# Size of the universe from a different perspective

1. Dec 11, 2008

### WaveJumper

One of the postulates of the Big Bang theory taken from GR says that the universe is not expanding into anything, but that it's the metric that's expanding. The idea of metric expansion says that two points in space remain at the same spots but the distance between them grows(while these two points remain at their same locations).

Extrapolating this back to the Big Bang we have a universe that did not change in size since the Singularity if we were able to view it from the "outside". If such an "outside of the universe" viewpoint were possible, the universe would still be a zero-dimensional "point"(aka Singularity), that only when viewed from the inside would show internal metric expansion and size that appears to be different than zero.

What are your thoughts on this?

Last edited: Dec 11, 2008
2. Dec 11, 2008

### George Jones

Staff Emeritus
This seems close to the concept of co-moving coordinates.
I can't make much sense of this.

3. Dec 11, 2008

### johan01

"The idea of metric expansion says that two points in space remain at the same spots but the distance between them grows(while these two points remain at their same locations)."

The only way i can see this happening is if the two points themselves are expanding proportionately

4. Dec 11, 2008

### WaveJumper

If the stars in the universe were represented by these symbols, say 5 billion years ago:

@ @

@

now they'd sit in the same spots, just the distance(space) between them would increase, thus they are still where they once were:

@ @

@

The point is these 3 dots/symbols did not move. My uncertainty is whether we can extrapolate this metric expansion all the way back to the singularity because if we could, the size of the universe, when viewed from the "outside"(if it were possible) would still be zero, as it is assumed to have been 13.7 billion years ago.

Last edited: Dec 11, 2008
5. Dec 11, 2008

### marcus

Singularity does not mean "point", it means the breakdown of a math model. We have no reason to suppose that singularities actually exist in nature.

You might get something out of reading "A Tale of Two Singularities" at Einstein-online. It is just a page. The E-o index is in my sig.

Quite a lot of current research in cosmology is with non-singular models. These are math models that don't blow up and stop computing, as you work back in time. In other words people are interested in what really happened around the big bang, so they are attempting to develop models that are more realistic.

The classic 1915 theory had breakdowns of various shapes and sizes. Not all its singularities were zero dimensional points. That is another reason why it is a bad idea to equate singularity with point. Singularities exist in theoretical models, not in nature, and even in the context of a model, a singularity is not necessarily a point. There can be an extensive region of breakdown. A breakdown usually involves something that ought to be finite running off to infinity---the model stops computing sensible answers.
=======================

That's right! And GR says space has no physical existence. It does not attribute objective reality to points, or spots, or locations whether in space or spacetime. You only get points when you fix on some definite artificial coordinate system.

In the most basic sense, to say that an observer, or a star, or a galaxy is stationary, means that it is at rest with respect to the matter of the early universe---the source of the background radiation. It doesn't mean that the observer "stays at the same point" because there are no points. In artificial coordinate systems yes, but not in nature.

Points/locations are an artificial human invention and to define them you have to go thru a whole rigamarole of establishing a coordinate system, which in the end will probably involve anchoring to some material thing like a star or referring to the background radiation. We wave our arms but in the end our feet are still on the ground.

This doesn't make sense to me. What are points? What are spots? What are locations?
What does it mean to say that a point stays at the same point? Or that a spot stays at the same spot?

I like your mentioning metric expansion, but I imagine it differently. I picture two galaxies (or two observers) both of which are at rest relative to background. Their being at rest just means that neither is seeing a doppler hotspot in the background radiation. The distance between them is measured and found to be increasing.

What I'm trying to show here is a way to picture metric expansion in a completely non-abstract way. It is supposed to be operational. Two real observers, they each look around and discover that the background is the same temperature in all directions, so they are both at rest. Then they proceed to measure the distance between them, which I agree is a technical problem, radar, synchronizing clocks etc. It isn't trivial, but somehow they manage to measure and keep track. Maybe other observers help. Anyway these two stationary observers discover the distance between them is increasing.

So far, nothing as abstract as a point, or a coordinate system, or spacetime, has been introduced into the story. You could do that though. You could introduce a system of socalled comoving coordinates. They are technically useful as long as you stay within the range where they are applicable. Abstractions have limits to their applicability. Comoving coordinates break down if you go back too far. At least the ones I'm used to. With abstractions you have to know when to stop.

I think your post has a good idea, metric expansion, but it suffers from pushing an abstraction too far---to where the classic model develops a singularity.

========================

Now I'm going to contradict what I've said, and say that your post is right in a way. Some of the people who work on non-singular cosmology models actually do construct coordinate systems that don't break down! The metric bounces. There is a contraction which never goes singular (the density never blows up) and when the density reaches a very high level there's a bounce and expansion starts.
In those bounce models you really could have two mathematically defined points which would get closer and closer for a while, and then farther and farther apart. I have to admit that this looks very similar in some respects to what you were talking about.

So it looks like I'm hemming and hawing a lot on this one. Fence sitting. Maybe someone else will have a more definite reaction.

6. Dec 12, 2008

### Nick666

Well maybe its 1 cubic inch in volume and somebody plays ping-pong with it.

7. Dec 12, 2008

### WaveJumper

No it's not the point i had in mind. The point is the universe appears not to be expanding into anything(as in the old question - what's the universe expanding into?), but expanding into itself(whether this volume is zero or another number). It's very counter intuitive and quite mind boggling.

Last edited: Dec 12, 2008
8. Dec 13, 2008

### Nick666

So if we are in a singularity, can we ever escape it ? (assuming there actually is something outside of it)

If the universe/singularity we live in is everything, isnt these type of question "if we were outside of our universe.............." non-sense ?

9. Dec 13, 2008

### Chronos

It may be appropriate to steer the discussion in a different direction. It is not useful to discuss spacetime before you define it. That is what GR is about. Imposing a coordinate system is a useful way of thinking about it, but not necessarily adequate as a description. If you allow the possibility that any coordinate system you overlay on the universe is unbounded, things start to fall into perspective.

10. Dec 15, 2008

### johan01

is it not coincidence hat all theories formulas and theorems break dow at some point in their definition to explain what we observe collectively.

Is this mabey because what we observe is unique to us only . and everybody observes events from a different viewpoint allowing different possible statesin different frames of reference.

11. Dec 16, 2008

### oldman

This section of your post should be read by anyone who finds it difficult to understand cosmological expansion --- which is just about everybody. It's a model of clarity compared with the irrelevant analogies with curvature that clutter texts on GR. I particularly like the operational bit. Percy Bridgman would have approved heartily.

12. Dec 16, 2008

### marcus

Thanks for your comment, oldman. I've acquired a high regard for your critical faculty, so am glad you liked the post. I'll go back and re-read it, to see what I can learn.

13. Dec 17, 2008

### The-BRA!N

And yet, if the distance in between them has grown, how can they not move away from each other? For the distance in between them to grow, they would HAVE to move apart, it's only logic.

Maybe I've missed something here?

14. Dec 17, 2008

### marcus

The idea you are missing is the concept of an object or observer being at rest relative to the Background.

The idea of being stationary with respect to the CMB (cosmic microwave background.)

This corresponds to a couple of other criteria of being at rest which are used in cosmology, no need to elaborate. This is sufficient. You are at rest relative to CMB if you see the CMB have nearly the same temp in all directions. It varies less than 1/1000 of one percent.
Less than ten parts per million.

If you were moving you would see a doppler hotspot in the microwave sky ahead of you. This has all been checked out repeatedly since the 1970s. Smoot and Mather got the 2006 Nobel for it.
====================

People in this thread are attempting to assimilate a simple law called Hubble law which is about the present rate of increase in distances between stationary objects. The law is only about stationary objects, those at rest relative to Background.

It says the present rate of increase, v, is proportional to the present distance D.
Namely v = HD

H is the current value of the ratio. You multiply the distance D by H and you get the rate that the distance is increasing---in km/second if you like, or some other units.
======================

The-B,
keep in mind that Gen Rel says you have no right to expect distance between two stationary objects to stay the same. Gen Rel is a model of dynamic (changing) geometry. If you try to impose prejudices and expectations based on static geometry, you just get confused and spin your wheels.

15. Dec 17, 2008

### johan01

hi marcus
i have a question.

in your view is the CBR at every point in space. have these photons propergated from some distant place- i.e from the edge of the universe- and still propergating somewhere ?

OR

are they everywhere you go - ie at every geometric point in space- if so where are they propergating to , back to the edge of the universe?

16. Dec 18, 2008

### Chronos

CBR photons are, and always have been everywhere in the universe. The only thing that changes is their temperature [wavelength]. This has been affirmed via observations of excitation of molecules in intergalactic space. We happen to reside in the coldest possible region of the entire universe. But this is nothing special. Every other observer everywhere and everywhen else in the universe would reach the same conclusion.

17. Dec 18, 2008

### johan01

CBR photons are, and always have been everywhere in the universe

i think this is where i am getting stuck,
as i see it, they are all just moving around at the speed of light, in "ALL" directions.
And just getting more redshifted and weaker, due to expansion.
Do they not get absorbed by atoms, as they crash into our eyeballs , do those origoinal CBR photons not become less. since we now radiate other energies from our bodies "NEW PHOTONS".

How can those CBR photons "OCCUPY" every point in space geometry 5 billion years ago.
And now that the space geometry has more than doubled , those origoinal CBR photons still occupy , every point in this larger space geometry.

Have i posed my question correctly, can you understand the question ?

18. Dec 18, 2008

### WaveJumper

I don't want to scare anyone, as it's kind of disturbing and this will send the thread over to the Philosophy section, but if you are willing to go all the way, send me a PM, i'll give you more hints. For starters, you might want to have a look at Bell's theorem non-locality(the non-local nature of quantum mechanics). Thus you'll find out what Einstein meant by the following:

"A human being is a part of the whole called by us "the universe," a part limited in time and space. He experiences himself, his thoughts and feelings, as something separate from the rest - a kind of optical illusion of consciousness. This delusion is a kind of prison for us, restricting us to our personal desires and affection for a few persons nearest to us. Our task must be to free ourselves from this prison by widening the circle of understanding and compassion to embrace all living creatures and the whole of nature in its beauty."

If you are not comfortable, don't even bother.

Last edited: Dec 18, 2008
19. Dec 18, 2008

### WaveJumper

It is not.

20. Dec 18, 2008

### johan01

wave jumper
i agree with your views ,

It not coincidence hat all theories formulas and theorems break dow at some point in their definition to explain what we observe collectively.

It is not.
Furthermore: if all the universe could be explained by the "theory of everything ", encapsulated in a few laws.
Then by the very definition of Goedel's incompleteness theorem,
our theory is incomplete and is part of a grander theory!

"send me a PM, i'll give you more hints"
what is a PM?