Does a finite universe make sense to you?

[marcus]

I must confess that this is an issue I have the most problems with comprehending.

Here is a thread with some quotes from Einstein.
https://www.physicsforums.com/showthread.php?p=1386960
Let's see if we can pinpoint the source of confusion with their help.

Here's post #24 by George Jones
https://www.physicsforums.com/showthread.php?p=1386555#post1386555
It has an interesting Einstein quote.

then I contributed #25 which has the following:
==quote==
“Dadurch verlieren Zeit & Raum den letzter Rest von physikalischer Realität. ..."

“Thereby time and space lose the last vestige of physical reality”.

(To try to paraphrase, I guess you could say space does not have physical existence, but is more like a bunch of relationships between events)

In case anyone wants an online source, see page 43 of this pdf at a University of Minnesota website
www.tc.umn.edu/~janss011/pdf%20files/Besso-memo.pdf[/URL]

"...
...In the introduction of the paper on the perihelion motion presented on 18 November 1915, Einstein wrote about the assumption of general covariance “[b]by which time and space are robbed of the last trace of objective reality[/b]” (“[color=blue]durch welche Zeit und Raum der letzten Spur objektiver Realität beraubt werden,[/color]” Einstein 1915b, 831). In a letter to Schlick, he again wrote about general covariance that
“[b]thereby time and space lose the last vestige of physical reality[/b]” (“[color=blue]Dadurch verlieren Zeit & Raum den letzter Rest von physikalischer Realität.[/color]” Einstein to Moritz Schlick, 14 December 1915 [CPAE 8, Doc. 165]).
..."

Both quotes are from Nov-Dec 1915, one being from a paper on perihelion motion. and the other from a letter to Moritz Schlick a few weeks later.
==endquote==

One way to say the significance is you have to [B]wean your mind away from thinking in the English language and focus on the distance function, the metric[/B]. And even more, focus on the web of distance relationships between events.

Events, like the collision between particles A and B, like the arrival of a flash of light at a telescope on Mount Palomar.
Maybe events are more real than points in space. Maybe, as Einstein suggested, points in space have no physical reality.
Only events and the relations (like distance) between events have objective reality.

In General Relativity, the gravitational field IS A METRIC, a distance function that allows you to compute distances between events.
It is nothing else besides the metric. And the metric set of distances determines the geometry (gravity is geometry, so the metric can serve as gravity, which is what he makes it do.)

It is a very economical theory. There is nothing extra, that one could do without. (Even more economical than I've said. Even the metric is boiled down. Two that are the same except for trivial differences are treated as one. All equivalent ones lumped together. All redundancy is gotten rid of.)

So he says, don't believe in the existence of space and time. Believe in the field---the relationships between events---for example, distances.

when someone says space expands, don't believe them, don't even listen to them. think: the DISTANCES are expanding.
the expansion is [B]seen in the metric---the distance function---and nowhere else[/B] because space has not even a shred of phsical reality so there is nowhere else for the expansion to be make itself evident.

Learn to use your confusion. Discover what is the focus of it, what intensifies your confusion. Maybe these Einstein quotes can help distill the essence of it for you.

The spoken languages were invented by primitive tribesmen. There are some things if you insist on thinking purely in words you will always be misled.

 

[BoomBoom]

One way to say the significance is you have to wean your mind away from thinking in the English language and focus on the distance function, the metric. And even more, focus on the web of distance relationships between events.

Nice post Marcus...that was helpful.

It does seem that a problem is the misleading words. But these words are continually used by many trying to describe an expanding universe. It is certainly no wonder why there is so much confusion with the subject.

 

[sketchtrack]

My intuition wants me to think that space isn't expanding, and things are just moving apart through space. Is the reason that that idea is false because our theory of gravity tells us that galaxies have no physical reason to be moving the way they would need to be?

 

[MiltMeyers]

Marcus I disagree and believe that space time is something. It is a quantum foam were virtual particle pop in and out of existence. It is what "Blew up" in the beginning and is still expanding with each passing day. ST consists of at least 4 dimensions and more I'm almost sure. The matter we see around us in in the far past was carried to were it is by ST in the beginning and now as it exspanses. ST has zero point energy and can create matter even now. As it in the beginning created matter and anti matter which may have repealed each other by gravity. This created neutrinoes which condensed into Hydrogen and some helium. The creation of matter from ST is still going on. In the beginning ST exspanded faster than light and that is how the temparature of ST is the same all over the viewable universe. Before ST there was nothing and that means time before the initial impulse function of space time was nothing. Zip nada nothing. Now that said, I stand in respect of what you have to say Marcus so don't rain down fire and brim stone on me. Also forgive my spelling as I only passed English 101 with a C and alway drew the red undrerlined comment SPELLING. Ahhhhh memories.

 

[marcus]

Milt did you see the recent Scientific American article about spacetime foam and the emergence of classical deSitter spacetime at large scale (from the micro-scale foam)?

The people who are farthest along with computer models of spacetime foam are Renate Loll's group at Utrecht and their collaborators (Athens, Tokyo, Reykjavik, Warsaw, Copenhagen etc.)

it's a strong group. You should know about their work if you are interested in the quest to find out what space time and matter are made of----what the fundamental degrees of freedom are. Maybe things can be made out of pure geometry (includng topology)---pure relationship and interconnection. I wouldn't exclude the possibility.

anyway they do computer modeling of quantum spacetime-----and big averages like Feynman path integrals, where they average up many random quantum spacetimes. Even the dimensionality of the spacetime is up for grabs and not always the same.

the article is available free, if you follow a link at Renate Loll's website.
http://www.phys.uu.nl/~loll/Web/title/title.html
Or you can read it in the July 2008 Scientific American.

========
BTW I don't think you contradicted what the Einstein quotes said. All the things you mentioned can take place in the context of the gravitational field. they don't require a new kind of material called space in which to occur, they don't require space to have object-like reality so that it expands and more is created etc.---all the things people say about it here when they think of it as a substance.

the things you mentioned, events, occur without question, I am saying that points of space don't have to have an independent existence so that these events can occur at those points. there can simply be a web of distance relation and other geometric relations----mere information. Isn't that enough for the things you mentioned to take place in that context? Or do you insist on more? Be careful or Occam will get you
=============

About brimstone. that is the Mentor's job. Guru is an unofficial democratically elected annual party-hat. It rotates. Be listening to what other rankandfile non-Mentor members are saying and get an idea of who you want to elect to wear the hat next year!
In any case you wouldn't get any brimstone even if I had it to hand out.

 

[sketchtrack]

There are a few things that have me confused now.

1) Is space expanding equally everywhere, or is it only expanding in between galaxies. If it is only happening between galaxies, then why?

2) When space expands, molecules occupying that space would have to either break apart as distances between the bonds increase, or it would have to expand itself, or it would have to move inwards to compensate for the distance increasing. Which of these options is thought to be correct?

 

[marcus]

There are a few things that have me confused now.

1) Is space expanding equally everywhere, or is it only expanding in between galaxies. If it is only happening between galaxies, then why?

"Space expanding" is kind of a bad phrase to use. Distances increase in the normal natural course of things according to the best model of gravity we have.

Distances within our solar system and within our galaxy are distances between gravitationally bound objects. They don't increase as part of this pattern. The pattern is only largescale distances between objects that are not bound in orbits around each other.
Even some nearby galaxies can be bound together.

so the answer is NO. not all distances expand. the Hubble law relationship is only true ON AVERAGE FOR VERY LARGE distances.

the thing is, it is amazingly regular if you look on large scale. nearly everything is receding by the same percentage amount each year.
====================

the Einstein equation of Gen Rel governs the distance function. the distance function changes constantly and dynamically and is affected by the distribution of matter.
so its behavior is not totally regular------it is the solution to a differential equation. like the surface of the ocean or the winds in the atmosphere which have their differential equations governing them.
but the expansive pattern is very close to regular (matter, which affects the distance function, is distributed roughly uniform, so the expansion at large scale is roughly uniform too.)

Mostly what the distance function is doing these days is that all the largescale distances increase about 1/140 of a percent every million years.
=====================

the Einstein equation is our theory of gravity. until we get a better theory of gravity we have to accept that the gravitational field is the distance function and it is dynamic and changing---geometry is changing (or another way: spacetime is curved)

2) When space expands, molecules occupying that space would have to either break apart as distances between the bonds increase, or it would have to expand itself, or it would have to move inwards to compensate for the distance increasing. Which of these options is thought to be correct?

If that's the choice, I'd have to say move inward.
"space expands" is an unclear phrase that often confuses people, you could try thinking in terms of distances increasing
distances between bound-together things don't increase in General Relativity. like the two ends of a stick or the two sides of a crystal. or two things in circular orbit. those distances between bound-together things do not increase

But in a borderline case I would have to say that they move inward and in
some extreme cases stuff that was gravitationally bound can come unbound. It isn't typical. Some theoretical models allow for even chemical bonds to be broken like in those Big Rip scenarios. they have little to do with everyday astronomy. I tend to filter that stuff out.
The ordinary expansion of distances is very gentle and doesn't interfere with systems held together by atomic and molecular forces. (That is why we aren't used to seeing distances between stationary things change. The distance between New York and San Francisco is more or less constant, almost.)

Wallace and Cristo are the experts about this. I trust they will correct me if I'm seriously wrong about anything.

 

[robheus]

If that's the choice, I'd have to say move inward.
"space expands" is an unclear phrase that often confuses people, you could try thinking in terms of distances increasing
distances between bound-together things don't increase in General Relativity. like the two ends of a stick or the two sides of a crystal. or two things in circular orbit. those distances between bound-together things do not increase

But in a borderline case I would have to say that they move inward and in
some extreme cases stuff that was gravitationally bound can come unbound. It isn't typical. Some theoretical models allow for even chemical bonds to be broken like in those Big Rip scenarios. they have little to do with everyday astronomy. I tend to filter that stuff out.
The ordinary expansion of distances is very gentle and doesn't interfere with systems held together by atomic and molecular forces. (That is why we aren't used to seeing distances between stationary things change. The distance between New York and San Francisco is more or less constant, almost.)

Wallace and Cristo are the experts about this. I trust they will correct me if I'm seriously wrong about anything.

I have also always struggled with this (esp. if you are used to the ontological definition of space as merely distance relations between objects) and in most (popular) descriptions, the issues related to that (why only space expansion at large scales and not at small scales) are often not mentioned, side-stepped as not important, or only briefly mentioned and which we then have to take at faith value.

What is important of course first is that it is well-established (in the context of GR) what "space" is.
In the Newtonian sense, space is not "something". So, expansion of space or two bodies moving from each other can not be distringuished.
In GR it is taken that those are different notions of reality (which would lead to "space" being something, i.e. "some form of aether"). Yet, on the other hand, there is no "absolute frame of reference" acc. to GR.

All of this together however is not very obvious and seemingly contradictionary.
Would GR somehow say that - energetically - distantiating two bodies from each other (two far away galaxies) is somehow different in case of:
1. Two bodies moving "in" space and receding from each other
2. Two bodies stationary in (local) space, but with the space between them expading

Further, if normal stuff (molecules) etc. have to somehow compensate for the (local) expansion of space, wouldn't that mean that this produces energy? (at least that is the case for gravitational bound objects).

WRT terminology, in cosmology the expanding of space (in distinction with movement in space) is often termed as expansion of the spacetime metric and/or references as the increase of the scale factor

 

[ThomasT]

Starting from any point in the universe, shine light in all directions; given infinite time has passed, will it have reached the edge of the universe?

Infinite time isn't a physically meaningful term. Would light emitted in any direction ever reach the boundary of a bounded universe that is expanding at the speed of light? Is that a meaningful question? I don't know.

It doesn't make sense to me to define the universe as finite, as there is no edge of the universe to cross.

How might we possibly ascertain that the universe is or isn't bounded?

You could imagine the universe shaped like a sphere, and traveling a constant distance in a straight path would eventually get you back to your original position, but still you would never reach the edge of the universe.

I do imagine it as an isotropically expanding 3D sphere, with us and everything else that constitutes the contents of the universe inside the boundary surface of the sphere. So, if you travel any distance in a straight line, then you will end up somewhere other than where you began.

At the border of our universe lies a dimensionless quantity.

Or, maybe it's the expanding front of the big wave that defines the border of our universe.

What are your thoughts?

That, except for the evidence of apparent expansion, it's pretty much all speculative -- but interesting nonetheless.

 

[eg180]

I think that is why many ideas proposed by string theorists (multi-verses, parallel dimensions, etc.) seem so far off in "left-field" because they seem to ONLY see the math without any observation or logic to back it up.

Thank "God" many of the scientist that came before us didn't let what would appear to be "logical" hinder progressive ideas and fledgling theories that eventually were given more credence. When you think about it, we are the oddballs of the universe - things don't often go past light speed and our temperatures, densities, and velocities are quite mild in comparison with the universe's quite volatile, and violent nature. It is not surprising that our common sense fails to grasp the true universe...our common sense does NOT represent reality.

 

[DaveC426913]

...our temperatures, densities, and velocities are quite mild in comparison with the universe's quite volatile, and violent nature. It is not surprising that our common sense fails to grasp the true universe...our common sense does NOT represent reality.

Well said. This is something I find myself repeating over and over to people who think that our physical universe has to make common sense.

 

[eg180]

Well said. This is something I find myself repeating over and over to people who think that our physical universe has to make common sense.

Hey, Dave. I'm new here and I am by no means a scholar or well versed in physics or cosmology - I've just recently found a fascination with quantum physics/cosmology, etc at 28 years old, when I wish I would have been exposed to this in my early teens. (I was raised in a fundamentalist Christian household, so these topics rarely came up, unless they were in the form of a bible verse. ("In the beginning God created the heavens and the Earth..etc.)

I hope to learn a lot from everyone on this board. It's great to find an outlet on the net for these things that I've only recently become fascinated with. I'm only a pupil but it's never too late to learn. (I guess it would help if I were good at math though.) :)

 

[BoomBoom]

Thank "God" many of the scientist that came before us didn't let what would appear to be "logical" hinder progressive ideas and fledgling theories that eventually were given more credence.

I agree with this statement. Logic builds on knowledge and what may seem logical in one era may seem a foolish notion to a subsequent era. The old logic is replaced with new logic as knowledge is acquired.
But, generally speaking, things that do not make logical sense often turn out to be untrue. I have no doubt that future generations will look back on some of the cosmology theories of the turn of the 21st century (especially pertaining to string theory) and say, "now that's just silly...what were they thinking?".

 

[DaveC426913]

Hey, Dave. I'm new here and I am by no means a scholar or well versed in physics or cosmology - I've just recently found a fascination with quantum physics/cosmology, etc at 28 years old, when I wish I would have been exposed to this in my early teens.

I have no education in science since high school myself. All my knowledge is self-gained. It's never too late.

 

[MiltMeyers]

Glad to hear we are all about equal in knowledge. Now let me restate. that as we look out to a time and distance of the cosmic background that it fills the sky in every direction that we look. The universe is much smaller then and all directions we travel will take us back to that time. Now go beyound that event back to the singularity and it also would be in every direction we can go. So now I ask you what direction would you go to get to the edge of space time? To escape we need a new dimension a 5D but our universe is only 4D. I've always thought that space time was exspanding at C but of course the matter was at a slower rate. The real noodle problem is that we are in the oldest state of the universe and so is every man women or child. Any direction we go from us is back in time to a smaller universe. IE the Sun is in a universe 8 minutes smaller from were we are. This can only be if we are in a 4D sphere or bottle as I like to call it. Nothing is ever lost from it and since nothing can travel faster than light nothing is lost. Some have said that the greater the distance that the faster an object can go till it is going faster thanC, like maybe 2C. I say that that C is the limit and all you do when you add space time is lower the frequency. The faster an object goes fromus the lower the frequency and that is why the back ground is in the microwave range. That is why the red shift. That is the way I see things so feel free to jump in and straighten me out.

 

[DaveC426913]

Glad to hear we are all about equal in knowledge. Now let me restate. that as we look out to a time and distance of the cosmic background that it fills the sky in every direction that we look. The universe is much smaller then and all directions we travel will take us back to that time.

You are confusing travelling with looking. When we look outward we see back in time, but we can't travel there.

 

[mysearch]

I have only quickly read through all the contributions, so apologises if my point has been raised before and I missed it. However, I was wondering whether a finite universe would have a gravitational centre of mass?

When Newton first came up with his theory of gravitation, he was unsure whether gravity acted with respect to the surface or centre of mass. Subsequently, he formulated what has become known as the Newton’s Shells:
http://en.wikipedia.org/wiki/Shell_theorem

However, the flip side of this theorem shows that a particle within the cavity, surrounded by a uniform shell, would feel no net force of gravity, or possible spacetime curvature is more exact according to GR. However, the question being raised is whether an infinite universe would act as an infinite thick shell to any point in the visible universe and thus have no centre of gravity? While, in contrast, a finite universe must have some form of centre of gravity? Just a thought.

 

[MiltMeyers]

Dave Yes I agree and what I should have said if we could travel instantaneously which we can't but it is a way to describe what we see as that is the shape of the universe. It was late and I'm really not a bright bulb.

Mysearch, the only thing like a center is the spot were the singularity was and it is now spread all over the universe so my answer, if you care is there is no center. You have to visualize a 4d sphere and that is very hard, to see what I mean. So the universe has no center and no outside and nothing before the initial singularity.

 

[mysearch]

Response to #125

the only thing like a center is the spot were the singularity was and it is now spread all over the universe so my answer, if you care is there is no center. You have to visualize a 4d sphere and that is very hard, to see what I mean. So the universe has no center and no outside and nothing before the initial singularity.

I am not pretending that I know the actual answer, but would be genuinely interested in how a 4D-sphere changes the basic physics of gravitation. Newton’s shell theorem provides some tangible mechanism by which gravity might cancel out in an infinite universe, but not a finite universe. While Newton's laws of gravity are superseded by GR, I believe Newton’s basic laws still applied in this case. The terms centre of gravitational mass may be misleading as it is really only referring to a point corresponding to the net resultant of all gravitational forces/curvature in a finite universe. So my response is really just another question:

How does a finite 4D sphere explain there being no centre of gravitation?

 

[DaveC426913]

Newton’s shell theorem provides some tangible mechanism by which gravity might cancel out in an infinite universe, but not a finite universe.

You need to specify one more qualifier: boundary.

A finite bounded universe will have a bias in gravity, a finit but unbounded universe will not.

 

[mysearch]

Response to #127

Hi, accept the implication of the correction, but do not understand why. Can you qualify your statement about a "finite but unbounded universe" with any reference that explains the physics? Again, this is intended as a genuine inquiry and not as a smart-arse response. Thanks

 

[DaveC426913]

Hi, accept the implication of the correction, but do not understand why. Can you qualify your statement about a "finite but unbounded universe" with any reference that explains the physics? Again, this is intended as a genuine inquiry and not as a smart-arse response. Thanks

Well, that's where your 4D space comes in.

In the 2D "balloon" analogy the universe is finite (its width is the circumference of the balloon) yet unbounded (there is no edge, and no point on the surface is "privileged"). It also means no point on the surface is privileged with having a different mass distribution, and that means no point on the surface has a gravitational gradient differnt from anywhere else.

In the equivalent 4D universe, it has a finite size, yet, because it wraps around there is no boundary. This means no point is privielged with an different mass distribution because no point is "nearer an edge" than any other.

 

[MeJennifer]

Perhaps this is all confusing due to terminology but under GR a closed spacetime is always finite while an open spacetime is always infinite. In addition such spacetimes are also resp. spatially finite and spatially infinite.

 

[MiltMeyers]

Dave that's great as you have a way with words. Well said. Now as I see it space time is curved and exspanding even though the light we see looks like it is traveling a straight line. Light travels at C due to space exspanding at C so space time started first so it is the cause and light speed is the effect. I maintain this is not like either but space time is something and has a quantum foam were particles appear from space time and then disappear. It has a zero point energy. It seems to be that everything inside our universe is something and there is nothing outside not even nothing. Maybe there is an outside but it would have to be in the 5th demension. Okay who are you voting for and how much money do you make and is there a God? Please don't answer that as I was just kidding.

 

[MeJennifer]

Now as I see it space time is curved and exspanding even though the light we see looks like it is traveling a straight line.

Spacetime does definitely not expand.

Light travels at C due to space exspanding at C so space time started first so it is the cause and light speed is the effect.

No, you got that wrong.

 

[MiltMeyers]

Jennifer, hmmm if space time doesn't expand, why is the universe getting bigger? Also it is accelerating as time goes on. Does not the space between the galaxys make the universe bigger now than in the past? Maybe I'm using the wrong words? Please let me know were I'm going wrong.

I know that the speed of light C is not due to space time exspanding. So please explain how that works. Why is the c just about 186,000 mps and not 200000 mps? I'm truly happy as I think I'm going to learn something.

Thankyou;
milt

 

[DaveC426913]

Okay who are you voting for?

The only sane choice: I live in Canada.

 

[MeJennifer]

Jennifer, hmmm if space time doesn't expand, why is the universe getting bigger? Also it is accelerating as time goes on. Does not the space between the galaxys make the universe bigger now than in the past? Maybe I'm using the wrong words? Please let me know were I'm going wrong.

Don't mistake spacetime for space.

Why is the c just about 186,000 mps and not 200000 mps? I'm truly happy as I think I'm going to learn something.

Actually it could be any value it just depends on the units of measurement you use.

 

[MiltMeyers]

Don't mistake spacetime for space.
Oh are you saying that space is the 3 demensional kind and spacetime the 4 demensional kind? So space is exspanding not space time? Please help me to see that would you please?


Actually it could be any value it just depends on the units of measurement you use.

What keeps it from being faster or slower thru open space? Space is not an either or is it? I was taught many years ago that light propegated by each point on the wave front acts as a primary source and each point on that wave front acted as a primary wave source and so on. That was physics in 1959. Do you agree that the universe is exspanding at C?

Thankyou for your help.
milt

 

[MiltMeyers]

I'm so new here I didn't figure out how to post with a quote.

 

[epkid08]

Don't mistake spacetime for space.

Why wouldn't spacetime be expanding? Well for one, we assume space is expanding, so what does it mean for time to expand? Well, I'd say that if time wasn't 'expanding' we'd be frozen in time, but because spacetime is expanding, time and space continue to accelerate, as we continue traveling into the future.

 

[MiltMeyers]

MeJennifer---As far as I can tell when I think about it space time is 4 dimensions and space is 3 dementions but it exists only in my head. No jokes please. How can space exspand without bringing the 4th demension along with it? You do think that the universe is getting bigger and "exspanding"?

 

[Chronos]

An observationally finite universe makes sense to me. Mainly because there is no observational evidence to the contrary. Nominate the observation you have in mind that refute this proposition.

 

[mysearch]

Dave, thanks for the response in #129. However, if I could just push on a couple of points before I go away and do some more reading. The point of my questions is to try to understand what is generally accepted fact, albeit still subject to verification, and what is still speculative:

1) The universe is said to be expanding, based on redshift measurements, cepheid luminosity etc. This position is generally supported by CMB verification? Therefore, didn’t really understand the comments about space/spacetime not expanding in #132/135.

2) When people talk about curved spacetime, are they referring to gravitational spacetime curvature or the open/closed issue?

3) Given a density in the order of about 20 particle/m^3, a large-scale homogeneous universe would appear to be locally gravitationally flat, although this ignores the issue of whether there is an overall gravitational centre. See specific comments to #129 below?

4) The description of the universe being opened, closed or flat seems to be based on models of the universe using GR and the cosmological principle, e.g. homogeneous and isotropic, but ultimately dependent on the total energy-mass density assumptions of the universe. Today, the general assumption is that k=0, even though the level of speculation regarding the real nature of the energy-density is still high.

5) The case, k=0 is a special form of an open universe described as ‘flat’. Such a universe will expand forever, albeit at an ever-decreasing rate?

Ok, just wanted to get some assumptions in the open for clarification. I have snipped the following quotes from #129 for reference:

In the 2D "balloon" analogy the universe is yet unbounded (there is no edge, and no point on the surface is "privileged"). It also means no point on the surface is privileged with having a different mass distribution, and that means no point on the surface has a gravitational gradient different from anywhere else. In the equivalent 4D universe, it has a finite size, yet, because it wraps around there is no boundary. This means no point is privileged with a different mass distribution because no point is "nearer an edge" than any other.

Given the statements in 3) and 5), what evidence supports your 2D analogy that leads you to believe that a 4D universe ‘wraps around’ in the manner you describe?

While I think I understand the implication that the balloon analogy closes the curvature of spacetime, hence avoids any ‘gravitational gradient difference’ on the scale of the universe, it would seem that you must physically link the gravitational effects on one side of the universe to the other? Finally, one last question with respect to the following quote in #140

An observationally finite universe makes sense to me. Mainly because there is no observational evidence to the contrary. Nominate the observation you have in mind that refute this proposition.

While I agree that there may well be limits to what we can observe of the universe, this does not necessarily imply that the universe is not much bigger and possibly infinite. One of the reasons for raising the Newton Shells issues was to see whether it could support the notion of an infinite universe in the absence of any observed graviational centre. However, it is only a 'speculative notion' on my part and I accept that there is no evidence that supports, or refutes (?), this position. Therefore, would be really interested in any references, which describes the physics that supports any of the other positions forwarded. Many thanks.

P.S. Just for the record, I am actually agnostic on the question raised in this thread, simply because there does not seem to be sufficient evidence, as yet, to be conclusive. However, somebody in the forum may be able to correct me on this assumption.

 

[yuiop]

...

1) The universe is said to be expanding, based on redshift measurements, cepheid luminosity etc. This position is generally supported by CMB verification? Therefore, didn’t really understand the comments about space/spacetime not expanding in #132/135.

Hi mysearch. Long time no see! I think Jennifer was making a distinction between spacetime and space, where space expands while spacetime does not. I am not clear on how that distinction is defined but Jennifer is usually pretty well informed on this stuff.

...
2) When people talk about curved spacetime, are they referring to gravitational spacetime curvature or the open/closed issue?

In my understanding they are synonomous in the context of cosmology but hopefully someone will clear that up. In a closed universe Omega(total) is greater than one and the total interior angles of a large scale triangle adds up to less than 180 degrees and the universe is finite and has the potential to collapse gravitationally. In an open universe with Omega(total) less than one the interior angles add up to more than 180 degrees and the density is insuffient to collapse the universe gravitationally. It is worth noting that an exactly flat universe only requires the universe to be infinite if the cosmological constant is zero. A value of Omega(total)=1 which is partly made up of Omega(mass) and non zero Omega(dark energy) does not require the universe to be infinite.

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5) The case, k=0 is a special form of an open universe described as ‘flat’. Such a universe will expand forever, albeit at an ever-decreasing rate?

The flat universe has large scale triangles with interior angles that add up exactly to 180 degrees as if there is no gravity at all and the geometry of space is classically Euclidean. The current observational data is just on the closed side of being exactly flat but possibly too close to call at the moment. The apparent lack of gravity despite the obvious fact that there are bodies with mass in the universe is explained by the anti-gravitational effect of the cosmological constant otherwise known as dark energy. Einstein originally introduced the cosmological constant to satisfy his belief that the universe was eternal and static (which was more a religious consideration than a scientific one) it was pointed out that such a static model was inherently unstable and the slightest deviation from perfect balance would cause the universe to rapidly collapse or expand exponentially. That consideration together with Hubble's observation caused Einstein to withdraw the arbitary cosmological parameter and call it his greatest blunder. Note that he did not simply keep the cosmological constant and change the arbitary value to match observation. One problem with the cosmological constant is the enormous coincidence that the anti gravity effect exactly balances the gravity effect to give an apparent flat universe at only one epoch in the history of the universe and that happens to be now. Statistically the coincidence is of the order of billions to one against.

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While I agree that there may well be limits to what we can observe of the universe, this does not necessarily imply that the universe is not much bigger and possibly infinite. One of the reasons for raising the Newton Shells issues was to see whether it could support the notion of an infinite universe in the absence of any observed graviational centre. However, it is only a 'speculative notion' on my part and I accept that there is no evidence that supports, or refutes (?), this position. Therefore, would be really interested in any references, which describes the physics that supports any of the other positions forwarded. Many thanks...

On the Newtonian shells issue I would just like to add that in relativity the mass in the shells external to the shells where measurements are being made does have to be taken into account. The interior Schwarzschild solution has to be used in the case of the universe as the normal exterior Schwarzschild solution is only valid when there is no mass exterior to where the measurements are being made. The significance of the exterior shells is easily seen when you consider a clock in a hollow cavity at the centre of the Earth. It will be running slower that a clock on the surface of the Earth despite the fact that the Newtonian shell theorum sugggests there is no gravitational acceleration or force inside a hollow shell. The gravitational time dilation is a function of gravitational potential and not of gravitational acceleration. Gravitational potential is not independent of mass in external concentric shells.