[g__day]

Here's an interesting observation. Science believes the Universe inflated past light speed for a fraction of a second during its creation (i.e. its age 13.8 billion years, but its diameter is 40 billion light years, radius 20 billion light years).

Connections or interactions with something only happen because of force carriers (light gravity etc) - and force carriers can only move at light speed (bosons and relativity).

So we can ask - how much of the Universe is causally disconnected (segments that are far enough away and receeding so fast from each other that light or gravity or any force can never bridge the gap to reach another segment ) meaning forever these segments simply don't exist to each other nor can ever influence each other.

At maximum connectedness is the original epi-centre of the big bang. At this point one could observe a sphere of light equal to the age of our Universe, i.e. 13.8 billion lightyears in radius of the Universe's 20 billion lightyear radius - so by simple maths the volume of a sphere is 4/3 * pi * r^3 that means at the centre you could be affected by 13.8^3 / 20^3 = 33% of the known Universe.

Also from simple maths the percentage disconnect increases as you move from the past epicenter of the big bang to the edge of the Universe today.

If you were at a point closer than 13.8 billion lightyears to the edge of the Universe this figure would be even lower. Close to the edge you'd would be affected by less than half a sphere so you would be affected by less than 12% of the Universe.

As the Universe's expansion is accelerating I would guess over time this figure is continually decreasing, not static. So at 1 billion years old the causal connectivity of the epicentre of the big bang to the rest of creation I would view would be significantly higher than 33% (must check this)!


* * *

So is may be true to say the Universe is largely and significantly causally disconnected from itself! Maybe this is a prime factor leading to the increasing expansion of space itself.

Makes you wonder what is the Universe if between one and two thirds of itself is disconnected and its only getting more disconnected as time progresses.


* * * LINKS

I can give you plenty of links, because the premises are simple, only the conclusion is profound:


Size / Age of Universe:

http://www.wordwizz.com/pwrsof10.htm

http://www.technovelgy.com/ct/Scienc...sp?NewsNum=149

Inflation:

http://www.nap.edu/readingroom/books/cosmology/1.html

The 4 four forces (all bosons - w, z, Gluons and Photons) and when they came into existence:

http://pdg.lbl.gov/fireworks/intro_eng.swf

http://hyperphysics.phy-astr.gsu.edu.../unify.html#c1

http://particleadventure.org/particl...art_print.html

http://encyclopedia.thefreedictionar...orce%20carrier

Speed of force carriers - relativity!

http://www.google.com.au/search?q=ca...sons&hl=en

Other interesting facts:

http://www.astronomycafe.net/qadir/acosmbb.html


The rest is simple maths... (assuming the Universe is only 3 dimensional)

So I posed this in the advanced physics forums to see what folk think there - but that will probably take a week to get significant comment.

http://www.advancedphysics.org/viewthread.php?tid=834

[Vadi]

The universe has no finite radius.

[K.I.L.E.R]

But the contents inside are finite?

[Vadi]

I don't know. There ain't an upper limit of density though?

[Fred]

Ok, theres a few problems here..

One, the universe we see is by definition causally connected to us, what we don't see could be infinite.

Two, the big bang has no epicentre, it happens everywhere.

Now, the question is good, take 2 parts of the visible universe in different directions and ask yourself, were they causally connected in the past? Answer, on average yes, b/c we see an extraordinary homogeneity in the night sky (by experiment the CMB is what you look at), so much so that it was a problem for the usual FRW universe of general relativity. Things were too even, and this is what is known as the horizon problem.

This was more or less solved by inflation theory. Here spacetime inflates exponentially so to speak, and if you solve the equations, you will see that everything will have had time to settle in thermal equilibrium more or less. Then the universe pops out of inflation, and we are left with a nice smooth isotropic and homogenous universe governed by the usual friedmann equations.

One source of confusion that I think you might be struggling over is exactly what you mean by 'causally connected', and what you use as a clock. This is a little less simple than using Euclidean geometry, you need full General relativity to deal with it appropriately.

[g__day]

fred - thanks

Few scientists view the Universe as infinite (I can't name any credible ones)

The big bang of course happened everywhere, (past tense) because that is all there was. Its epi-centre can not be detected but still exists (to conserve laws of energy, mass and momentum) is the distinction you need to understand. We - nor anyone else - can detect where it was if it is outside our Hubble Sphere (apparently the term specifically used to describe how far light / gravity or any other force can travel over the age of the universe). So yes spacetime unfolded and to the layperson scientists say is centre is undectable, or there remains an unfindable centre - or the question can't be answered ... but the technically more correct answer is it should still exist but our physics can't hope to find it - we are Hubble sphere bound.

Parts of the visible sky - in opposite directions - were casually connected and may still so be. But receding parts that are slightly beyond what is visible to us in opposite directions definitely aren't casually connected.

Your comments on COBE and background radiation and homogenity are correct. Your statements linking inflation to the observed distributions of background radiation are also correct, although irrelevant to the statement at hand.

Casually connected is simply putting together two facts - 1) forces can not instantenously transmit, they travel at lightspeed at best and 2) during inflation the Universe unfolded 50,000 times faster than lightspeed until the laws of relativity took over - around 10 ^ -34 seconds after the big bang. So anything outside our Hubble Sphere can't interact with us and because of inflation most of the Universe is outside our - or any other - Hubble Sphere.

Time from a relativity POV doesn't enter this framework of analysis.

Thanks for you points!

[Vadi]

I meant that the universe has no boundaries so the can't be an epicentre. Also quantum pyhsics smear it out.

And parts of the universe can be causally connected through wormholes; in both directons since black holes seem to let information escape them.

[g__day]

The Universe may well have boundaries.

The wormhole connectedness pitch is so theoretically incomplete it has only the vaguest of frameworks - it can't even tell the typology of other dimensions so far. We can speak more reliabiliy about heaven then wormholes at the moment!

[Diplo]

g__day, are you talking about the universe being causally connected or casually connected? You use both and they imply different things to me (a relative layman in these things).

[Fred]

'Few scientists view the Universe as infinite (I can't name any credible ones) '

Again what most people mean when they say 'the universe' is precisely 'the visible universe'. That of course cannot be infinite.

This is actually a question of topology, and unfortunately experiment has ruled out a few possibilities (the closed universe with a spherical topology). However, our universe *can* be more or less an infinite plane. This is consistent with a FRW solution that is accelerating (COBE/WMAP). It also could be something that looks like a Torus, with a hyperbolic metric. That would be in principle observable, and things in this picture actually do collapse (by homotopy) to a point.

However, if its the simplest case, the flat plane, the Big bang has no point like compactification, and well you're singularity is sitting throughout all points in space, even points infinitely *far* apart (with zero proper length... chew on that for a minute or two).

There are other possibilities for topology choice, including some rather complicated nonsimply connected stuff. But most people use Occams razor.

"But receding parts that are slightly beyond what is visible to us in opposite directions definitely aren't casually connected"

No thats not necessarily true, (though it is on average). One reason could be a nontrivial topology as I pointed out (a Torus for isntance). Another could be a nontrivial local metric describing the patch.

btw, the definition of causal connection is not quite that simple in GR, i'll call it horizon distance.

it is for the Robertson Walker metric something like d(t) = R(t) integral ( 0--t) c dt'/R(t').. Where R(t) is the scale factor.

For an open universe, in the matter era, this will give a completely nontrivial looking distance for causal connection, not at all a euclidean looking thing.

[g__day]

Fred can you elaborate on "if its ... the flat plane, the Big bang has no point like compactification, and well you're singularity is sitting throughout all points in space, even points infinitely *far* apart " please, as I read yesterday the latest Cosmic Background Radiation Studies from the South Pole show the predicted polarisation, giving both alot of support for inflation and a flat Universe topology.

Scientists believe the sum matter / energy of the Universe from the moment of the Big Bang - if once again concentrated into a localised area to produce gravitational collapse - would give a Black Hole with the equivalent Schwartzschild radius about 40% bigger than we estimate the entire Universe has today. So the fact that the Big Bang didn't implode under that kind of pressure means simply and greater force stopped it. By definition nothing was outside this singularity so the force that created reality must have allowed expansion forces to outpace the propogation of the gravity field that would have stopped things cold in the first pico second. Inflation accounts for this, but as you say it allows very complex possibilities to occur when it comes to the shape or topology of the Universe.

So the singularity was likely uniform - but not for too long - inflation ripped that apart and although we see great uniformity possibly this is allowed even with dis-continous connectivity (causality).

I ponder how reliable are our estimates of the size and topology of the Universe are given we accept it is much larger than our Hubble Sphere.

It leads me to ponder greatly the meaning of a whole Universe that may really be just a giantic series of mainly dis-connected super cluster galaxies. Thinking about the 'edges' of the Universe - well the expression "You can't get there from here" never seemed more relevant!

[Fred]

" if once again concentrated into a localised area to produce gravitational collapse"

The problem here again, is what you mean exactly by 'area'.

One of the perpetual confusions, students of mine have when I teach GR, is precisely what mass, energy, length, area, time and volume correspond too exactly. In general, these things have several definitions depending on what you are trying to accomplish, and the level of abstraction.

I don't know how much I can help you in this type of forum, i'd really need to explain a little bit about pointset topology, manifolds, etc and giving length a meaning in topology (in fact in general, topologies that give a good meaning to length are a small subset of possibilities).

The way I like to think about it physically, is the topology of our universe is fixed, but length and what not will vary depending on the metric and the parameters that are there.

So in the case of a flat plane topology, what you see at all moments is still a flat plane, but the way you measure length is shrinking as you approach the physical singularities (where energy blows up).

On one hand, its sorta artificial, in the sense that we are sure quantum corrections are going to replace the classical theory at one point, inflation happens sorta by hand in such a regime.

Here is an explanation Brian Greene gave me. Consider a number epsilon (which is small) after the big bang. Galaxies and stuff are going to still be seperated topologically in the sense that the corresponding points will be outside balls of radius epsilon. However, the way we measure length via the metric is shrinking to zero. So send a photon out, and you will see that the distance it needs to travel goes to zero. But they are still physically apart.

So the big bang (better known as the big stretch) happens throughout the entire topology, even though there is a singularity of the metric, and how you measure physical quantities goes to zero.

This whole thing is quite subtle. Consider for instance a closed universe (the big crunch).. Normally we like to think of it as a spherical R^4 type thing. What they usually don't tell you in layman presentations of the subject, is that this too admits a flat plane interpretation topologically.

Consider a 3 sphere as an analogy. Remove the north pole, you will see by a smart relabeling of coordinates that you can make flat plane(s) out of the rest of the points. And by another patch, this time with the north pole included, but with the south pole removed, you get the entire information of the topology. But they are distinct physically, even though the sphere is related to two patches of flat planes by a homeomorphism.

So we have an indeterminism or an ambiguity at a very fundamental level, only very subtle experiment can distinguish things, and sometimes not even that is possible.

[g__day]

I should of course said volume - not area. The point I was making was most folk never ask why the Big Bang actually banged rather than imploded. Only after some consideration they might say hang on all that energy or mass so tightly concentrated is the very definition of a black hole! Why when the Universe was moments old its Schwartzchild radius (black hole event hozion) would equal about 30 billion light years - so why wasn't it crushed - the explosive forces simply couldn't have been anywhere near powerful enough to overcome gravity!

It takes them a while to realise:

1) The four forces were Unified to start with (and yes gravity did seperate first)

2) Gravity takes awhile to propogate, the enormous gravity field propogating outwards simply lagged too far behind the shockwave front of our creation event.

3) The non relativistic beginning of the Universe disconnected it under relativity. By the time relativity transitioned in (and we had the four forces with lightspeed limits) most of creation was already outside the spherical gravitational crush cone that would have then formed.

Take point 1) - by the time the Universe had moved into the control of relativity and the four forces it would have been a bit bigger than a basketball. If the Earth was compressed to the size of a sphere an inch in diameter it would form a black hole. An entire Universe the size of a basketball should have been that's all she wrote - but relativity didn't hold sway at these initial energy densities.

So the topology of the Universe was set before the first second of existence had ticked by. Of course it expanded - but by then its topology is determined.

Without getting hung up on topology or streching of dimensions underlying reality, or how static are our hundreds of physical constants - we don't need it to comprehend the central tenant of this subject.

The Universe started its existence obeying quantum mechanics and possibly the laws of other physics systems until the energy densities fell enough to let relativity kick in. If the Universe had less mass/energy at creation it might have transitioned straigth to relativity on creation and have never been born - because it would have been crushed on creation. But for us the energy levels were so high our Universe exploded on big bang, and this interlude gave us a head start before relativity took over.

So this phase change of physics allowed our Universe to exist - but means it is largely disconnected (under relativity) forever more.

If anyone is interested when we moved from Quantum Gravity -> Inflation -> Relativity and how the forces split from one into four - the following diagram describes this well: