Martin

As tangential velocities are difficult to measure for galaxies there is some doubt over the event.

...

Exactly, I think that's a good point to bring out. Using dopplershift we can measure the radial velocity (of approach) very accurately. But any "sideways" drift is almost impossible to measure.

I remember some years back seeing a computer animated movie simulating the collision of the two galaxies and it was spectacular. Flinging different parts every whichway. Passing thru or around and then falling back together etc. And after quite a lot of milling around, we settled down into an elliptical galaxy (not as pretty as a spiral, you rightly note.)

But the computer simulation was made based on, I believe, some arbitrary assumption about the sideways component. The overall scenario is plausible but there is indeed "some doubt" as to details of the expected merger.

Incidentally our whole galactic supercluster is on a journey to and presumed collision course with something called 'The Great Attractor'.

I haven't kept up with the latest on estimated motions. My memory is that our galaxy (and indeed the Local Group we belong to) is going 500-600 km/s in the general direction of Hydra-Centaurus (the direction of the presumed G.A. concentration of mass). And the nearest really big cluster is the Virgo cluster, also estimated to be on roughly the same course.

The Local Group could be seen as a kind of minor satellite of the Virgo cluster and so we can think in terms of a Virgo supercluster, that we belong to (consisting of the Virgo cluster and surrounding smaller stuff like our Local Group.

So I guess the conjecture was that the Virgo supercluster was collectively going 500-600 km/s in the Hydra-Centaurus direction.

Could you review for us how we can tell? How are these velocities measured/estimated?

It is an interesting topic, I think.

The estimates I recall seeing were of velocities with respect to the microwave background rest frame. Is that your impression too?

I would say that the only velocities of this sort that we can measure reliably are the solar system's relative to CMB, and the solar system's relative to galactic center. Then doing a vector subtraction one gets the velocity of the Milky galactic center relative to CMB.

So Milky's velocity relative to the microwave background has been determined with pretty good precision.

But how to go from there to an estimate of the Virgo cluster's speed and direction? It seems bound to involve a lot more guesswork.

BTW I enjoyed Larry Niven's Ringworld---the characters especially Nessus associated with your namesake.

I hope you'll post some source material on these neighborhood velocities. I've lost track of whatever old links, and there has probably been some more recent stuff.

My hat is off to you, P. I did not stop to do a calculation. I am just on the point of going out and can't check your arithmetic, but assuming that is right then there seems time for only something on the order of one orbit, if that.

I will double check when I get back. My guess now is that you are not missing anything. Can't be more specific.

As I understand it, the galaxies moving towards us are in our local galactic cluster...

That's more or less right. If the distance to a galaxy is decreasing then chances are it is in some sense a "neighbor". Either in our local group, or in a neighboring cluster like the Virgo cluster. People talk about somewhat larger groupings called superclusters.

Galaxies do have random motions which could be towards or away or in any direction. You have to get fairly far away before the expansion effect completely dominates that random motion.

====

Now you are asking about inferring back in time---where was Andromeda relative to us?

I don't know of that kind of computer modeling being done and I don't know that it could be done with any reliability at present, because I don't think we know Andromeda's trajectory accurately enough.

All I can do is discuss possibilities with you. You know two objects can orbit each other indefinitely, getting closer and then farther and then closer and then farther, without ever colliding.

Two stars can do this---it is just a case of elliptical orbit.

Then after many orbits something could cause one of them to VEER and they may then collide. The random flyby of a third star could destabilize the orbit of the first two. I think you can picture that.

People do make computer models of the solar system and run them backwards in time as well as forwards.

But I never heard of someone modeling our local group of galaxies. It is complicated, I think there are some 10-20 large-ish things plus a lot of little bitties. I don't think we have observed these things enough to really know the speed and direction of each one. I don't see how we could expect to make a good model and run it back in time.

As far as I know, Milky and Andromeda have been orbiting each other, both members of this local group, for as long as they've existed.

Now the distance between M and A is closing, which by itself does not mean they will collide (a comet can approach the sun without hitting the sun). But some people predict collision on this pass, and that seems quite reasonable to expect. I've heard that a lot. But that doesn't mean that M and A haven't been orbiting each other in the past without colliding.

I have to pass, therefore. I don't have any hard information. Maybe DH or somebody else has some.

I'm having a problem with a photon not getting any closer or farther from us. A photon cannot ever be stationary, can it? Wouldn't this have repercussions on the bending of spacetime to make that photon travel at the speed c from or towards us?

In its local frame the photon is always traveling at normal speed c.

You should know that most galaxies we see with, say, the Hubble telescope are receding at rates greater than c. That means their current distance to us (if you could freeze expansion and take the time to measure it) is increasing at a rate faster than c.

You should learn how to use the simple online calculator (google "cosmos calculator") that converts redshift into recession rate.

These galaxies are not moving significantly in any conventional sense. They are not going anywhere. Just the distance to them is increasing, as allowed by General Rel, and specified by the Hubble law. v = Hd

(recession rate = H times distance)

So think of a galaxy which is sitting still in its local frame, and receding from us at rate c. So the distance from us to it is increasing at exactly the rate that light travels in the local frame. If that galaxy emits a photon in our direction, that photon will stay at the same distance from us, while the galaxy's distance from us grows at the rate c. The photon's local speed just cancels the recession rate.

If you google "cosmos calculator" and find Morgan's online redshift-to-distance-and-recession-rate converter, and if you want help using it, just ask.

Most of the galaxies we can see have redshifts greater than 2---that gives an idea how much their light has been stretched. The symbol for redshift is z. To use the converter you need to plug in 3 standard numbers that describe our universe's expansion

.27 for the matter fraction

.73 for the cosmological constant

71 for the current Hubble rate.

Once those 3 numbers are in the proper boxes, you just type in any z, any redshift you please, and it will tell you the distance to the galaxy that we see with that redshift, and its recession rate (which is a rate of distance increase, not a speed of ordinary conventional motion).

If you don't learn how to use that simple calculator your soul is forever doomed to darkness. Ask questions. Have fun.

...

Now it seems that more scientists are considering the possibility that it has actual dimensions. Describing a BH by it's 'radius' means the Schwarzschild Radius.

Misleading. The singularity AND the event horizon with its Schwarzschild radius have always been parts of the classical description. There has been no shift by "more scientists considering" some possibility. The Schw. radius has been with us since the 1918 work of Karl Schw. The event horizon was already a big deal in the 1970s with Bekenstein entropy and Hawking radiation.

I'm sure I have mentioned this before, but if we could park our space ship a few hundred miles outside the event horizon of a BH with an ACTUAL physical diameter of a MILLION kilometers and stare directly at it ... we would see nothing. The light coming from the stars BEHIND the BH would bend around the gravitational well, so it would no different than looking at any starry section of space. ( This assumes it is not 'feeding' ... no jets of radiation coming from the poles ... and that there is no accretion disc to give away the location.)

Misinformation.

Already with a stellar BH, like the 30 solarmass one in Andy Hamilton's graphic illustrations, looking in the direction of the BH you see something HUGELY DIFFERENT from an ordinary patch of starry sky.

This assumes the BH is not "feeding" but is completely quiet. A quiet BH still reveals its presence by gross optical distortion of whatever is behind it.

http://vixra.org/disclaimer

Icarus, I want to convey congratulations on this interesting thread discussing your highly speculative theory.

I appreciate your bringing it here to SFN, and the large amount of work put into graphic illustration, and the Latex typography.

Because the work is so highly speculative, it belongs in the Speculations forum. I will move it there.

This does not indicate disapproval. I encourage you to continue discussing and explaining your interesting idea.

The Astronomy/Cosmology forum is more focused on questions and answers regarding mainstream A/C.

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

I don't want to get into a discussion of your ideas, myself. There are several people who are already interested and it's up to them to ask questions. Nevertheless, I did want to toss in a comment---and to mention what seems like a peculiarity of your "Laws of Motion" in post #8.

It seems to require a distinguished frame of reference simply to be able to state your laws of motion. Or am I missing something?

I see no Newtonian "equal and opposite reaction" assumption regarding forces.

Would momentum be conserved in a universe which obeyed your laws?

... concentrated in a single point of infinite density. Most likely this is not the actual case due to quantum effects, but what actually happens is not resolved.

This is the key thing. It what is so interesting.

Gravity=geometry. Quantum gravity = quantum (therefore uncertain) geometry.

When QG is used to analyze what happens in a black hole, typically the singularity goes away and is replaced by something else. But so far different researchers have not resolved the issue of what.

In order to resolve, it must be possible to test ideas. For instance, the different QG models of BH collapse must lead to different predictions about gammaray bursts, say. If gammaray bursts are radiation from a BH collapse event. Then one must make detailed observations of the bursts in order to confirm or eliminate models.

If anyone is curious about the current QG research into BHs, they can look up papers on arxiv.org by various authors. Three young researchers that come to mind are

Kevin Vandersloot

Dah-wei Chiou

Leonardo Modesto

Personally I would not bother with any papers from before 2007 because the quantum black hole research is in transition. It is a high-risk area of research. There is so far no stable authoritative treatment that I know of.

Wouldn't the stuff above you be blue-shifted?

No Sir, I think not. It seems like it would, at first sight. But the photons from outside that came in thru the horizon after you are having a hard time catching up with you and are actually redshifted. As I recall, Andy Hamilton explains that somewhere at the Boulder black hole site.

http://casa.colorado.edu/~ajsh/schw.shtml

 

Interesting stuff.

You are absolutely right! It is interesting indeed. Hard. But Andy's a determined and visual explainer.

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

Intuitively, you are closer to center so you are pulling away from the stuff that fell in after you, and the stuff ahead of you is closer to center so it is pulling away from you. This is just halfwitted Newtonian intuition, not to take literally, but it sort of explains why both the stuff ahead and the stuff behind is redshifted.

...

That means our guy at the BH proximity would be in a state of free fall in a huge gravitational well. Instead of walking on the Moon, where his body wheights less than on Earth due to the lower gravity on the Moon, in the BH case the human body would turn into billions & billions of tons. Knowing that the human body can stand acceleration only a few g's ("a constant 16 g for a minute, however, may be deadly. from http://en.wikipedia.org/wiki/G-force#Human_tolerance_of_g-force), I suppose our guy would be dead before reaching the BH event horizon. Or am I wrong somewhere?

Well just to have a concrete example, suppose it is a billion solarmass BH, like you find at the core of some galaxies. Some galaxies' BH are bigger than that, but take a billion solar for round numbers.

Someone falling towards the event horizon would not feel any acceleration and not be stressed. Free fall is zero G. The sucker is too big to generate tidal forces on you at this point. It pulls your feet with about as much force as it pulls your kidneys or your brain or your ears. You are small compared to it, like a point particle, so no tidal stretching and no feeling of acceleration.

And you would fall thru the horizon without noticing it. It wouldn't hurt.

Now you are inside. You don't feel any tidal stretching yet. There is a long way to fall, on the order of two billion miles or three billion kilometers.

You don't feel like you weigh "billions & billions of tons".

You are still in free fall, which means zero G.

So you have some time to look around and see and think before you start to feel uncomfortable and start to get shredded by tidal forces (unequal attraction on different body parts). It is an interesting question what do you SEE. Because the hole geometry bends light in funhouse ways. Your world is going to be optically distorted.

Somebody else should discuss this. I haven't thought about the visual experience. intuitively, the central singularity would not be something you can SEE. It would be like in your future, and you can't see your future. But you would be able to see lots of other stuff. Like maybe busloads of Japanese tourists that fell in at the same time you did, all taking pictures of each other. Or used television sets that somebody dropped in because he couldn't figure out what else to do with them. And the stars outside the event horizon, behind you. You could see lots of stuff. But because of the funny optics I can't intuitively picture it.

The way I'm thinking about it, if your feet are pointing down inwards, then your visual world becomes more and more concentrated into a 360 degree band around your head at eye-level. Looking around you at eye-level you see stuff. But tilting your head to look up you see less and less (and it is redshifted to invisibility) and tilting your head to look down you also see less and less (and it is redshifted). So the tourist busses and broken television sets all around you increasingly concentrated at eye-level.

Someone who has thought this through may hopefully take over. I know Andy Hamilton at the U of Colorado has done some graphics showing what it looks like to fall into a BH. Some of Andy's stuff is online. Maybe someone here has checked that site out.

BTW, someone might check this estimate---I estimate that if you were taken near the event horizon of a billion solar BH and dropped thru your fall from the horizon to the singularity would last about 6000 seconds (by your own subjective time sense.)

That's called your proper time. The time as you experience it, the clock that your body processes are running on. 6000 seconds according to your own wrist-watch if you wear one.

Since I'm not being precise and am not so sure of my estimate, maybe I better say "something over an hour" of subjective time.

There is a short animated film of the formation of a dwarf galaxy, based on supercomputer simulation.

http://www.sciencenews.org/view/generic/id/54015/title/Supernova_winds_blow_galaxies_into_shape

In the video you see occasional supernovae exploding, each time blowing away part of the ordinary matter that is trying to gather together. Time is speeded up and the video gradually zooms out, as the small protogalaxy blobs collide, coalesce, as the galaxy grows, and as its spiral structure develops.

Finally the galaxy grows massive enough so that its own supernovae do not disrupt it.

The animation is part of a proposed solution to a long-standing puzzle about structure formation, published in the current issue of Nature.

http://arxiv.org/abs/0911.2237

Dark matter dynamics (with supercomputer simulations) has already explained a lot about structure formation. If you haven't seen this, George Smoot has an excellent 18 minute talk on it---google "Smoot TED".

Earlier simulations successfully reproduced a realistic picture of largescale filamentary (cobwebby) structure of matter, correctly predicted the size and distribution of clusters of galaxies, and the typical shape of individual large galaxies. But the simulations did not give a realistic picture of the dwarf galaxies which have a lower concentration stars and other forms of ordinary matter in their centers than the sims predicted. Overall the dark matter explanation of largescale structure worked remarkably well but there was this nagging discrepancy.

The article in Nature addresses that problem and explains the observed appearance and characteristics of a dwarf galaxies.

Hi Martin,

 

I am not sure if my interpretation of my reading on the subject is right. However, in the decelerating model of the Universe, the Hubble volume indeed is expanding and so the photons outside its past boundary will eventually fall within the Hubble limit and be seen by us...

I agree with this part of your post. In a non-accelerating expansion there is no event which we would not eventually get to see. There is no horizon.

But I'm not sure I understand this, and probably don't agree:

In the accelerating model, this will not be the case and once the stars fall outside the Hubble limit they are gone forever.

The Hubble distance is estimated some 13.8 billion LY. The cosmogical event horizon is estimated at 15-16 billion LY. There are plenty of stars which are today outside the Hubble sphere (the radius c/H sphere) but not outside the event horizon.

If something happens, like a supernova event, TODAY, at a star which is say 14.5 billion LY from here, WE WOULD SEE IT. If our civilzation continued to point good telescopes at the sky. It is not "gone forever" even though it is outside the Hubble sphere.

All that means is that the photons from that supernova would eventually be gradually swept back and would not get closer to us for some time. But they would stay nearly the same distance from us and eventually the Hubble radius c/H would extend far enough out to include them.

This is according to the standard model with the typical parameters people use. If you have specific questions please ask. I'll try to help.

The Universe is constantly expanding and as a consequence some very distant stars are moving away from us at speeds greater than the speed of light. This means that these stars will never be seen by us...

What you say here contains a misunderstanding. One thing you could do is read a popular article by two Aussie scientists, Charles Lineweaver and Tamara Davis, that was originally published in the Sci. Am. of March 2005.

I have a link in my signature at the end of the post. Anyone who calls him or herself "astro geek" should certainly know everything in that article. It is basic stuff about the standard cosmo model, with good pictures and diagrams.

If you have trouble with the link, or any questions, please let us know.

MOST OF THE GALAXIES THAT WE SEE were receding from us faster than the speed of light when they emitted the light that we are now receiving from them.

If you don't see how that works, read the Lineweaver article. If you still don't understand, ask here.

Also most of the galaxies that we see and photograph with telescopes etc are NOW receding at rates greater than c.

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

I have to go out, I'll check back later.

There are models where the universe expands, stops expanding, and starts contracting more or less at the same rate. It takes tens or hundreds of billions of years for anything uncomfortable to develop. Finally there is a crunch. Those models are not anything to worry about.

The main thing is to get straight on the first part of your post, about recession rates.

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

I'm only back for a moment. Have to leave for the day. Things to understand about the standard cosmo model:

1. Acceleration does not mean the Hubble rate H(t) is increasing. It has been decreasing and is predicted (in the std. model) to continue decreasing. What accelerates is the scale factor. Learn about this. The Friedman model is based on the scale factor.

2. Because the Hubble rate is decreasing, the Hubble distance is increasing. It is the reciprocal c/H.

3. The Hubble distance is the distance that is currently increasing at rate c. It is the distance to a galaxy which is receding at rate c. IF A PHOTON CAN GET WITHIN HUBBLE DISTANCE OF US, IT WILL EVENTUALLY REACH US.

4. Because the Hubble distance has been increasing rapidly it has kind of "reached out" to photons that were trying to get to us but were being swept back by the expansion. Thus we have received and are now receiving a whole lot of light which was initially being swept back, getting farther away rather than nearer.

5. As Lineweaver etc explain we currently see with our telescopes many galaxies which were receding faster than c when they emitted the light, and which are still to this day receding faster than c. Indeed that is typical.

As I recall, anything with a redshift z > 1.6.

You can check this using the online cosmos calculator. Google "cosmos calculator" and get someone to explain what numbers to put in, to get started.

...

It's possible I'm wrong and they've mostly accounted for changes in position when making the filaments diagram....

 

...their actual positions millions and billions of years later (i.e. today). Would the filaments retain their shape afterward?[/i]

...

To the extent possible differences in position are already accounted for. The filamentary structure is observed.

It was intelligent of you to think that you might have been wrong in supposing that radial distances had not been brought up to date. You must have used the Ned Wright calculator. If you plug in an observed redshift it calculates the today distance for you.

That's the whole point. If you haven't played around with the cosmo calculator, you should spend some time doing that and get used to it.

...

 

 

There some bigger problems with the balloon analogy:

It assumes a finite universe. That remains an open question as far is I know.

I agree. To my mind that is the main problem. To include the infinite case one has to stretch one's imagination to include an infinitely big (but nevertheless expanding) balloon. A tall order:D

It implies that the universe is embedded in a higher order Euclidean space; that a Euclidean point of view is somehow preferential to a non-Euclidean description.

When I've presented the balloon analogy I usually stress that when you use it you have to concentrate on the surface itself. Ignore the outside, the inside, the rubber, pretend they don't exist.

All existence is concentrated on the 2D surface itself.

To use the analogy properly, one should think of the surface as NOT embedded in a higher dimensional Euclidean space. The geometry can be described in a purely internal way, from the point of view of a 2D creature living entirely in the surface (for whom no other spatial directions exist besides those lying in the surface.)

Including some additional discussion like that can help to offset the drawbacks you mentioned.

The Cold Dark Matter theory, found here http://en.wikipedia.org/wiki/Cold_dark_matter , has been used to explain how the universe formed into a cosmic array of galaxies from the moment of the big bang.

 

This is from the above link:

 

"In the cold dark matter theory, structure grows hierarchically, with small objects collapsing first and merging in a continuous hierarchy to form more and more massive objects...

Have to be careful with Wikipedia. Pick and choose your articles. Some articles have stuff which is wrong, or partly wrong, or misleading.

The first danger signal with a Wikipedia article is if there is a self-critical warning banner at the top. The Wikipedia organization has the policy of putting warnings at the top of their own articles which they consider inadequate or possibly unreliable for some reason. The staff doesn't have time to fix everything which some incompetent or biased contributors might post. So they just tag it.

The one you cited has a banner like that.

I would normally advise ignoring such an article. It's kind of like seeing "proceed at your own risk." This particular warning is because the article lacks references to reliable sources.

But even if someone fixed that and put in some links to something that passed for reliable, the article would still be misleading because of that business about stars forming first.

That is not how modern theory of structure formation goes. It is not hierarchical with small objects forming first, and then building up. The article refers to some ideas some people had back in the 1980s. AFAIK contemporary models of CDM structure formation do not have small objects forming first.

So if the article gives you the impression that it is talking about contemporary astronomy, and is relevant, then it seems misleading. It somehow should include mention of what current scenarios are, current models of structure formation.

A good source at a popular level might be George Smoot's talk. Google "Smoot TED". It talks a lot about CDM and structure formation but it is definitely not hierarchical bottom up with small objects first. They run computer models and that is not what happens.

I can't give you an authoritative picture. Have to go. I'll try to get back later and add some detail. Maybe someone else can fill in the picture in the meanwhile.

There are no universal diagonals, either.

That's fairly deep. I'd be interested in hearing you elaborate some on that.

One thing that comes to mind is the Shapiro observation. Lightrays passing near the sun are actually slowed down by the fact that time is slower as you go deeper down in the gravity well. So the speed of light appears to be contingent.

So the "diagonals", which symbolize the lightcone structure of spacetime, could be seen as contingent, somehow not absolute.

The smallest gravitywave ripple would in principle (infinitesimally) alter the lightcone structure of causality.

Or am I off track? Do you want to add some detail?

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

Edtharan, I think you know that in cosmology we do have an (approximate) universal Now. Given (approximately) by the CMB.

We have discussed that. But in pure General Relativity, in the abstract, not including features of our universe like the CMB and Hubble expansion, there is no universal Now. So you are right in that respect.

As soon as you include even Hubble expansion, you have implicitly accepted a Now. The Hubble law depends on being able to measure distances at a given moment, it contains a universal time coordinate

v = H(t) d

Now in response to Ellis. I doubt anyone thinks that general relativity is the final word on the structure of space-time.

Exactly.

Ellis is recognized as a top Relativist and Cosmologist and the papers I refer to are aimed at a specific modification of the GR block universe idea to make it more compatible with QM. You cannot "respond" to Ellis without studying his specific proposal.

Anyone interested can look up G Ellis on arxiv.

As for the block universe, IMVH it is a stupid concept,...

Why stupid?

_because energy would be infinite...

Not so. The volume of space does not have to be infinite in block universe.

The quantity of matter/energy does not have to be infinite.

One version of block universe can be visualized as a solid ball, layered like an onion---into time-layers.

(heh heh some jerk could point out that the slicing into time layers is typically to some extent observer-dependent or arbitrary---that's right---but we are used to time-slicing in cosmology )

Logically there is no essential difference but call it a ball universe, if you want.

The balloon model is just another (necessarily imperfect) way of looking at the ball universe. As the balloon inflates, it represents successive layers of the ball.

So the balloon model is essentially a 3D model.

It gives a way to think of a full 4D model. Think of a 3D hypersphere (in place of the 2D balloon surface) and think of the 3D hypersphere inflating.

Watch the movie of photons creeping over the 2D balloon surface, as distances on it grow. Extend that in imagination to photons creeping through an expanding 3D hypersphere.

Specific visualization-aid concepts are not inherently stupid. Picking and choosing can be stupid. Rejecting and favoring can be stupid. Since various ones can be useful in various contexts, one should be ready to use whichever aid to the imagination is appropriate. As for the concept itself, obviously what most matters is how you use it.

What a nice bit of news! Thanks for sharing it with us.

You must be on the point of taking a postdoc position somewhere.

Cordial best wishes and many (as Severian says) happy returns.

Heh heh. Nice way to put it.

Later space is bigger.

So it expanded into "later" (rather than into some imagined surrounding space).

Yes I reckon so. Must be, because the best they have done so far with 95% confidence is say the circumference has to be at least 628. (you know the units I mean).

Compliments on getting an understanding of it with the help of visual intuition. Good intuition---I mean about the 7% horizon and the 2% error margin.

Martin, Perhaps you should add "with sugar on top" to your plea for 'good measure'.

Heh heh. Absolutely.

Please understand what the standard cosmo model says---get familiar with it---before you start criticising or making up your own. Pretty pretty please with LOTS of sugar on it

Everybody who posts in Astro/Cosmo should have tried out the Ned Wright calculator: google "Wright calculator"

and watched Wright's balloon model animation:

google "Wright balloon model"

Calculators like that and like Morgan's "cosmos calculator" I link to in my sig---calculators like that embody the equations of the standard model.

You dont know the model if you just know some words.

Basic shared cultural experience. A first exposure just takes 15-20 minutes.

And there's the Lineweaver Davis SciAm article. Generally recommended by many of us at SFN over the years.

This is reminiscent of Galileo's 'result', after his attempts to measure the speed of light using men with lanterns on distant mountaintops: "Extraordinarily fast, if not instantaneous."

To have had the balls to try to experimentally determine the speed of light in william shakespearse's day or 1620 or whenever. the guy was awesome!

And within 50-60 years from Galileo's experiment a young Dane in Paris actually measured it! inspired by Galileo.

He got within about 10 percent of the right answer by timing the eclipses of one of Jupiter's moons.

Galileo put the idea out there, that it could have a finite speed and you could measure it. And Olaus Roemer followed up within 50-60 years.

In your picture space is 1 dimensional. A circle. And instead of an expanding circle you say picture a cone. A cone is a static picture of an expanding circle. You can slice a cone into a series of larger and larger circles.

...

The analogy I like is the cone. Lets cut out the conical singularity. Then globally the cone looks like a circle times an interval (part of the line). Orientate it so that the smaller circle is facing down. Now do some space-time cuts, that is cut up the cone into a series of circles. You see that they are all of different sizes.

...

Some people make the same analogy but with 2D space. Their spacetime is a solid ball. They imagine it as made of spherical layers, like an onion.

Each layer is space at some particular time.

Each analogy has some enlightening or convenient feature. Each is useful and all, as you suggest, have problems. No perfect analogy.

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

Basically what you have presented, AJB, is a toy version of the block universe concept.

It could be interesting to discuss the pros and cons of that 4D way of picturing the universe---its degree of realism or not.

George Ellis, a worldclass cosmologist and relativist has written about the block universe recently. A couple of papers in the past two years. You may know of him: he co-authored The Large Scale Structure of Space Time with Stephen Hawking back around 1960.

Part of George Ellis' message in these papers is that a simple thought experiment involving two weights and a radioactive isotope can show that the block universe concept must be wrong. It cannot correspond to reality because it does not include quantum uncertainty.

In the standard block universe picture space time including past and future are part of a single 4D crystal-like entity. Particles have their world-lines snaking through the block.

You can slice the block into time-slices according to some observer's time, or anyway some chosen time.

I have to go. Back later

I'm assuming the visible universe has radius 13.7 billion lightyears (it's 13.7 billion years old, and so the farthest light could have traveled is 13.7 billion lightyears, and so the farthest we can see is 13.7 billion lightyears away, and that defines the "visible universe").

The farthest stuff we can see is what emitted the CMB light. The microwave background. The current distance to that stuff is 45 billion light years.

Think of freezing expansion and then timing a radar signal. It would take 45 to reach that matter (which we see as it was over 13 billion years ago) and 45 to get back. A round trip time of 90.

Don't think of it as 13.7 billion lightyears away. In terms of today's distance it is much more because of expansion.

45 billion lightyears is what astronomers call the particle horizon. The present distance of the most distant particles which we can see (from the light they emitted in the past).

If the minimum radius of the universe is roughly 100 billion lightyears as you say...

I said the radius of curvature was estimated at least that. RoC is a technical mathematical concept. It is used as a measure of curvature.

The RoC doesn't correspond to any actual distance in our space.

If you imagine embedding our space as a hypersphere in a space of higher dimension, then it would have a center and every point of our space would be the same distance (100) from that imagined center.

I thought you were calculating the circumference and got the wrong numbers, so that all this would be familiar to you. You would understand what the radius of curvature means. Sorry I mentioned it, if it caused you confusion.

Think of it this way. In the smallest finite case, the circumference is 628.

And the farthest distance we can see is 45, in all directions.

That 45 is along the curved hypersphere surface.

So the farthest distance we can see is 45/628 of the circumference.

Light follows the curvature of space, so it travels along the "balloon surface". So distances we measure are like great circle airplane routes, and should be compared with the circumference, not the imagined radius (which if it existed would be outside our 3D world.)

And the 628 is a lower bound. Could be much more.

Thank you for enlightening me with this thread

You are most heartily welcome, but in truth I think sincere (not feigned) thanks are due to Chuck Lineweaver and Tammy Davis. They did a great job.