Here are grouped together 3 of my posts from Universal Expansion edited into a complete and concise hypothesis.

Part 1

The universe is not expanding in the sense that we usuallyunderstand expansion.

It's expanding "into itself".

How can that be? you ask.

The universe is described as boundless but at the same time finite in 3 dimensions

(forget the other rolled up 8 or so dimensions in string theory for now as we're dealing with a concept or a mental picture if you will.)

Imagine a one dimensional universe. It has to be a line, right? OK.

Now lets imagine that the "space" occupied by the line is curved (we wont say by what yet).

The line could complete a circle and come back on itself. This is not 2 dimensions!!

This is one dimension in curved space. The circle per se is a 2 dimensional object that helps us visualise the 1D universe in curved space.

Now imagine a two dimensional universe. It has to be a plane yes? OK.

Now lets imagine that the "space" where this universe exists is also curved.

If you think of the surface of a globe then you,re doing well.

The surface curves with the space and "comes back on itself" thus is unbounded i.e. has no boundary (be careful not to think that inwards to the centre and outwards away from the centre exist for this universe. They do not!

The Globe is just a visualising tool that lets us imagine a two dimensional universe in curved space.

Now we have the first hard part.

Moving up a dimension into a three dimensional universe (ours by the way)

we find ourselves in the embarrasing position of having no four dimensional tool to help us visualise how we can have a boundless universe in curved space.

We are forced to go back and look at the 2D universe and extrapolate from there.

The problem is that in a 2D model the expansion is visible like a baloon being blown up. The surface of the balloon seems to expand outwards. But we have said that outwards does not exist for the 2D universe! so what's realy happening?

Well the way I see it is that the curavature of space is decreasing.

the actual universe itself observes a spreading effect of all the material in it but it cannot say where it is going because there is no dimensional concept of outward!

It can only say that it is expanding in a manner that seems to go somehow into itself with out ever crashing into itself from behind!

Now for the second hard part.

Move all this up a dimension!

Now for the realy hard part.

Beleive that for us the extra dimension needed to build our model of the expanding 3D universe does not exist. (it's curved space-time)

I mean realy does not exist, not zero, not a vacuum, not space somwhere else, but realy not there at all!!!

Get your head round that and you're on your way to understanding universal expansion as envisiged by true relativists.

part 2

I think I have a four dimensional model to explain expansion in 3 dimensions as a reduction in curvature. It also explains why the visible universe seems to be physically expanding.

If I may simplify the visible universe into a sphere (3D) which is surrounded by an infinite number of doughnut shapes that intersect ous visible universe which fills the cross section of the rings. (These doughnuts are of course just an aid to visualisation for the moment.)

Imagine stopping time and then traveling from where we are (the centre of the visible universe) in what seems to us a straight line to the edge of the universe we are actually moving along a line in curved space which is the equivalent to the central circle of one of the doughnuts.

As we travel towards the edge we start to see that things exists beyond the point that we considered the edge of the universe.

Remember time has stopped so all the light in the universe is stuck in the same place. so we hypothetically see what is beyond the edge.

Remember in the 3 dimentional model of the 2D universe the curavature was decreasing as the balloon expanded. The second thing to notice here is that if you were in this 2D universe you would also observe that your horizon was becoming farther and farther away but the objects on the horizon were always the same objects. No new objects would come into sight! This happens in our universe and is represented as the edge of the visible universe moving awy from us at almost the speed of light. If things were moving away from us faster than the speed of light then the light would never reach us! ( like throwing a ball backward out of a moving train window-the ball still moves in the same direction as the train only slower, there is now way it can hit a stationary object behind the train)

Our "horizon" is the edge of the visible universe and is always receeding but no new objects will apear on it from where we stand.

If wew move instantaeously to the "horizon" we will see another "horizon" and it behave just like the one we see from here.

instantaneously traveling along our line out of the visible universe the curvature of the doughnut's central line will bring us round upon ourselves from behind(like going round the balloon).

Going off in any direction from the centre of the universe i.e. where you are now, you will alway enter into a doughnut central line because there are an infinite number of them. (remember they are just a model to help think of a 3D universe in curved space) And you will always end up where you started.

Now add TIME!

We cannot move faster than light.

We can never overtake the edge of the universe or get any closer to any part of it than we already are.

The edge or "horizon" is expanding into itself and the curvature which causes this phenomena is decreasing continuously at the speed of light.

What causes the curvature is another question but mass and time and gravity which are inter-related in a such marvelous way are the leading candidates in modern physics.

Part 3

When I postulated about the infinite series of imaginary doughnuts as an aid to visualise the curvature of space I only touched on the Idea of expansion.

Here is a fuller examination.

As we know a shpere is a special case torus where the central ring has zero diameter. Picture this torus as having the diameter of the current visable universe.

This is the state of the curvature of space at the time of the Big Bang.

As the torus expands (and it, which is one of an infinite series, expands in a special way: the central ring increases in diameter but the cross section remains the same, if it just blew up like a linear projection then the curvature in the cross section would remain the same.) matter, energy and time all begin to unfurl.

The visual appearance of each torus changes as time goes by: From a sphere it begins to resemble an apple with the poles pinched then as the radius increases the hole in the centre appears then it starts to look like a dough nut and from there it starts to look more and more like a bicycle inner tube.

I measure the curvature of space as the tan function of the angle created by

3 points. They are:

A: the centre of the universe

B: the point on the extreme outside edge of the torus farthest away from point A.

C: the point where the imaginary line from point B passes tangentially the edge of the visible universe.

The angle ABC we will call "a" for apoklisis which means deviation.

tan a is the measure of curvature of the space occupied by the universe.

Lets look at each case along the time line of this dynamic model.

1. The sphere: at this point apoklisis is 90 degrees and the curvature is infinite.

no straight line can ever leave it's starting point and everything is seemingly curled up into an infinitely small space.

The universe is howver the same size as it is now! (Remember this is a 4 dimensional model not reality!

2. The apple shaped torus: The centre of the torus is still with in our universe and if we take 2 examples we will see two different behaviours.

type a: The centre of the torus is less than half way from us to the edge of the universe. At this point in the expansion straight lines will not reach the edge of our universe and the resulting condition is that the matter,energy and time have yet to unfurl to the point where the universe seems to be visually expanding, i.e. light always came back to the point of origin within the universe.

type b: The centre of the torus is more than half way to the edge of the universe.

in this state the model starts to display what can be considered visual expansion (the type of expansion we can easily imagine like a ball being blown up in 3 dimesions). Straight lines from the centre now reach the edge of the universe and can be mentally projected outward beyond the edge. This is the formation of the "horizon" which I mentioned before.

3. The doughnut with the infinitely small hole. The apoklisis is now 30 degrees and the curvature is 1

4. The inner tube and beyond. The curvature dereases below 1 as the diameter of the hole expands until at a time infinitely distant from us the curvature becomes 0, Everything is straightened out and dimensions are infinitely large.

At this point everything goes into reverse and the expansion becomes compression

like the piston in a car engine eaching the apex of it's cycle.

Remember this is just a model to explain a bounded infinite universe whose decreasing spacial curvature creates the illusion of 3 dimensional expansion.

Now my head realy hurts!

Cheers

Ferg