# A question about distance and time(2nd)

1. Dec 30, 2008

### BoyangQin

Marcus, i'm back, now waiting for offers from college.
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last night, i re-mused about the balloon model and expansion of space

On that expanding balloon,
a galaxy has a constant coordination;
only the distance between them expands.
the light that travel between the galaxy is lucky to gain interest on the distance it already travelled(it travels 1ly and that 1ly expands to 1.4 ly), so the light can travel faster than c.

but what about the distance untravelled? Didn't that distance also expanded?

put it into the bank analogy,
it's like the interest of the savings(distance already travelled) makes more money,
but the interest of the loan(untravelled distance) cuts off that money.
shouldn't it balance after all?

2. Dec 30, 2008

### BoyangQin

Or actually, wouldn't it takes more time for light to travel a distance?
Everytime the light travel a little distance, the distance left to travel expands
the unlucky photon would need to cover more distance ahead,and takes more time...

3. Dec 31, 2008

### marcus

That is right. Fortunately you have imagined clearly and carefully, so that the imagination gives you the right answer without using numbers. It is true that expansion causes to take more time to reach any given stationary target.

We can check this (even though we know it already) using a calculator like Ned Wright cosmo calculator*. Put in z=1090 and press "general". CMB light has z=1090.
It will tell you that the light has been traveling 13.7 billion years to get to us.

And we the target were 41.6 million LY away from the source matter back when it emitted the light.

And we are now 45.6 billion LY from the source matter.

If expansion had been frozen it would only have taken 41.6 million years for the light to get from "their" matter (the source) to "our" matter (the target).
But because of expansion it took much longer, namely 13.7 billion years, which is 330 times longer.
You could try using the calculator to construct examples like that for yourself with other redshift numbers z.
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if you want to think about it in bank savings account terms, I would say it is like saving money at a time when there is price inflation. A man wants to save up money to buy a sailboat, which costs 10,000 dollars. If there were no expansion, and he saves 1000 dollars a year, then in 10 years he could buy the sailboat.

But if there is expansion, then well he will have a lot more money at the end of 10 years (because of the bank interest) but on the other hand the sailboat will cost a lot more.
So after 10 years he will still not have enough to buy the boat. Even if the bank interest rate is equal to the inflation rate it will take longer for him to save up enough. In your post you explained why, so I will not repeat.
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*to get Wright calculator just google "wright calculator" or use this link
http://www.astro.ucla.edu/~wright/CosmoCalc.html

Last edited: Dec 31, 2008
4. Dec 31, 2008

### BoyangQin

ok, I get the other half of the picture: the light must travel further (even though it travels faster than c)
thx a lot
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well, people usually loan money to buy sailboats,don't they, so they can sail in it while trying to foot the bill...
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5. Dec 31, 2008

### marcus

That's right, Boyang, but this guy is a former Wall Street financial analyst and his credit rating is zero. People won't let him borrow and buy the boat on credit, so he has to save up for it

6. Dec 31, 2008

### BoyangQin

1. How much is H really? there are so many difference values of Hubble constant on the tutuorial...(72+/-8 km/s/Mpc, 57+/-4 km/s/Mpc, 71+/-3.5 km/s/Mpc...)

2. How come 1/H is approximately the age of universe? by coincidence or by some obvious reason?

3.
Quote Wright Tutorial part 1:
" ...An observer with a large motion with respect to the Hubble flow would measure blueshift in front and large redshift behind, instead of the same redshifts proportional to all distance..."

What is the 'Hubble flow'? Wright seems to imply that this 'Hubble flow' has a direction---an observer moving with respect to the flow experience blueshift in front and redshift behind. Is this implication conflicting with the balloon model(where the space is expanding in virtually all direction)?

Sorry for the barrage of questions... :)

7. Jan 1, 2009

### marcus

"Hubble flow" is an old terminology from long before the discovery of the CMB
to be at rest with respect to the H.F. is a way of saying be at rest with respect to the process of expansion that Hubble noticed

the H.F. has no direction and it is a bad terminology because it visually suggests the wrong thing.

after discovery of CMB in 1960s one can say "at rest w.r.t. CMB" and I think that is much clearer and more intuitive. If relative to CMB you are moving 370 km/s in the direction of Leo (as the solar system is) then the CMB will be fractionally hotter than average 2.728 kelvin in that direction, by the fraction 370/300000...and colder behind you by same tiny fraction...it is just normal Doppler effect.

But already thirty years earlier in the 1930s Hubble knew that the solar system had some motion (like 370 km/s but I don't know what he estimated) with respect to the overall matter of the universe which was dispersing or flowing apart. He knew this because in one direction of the sky he didn't see as much redshift as average. (that was the Leo direction, I don't know his estimated coordinates) and in the opposite direction he saw more redshift than average. So he knew. He realized there was an idea of being at rest.

The Hubble law v = Hd is actually about distances between observers at rest w.r.t. whatever you call it (the CMB, the bulk average matter of the U, the expansion process itself, the flow, the ancient matter that emitted the CMB, whatever name) the idea of being at rest is the same by whatever name.

Too bad they got the jargon habit of saying at rest wrt "Hubble flow" because it does sound like it should have a direction and also to some extent it is expert-only secret code.

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I wish somebody else would answer 1 and 2. I think Hubble rate is 71 km/s per Mpc and I can't remember the plus/minus.
This 71 is what I am always seeing.

And to me it is a puzzling (even a bit disturbing) coincidence that the Hubble time 1/H is so close to the estimated age of the universe.
There are people around here whose opinion I value and who might have an explanation. I would like to hear what they think.

Last edited: Jan 1, 2009