# Age versus size of the universe

1. Apr 8, 2011

### MCPO John-117

whenever i think about the age of the universe compared to the size of it i get frustrated. how can a 50 billion+ light year universe fit in 14 billion years of space? my younger self said nothing can go faster than light so the universe couldn't have grown more light years in size than years in age. as i got older i learned of inflation and expansion allowing faster than light growth but is the difference really that large? has it been proven that the age and size are consistent with accelerating expansion? is the 14 billion year old age the age of the observable universe? i just have this overwhelming gut feeling that the universe is much older than we think but i cant explain it to myself. help please so i can stop losing sleep :) thanks

2. Apr 8, 2011

### Calimero

Radius of our observable universe is 46 BLY. That is, distance now from us to the surface of last scattering (you can look it up at wikipedia if you want to know what surface of last scattering is). Object (hot plasma) which emitted that light was only 0.042 BLY from us when that light was emitted, and was receding from us at 57 times the speed of light. Now that object is 46 BLY from us, and is receding at 3.3 times the speed of light. If you divide 46 with 0.042 you will get 1090, which is the number that tells us how many folds universe has expanded since then, and also it is the value of the redshift of that light (subtract 1 from it, which at high redshifts is not that important).

Now to the things that keep you awake:

1. Size of whole universe is not known neither now, neither at the time of Big Bang.

2. There are many ways to define distance and velocity on large scales. If you do it in so called comoving coordinates then

3. things can, and do, separate faster then light.

3. Apr 8, 2011

### bcrowell

Staff Emeritus
FAQ: Why is the radius of the observable universe in light-years greater than its age in years?

The radius of the observable universe is about 46 billion light years, which is considerably greater than its age of about 14 billion years. Since the radius of the observable universe is defined by the greatest distance from which light would have had time to reach us since the Big Bang, you might think that it would only lie at a distance of only 14 billion light years, since x=ct for motion at a constant velocity c. However, a relation like x=ct is only valid in special relativity. When we write down such a relation, we imagine a Cartesian coordinate system (t,x,y,z), which in Newtonian mechanics would be associated with a particular observer's frame of reference. In general relativity, the counterpart of this would be a Minkowski coordinate frame, but such frames only exist locally. It is not possible to make a single frame of reference that encompasses both our galaxy and a cosmologically distant galaxy. General relativity is able to describe cosmology using cosmological models, and this description is successful in matching up with observations to a high level of precision. In particular, no objects are observed whose apparent ages are inconsistent with their distances from us.

One way of describing this difference between special relativity's x=ct and the actual distance-time relationship is that we can think of the space between the galaxies as expanding. In this verbal description, we can imagine that as a ray of light travels from galaxy A to galaxy B, extra space is being created in between A and B, so that by the time the light arrives, the distance is greater than ct.

4. Apr 13, 2011

### Andrew Mason

Conceptually, I have trouble differentiating between the expansion of space and simple relative motion in which the space between two objects A and B "expands" as they move farther apart.

But my question is simply this: How does one measure the difference? How would one measure the expansion of space?

If space is expanding significantly over 13 billion light years, should we not be able to measure just a little bit of expansion of space over shorter distances?

AM

5. Apr 13, 2011

### bcrowell

Staff Emeritus
They are just two different verbal descriptions of the same thing. They are not statements that make contradictory predictions about observation.

Yes. However, you do not get significant expansion of strongly bound systems.

http://www.lightandmatter.com/html_books/genrel/ch08/ch08.html#Section8.2

See subsection 8.2.6.

6. Apr 14, 2011

### Andrew Mason

Well, if space is not expanding, SR applies. What, physically, is different when space expands as opposed to simple relative motion?

I realize that it is not significant. But the question is whether it is measurable. The Michelson-Morley experiment was set up to detect a very small difference between the speeds of light moving in directions parallel to and transverse to the ether.

AM

7. Apr 14, 2011

### marcus

Andrew, see if this helps:
https://www.physicsforums.com/showthread.php?p=3245869#post3245869

And keep in mind that the two static geometries we tend to think of are unrealistic. Euclidean geometry is not how the world behaves. And the static geometry of 1905 Special Relativty is not either, it is only realistic in an approximate sense, if you understand its limitations and don't try to apply it on too large a spacetime scale, or in regions of strong gravity.

In realistic geometry you have no right to automatically expect that the distance between stationary observers will not change. If you want to talk about motion or about being at rest then you have to carefully define---and then you cannot assume that a changing distance corresponds to motion.

Fortunately in Cosmology there are some standard definitions that are widely understood. (Universe time and proper distance)
That gives an easy way into the subject. If you can assimilate them you can avoid some confusion about expansion of distance versus actual motion relative to Background.

That is what my post is about, that the link is to: trying to communicate that point of view.
Check it out if you want----it may help or it may not, depends on you and what works for you.

8. Apr 14, 2011

### bcrowell

Staff Emeritus
There is no expansion in the Schwarzschild spacetime, but SR doesn't apply to the Schwarzschild spacetime.

http://arxiv.org/abs/astro-ph/9803097v1

Last edited: Apr 14, 2011
9. Apr 14, 2011

### Andrew Mason

It appears to me that you are suggesting that I accept a concept of the expansion of space as being distinct from simple relative motion, even though such a distinction a) is not measureable b) cannot be tested c) is not conceptually very clear.

This may be an inherent problem with cosmology. We can develop interesting theories but without being able to subject these theories to rigorous testing we can easily persuade ourselves to accept something as fact which is really nothing more than a good guess based on a very limited amount of information.

AM

10. Apr 14, 2011

### marcus

Thanks so much for your reply! I never say "expansion of space". I don't think of space as a "thing", I think of geometry, geometrical measurements, distances. I try always to be clear about what DEFINITION of distance is being used.

There is, in the real world, no one preferred definition of distance, or of motion, or of speed. In order to think clearly one must first define operationally. Concretely visualize the meaning, imagine how something would be measured.

People get into trouble when they make unconsidered assumptions, like about distance, that don't apply to the real world, or apply only ambiguously or in a limited way, and then try to reason from those assumptions.

A good way to begin to understand cosmo is to focus on what is called PROPER distance or "freezeframe" or "instantaneous" distance, where you imagine you can stop the expansion process and then use ordinary means like radar, or a long measuring tape. You freeze the expansion at a moment in time and stretch a long cord or send a radar signal.

That is the distance idea inherent in the Hubble Law v(t) = H(t)d(t). It is the language in which the Law is stated. So, since that law is central and involved in everybody's first acquaintance with cosmology, it seems like a good llace to begin. Expansion of proper distance is usually the first thing people hear about and the first thing that confuses them.

You are welcome to dismiss all this without first trying to understand it!

I don't think Feynman advised that sort of behavior, but I am happy for you either way.

If you want to make the effort and give it a chance, in your mind, then I have made a post for you about the month of April and the ancient light. It is really the first place to start. The sky has a doppler warm spot around the constellation of Leo.

At this point I am not suggesting you believe ANYTHING except that if you had a sensitive microwave antenna you could detect the warm spot.

You don't seem to understand anything yet, that we are talking about, so why should I be urging you to BELIEVE something. Personally I go light on belief anyway. Models and theories are meant to be tested and used provisionally for prediction. One never verifies, only eventually falsifies and replaces with an improved model.

If you want to venture to understand today's cosmo all I can do is suggest you go to that post.
https://www.physicsforums.com/showthread.php?t=490133

And then go out tonight around 9 PM and look nearly overhead, at the Leo area, and think about how that has a doppler warm spot (about one tenth percent warmer than the average sky).

And how, from there, one can translate to a frame of reference that is not moving relative to the universe as a whole. I.e. relative to the bath of ancient light that fills the U.

But if you want to totally shut that out and not make that mental venture, that is also fine. I'm good with that.

Last edited: Apr 14, 2011
11. Apr 14, 2011

### Andrew Mason

All I asked was a simple explanation of the DIFFERENCE between relative motion, in which the distance between objects increases, and expanding distance (or space) in which the distance between objects increases. The difference is alluded to but never explained.

That is why I asked: how does one detect and measure the difference between expansion of distance and relative motion?

So far, this explains nothing except that there is a difference.

How does that warm spot tell us anything about expansion of distance (or space) as opposed to simple relative motion? Doppler shift proves that there is relative motion between the light source and the receiver. How does that doppler shift tell us that space is expanding as opposed to telling us that there is simply relative motion between source and observer?

I am trying to understand what the physical difference is between, on the one hand, expansion and, on the other, relative motion, and, most important, how it is detected/measured. So far no one has been able to explain to me how it is done. It is a very simple question.

By the way, the ad hominem approach to argument is usually the sign of a weak case so I suggest you try something else.

AM

Last edited: Apr 14, 2011
12. Apr 14, 2011

### bcrowell

Staff Emeritus
I think you're getting a consistent answer from both me and Marcus.

I'm telling you there is no distinction between the two, that they are just two verbal ways of describing the same observables.

If I'm reading Marcus's posts correctly, he's telling you the same thing:

Marcus, if I'm misrepresenting your opinions, please let me know.

Andrew Mason, here's a way of looking at it that may help to clarify the discussion. If you can take the set of all points in a spacetime and write them as the union of timelike world-lines, that's called a congruence. Given a congruence, there is a quantity called the expansion scalar that you can define; see http://www.lightandmatter.com/html_books/genrel/ch08/ch08.html#Section8.1 , subsection 8.1.3. Since it's a scalar, it's independent of observers or choices of coordinates. The expansion scalar can be interpreted as telling us whether there's expansion going on. However, the value of the expansion scalar depends on the choice of the congruence. Now there happens to be a pretty important congruence that one would naturally want to talk about in a cosmological context, and that is the congruence formed by the world-lines of all observers who are at rest relative to the Hubble flow. If you pick that congruence, the expansion scalar is positive, as you'd expect from the usual verbal description of cosmological expansion as an expansion of space. But this all depends on whether you think that congruence is the right one to pick. Some people prefer the verbal description of cosmological expansion in terms of motion of galaxies, and those people would probably have objections to giving that particular congruence special status, or else they would object to the verbal description of the expansion scalar as a measure of expansion of space. There is no way to decide which description is right or wrong, because everybody agrees on all the observables.

-Ben

13. Apr 14, 2011

### marcus

For starters let's stop talking about "the" distance as if it had some unique meaning. If you want to meet me half way then let's agree that we are talking about proper distance. That's technical terminology for one of the definitions. I called it instantaneous or freezeframe. I don't yet know if you understand the definition and are willing to continue discussion on those terms.

All measures of distance are model dependent. You fit a model to data and get the best fit and then use the model to convert from redshift. A big mass of overlapping data is used to corroborate the model, which is constantly under critical examination. Your job at this point is to understand the ideas---understand first, criticize later, if/when you reach that point.
And there is no question of belief. In a mathematical science, models are meant to be test and used, not believed in.

"Doppler shift proves that there is relative motion between the light source and the receiver"

When is this relative motion that you say "there is"? The matter emitted the light 13.6 billion years ago. I don't know anything about what the matter is doing now.

What I know is there is a uniform bath of light, amazingly uniform, with an ideal thermal spectrum, the same coolish heat glow from all directions. Except in one direction where it is a tenth percent warmer. And another opposite where it is tenth percent colder.

What I mean by Doppler is that we are approaching the light. The light has been there uniformly filling the universe for 13.6 billion years. I don't know anything about what the trillions of jillions of different sources are doing, now or back then.

The basic fact is we are moving today in this uniform bath of light, and we are moving at a tenth percent speed of light. (approximately)

How about that for starters?

We are talking about Humanity's immediate experience of the sea of ancient light that we are swimming in, today. That we feel with directional antennas and make temperature maps of.

If you are OK with that, let's also say the distance we are talking about is what the professionals call "proper" distance----the instantaneous kind where it would be what you get if you could freeze expansion long enough to measure it, calculated by model from observed redshift.

You OK with those two things?
==============================

EDIT:
Ben, I think we are in pretty close agreement. Probably I just get in the way. I will try NOT replying so I don't get your way.

I started another thread so that Andrew could discuss there if he wanted to pursue a second line and it wouldn't interfere with this thread.
The title is something like "April is the month to see the CMB warmspot"

It's a nice coincidence that we are talking about motion relative to the CMB radiation and it happens to be the time of year when Leo is in the evening sky.

I yield the floor to you.

Last edited: Apr 14, 2011
14. Apr 14, 2011

### dm4b

Well, I might as well just complicate the matter even more.

In Carroll's text, he mentions that even talking about relative motion between objects that are seperated by cosmological distances is nonsense. There is no way to precisely define relative velocity between two objects in a curved space.

He then goes on to explain that the redshifts from extremely remote galaxies are NOT Doppler Shifts. They are cosmological redshifts. In other words, they are due more from the expansion of space, then from relative motions. (for local galaxies, it would be more from Doppler effect though)

However, as I understand it, this position is ... well, maybe not controversial ... let's just say it's not totally agreed upon.

But, I'm with AM ... I don't think a simple answer has been given yet .... has it? Maybe there isn't one?

15. Apr 14, 2011

### bcrowell

Staff Emeritus
Right. Which is why there's no way to define whether cosmological redshifts are kinematic or not.

The only thing I'd disagree on here is a shade of meaning. When you say "more from the expansion of space, then from relative motions," you make it sound as though one can say what percentage is one effect and what percentage is the other. You can't.

I'm not aware of any controversy. Some people prefer one verbal description over another, but that's just a preference, not a controversy.

If the question is how to distinguish kinematic from gravitational Doppler shifts on cosmological scales, then there isn't a simple answer. There isn't an answer at all. It's like asking whether democracy tastes more like peppermint, or more like spearmint.

-Ben

16. Apr 14, 2011

### Andrew Mason

Well, not exactly. The difference in theory is that light travels at c if space is not expanding regardless of the speed of the source and the receiver. If it is expanding at a rate v in a region between object and observer then light travels at $c - v$ in that region from source to observer. My question is quite simple: how do we measure or detect that? One problem, it seems to me, is that if space is not expanding in our local environment (eg. our galaxy) it is very difficult to detect/measure a distant expansion.
If this is science, there must be a way to tell whether the description is wrong.

AM

17. Apr 14, 2011

### dm4b

I agree - I just didn't phrase things as best they could be ... sry bout that!

I guess the key point is that locally, the cosmological effects are neglible compared to (relative motion) Doppler, and vice versa.

It definitely was more of a conceptual disagreement. But, it seemed like there was disagreement on a fundamental level on a point or two. I just don't remember the details.

This was in a paper from arxiv and I can't seem to locate it again :(

Well, I like democracy, but I hate spearmint ... so, clearly, democracy would taste more like peppermint ;-)

18. Apr 14, 2011

### dm4b

On second thought, I'm not sure about this now.

For example, in Carrol's book he calculates an expected redshift due the expansion of space defined by a simplified Robertson-Walker metric containing a dynamical scale factor. During the derivation and from the final equation for the redshift, one can see that relative motion is not brought in anywhere.

So, could we not use the real RW metric to calculate what we think should be the red shift due to cosmological effects (i.e. expansion of space) and any discrepancy from the observed redshift could then be chalked up to a relative-motion Doppler Effect?

I guess not, or there would be no disagreement on the issue, huh?

It seems like in certain regimes, like the local neighborhood, you could definitely claim that the Doppler shift is mostly kinematic (relative motion). The curvature and expansion rate is just too darn tiny at a local scale to have any substantial effect.

19. Apr 14, 2011

### bcrowell

Staff Emeritus
This has nothing to do with whether space is expanding. Locally, light travels at c regardless of whether space is expanding. Globally, you can't define speeds in GR, and this is true regardless of whether space is expanding.

No, this is incorrect.

Right. The description in terms of kinematic or gravitational Doppler shifts isn't science.

20. Apr 15, 2011

### Haelfix

So you might look for departures from Hubble's law. And indeed this can happen.

For instance there is a famous observational effect called 'Fingers of God' whereby clusters of galaxies develop large peculiar velocities relative to some local gravitational point and the effect is that these individual motions can become quite large and in fact produce what looks like a long "finger" pointed towards you in redshift space.

So yes, something like this does happen.

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