
You can't just add relativistic velocities as if they were apples.

[Halc]

no matter how often you ignore the issue, things don't travel faster than light.

You're both wrong.  From https://arxiv.org/pdf/astro-ph/0310808.pdf  Davis, Lieweaver
"Expanding Confusion: Common misconceptions of cosmological horizons
and the superluminal expansion of the universe"
They go on to list four misconceptions about the universe expansion, and then go on to list accepted/published papers/texts that make these misconceptions.

B C, you're making the mistake of modeling the universe using a special relativity model, which assumes flat non-expanding spacetime.

In Section 4 we provide explicit observational tests demonstrating that attempts to apply special relativistic concepts to the Universe are in conflict with observations.
...
3.1 Misconception #1: Recession velocities cannot exceed the speed of light.
...
When observables are calculated using special relativity, contradictions with observations quickly arise (Section 4).

Dave meanwhile is pretty much making up all his physics on the fly, and describes a universe that was falsified about 130 years ago, long before they even knew about expansion.

Here's a graph of redshift vs present velocity for a distant comoving object:

Notice that all curves are the same locally, only beginning to diverge as speeds get up to relativistic velocities.
BC, you are advocating the SR line that approaches 1c on the lower right. The paper I linked goes into detail about why this view quickly produces contradictions with observervations.
Dave is pushing the linear view of v=cz, which is the leftmost line going off the top of the page, which also contradicts observations, but the paper doesn't so much go into debunking this one since it is not a common misconception asserted by accepted scientific literature.

The empirical observations fall withing the grey area, and the favored model is the (0, 3, 0, 7) one, which is the 2nd from the top of the 4 lines. It yields a present recession velocity of about 2c for an object with redshift of 10.

[Bored chemist]

B C, you're making the mistake of modeling the universe using a special relativity model, which assumes flat non-expanding spacetime.

I grant you it's not correct, but it's not a mistake per se, it's a simplification. (And a lack of clarity about proper velocity).
I really don't think the OP is up to the detailed version.

[Dave Lev (OP)]

Dave is pushing the linear view of v=cz, which is the leftmost line going off the top of the page, which also contradicts observations, but the paper doesn't so much go into debunking this one since it is not a common misconception asserted by accepted scientific literature.

Thanks Halc
Don't you agree that only the linear view of v=cz is applicable for homogenous and isotropic Universe?
Let's focus in your example:

he empirical observations fall withing the grey area, and the favored model is the (0, 3, 0, 7) one, which is the 2nd from the top of the 4 lines. It yields a present recession velocity of about 2c for an object with redshift of 10.

That gray line that yields a recession velocity of 2c for redshift 10, also yields recession velocity of 0.6c at redshift 1 (let's call it galaxy B) and 0.8c at redshift 2 (galaxy C).
So, while the recession velocity of galaxy B (from earth) is  0.6c at redshift 1, the recession velocity of galaxy C (from earth) is  0.8c at redshift 2.
If we could jump to B and monitor the recession velocity of C than what shall we see?
Based on the gray line, the recession velocity between B to C is (0.8-0.6)c =0.2c, while the redshift should be (2-1)=1
So, while we see a nearby galaxy (B) with redshift 1 moving away at a recession velocity of 0.6c, that galaxy see other one (galaxy C) with a redshift 1 moving away at 0.2c (instead of 0.6 as we see).
How can you explain this phenomenon?
How can we still consider the universe as Homogenous and isotropic under this observation?

[Kryptid]

Based on the gray line, the recession velocity between B to C is (0.8-0.6)c =0.2c, while the redshift should be (2-1)=1

Wrong. You can't just subtract those from each other.

[Dave Lev (OP)]

I get 0.8c at z=1 and ~1.25c at z=2, using 2nd line from top in grey area. Somewhere there's probably a color version of that chart that makes it more clear which line is which model.

So it should be as follow:
With regards to location (galaxy A)
Galaxy B - Recession velocity of  0.8c with  Redshift z(ab)=1
Galaxy C - Recession velocity of 1.25c at Redshift z(ac)=2
It also seems to me that:
Galaxy D - Recession velocity of 1.4c at Redshift z(ad)=3
 

Quote
So, while the recession velocity of galaxy B (from earth) is  0.6c at redshift 1, the recession velocity of galaxy C (from earth) is  0.8c at redshift 2.
If we could jump to B and monitor the recession velocity of C than what shall we see?
Based on the gray line, the recession velocity between B to C is (0.8-0.6)c =0.2c

These are proper recession speeds, and they actually do add that way, so 1.25c-0.8c is about 0.45c between B and C.

Thanks

With regards to (galaxy B)
Galaxy C - Proper Recession velocity of 1.25c-0.8c= 0.45c
Galaxy D - Proper Recession velocity of 1.4c-0.8c = 0.6c

With regards to redshift:

Redshift at 0.45c is z=0.5 or so.  Kryptid points out that redshifts don't add like you're doing.

You claim that the redshift between B to C is z = 0.5 as the proper recession velocity between B to C is 0.45c?
So, how could it be that we see B at redshift 1 and C at redshift 2 while the redshift between B to C is only 0.5?

[Dave Lev (OP)]

Quote from: Dave Lev on Today at 06:03:19
So, how could it be that we see B at redshift 1 and C at redshift 2 while the redshift between B to C is only 0.5?

I did indeed make a mistake there.  The redshift at 0.45c is a bit under 0.4.  The resolution of the chart is near unreadable at such slow speeds.Maybe the numbers would be more clear if you picked galaxies a little further away, like one at hypothetical z=100 (v=~2.9c) and another receding at half that speed, z=3. Of course there's nothing visible at z=100 since any galaxy there is in the middle of the dark ages, so it emits no light.  Hence it being hypothetical.  We can see the recombination event at z=1100, which is just off the right side of that graph, which ends close to the edge of the visible universe.

Dear Halc
You didn't answer my question.
So, let me ask again:
If galaxy B is located at almost the same direct line from A (our location) to C.
How could it be that we see B at redshift 1 and C at redshift 2 while the redshift between B to C is only 0.5 (or at least lower than 2-1=1?

[Dave Lev (OP)]

Quote from: Dave Lev on Yesterday at 15:19:19
You didn't answer my question.
So, let me ask again:
If galaxy B is located at almost the same direct line from A (our location) to C.
How could it be that we see B at redshift 1 and C at redshift 2 while the redshift between B to C is only 0.5 (or at least lower than 2-1=1?

Because the mathematics puts it at about 0.5.  You subtracting 1 from 2 is completely irrelevant, since we're not counting apples here.

OK
With regards to galaxy B
Light from B is emitted and moving at the speed of light in the direction of the milky way (galaxy A). Let's call it light B
At the first moment after the emission, Light B has a redshift value of zero.
However, after crossing the distance between B to A at the speed of light,  we get it in redshift z(ab)=1

With regards to galaxy C
The light from C also emited at redshift zero. Let's call it light C.
It gets to B at a redshift of z(bc) = 0.5.
Than both lights (C and B) are starting to move almost together at the same speed of light in the direction of the milky way.
However, at the first moment (from B) light C has already redshift of z(bc)=0.5 while Light B has a redshift of 0.
Llight B and light C cross exactly the same distance between B to A and exactly at the same speed of light.
So why the redshift of light B had increased by 1 (from Zero to 1) while the redshift of light C had increased by 1.5 (from 0.5 to 2)? (Remember - same distance at the same speed of light)
Can you please explain the mathematics for that?