A question about the universe from a non-physicist?

[ultrasquid]

I am by no means a physicist but have a great desire to better understand the nature of our universe. I have had a question that has been bothering me and hoped that maybe someone could shed some light on or maybe just give me their best explanation. This is also my first post here so hello all

I am taking for granted what I feel to be our best commonly held understandings @ the current time but if I make an error in my assumptions as to what is commonly held as correct, by all means point out my errors.So here is my question.

If the universe is approximately 13.5 - 14 billion years old and started from and started from an infinitely dense singularity (*seems to be the best guess @ the moment) that has been expanding and accelerating in it's expansion in all directions, how is it that we can see a galaxy that is 13,230 million light-years away?

Perhaps I am just thinking of it wrong but to my understanding that universe (Abell 1835 IR1916) 13,230 million years ago was much closer to our vantage point and by my reasoning 13,230 million light years closer. I guess what I am trying to say is that if the light has been traveling for that length of time to reach us , how is it that the distance between that galaxy and our vantage point was that much shorter and yet we are seeing it now? Another way to look at it would be to say photons left point A 13,230 million years ago. @ that time point A. & B. were much closer. If there are 31,556,926 seconds in a year and the photons have been traveling for 13,230,000,000 years, then they have been traveling for 417,498,130,980,000,000 seconds. If they have been traveling for that many seconds @ the speed of light they have covered 125,162,599,682,756,160,000,000 kilometers. If the
universe is expanding @ a current rate of 74.2 km/sec (*best figure I could find) perhaps speeding up from the time the photons left point A. then it seems the distance between points A. & B. must be < 125,131,621,321,437,444,000,000 kilometers.

So if the universe is @ it's oldest 14 billion years old, then it was @ it's oldest 770000000 years old when those photons left on their trip. Assuming that @ no point the expansion of the universe exceeded the speed of light the furthest possible distance from outside of the universe to outside (diameter) would be 14,569,191,497,463,680,000,000 kilometers.

So to summarize,

A. Galaxy the photons left

B. Our vantage point that they were detected @

125,162,599,682,756,160,000,000 = Distance covered by photons in kilometers traveling @ speed of light.

< 125,131,621,321,437,444,000,000 = Distance in kilometers between point A. and point B. when the photons started their journey. (

14,569,191,497,463,680,000,000 = Maximum diameter of universe in kilometers when photons left point A. (assuming that matter can not exceed speed of light and the universe is < 14 billion years old)

74.2 km/sec = Current Rate of expansion

< 30,978,361,318,716,000,000 = distance space has expanded during the photons journey using the current rate

299792 km/s (kilometers per second) = speed of light

31,556,926 = seconds in a year.

In short even if the matter in the universe was expanding @ the speed of light from the the big bang to the moment the photon left the furthest known galaxy the furthest it could have been from us is 14,569,191,497,463,680,000,000 kilometers. In the time the photons have been traveling they should have covered 125,162,599,682,756,160,000,000 kilometers.
Even adding in the distance space has expanded during the photons journey using the current rate (< 30,978,361,318,716,000,000 kilometers)

125,162,599,682,756,160,000,000
- 30,978,361,318,716,000,000
- 14,569,191,497,463,680,000,000
= 110562429823973764000000 too many kilometers

I suppose I am not factoring in the fact that it is possible that the universe started out expanding faster than it is now @ the big bang, slowed down, and then started speeding up again?! Maybe i screwed up my numbers somewhere along the way while trying to think about the best way to explain the question. Maybe I am just looking @ it wrong logically.

I hope I have conveyed my question in a reasonable manner that's not too convoluted. Like I said, I am not a physicist, that's why I came here for insight. If I am looking at it wrong please let me know why.
Thanks in advance for your time :)

 

[S.Vasojevic]

If the universe is expanding @ a current rate of 74.2 km/sec (*best figure I could find)

That would be 74 (km/sec)/Mpc (megaparsec). Meaning that further is galaxy it is receding faster.

 

[ultrasquid]

That would be 74 (km/sec)/Mpc (megaparsec). Meaning that further is galaxy it is receding faster.

Thanks for your input, I see the flaw I made in thinking 74 km/sec was the same thing as 74 (km/sec)/Mpc. In looking into it I found out that means for every megaparsec (3.26156377696 million light years) you go out, the Universe is expanding 74.2 km/sec faster.

Ok so on that note, (13.23 billion ly (light years))/(Mpc (megaparsec)) = 4056.33644004

4056.33644004 * 74.2 km/sec = 300980 km/sec
speed of light = 299792 km/s

Is that galaxy speeding away from us faster than the speed of light?!

 

[HossamCFD]

1.As S.Vasojevic pointed out, the rate of expansion is directly proportional to the distance. so at greater distances space does expand faster than the speed of light (yes this does not violate special relativity or any law of physics for that matter). this "light horizon" will hinder any calculation that you may do about the size of universe, though you may do some calculations about the size of the "observed universe".

2. You said: the furthest possible distance from outside of the universe to outside (diameter) would be...

the keywords here are outside and diameter. In principle there is no such thing as outside the universe nor does the universe has an edge (as far as mainstream physics is concerned). Also by saying diameter you're implying that the universe is a sphere which we don't have sufficient evidence to say so.

3. the region from which light was emitted almost 13.5 billion years ago and reaching us now is called the last scattering surface (I believe it's almost 50 billion light years away) and this is the boundary to our observation. it's getting bigger as time is passing since light from more distant regions would have time to reach us. this observed universe appears to be flat not spherical but one may argue that the universe as a whole can well be spherical while only this small portion (the observed universe) appears to be flat. I also don't know how big the actual universe may be comparing to those 50 billion light years of observed universe (I don't know if there is any speculation about it)

4. I am somehow new to astrophysics and I would appreciate corrections/confirmations from more knowledgeable members.

 

[blkqi]

Assuming a constant rate of expansion, the approximate age of the universe is 1/H by backward extrapolation.
The quantity c/H is the Hubble radius, the radius of the Hubble sphere which contains all of our causally connected, observable universe. Note that this is not a boundary of the universe, but simply our observable universe.
These are cosmological approximations with uncertainty on the order of magnitudes. We can't observe a galaxy with a velocity greater than c.

 

[ultrasquid]

These are cosmological approximations with uncertainty on the order of magnitudes. We can't observe a galaxy with a velocity greater than c.

I am aware that the figures that I used are very rough and uncertain, like I said, I am not a physicist. I am just trying to better understand. I was simply trying to show roughly how I thought of the question.

 

[Constantin]

For cosmological distances don't use kilometers, use light years or parsecs.

The light we receive is 13.2 billion years old, it doesn't mean the galaxy was 13.2 billion light years away when the light was emitted.
I don't see any problem.

For a better understanding read:
http://www.astro.ucla.edu/~wright/cosmo_02.htm

 

[S.Vasojevic]

Ok so on that note, (13.23 billion ly (light years))/(Mpc (megaparsec)) = 4056.33644004

4056.33644004 * 74.2 km/sec = 300980 km/sec
speed of light = 299792 km/s

Is that galaxy speeding away from us faster than the speed of light?!

Yes it is. Wiki or google 'cosmological redshift', and read Ned Wright's pages (link that Constantin gave). You can also search through PF's cosmology forum, there are good threads about this.