Dear Marcus: Your View on Two Properties of the Universe

[Petradog]

Dear Marcus

If you could answer your opinion on these two questions that would be great.

1. Is the universe infinite in space or whatever space seems to be expanding in or morphing into?

2. Is the universe infinite in time? Is time always present before the big bang and before those complex physics laws, and is there a time infinitely after the merging of our galaxy with Virgo? Time of course referring to change occurred within the thing that space expands or morphs with.

I am by no means a physicist or a mathematician, but if you've explained good science to so many people here, I think you would have great wisdom on the true reality.

What is your belief? If you had to choose finite or infinite for both questions, which would it be, and why? You make the call, you're the biggest poster here!

Oh, and there is no answering neither or both.

Thank you, respond when you have the time

 

[marcus]

Dear Marcus

1. Is the universe infinite in space or whatever space seems to be expanding in or morphing into?

2. Is the universe infinite in time? ...

Petradog, I'm delighted by your questions. The idea of being forced to guess (when I don't know enough to guess rationally and really have to guess guess) somehow tickles!

I'm a spectator. I watch cosmology research (and quantum cosmology) as avidly as some people watch basketball or Humphrey Bogart movies. I don't pick winners!
The reason I like research to watch is that it is more surprising than anything else I know.
It has more surprises stored up for you.
Because if they knew the answers already they wouldn't be trying to find out.

I could tell you what answers I think I would LIKE the best We all have biases, I guess. Do you want that?
I know what kind of universe picture would appeal to me the most, so I'd be gladest if it turned out that way. Biases count for little however.
And the pleasure of getting any kind of answer at all outweighs any satisfaction of bias. Personal taste preference really does count for nothing. Nature decides how it's going to be and what she'll let us know and how much we have to work for it.

 

[marcus]

I ought to be able to make a clean concise declaration of my cosmo biases.
To make this fair, it would be nice if we could re-title the thread so it is for everybody to confess their leanings one way or another. Maybe Petradog you will let us know yours, so it is not onesided.

Warning: this is not a statement of probability about what is likely. It is personal favorites which has no bearing on how things turn out.

A. Finite volume space. Bumpy 3-sphere. Radius of curvature currently something over 100 billion lightyears. (this was the WMAP 95% confidence lowerbound estimate in 2008).

This is what people call a hypersphere. The 3D analog of the 2D surface of a balloon.
All existence concentrated on the 3-sphere, no surrounding space. So space has to be experienced and measured from within, not contemplated from the outside.

B. No limits on time-evolution. Go back in time as far as you like. Use a model that doesn't blow up. Could turn out there was a bounce, a rebound from some type of contraction. Have to test this against what we can observe today. I'd love it if the bounce model passed some observational tests.

I might have to revise this tomorrow. Getting late now. Other people should state their biases if they want. Thanks for asking Petradog.

 

[Petradog]

thank you very much marcus. I have no cosmo learnings unfortunately. I'm trying to be a spectator of cutting edge research too, except I have no idea what they're talking about, which is why I go here for a plain english understanding of what these papers mean.

Your favorite has great significance to me.

 

[tmoan]

2.
I know about other models of the spatial universe but i do not want to delve any deeper than i can pry for the moment.
but i recently teared a piece of cloth in two.That got me thinking of the expanding universe with accelerations and decelerations(shrinking) in that expansion.I have not yet thought of the physical aspect of it but i think it can be formulated into a good model.
Where the universe can have a constant of expansion over a large change of time but can go through fluctuations that decelerate and then accelerate its expansion.this can be symbolized by the overall change of entropy,a state function, over billions of years which is by all means increasing.But fluctuations will change its rate and in some cases reverse it just like the snapping of every string in the piece of cloth i teared up earlier.Surely the cloth will be torn but the rate is ever changing because of the quantum bundles of strings in it.if this model is expanded to higher dimensions than cloth and a more variable texture than identical strands.I think in some way this analogy can give rise to a more sensible thinking of expansion than balloons and raisins at least to me.

of course this is a model and strings(strands) here are of no relevance to the p-brane string theory.

also i am sure there are a lot of glitches in what i just wrote this is because i am in no context a cosmologist but rather a physicist in his early interests in cosmology so forgive my technical flaws!

1.
i believe in the time ending and beginning with space itself because an infinite time scale stretching backwards and forward will simply challenge GR which is consistent to date with many experimental evidence.Curling of space and time into linear spacetime is my bias today because to me it makes sense.Yet, just like before this understanding GR didn't make sense i am open to newer ideas that do not PRESENTLY.I only fully understanded GR when i plotted time varying with and x-y plane and saw with my own eyes what power it has on a 2-D scale let alone adding the 3rd.

 

[TalonD]

Marcus, what's your backgound if you don't mind telling? Are you a university professor? or just a joe the plumber with an amazing aptitude for this stuff?

as for my persoanl bias... there is a lot I'd like to say, but bias borders on speculation and I've learned not to do that :P

 

[marcus]

...

as for my personal bias... there is a lot I'd like to say, but bias borders on speculation and I've learned not to do that :P

Talon you just reminded me! It's very important in this forum not to indulge in speculation. The main educational goal I think is focused around getting a better understanding of current mainstream cosmology---with the professional research lit a background or guide.

Also we should never let personalities become the issue. In cosmo forum the focus is always got to be on what is known about the universe (early conditions, largescale structure, expected evolution in future...) and also on what is not known: what the professionals are currently trying to discover---the open questions.

So why would I think there would be some purpose to morally re-define this thread to be inclusive of everybody who wants---and to ask what are your biases?
How would you like it to be?

And there's the related question what would you guess, if forced to guess, about open questions (where there is as yet no rational scientific grounds to assume one thing or another)?

In between what your bias is and what you'd guess (nobody has to make a guess where there are no grounds, but if some alien inquisitor aimed his phaser at you and said "Guess!")---in between bias and guess there is this fuzzy land of wishful thinking.

So what's the purpose of venturing into talk about how you'd like the universe to be?
Petradog in effect challenges us (let's extend it to be inclusive) to be open about our biases. Could this be constructive? Or should we hush it up and move on to more objective stuff?

OK, stop dithering. Get your courage up and answer Petradog directly. Guess where cosmology and astroparticle research will be in 10 years from now.

(We can never know the final truth, research at best just converges towards it. So at best we can only guess where research will be at some time in the future.) this is a bit scary.

OK. *deep breath* By 2020 quantum geometrical gravity (essentially quantum GR) will be fully unified with quantum cosmology. The prevailing model will replace the bang singularity with a bounce. Predictions of stuff to look for in CMB and other background signals will be derived and checked. The Planck mission will have provided more CMB data, beyond what we have from WMAP. The universe will turn out to be spatially finite with 95% confidence--that is the errorbar for Omega will be all on the upside of 1. At present 1 is in the 95% confidence interval (so the infinite flat case is included.) By 2020 it won't be.

We already have weak lensing contour maps of dark matter density---the clouds of DM surrounding clusters are being mapped. By 2020 we might have a pretty good idea of what the DM is. But this is straying away from the two main questions Petradog asked---the extent (finite or otherwise) of space and of time-evolution.

BTW to me time-evolution basically means the process of cranking models back into the past, or forwards into the future, and the issue is do the empirically confirmed models break down or blow up at some point. If they don't then time-evo is infinite at both ends. I am not assuming that time is spatialized or geometrized because we don't really know that (the recent FQXi winners suggest not )

I don't guess that the issues around dark energy will be fully resolved by 2020. So I'll leave that on the table for somebody else to make a guess about.

Heh, heh. That was fun actually. Why don't you all try it?

 

[TalonD]

well, I'm full of questions, some very fundamental for which no one yet has an answer. Although I have my own ideas. I will agree with you Marcus to a certain extent especially since you are far beyond me in your understanding of the subject. I do like the idea of an infinite universe however, and an infinite progression of time. For the bounce to happen, time had to exist. Without time, nothing can happen. Time after all is a sequence of events and without it, there can be no events. No expansion from a singularity. Well I think maybe we can agree that there was no singularity, that it was instead vastly dense but not infinitely so. I would suggest a plank density beyond which you can not get any more dense. Well getting off track a there a little.
Consider the Copernicus view or whatever you call it. we use to think the Earth was the center of the universe, then we discovered that the Sun is! Then we found it was only a little star and we thought the milky way was everthing, then we found out there were other milkyways. So extending that thought to the whole universe, is it the only one? or is the part we can see, all that there is? Well there could be an infinite number of universes or this could be the only one and it could be infinite in size, or it could be the only one and finite in size with no inside and no outside, just a 3d spherical surface. I still like the infinite universe, it is more aesthetically pleasing to me for some reason. So that's what I would choose if the alien were pointing his phaser at me.
ok, a prediction, hope this doesn't get me a ding from the moderators.. I predict that someday we will discover that time itself has a granular quantum nature... hmmm...
whataya think?

and why so secretive? I'm just a lowly computer programmer by way of introducing myself... :)

 

[marcus]

well, I'm full of questions, some very fundamental for which no one yet has an answer. Although I have my own ideas. I will agree with you Marcus to a certain extent especially since you are far beyond me in your understanding of the subject. I do like the idea of an infinite universe however, and an infinite progression of time. For the bounce to happen, time had to exist. Without time, nothing can happen. Time after all is a sequence of events and without it, there can be no events. No expansion from a singularity. Well I think maybe we can agree that there was no singularity, that it was instead vastly dense but not infinitely so. I would suggest a plank density beyond which you can not get any more dense. Well getting off track a there a little.
Consider the Copernicus view or whatever you call it. we use to think the Earth was the center of the universe, then we discovered that the Sun is! Then we found it was only a little star and we thought the milky way was everthing, then we found out there were other milkyways. So extending that thought to the whole universe, is it the only one? or is the part we can see, all that there is? Well there could be an infinite number of universes or this could be the only one and it could be infinite in size, or it could be the only one and finite in size with no inside and no outside, just a 3d spherical surface. I still like the infinite universe, it is more aesthetically pleasing to me for some reason. So that's what I would choose if the alien were pointing his phaser at me.
ok, a prediction, hope this doesn't get me a ding from the moderators.. I predict that someday we will discover that time itself has a granular quantum nature... hmmm...
whataya think?

and why so secretive? I'm just a lowly computer programmer by way of introducing myself... :)

no particular reason, just am secretive. lowly retired mathematician.

I don't want to discuss the granular structure idea. If interested in time you should read Rovelli's essay, maybe also Barbour's. Did you already?
http://arxiv.org/abs/0903.3832
http://arxiv.org/abs/0903.3489 (Barbour's is simpler.)
Parts of Rovelli's essay I don't understand, but still like it, think it's good.

Ashtekar's group found the bounce occurred at around 40percent of Planck density. That is, to me, an unimaginably almost inconceivably high density.
That's what you casually estimate.

the title of thread is somewhat embarrassing. I wish the title could be something impersonal and objective. I don't criticize or blame Petradog, it's just how it is.

I still like the infinite universe, it is more aesthetically pleasing to me for some reason. So that's what I would choose if the alien were pointing his phaser at me.

Good! We disagree! That is somehow better than agreeing, when people are making crazyass guesses. OK. Yes. If the confidence interval on Omega could be narrowed and instead of converging on the up side it narrowed down on exactly one. So it began to look like we had the flat infinite case? Believe me I would be so happy! Getting any more definite answer totally outclasses the issue of whether it is your pet favorite or not!
I agree. Infinite would be just fine.

You should get used to consulting primary sources in cosmo, if not already. Look at table 2 of the 2008 WMAP report see if you can find the 95% confidence interval for Omega. Ask for help interpreting if you need it.
http://arXiv.org/abs/0803.0547
Look at how the different WMAP reports stack up citation-wise. It is this one that has 62 cites already and the next highest is only 28.
http://wmap.gsfc.nasa.gov/references_5yr.html
This one is the most useful of the set. Table 2 is on page 4. Omega_k is a conventional symbol for 1 - Omega_total.
The flat case corresponds to Omega_k = 0
While Omega_k < 0 corresponds to the positive curved case, finite volume, the usual Omega > 1. Obscure notation but essentially dirt simple.
Can you make sense of some of the table? I hope I hope.

 

[TalonD]

The thread title is understandable, you do seem to be one of the most prolific and knowledgeable posters here. I'll take a look at those links, thanks! especially Barbour's if it's simpler :P

 

[marcus]

The thread title is understandable, you do seem to be one of the most prolific and knowledgeable posters here. I'll take a look at those links, thanks! especially Barbour's if it's simpler :P

Talon if you just have 5 minutes to look at one thing I wish you'd look at table 2 on page 4 of http://arXiv.org/abs/0803.0547
like the second or third line
It is telling you the status of our knowledge about is space finite volume or infinite.
We know something about that.

Time on the other hand, what Barbour is talking about, is an endless conundrum. Only bother with the time essays if driven by a compelling interest in time.

 

[TalonD]

Hi Marcus, I took a look at that table and read.. skimmed through the text. Mind telling me what it says in plain English? It's a little bit beyond me.

I am quite interested in time. I like to ponder the things like that... Things that we don't have answers to yet.


side note off topic, speaking of time, it seems remarkable to me that we are here so soon after the BB. 13.7 gyrs is a long time but not so long geologically. After all the Earth is nearly half that age. Would that make our sun only a second generation star?

 

[marcus]

Hi Marcus, I took a look at that table and read.. skimmed through the text. Mind telling me what it says in plain English? ...

Here's some notation:
there's the actual average energy density rho
and the critical density rho_crit required for space to be flat
and the ratio Omega = rho/rho_crit

Also written Omega_tot, for total.

If Omega = 1 it means the actual density equals the critical level needed for flatness.
If Omega > 1 it means a bit too much density to remain flat, and she curls around and closes on herself----the hypersphere. the balloon analog.

If Omega <1 most likely infinite but possibility not taken too seriously for some reason. Seems like 1 or > 1.

So Petradog asks is space finite volume or infinite volume. Slightly oversimplified ( dn't want to get into all ramifications) it boils down to what do we know about Omega?

WMAP is the blue ribbon mission and they are the people to ask. I told you what Omega_k is, so you can translate their C.I. for that into a C.I. for Omega.
−0.0179 < Ω_k < 0.0081
means the same as

0.0919 < Ω < 1.179

I took the column labeled WMAP+BAO+SN because that is WMAP put together with other highquality data. the distribution of galaxies, their density has a large scale BAO wave component, SN stands for supernova. So that C.I. is even better than the pure WMAP confidence interval.

Basically it says
0.9 < Ω < 1.2

That means largescale space is *nearly* flat and either infinite volume or very large. (circumf > 600 billion lightyears and increasing)

And a new satellite observatory named Planck goes up in April, just next month! We'll watch and see if and how this confidence interval narrows down. This is how the question that Petradog posed is to be addressed quantitatively.

That's a simplification but it gets some of the essential gist across.

You might prefer the next round of measurement to narrow it down to [0.95, 1.1]
and I might prefer it narrowed down to [1.01, 1.15]. But it doesn't care which we prefer and we'll probably be pretty happy if it just gets narrowed down in whatever fashion.

 

[TalonD]

ah, ok, now I understand. Thanks for that explanation.

question
if the universe turns out to be a 3 sphere. does that mean that if you take off in a rocket in any direction, you would eventually end up back where you started like you would if you flew around the Earth ? Assuming you could outrun the expansion that is. In a thought experiment you can do that sort of thing. But am I understanding the geometry of it correctly?

 

[marcus]

Assuming you could outrun the expansion that is. In a thought experiment you can do that sort of thing. But am I understanding the geometry of it correctly?

You understand. As a thought experiment imagine you could freeze the expansion, and then go around.

That same Table 2 of the 2008 WMAP report gives a lowerbound estimate for the radius of curvature that translates to slightly over 100 billion lightyears. The circumference would be 2 pi times that----about 600 billion. 95% confidence lower bound. At least that big a circumference.

So it would take a long time even if you didn't have to face expansion.

 

[Petradog]

Marcus you are a great contributor to this forum, but I think you should look into becoming a researcher that works at an observatory or a scientist on a team at a university. Not only would you learn more, but you'd advanced the rate of progress for science itself by directly aiding research initiatives.

You also always have time to respond to people, which is very uncommon for intellectuals as they're usually doing other things. I dont' know why you care so much as to delve into the actual data that the researchers have measured and explain it in plain english as that takes quite a lot of thinking. I guess you enjoy teaching people and that's it. Everyone here probably appreciates it more than you think they do!

 

[Chronos]

Even the occasional head-butters here would agree with you on that point, petradog. I rarely disagree with Marcus to any material extent, but quibbling over details is great fun.

 

[TalonD]

WMAP is the blue ribbon mission and they are the people to ask. I told you what Omega_k is, so you can translate their C.I. for that into a C.I. for Omega.
−0.0179 < Ω_k < 0.0081
means the same as

0.0919 < Ω < 1.179

I took the column labeled WMAP+BAO+SN because that is WMAP put together with other highquality data. the distribution of galaxies, their density has a large scale BAO wave component, SN stands for supernova. So that C.I. is even better than the pure WMAP confidence interval.

Basically it says
0.9 < Ω < 1.2

That means largescale space is *nearly* flat and either infinite volume or very large. (circumf > 600 billion lightyears and increasing)

Ok, you understand this stuff so explain please.
what is C.I. ? what is Omega_k ?

I see −0.0179 < Ω_k < 0.0081 in the table but how do you get from that to
0.0919 < Ω < 1.179
and
0.9 < Ω < 1.2

and how do you calculate the 600gly circumference? or where do you get the figure of 100 plus radius of curvature?

Just because I developed a new prime number theorem doesn't mean I'm all that good at math. Wish I was better at it. I'd like to be able to read some of those technical papers and understand them better. :P

 

[marcus]

Ok, you understand this stuff so explain please.
what is C.I. ? what is Omega_k ?

I see −0.0179 < Ω_k < 0.0081 in the table but how do you get from that to
0.0919 < Ω < 1.179
and
0.9 < Ω < 1.2

and how do you calculate the 600gly circumference? or where do you get the figure of 100 plus radius of curvature?
...

Thanks for asking for clarification. I was typing fast and made typos in the earlier post!
What a mess! Should have been
0.9919 < Ω < 1.0179

The rounded off confidence interval I gave should have been:
0.99 < Ω < 1.02

That is just a rounded-off version of the preceeding line, to make it easier to read and remember.

95% C.I. means 95% confidence interval. You are 95% sure that the true number (out in the real world of Nature) is in that range. If it is done competently then it will turn out that next years' data will only narrow down the C.I. but won't contradict it by jumping out of that range.

Omega_k is just a variable that is arbitrarily defined to be 1 - Omega.so if Omega_k = 0.01 then Omega has to equal 0.99
and if Omega_k = -0.015 then Omega has to equal 1.015
Saying that Omega_k is in the range [-0.018, 0.008] is the same thing by definition as
saying that Omega is in the range [0.992, 1.018]

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

now you want to know how to get the estimated lowerbound for radius of curvature in lightyears. They give it in parsecs and a parsec is 3.26 lightyears. they also use a parameter "h" which stands for 0.71. I have to go but I will get back. You can probably do the units conversion but I will go thru it with you as soon as time permits.

 

[marcus]

Talon, thanks again for catching the sloppy arithmetic! I must have been in a rush and planning to come back and edit, to get the numbers right. The earlier numbers stink.

But anyway I am glad you took a look at
http://arXiv.org/abs/0803.0547
Now let's look again at Table 2 and do that units conversion to find the radius of curvature estimate.
In the WMAP+BAO+SN column, taking the positive curvature case, we have
R_curv > 22 h^-1 Gpc

Cosmologists use the funny h parameter because they like the freedom to try different values of the Hubble rate H. Funny h is just H written in the usual units (km/s per Mpc) divided by 100!
So if you think H should be 72 km/s per Mpc, then you put in 0.72 for the funny h.

In that case
22 h^-1 Gpc = (22/0.72)*3.26 billion lightyears = 99.6 billion lightyears.

Earlier when I looked at this I was thinking h = 0.71 and I got a bit over 100 billion.

So you can see where the figure for the circumference comes from. If you could freeze expansion and circumnavigate the hypersphere in a great circle you'd go 2 pi times that radius.

The volume of a hypersphere (analogous to the area of the balloon surface) is
2 pi^2 R^3
This is not the 4D volume contained "inside" the hypersphere. It is the 3D size analogous to surface area of balloon. You can use that formula to find the 3D volume of space as it would be today if the radius of curvature were in fact about 100 billion lightyears. Just plug it in and you get something in cubic lightyears.

The coefficient 2 pi^2 is about 20.

And this is lower bound estimate, the true radius of curvature is at least the 100 billion figure so the volume is at least that.
==================

A minor detail in Table 2 is the confidence interval for Omega in the case where one assumes that the cosmo constant really is the cosmo constant---dark energy actually comes from a Lambda in the einstein equation and accordingly has an equation of state with w=-1
Footnote "f" says that for the w = -1 case, and the combined WMAP+BAO+SN data, we have
−0.0178 < Ω_k < 0.0066 (95% CL)
So that means
0.9934 < Ω < 1.0178
slightly less downside range and more upside range

 

[TalonD]

Hey Marcus..

that -1 exponent on the h kinda threw me. to multiply by h^-1 you simply divide by h ?
I need to brush up on algebra.



(2 * (pi^2)) * (100^3) = 19 739 208.8
from google calculator
would that be 19 billion billion cubic light years?

even though it is slightly to the upside of the range, it seems incredible to me that it can be such a small range close to 1 and not turn out to be exactly 1 but like you said, we shall see... stay tuned...

You know. this stuff is easier to understand when you know what the cryptic letters (h) and the acronyms mean. Thanks for explaining some of that to me.

I'm going to look back over that table...



I have a question about DE and expansion but maybe a new thread would be appropriate.

 

[marcus]

Hey Marcus..

that -1 exponent on the h kinda threw me. to multiply by h^-1 you simply divide by h ?
I need to brush up on algebra.

You are doing all right! Yes you simply divide by h. Divide by 0.71 or 0.72 (whatever you think the Hubble parameter is).

even though it is slightly to the upside of the range, it seems incredible to me that it can be such a small range close to 1 and not turn out to be exactly 1 but like you said, we shall see... stay tuned...

You are right. A lot of people think it is so close to one that it has got to be exactly one. That's a popular view among cosmologists! But we don't know and better measurements are in store (like from Planck mission). So as you suggest, we wait and see.

(2 * (pi^2)) * (100^3) = 19 739 208.8
from google calculator
would that be 19 billion billion cubic light years?

You show a lot of gumption to do that volume calculation. You may have missed some zeros. One billion cubed is one billion billion billion.
And 100 cubed is a million.
So the answer is about 20 million billion billion billion cubic light years.
Or 19 depend on whether you round up or round down.

I would write it 20 x 10³³ cubic lightyears.

Silly as such a large number looks, it actually turns out to be useful in calculating such things as the mass of the universe, and the volume it would occupy at the moment of bounce (if an earlier collapse rebounded on reaching the Planck density---a kind of theoretical limiting density)

I have a question about DE and expansion but maybe a new thread would be appropriate.

Sure, it will make it a general question aimed at all those with expertise at PF. There are quite a bunch of knowledgeable people. Everybody should get a turn.

 

[Ich]

If I may jump in,
my personal view is:
If it looks like a duck, swims like a duck and quacks like a duck, then it probably is a duck.
So I'd say the universe is flat, and ends boringly after a long time.
The initial singularity should be something much funnier than the LQG calculations imply. Something like Penrose's cyclic universe model. Something natural - after you learned it's true.
And I do not think that they will solve the puzzle in the next 20 years. This will take at least another 100 years full of surprises.

 

[TalonD]

wow! I did miss some zeros! so if we assume the universe is finite and we have just calculated it's volume then we can calculate it's volume at plank density or 40% of that if that is where it bounced... if it bounced. and we can also calculate the volume of our 45gly radius visible part was at that time. I would do it, but I'm afraid I would miss more zeros :P