Size of the universe from a different perspective

[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?

 

[George Jones]

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).

This seems close to the concept of co-moving coordinates.

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?

I can't make much sense of this.

 

[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

 

[WaveJumper]

I can't make much sense of this.

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.

 

[marcus]

...the universe would still be a zero-dimensional "point"(aka Singularity), ...
What are your thoughts on this?

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.
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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.

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.

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).

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.

 

[Nick666]

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

 

[WaveJumper]

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

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.

 

[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, isn't these type of question "if we were outside of our universe....." non-sense ?

 

[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.

 

[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.

 

[oldman]

...GR says space has no physical existence. It does not attribute objective reality to points, or spots, or locations ...picture metric expansion in a completely non-abstract way (that) is ...operational. ...With abstractions you have to know when to stop.

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.

 

[marcus]

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.

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.
https://www.physicsforums.com/showthread.php?p=1997345#post1997345

 

[The-BRA!N]

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:

@ @

@

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?

 

[marcus]

Maybe I've missed something here?

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.

 

[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?

 

[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.

 

[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 ?

 

[WaveJumper]

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?

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.

 

[WaveJumper]

is 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.

 

[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?

 

[Einbeermug]

Only things that are finite have size.

The sphere/balloon analogy presumes space is being added to the spaces within the cosmos and that although it is unbounded (like the surface of the sphere) it is finite.

From any given point on the surface of (or even within) a sphere, there exists another point at which motion in any available direction does not increase the distance between the two.

If ther cosmos is finite then for any given point within it there must exist another point within a finite distance at which motion in any available direction does not increase the distance between the two.

I know of no such point having been discovered nor any calculation that would demonstrate that such a point is possible.

 

[The-BRA!N]

Gotcha, thanks for the clarification, marcus.

In some ways, I see it similar to a tesseract (concept, not object): rather than seeing the fastest way between two points as being a straight line, instead "bringing two points closer together" to eliminate distance.

Reference: "transport[ing] [oneself] ... through the galaxy by means of tesseract, a fifth dimensional concept which is explained as being similar to folding the fabric of space and time."
-Wikipedia, http://en.wikipedia.org/wiki/A_Wrinkle_in_Time

 

[marcus]

If the cosmos is finite then for any given point within it there must exist another point within a finite distance at which motion in any available direction does not increase the distance between the two.
I know of no ... calculation that would demonstrate that such a point is possible.

You yourself have shown the mathematical possibility.

It's an established possibility that the universe has finite spatial volume. Ordinary working cosmologists deal with that case along with the infinite volume case. At present there is no scientific reason to rule either case out.

The most recent report on current best estimates of cosmological parameters was the 2008 WMAP report. In that report the authors specifically dealt with the finite volume case and gave a lower bound on the radius of curvature.
As I recall the radius of curvature estimate came to around 105 billion LY.

You seem to like the idea of a point at maximum distance from us. The existence of such a point is mathematically necessary because of the compactness of S³ but that's just a technical proof. You can take for granted that such a point exists in the finite-volume case. And we can give an estimate of HOW FAR AWAY IT IS at the current moment.
If my memory of 105 billion LY is right, the maximal distance would be at least pi time the radius of curvature---so at least something like 320 billion LY.

Basically these estimates come from the galaxy surveys, the CMB (cosmic microwave background) and other stuff that let's you measure curvature. The largescale curvature is something we can measure, fortunately, and the measurements of it are gradually getting more precise.
At some point we will know if it is positive. (If the 95% confidence interval is all on the up side of zero.)

 

[Einbeermug]

Basically these estimates come from the galaxy surveys, the CMB (cosmic microwave background) and other stuff that let's you measure curvature. The largescale curvature is something we can measure, fortunately, and the measurements of it are gradually getting more precise.
At some point we will know if it is positive. (If the 95% confidence interval is all on the up side of zero.)

If curvature is being measured, then a center can be calculated. Curvature implies a finite symmetrical limit and if our earthly point of observation seems to be at or near the 'center' of cosmologists' calculations then the apparent curvature can be explained as being the limit of our ability to observe rather than the limit of the universe. Only if the 'limit' appears to be significantly (more than 'margin of error') closer on one 'side' of the universe (from earth) than the other would the observation hold any credence. And even then, unless the density of the universe were constant, it would still be questionable.
Indeed, if the universe is infinite, it would still have the 'nature' of being spherical. If, from any point, you drew equidistant lines to infinity through all the X,Y,Z, axes, you would encompass the universe. By definition, the procedure describes a sphere for which the selected point is the center - BUT, you would be able to do so for any given point.