The speed of light and Hubble Flow

[Stephanus]

Dear PF Forum,
I've been wondering about how on Earth (and I do mean it, from earth ) that we know there's a galaxy 20 billions light away. Considering that https://en.wikipedia.org/wiki/Age_of_the_universe is 13.8 billions years old. But before I'm asking about Supernova Ia and Hubble Flow, I'd like to ask the following question.

There are two comoving observers W at west and E at east, separated 100 light years away. A third observer, R, is running away from east to west at 0.6c.
The moment R reaches W, R sends a signal to E. This signal will reach E in 100 years wrt E and W clock. Not in 100/(1-0.6) = 250 years wrt EW!
This I already learned from PF Forum

And supposed E and W are separated 100 millions light years away.
And again supposed, just supposed that the sepace between them is not expanding the moment W sends a signal to E.
Then after that space is expanding between them at, say 0.6c. That means that now W travels to the west at 0.6c wrt E.

Perhaps I can draw a simple picture. s is the signal sent by W
W....s..........E
then the space between them is expanding at x
W....s.....xx......E
W....s.....x..x......E
W....s.....x...x......E
W....s.....x...x......E

Now I'm lost here. Not in space but in thought.
How is s speed?
s relative to W is 300,000 km per second? I think so.
But what is s speed relative to E?
300,000 km/s or 120,000 km/s.
But the motion of everything to light is always 300,000 km/s, right?
For example.
Alice move to the west wrt Bob 100,000km/s. Bob moves to the west wrt Charlie 50,000 km/s, Charlie moves 200,000 km/s wrt Delta to the east.
And then Alice, Bob and Charlie sends a signal to Delta. All of their signals travel at 300,000 km/s wrt Delta.

Now, my question is this
=====================================================
What is s speed to E?
=====================================================
Thank you very much.

 

[m4r35n357]

Now I'm lost here. Not in space but in thought.

Don't know if this is helpful, but I think the sort of mathematics that you need to analyze this sort of problem (ant on a rubber rope) is outlined here.

 

[BvU]

Or this on size of universe

 

[Stephanus]

Don't know if this is helpful, but I think the sort of mathematics that you need to analyze this sort of problem (ant on a rubber rope)

The mathematic?

Dear PF Forum,
While learning why the net energy of the universe is zero. I've been reading about the expansion of the universe, and of course in it, Hubble Flow.
...
So t = distance/velocity or t = m/v
But this velocity changes over distance, so I have to use integral.
t = m/v in dm
while v = m {distance}*H
so
##t = \int\frac{1}{Hx}dx##
This is my integral
##t = \int\frac{1}{Hx}dx##

You are making a large number of unjustified assumptions among them:

• The expansion of the universe occurs with a constant Hubble parameter.
• The Hubble flow starts out at a distance of 1 m. (This sets the lower limit of your integral.)

Obviously, the latter of these assumptions directly implies zero time to reach a distance of 1 m. The fact that your final expression contains a logarithm of a parameter with physical dimension should be a huge warning sign.

Tell me about it.

is outlined here.

But this is not an ant climbing a rope. This is something with ##w=\frac{u+v}{1+u*v}## Ant vs rope is like Achilles vs turtle.

 

[m4r35n357]

The mathematic?

I am from the UK, mathematics/maths is the word we use ;)

Tell me about it.

I don't recognize that quoted text, is it from another thread?

But this is not an ant climbing a rope. This is something with ##w=\frac{u+v}{1+u*v}## Ant vs rope is like Achilles vs turtle.

You might need to include relativistic addition (I'm not 100% sure about this though, as motion of space itself is sometimes not restricted in this manner, as in the waterfall model of black holes). Of course, if so that will make the maths even more involved. The wikipedia article I linked to specifically mentions the metric expansion of space, but I haven't yet seen a worked analysis of particle motion in an expanding universe. I think that is as far as I can go with this.

 

[Stephanus]

I am from the UK, mathematics/maths is the word we use ;)

Oh yes? Nice to know you

I don't recognize that quoted text, is it from another thread?

Yes

You might need to include relativistic addition (I'm not 100% sure about this though, as motion of space itself is sometimes not restricted in this manner, as in the waterfall model of black holes). Of course, if so that will make the maths even more involved. The wikipedia article I linked to specifically mentions the metric expansion of space, but I haven't yet seen a worked analysis of particle motion in an expanding universe. I think that is as far as I can go with this.

But what confuses me is this.
Anything motion relative to light is c. And it seems that IF the galaxy is recedings from us, it's light speed from us recedes? I'm really lost here. But thanks anyway for your answer.

 

[PeterDonis]

[Moderator's Note: Moved to Cosmology forum.]

 

[Jorrie]

But what confuses me is this.
Anything motion relative to light is c. And it seems that IF the galaxy is recedings from us, it's light speed from us recedes? I'm really lost here. But thanks anyway for your answer.

Yes, the photons emitted by any galaxy that, at the time of emission, are (or were) outside of our Hubble radius (where recession speed equals c) at that time, would have been receding from us. The photons always travel at c relative to their 'local space' (loosely speaking). The only reason why they could reach us is because the Hubble radius is increasing as time goes on and for some 'nearer' galaxies, the photons eventually found themselves inside our Hubble radius. From there on they could make headway towards us.

The details may a bit heavy for beginner level, but if you already have read and digested the 'balloon analogy', please ask specific questions.