# Theoritically how far can one see in the universe

1. Sep 5, 2009

### mviswanathan

As I understand, when we say that an object is 1 Million light years away, it means that the object was that far away when the radiation left that object. Please correct me here.

Considering that the object is also moving away from us as some velocity (at the moment the radiation originated from it), that object must have been very near us some time earlier than 1 Million years. Could that point in time be the origin of universe?

On the same count, considering the origin of the universe as 13 Billion years, there must be some theoretical limit the maximum distance from which one could receive radiation now. This limiting distance has to be much less than 6.5 million years since the velocity of separation from us is less than the speed of light, where as we receive the radiation from th object at the speed of light.

With this, I am unable to understand when it is said that we have observed the Cosmic Background Radiation, which gives us the glimpse of the universe when it was 380,000 years old. (Scientific American, India - September 2009 - 'In the beginning - The Universe'.

I am not sure, I am expressing my confusion properly. I may be able to clarify if here from some one.
Thanks

2. Sep 5, 2009

### marcus

Viswa, most questions about this are really about Hubble Law, which is stated as v = Hd and refers to the current distance (the "now" distance d) and the current rate of increase v, of the current distance.

The law describes a pattern of increasing distances between objects which are stationary in the sense that none of them are going anywhere. A rate of increase of the distance between two stationary observers or objects must be distinguished from ordinary motion (which always approaches some destination.)

The Hubble Law has built into it an idea of universal rest---being at rest with respect to the Cosmic Background, so that there is no doppler hotspot in the sky----so that except for tiny fluctuations the background radiation is the same temperature in all directions.

The Law v = Hd only makes sense for a universe of observers who are at rest relative to background. Sharing a common idea of rest, they can agree on distances, and on what is the present moment, the "today" when the distances are to be measured and their present rates of increase determined. If the observers were moving randomly relative to each other they would constantly be disagreeing about such things.

The distant galaxies are assumed to be essentially at rest relative to background---they have only negligible "proper" (i.e. individual) motions. This checks out pretty well with observation. As well as we can determine, galaxies tend to have only slight individual motions relative to background.

The observation of the background is the single most basic and important observation in cosmology. I would suggest that you keep asking questions until you do understand---until you have a mental picture.

The background light was radiated from the hot gas that filled space, at the moment when space had expanded enough, and the gas had cooled enough, that it became transparent.
The temperature everywhere was then about 3000 kelvin.

Before that, the gas was effectively opaque---too dense, too glowing hot for light to travel very far through it. The earlier light was, in effect, trapped in the fog. Then at that moment when expansion was about 380,000 years old, and the fog cooled and thinned out enough, the light got loose. A moment of liberation.

And we still see that light, coming from all directions.

However since that moment, distances have increased by a factor of z=1090 and the wavelengths of the light have all been expanded by the same factor. So that reddish glow of 3000 kelvin light has been stretched out to be microwaves of wavelengths which are longer by a factor of 1090. It is still coming to us from all directions but it is no longer visible. Special antennas and instruments are required to see it.

When the light was emitted by the atoms in the gas, those atoms were 41 million LY from "us" (that is, from the matter that eventually condensed to form the earth and its creatures.)

Now those same atoms are 1090 times farther away, at a distance of 45 billion LY.

So in a sense when we study the background we are seeing atoms which were 41 million LY from us THEN and which are 45 billion LY from us NOW.

Much of the Hubble Law expansion is at rates v > c. This should not worry you because the expansion of distances described by the Law is not ordinary motion. It does not interfere with the transmission of light in the same way that ordinary motion would.
The expansion of distance affects both the distance the light has already traveled and the distance it has yet to travel. So it can both help and hinder, in a sense. Depending on details it is possible for light to get from one object to another even though the distance between the objects was increasing at a rate greater than c for some or all of the time the light was in transit. The key to this is the fact that the factor H has changed over time.
That is a fine point---involving some additional technical detail. Get the main picture first, and then ask questions to fill in the rest.

3. Sep 5, 2009

### jambaugh

My father used to tell about a local trial where the defending attorney was trying to cross-examine an eye-witness's testemony. The attorney was exclaiming in a mocking tone at how remarkable it was that the witness could identify the defendent from such a long distance away. He asks:
"Well Mr. Jones, exactly how far CAN you see?"
to which the witness replied
"Well I can see the Moon! How far is THAT!?"
That ended the cross examination and the man was later found guilty. My dad always got a chuckle out of retelling that story.

4. Sep 5, 2009

### mviswanathan

Marcus, thanks for the response.
I did not understand the following
Could you explain as to how distance THEN and NOW both can be 45 billion ...

I was analysing like this:
1. Some time back all objetcs were together
2. The farthest object estimated to be 'd' light years distance (assuming) away base on radiation data. That means the object was 'd' distance when the radiation left the object. At the current moment it will be further away due its separation velocity (either constanct or varying)
3. The light from the object took 'd' years
4. Since Object now could be more than 'd' lighyears. The radiation from the currentt relative postion will take some years to reach us.
5. Since the initial separation was 0, the object must have taken some time to readh the current separation.
6 A hence the age of the universe must be much more than 'd' years. even neglecting 4 above.

I know, the above considers us at the center of the curest universe, which is wrong. But still, the age must be more than 'd' years.

5. Sep 5, 2009

### Sorry!

The age of the universe is currently estimated to be about 13.5-14 billion years.

I'm pretty sure what marcus is explaining to you is that when the light escaped from being 'trapped in the fog,' as he put it, it was 41 million light years away from the position of where Earth is (would be). However since then the universe has continually been expanding including the position where the light came, so it is now 45 billion light years away (a factor of z=1090). (So if the light from the radiation had started to make its way to Earth RIGHT NOW from its current distance then we would not see it ATM as there has not been enough time since the light was emitted to travel to our location.)

This means that the background radiation spoken of that emitted light when the universe was around 380 000 years old WAS 41 million light years away when the light was coming towards Earth and at the current moment in time it is 45 billion light years away.

So the age of the universe is older than the distance that the light was emitted from.

Now since the universe has been expanding the light has also been expanding. Marcus said that initially red wavelengths have been stretched by a factor of 1090. If you look at this image:

http://www.artlex.com/ArtLex/wxyz/images/wavelengths_1.jpg [Broken]

you can see that microwaves are stretched longer than the visible spectrum.

Hopefully I shed some light on the topic and didn't spread any misinformation. I've been interested in cosmology for sometime now (actually it's why I first came to these forums) but I started off with pretty much zero knowledge so I had similar questions to what you're asking, macus has always been a great help. :)
If anything I've said is wrong/confusing just lemme know.

EDIT: Having re-reading your post I think you're confused as to how the object has travelled so far when it hasn't had enough time to reach that destination... The reason has to do with points of recession being greater than the speed of light. This is possible because expansion is of SPACE itself. So the objects are moving WITH space. Speed of light is for objects moving through space. (simplification)

Last edited by a moderator: May 4, 2017
6. Sep 5, 2009

### mviswanathan

Sorry!,
Thanks.
Made me re-read Marcus's message again. I had missed the M and the B. Was in a hurry to message since felt obliged to respond immediately for fast response to my message.
I have to respect the reply by giving time to understand it to the extend possible.

I am doing that now :) and will come back

7. Sep 6, 2009

### Chalnoth

Things aren't quite so simple in curved space-time. With the CMB, for instance, the photons that we see today were emitted about 43 million light years away. The matter that emitted those photons is today around 47 billion light years away.

How is this possible? Well, basically it all comes down to the details of how the universe expanded. As our universe expanded, the photons that were emitted 43 million light years away were at first carried away by the expansion so fast that they actually moved away from us. However, since then the expansion rate rapidly slowed down, and as they traversed more and more space they finally got to the point where they started moving towards us again. When you work this out in detail, you get that when those photons were emitted, they were about 43 million light years out.

8. Sep 6, 2009

### mviswanathan

The replies made me look around for more basics to understand that Cosmological Redshift is differenct from Doppler Redshift (Doppler was easy to understand)
Regarding Marcus's none of them are going anywhere:
1)I understand, now, that the separation is not the usual velocity but stretching of space itself.
2)Considering some equal distance grids, is it like that, between any two stationary objects the number of grids remain same whereas the individual grid spacing is increasing.
3) When we say that it was 41 Million LY THEN and is 45 Billion LY NOW, does it mean that the THEN distance is 42 Million LY as meaured with the NOW grid spacing. Does it also mean that the THEN distance would also be 45 Million LY with the THEN grid spacing?
4)Is the velocity of light in 'grids/unit time' remains same irrespective of the changing grid spacing? Then I can understand
4)I am unable to undertand Cosmic Redshift, if the point 3 above is right, assuming, all this time, the time is unchanged. I am still in the process of phrasing my question on this.

9. Sep 6, 2009

### Chalnoth

Well, this is a major problem with respect to distance measures in cosmology: they're actually pretty arbitrary.

What this one means is that if you could freeze the universe in place and bounce some photons around while the expansion was halted, then those photons would take 43 million years to get here. If you then let the universe's expansion continue and halt it at the current time, then do the same photon bouncing while the expansion is frozen, then those photons would take some 47 billion light years to arrive.

10. Sep 6, 2009

### Sorry!

You're using the same grid its just the distances on the grid have increased in all directions.

11. Sep 6, 2009

### Chalnoth

Yes, that's another way of putting it.

12. Sep 8, 2009

### mviswanathan

I am still lost on
This is possible if the grid spacing is increasing but the speed of light in 'grids/s' remains constant. The expanding grid spacing drags the photon with it. It also mean that the light speed in m/s is changing when the grid is expanding?

I need some help!

13. Sep 8, 2009

### Chalnoth

No, it doesn't require this. The grid is increasing in size with time, but the speed of light is independent of the grid. It's just that any observer on the grid always measures photons traveling by them as moving at c. Thus whether the photons traveling in our direction are actually getting closer or further away depends upon two things:
1. The rate of expansion.
2. The current distance to the photon.

Remember that you can compute the rate of change of the distance between any two grid points through Hubble's law:

v = Hd

So if your current expansion rate is H, and your photon is currently traveling in your direction passing by a grid point that is currently at a distance d, then that rate of change of distance between you and the photon is c - v. So if the photon is passing right by you, then d = 0, v = 0, and you measure the photon's speed as c (as required by General Relativity). If the photon is far away, then c - v might be zero or negative: if it's negative, then instead of getting closer as it travels, it is actually getting further away because the grid spacing between us and the photon is getting bigger faster.

Whether or not the photon ever reaches us, then, depends upon how the expansion rate H changes with time. In our current universe, H is decreasing. This allows far-away photons that were traveling in our direction and yet still being carried further away by the expansion to eventually start moving towards us and reach us.

14. Sep 8, 2009

### mviswanathan

Ok, I was thinking (wrongly) that all the grid spacing are expanding uniformly. I now, understand the farther grid spacings expand faster than the near ones with 0 velocity at 0 grid point.

But considering then that rate of change of distance between you and the photon is c - v, the velocity of photon with respect to me is always less than c with a maximum of c. In that case the light which left an object 43 Million LY away THEN (43 Million years ago) will not reach me NOW.

Also I want to understand, when it is said that some object is x LY away, does it refer to NOW or THEN (when the light left the object)?

An after thought, my first statement above is wrong. The grid spacing could be increasing uniformly and still 'v= Hd'. The rest of the message remains.

Last edited: Sep 8, 2009
15. Sep 8, 2009

### Chalnoth

Well, first of all the rate of change of distance to the photon could easily be more than c if either the photon is very far away, or is simply moving in the other direction.

As for what the distance means, well, usually we make use of the comoving distance, which is the distance now, not when it was emitted.

Other distance measured are more closely related to observables, such as the angular diameter distance (which is the apparent distance as measured by the angular size of the object) and the luminosity distance (which is the apparent distance as measured by the brightness of the object).

For example, let's say that we know that the a particular object has an intrinsic size a. This might be the size in light years of a galaxy, for instance, or of a galaxy cluster. When we look at the object in a telescope, we measure the angle across the size of the object. If we know the angle across an object and its intrinsic size, then we can produce a triangle. The long arms of said triangle make up the distance to the object:

$$d_a = \frac{a}{\mathrm{sin}\left(\theta\right)}$$

This distance $$d_a$$ is the angular diameter distance. And it turns out that this distance is the grid spacing between us and the observed object at the time the light was emitted.

We can therefore multiply the above distance by the amount the universe has expanded since then to get the current grid spacing between us and the object.

In a similar fashion, we can take the luminosity distance. In this case, let's say we know the intrinsic brightness of an object, and we also know how bright it appears to be to us. We also know that the brightness drops off as the square of the distance. So if we know the intrinsic brightness B, and we know its observed brightness L (short for luminosity, the more often-used term in astronomy), then we have a distance:

$$L = \frac{B}{4\pi d_L^2}$$

Thus the luminosity distance is:

$$d_L = \sqrt{\frac{B}{4\pi L}}$$

As it turns out, this luminosity distance is also simply-related to those above. First, consider the dilution of the photons just through the fact that they're spreading out through space. The photons that were emitted in a sphere from the source long ago are now in a sphere with a radius equal to the current grid distance between us and the object in question. But the photons have also been reduced in energy by the expansion, so the luminosity distance $$d_L$$ is equal to the current grid distance (the co-moving angular diameter distance) times an additional factor of the increase in size since the time the light was emitted.

For more on distance measures in cosmology, see this paper:
http://arxiv.org/abs/astro-ph/9905116

So yes, it's a bit confusing, and it's all down to the simple fact that there is no one way to determine distances in cosmology.

16. Sep 8, 2009

### ranrod

Hi, I have a very simple question about this. So the Whirlpool galaxy, for example, which is supposed to be about 23mly away, could be much farther than 23mly away because of the expansion of the universe? Could've been much closer than 23mly away when it emitted the light that got to us?

Last edited: Sep 8, 2009
17. Sep 8, 2009

### Chalnoth

Well, the expansion isn't that fast. The change in distance between us and that galaxy due to the expansion would only be about 40,000 light years in the time it takes the light to get to us. You have to go to galaxies billions of light years away before the effects of expansion really start to muck up distance measures.

18. Sep 8, 2009

### mviswanathan

Thanks, I am clear about 'distance means - NOW distance' (extrapolated using theory).

But in
I am refereing to the approach velocity of the photon towards me. This velocity (c - v) is always less <= +c. I can be negative(that is moving away) if v is greater than c. It means that
Is this statement correct?

19. Sep 8, 2009

### Chalnoth

I'd have to run through the numbers. As time goes on, the CMB that we see will be made of photons that originated further and further away (all at the same time, of course).

20. Sep 8, 2009

### Carid

Not like Chalnoth to make a mistake!

21. Sep 8, 2009

### Chalnoth

Haha, I make mistakes all the time, but I don't think I did there :) I was talking about a very specific, non-physical scenario (freezing the expansion), in which case I'm pretty sure it's correct.

22. Sep 17, 2009

### marcus

People don't always use language consistently. Here's a way you can get clear on the concepts. Go to Wright's calculator:
http://www.astro.ucla.edu/~wright/CosmoCalc.html

Look at it just as it comes up on the screen. You can play around and try different numbers later, but just look at the example as it comes up.

The number z = 3 is the redshift of light from some galaxy, coming in to our telescope today.

The "comoving radial distance" is the distance to that galaxy NOW which you would measure if you could freeze expansion. It says 21.07... Gly---which means about 21 billion light years.
That means if you could freeze expansion and send a flash of light to them it would take 21 billion years to get there.

The "angular size distance" is the distance to that galaxy THEN when the light we are now seeing started on its way. It says 5.26... Gly---which means about 5.3 billion light years.
That means that if you could have frozen expansion on the day the light started out on its journey, it would have taken 5.3 billion years to get here.

The light's actual travel time is given by a different number from the now distance and the then distance. You can see it is 11.46... Gyr, which is not a distance, it is a TIME.
It means that the light from that galaxy took around 11.5 billion years to get here.

You can try different numbers in the z box later. Like the most distant star explosion that has been seen so far had redshift z = 8.3. The explosion was seen in April 2009. You can plug in 8.3 in the z box and find out how far the star was then. And how far the blasted remnants of it are from us now. (These are "if you could freeze expansion" distances.) And you can find out how long the light has been traveling---that is, how long ago the explosion happened.

But for now, I recommend not changing any of the numbers. Just look at the calculator as it comes up on the screen, with that z = 3 example showing. In the case of that example it is very clear. To summarize in round numbers:

1. 11.5 billion years ago some light was emitted from a galaxy and set off on its journey to us.

2. At that time the distance was 5.3 billion lightyears---so if you could have frozen expansion back then, the light would have taken only 5.3 billion years to get here (instead of 11.5.)

3. Now, after traveling for 11.5 billion years, the light gets here, and the distance to the galaxy today is 21 billion lightyears. That means if you could freeze expansion today it would take 21 billion years for light to travel to us from that galaxy. It is the distance now.

4. The distance to the galaxy has expanded by exactly the same factor as the wavelengths of light have increased by during their travel. This factor is always z + 1.
A redshift of z = 3 means that the wavelengths are now 4 times longer. Light that was 1 micron waves when emitted is now 4 micron waves when received.
And the now distance 21 Gly is 4 times greater than the then distance 5.3 Gly.

A good way to learn to visualize this is to study the animated movie of the balloon analogy.

23. Sep 18, 2009

### mviswanathan

Thanks Marcus.
Looks looks I am getting hang of it. :)
Still, I have something nagging. I will come back when I am able to express it.

24. Sep 18, 2009

### mviswanathan

I was plying with the Ned Writes calculator to see variation with Red-shift. All calculated with 'FLAT' choice.
I got the table in the attachment below.

Now, I am still to absorb that I am getting the light from an object that was 5.27 GLY away 11.5GY back at the same instant(NOW) as from an object that was only 0.042 GLY away earlier 13.67 GY back.

#### Attached Files:

• ###### From Ned Write.jpg
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25. Sep 18, 2009

### Chalnoth

The expansion rate was much, much faster in the early universe.