Is the universe bounded or unbounded?

[otseng]

In the Light, stars, and creationism thread, I proposed a theory to reconcile a young earth with being able to see stars that are billions of light years away. The theory assumes that the Big Bang is true, however, it also assumes that the universe is bounded. In typical cosmology, it is assumed that the universe is unbounded.

Bounded means that the universe has a boundary to it. There exists an "edge" to the universe in which beyond this boundary, our universe does not exist.

In an unbounded universe, there is no "edge". The universe "wraps" around itself. So, if you are to go in any direction in a straight line, you will eventually come back to the starting point.

This is hard to conceptualize, but can be explained like a surface of a sphere. On the surface of a sphere, if you start at any point and then go in a straight line, you will eventually come back to the starting point. Now, instead a 2-D surface on a sphere, the universe is a 3-D topology that curves in on itself.

The ramifications of either of these two assumptions make for drastically different cosmological conclusions.

So, the questions are:
1. Is the universe bounded or unbounded? Why?
2. What are the ramifications of whether it is bounded or unbounded?

[QED]

I already said something about the universe being both bounded and unbounded in the quantum field, infinite and non-existent, and all possibilities in between. Has anyone given some thought about this? We can be arguing about something that ourselves choose to become reality, along with all the consciousnesses in the universe. That is, the sum of conscious observation in the universe causes the collapse of the universal wavefunction. In a way, I can consider this indication (however feeble) that we're not alone in the universe and that we're far from being special. If it was just us, we would decide how the universe arises from the quantum field in each "now". Than again, perhaps we do. Perhaps the universe is as large as Humanity can observe.

Sorry Beto, I did miss that somehow. I'm not personally inclined towards the "conscious observer collapses the wave-function" interpretation. Unless it is augmented by Wheeler's kind of "backwards causation" that spans billions of years, it's difficult to picture a universe of proto-stars all busily churning out their fusion products in a universal state of coherence -- patiently waiting for the living products of their labours to make that all-important first observation that decoheres them into a reality. But then it's just as difficult picturing any of the Quantum interpretations.

I'm beginning to lose the gist of this debate. As a consequence of GR the metrics of distance as well as time are "up for grabs" as they are interchangeable. We can always choose a different "clock" to measure things with. For example, the density of the universe can be used to track an infinite number of events in a finite amount of time, so the significance of "boundaries" seems rather moot.

[Beto]

I'm not personally inclined towards the "conscious observer collapses the wave-function" interpretation. Unless it is augmented by Wheeler's kind of "backwards causation" that spans billions of years, it's difficult to picture a universe of proto-stars all busily churning out their fusion products in a universal state of coherence -- patiently waiting for the living products of their labours to make that all-important first observation that decoheres them into a reality. But then it's just as difficult picturing any of the Quantum interpretations.

You're quite right, although thinking back to the "double slit" I remember that a conscious observer isn't required. It's the measuring apparatus that collapses the wave function. This is accurate, right? It may be a subtle yet very important difference. The young universe you describe might only have existed has a possibility among all the others, until it was observed. In a sense it was "real" in the quantum field. Of course it may STILL be in the quantum field.

[otseng]

Well, it's a bit difficult keeping in mind a non-metric expansion given that the amount of observed red-shift has the most distantly observable galaxies moving at around two-thirds the speed of light. Such relativistic velocities would increase the mass of the galaxies in ways we could hardly fail to spot.

How would it fit in with Olber's paradox?

An expanding metric will subtract light that can't keep up with the expansion. Don't forget - the universe needn't be infinite for a dark sky to be a problem, just sufficiently big.

It would appear to me that a finite universe with a finite age would solve Oblers' paradox.

But yes, GR is all about describing space-time with variable metrics. The Friedmann-Lematre-Robertson-Walker (FLRW) metric is a solution of Einstein's equations that seems to give a good approximation to our universe.

We are definitely getting way over my head here. In layman's terms, what exactly does FLRW show?

From Goat's article about the universe being at least 156 Billion Light years wide...

However, 156 billion would not be considered large enough to explain why our observable universe is flat.

"The comoving distance from the Earth to the edge of the visible universe is about 46.5 billion light-years in any direction; this is the comoving radius of the visible universe. It is sometimes quoted as a diameter of 92.94 billion light-years."
http://en.wikipedia.org/wiki/Observable_universe

Now we're going over old ground again -- by being too big a radius to measure.

Yes, we've covered this before.

What is the evidence you have that rules out a finite but very very large universe?

Well, I don't think the burden is upon me to disprove something that has no evidence for.

But, I will say that I do challenge that the universe is metrically expanding. If the universe is not metrically expanding, then the size of the universe would be bound by the speed of light and cannot then be extremely large.

[QED]

It would appear to me that a finite universe with a finite age would solve Oblers' paradox.

Of course. I appreciate that a sufficiently small universe would satisfy the problem, and I also appreciate that if red-shift is not due to relativistic Doppler and if we are privileged enough to be stationary while distant galaxies recede all around us (not forgetting to add to everything the peculiar motion of three-thousand odd kilometers per second given by the CMBR dipole) and if some unknown force applies a greater acceleration to galaxies the further they are from the Earth and if distant Super Nova explosion happen in slow motion compared to local ones for reasons other than relativistic time dilation -- then putting all these "iffy" things together (and plenty more I've probably left out) we may be able to arrive at a radically alternative interpretation to the FLRW metric solution that has the Earth located at the centre of the universe.

But GR is experimentally verified to a very high degree and we mustn't forget that gravity isn't a force but a distortion of the space-time metric so we already know that space-time is "elastic". This is the main reason why I can't fit your pieces together. It's the same with the redshift interpretation: It's not just Doppler -- distant supernovae explosions appear to happen in "slow motion" -- a prediction of relativistic time dilation.

So how do you get a non-relativistic universe with a fixed metric that explains all the features so far observed? I think it's time you satrted explaining things in layman's terms

[otseng]

I appreciate that a sufficiently small universe would satisfy the problem, and I also appreciate that if red-shift is not due to relativistic Doppler and if we are privileged enough to be stationary while distant galaxies recede all around us (not forgetting to add to everything the peculiar motion of three-thousand odd kilometers per second given by the CMBR dipole) and if some unknown force applies a greater acceleration to galaxies the further they are from the Earth and if distant Super Nova explosion happen in slow motion compared to local ones for reasons other than relativistic time dilation -- then putting all these "iffy" things together (and plenty more I've probably left out) we may be able to arrive at a radically alternative interpretation to the FLRW metric solution that has the Earth located at the centre of the universe.

Let's break this down.

"a sufficiently small universe would satisfy the problem"

Only thing I'm asserting is that the size of the unobservable universe is not appreciably larger than the observable universe.

"red-shift is not due to relativistic Doppler"

Red-shifting would primarily be due to recession. But, my opinion is that other things might add to red-shifting. The recession would only be due to the movement of objects, not through the universal expansion of the space-time fabric.

"we are privileged enough to be stationary while distant galaxies recede all around us (not forgetting to add to everything the peculiar motion of three-thousand odd kilometers per second given by the CMBR dipole)"

Yes, this would be the conclusion.

"if some unknown force applies a greater acceleration to galaxies the further they are from the Earth "

I've offered dark energy as a possible explanation for this. Whereas I have yet to see a mechanism for the universal expansion of the space-time fabric.

"distant Super Nova explosion happen in slow motion compared to local ones for reasons other than relativistic time dilation"

This I don't have an explanation for. But I fail to see how metric expansion solves this either.

But GR is experimentally verified to a very high degree and we mustn't forget that gravity isn't a force but a distortion of the space-time metric so we already know that space-time is "elastic".

I'm not questioning that the space-time fabric is elastic. This has been demonstrated through experimental data. But, what I am questioning is that the entire universe is experiencing the same rate of metric expansion at every single point in space.

So how do you get a non-relativistic universe with a fixed metric that explains all the features so far observed?

Gravity can alter the metric locally, but I am not convinced that the entire universe has an expanding metric.

[QED]

Let's break this down.

"a sufficiently small universe would satisfy the problem"

Only thing I'm asserting is that the size of the unobservable universe is not appreciably larger than the observable universe.

Is that assertion based on anything in particular? All we know for sure is that more universe lies beyond. In a billion years time our horizon will be a billion light-years further away. Do you have reason to believe that this will "unveil" the edge of the universe?

"red-shift is not due to relativistic Doppler"

Red-shifting would primarily be due to recession. But, my opinion is that other things might add to red-shifting. The recession would only be due to the movement of objects, not through the universal expansion of the space-time fabric.

What are these other things that add to red-shift? The recession in your version of expansion takes place in an inertial frame extending to infinity. This Special Relativistic kind of expansion requires an unknown addition to red shift to account for superluminal amounts of redshift i.e. values of z>1.46 in equations relating to the Hubble flow. But we have routine observations of things with z around 10 not to mention the CMBR which has z=1089. None of this is a problem with GR expansion.

"we are privileged enough to be stationary while distant galaxies recede all around us (not forgetting to add to everything the peculiar motion of three-thousand odd kilometers per second given by the CMBR dipole)"

Yes, this would be the conclusion.

So why would all the rest of the universe be rushing past the origin of expansion? I wonder if you've properly got the picture you're describing in your mind... orthodoxy interprets the dipole as an indication of our velocity relative to the rest of the observable universe. You seem to think that we're at the origin of creation and the rest of the observable universe got flung out away from this origin -- but as the radius expands, its origin also drifts at a million miles per hour.

"if some unknown force applies a greater acceleration to galaxies the further they are from the Earth "

I've offered dark energy as a possible explanation for this. Whereas I have yet to see a mechanism for the universal expansion of the space-time fabric.

Perhaps you "couldn't see it" because you were already looking at it! The negative pressure of dark energy would be causing a metric expansion not just moving things around in a fixed metric:

Strangely, dark energy causes expansion because it has strong negative pressure.

A substance has positive pressure when it pushes outward on its surroundings. This is the usual situation for fluids. Negative pressure, or tension, exists when the substance instead pulls on its surroundings. A common example of negative pressure occurs when a solid is stretched to support a hanging weight.

According to the Friedmann-Lematre-Robertson-Walker metric, which is an application of General Relativity to cosmology, the pressure within a substance contributes to its gravitational attraction for other things just as its mass density does. Negative pressure causes a gravitational repulsion.

The gravitational repulsive effect of dark energy's negative pressure is greater than the gravitational attraction caused by the energy itself. At the cosmological scale, it also overwhelms all other forms of gravitational attraction, resulting in the accelerating expansion of the universe.

One might wonder, how can pushing cause attraction? How can pulling cause repulsion? This sounds like a contradiction. The solution is:

The pushing of positive pressure (and the pulling of negative pressure) are non-gravitational forces which just move substances around within space without changing space itself.
But the gravitational attraction (or repulsion) they cause operates on space itself, decreasing (or increasing) the amount of space between things. It is this which determines the size of the universe.
There is no necessity that these two effects should act in the same direction. In fact, they act in opposite directions.

"distant Super Nova explosion happen in slow motion compared to local ones for reasons other than relativistic time dilation"

This I don't have an explanation for. But I fail to see how metric expansion solves this either.

The relativistic red-shifting of the wavelength of light through which the observations are being made has the effect of increasing the temporal spacing of events in that observation. This stretching of time is peculiar to GR and cannot be accounted for by tired-light.

Gravity can alter the metric locally, but I am not convinced that the entire universe has an expanding metric.

This sounds a bit like the micro/macro evolution argument Gravity isn't a "local effect"! Its long-range action is one of the most significant factors in the shaping of the universe as a whole.

[otseng]

Is that assertion based on anything in particular? All we know for sure is that more universe lies beyond.

And I don't assert anything more than this.

What are these other things that add to red-shift?

OK, let me throw out some ideas.

It could be a result of gravitational redshifting.

"In physics, light or other forms of electromagnetic radiation of a certain wavelength originating from a source placed in a region of stronger gravitational field (and which could be said to have climbed "uphill" out of a gravity well) will be found to be of longer wavelength when received by an observer in a region of weaker gravitational field."

Why would this happen in a geocentric model? If the Earth is at the center of the universe and the universe is isotropic, then the net gravitional force on the Earth would be zero. The net gravitational force would be greater as you approach the boundary. At the boundary, the net gravitional force would be at its maximum. So, objects farther away from Earth would have greater redshifting.

I think this would also explain the time dilation of distant supernova explosions.

"the higher the local distortion of spacetime due to gravity, the slower time passes."
http://en.wikipedia.org/wiki/Gravitatio ... e_dilation

I also believe that "tired light" can be a factor, though it might only have a small effect.

Here's a thought experiment. Suppose we have a light source in the center of a sphere with a radius of 1 mile with a vacuum inside the sphere. And we are able to collect all the energy emitted from the light source that hit the sphere. Let's take this measured energy to be E1. Now suppose the radius is 1 billion light years and we measure the energy to be E2. Would E1 = E2? If tired light was not true, then it would be equal. Now let's take any radius, would E1 = En? What if the radius was infinity? I would just seem amazing to me that light would be able to travel an infinite distance with no loss in energy.

So why would all the rest of the universe be rushing past the origin of expansion? I wonder if you've properly got the picture you're describing in your mind... orthodoxy interprets the dipole as an indication of our velocity relative to the rest of the observable universe. You seem to think that we're at the origin of creation and the rest of the observable universe got flung out away from this origin -- but as the radius expands, its origin also drifts at a million miles per hour.

Actually, my view of this had only changed recently when you brought up the anisotropy data. Prior to this, I wasn't arguing that the Earth was stationary, but now I'm inclined to believe it.

Perhaps you "couldn't see it" because you were already looking at it! The negative pressure of dark energy would be causing a metric expansion not just moving things around in a fixed metric:

We're going to have to explore this area more and discuss the metric expansion of the universe.

So, first question:
Would it be true that the universe is metrically expanding at every single point in the universe at the exact same rate?

Gravity can alter the metric locally, but I am not convinced that the entire universe has an expanding metric.

This sounds a bit like the micro/macro evolution argument Gravity isn't a "local effect"! Its long-range action is one of the most significant factors in the shaping of the universe as a whole.

I don't disagree that gravity can have a long range effect.

[QED]

What are these other things that add to red-shift?

OK, let me throw out some ideas.

It could be a result of gravitational redshifting.

"In physics, light or other forms of electromagnetic radiation of a certain wavelength originating from a source placed in a region of stronger gravitational field (and which could be said to have climbed "uphill" out of a gravity well) will be found to be of longer wavelength when received by an observer in a region of weaker gravitational field."

Why would this happen in a geocentric model? If the Earth is at the center of the universe and the universe is isotropic, then the net gravitional force on the Earth would be zero. The net gravitational force would be greater as you approach the boundary. At the boundary, the net gravitional force would be at its maximum. So, objects farther away from Earth would have greater redshifting.

I think this would also explain the time dilation of distant supernova explosions.

"the higher the local distortion of spacetime due to gravity, the slower time passes."
http://en.wikipedia.org/wiki/Gravitatio ... e_dilation

Despite the huge mass of nearby Galaxies like Andromeda we see negligible amounts of redshift in escaping light and the large-scale structure of the universe is isotropic at all ranges so galaxies are not packed closer and closer the further we look out -- which is what you would need for apparent recession velocities at or beyond light-speed in your geocentric model. Here's how astronomers tell the difference between the different kinds of redshifts.

I also believe that "tired light" can be a factor, though it might only have a small effect.

Here's a thought experiment. Suppose we have a light source in the center of a sphere with a radius of 1 mile with a vacuum inside the sphere. And we are able to collect all the energy emitted from the light source that hit the sphere. Let's take this measured energy to be E1. Now suppose the radius is 1 billion light years and we measure the energy to be E2. Would E1 = E2? If tired light was not true, then it would be equal. Now let's take any radius, would E1 = En? What if the radius was infinity? I would just seem amazing to me that light would be able to travel an infinite distance with no loss in energy.

But what is a photon? This amazing property is part of its definition. Having a rest-mass of zero means it travels at the speed of light (whadday know -- a photon travels at the speed that photons travel at!) so photons don't experience the passage of time. As far as a photon is concerned infinity is no big deal. The only thing that seems to mess with it is an expanding or contracting metric and that's only as far as we, the observers of the photon, are concerned.

So why would all the rest of the universe be rushing past the origin of expansion? I wonder if you've properly got the picture you're describing in your mind... orthodoxy interprets the dipole as an indication of our velocity relative to the rest of the observable universe. You seem to think that we're at the origin of creation and the rest of the observable universe got flung out away from this origin -- but as the radius expands, its origin also drifts at a million miles per hour.

Actually, my view of this had only changed recently when you brought up the anisotropy data. Prior to this, I wasn't arguing that the Earth was stationary, but now I'm inclined to believe it.

Good for you! Perhaps you should set up another user group - contrarian

Perhaps you "couldn't see it" because you were already looking at it! The negative pressure of dark energy would be causing a metric expansion not just moving things around in a fixed metric:

We're going to have to explore this area more and discuss the metric expansion of the universe.

So, first question:
Would it be true that the universe is metrically expanding at every single point in the universe at the exact same rate?

Yes, the Hubble flow is the same on average everywhere. There is some talk of a local variation but as far as constants go, Hubble's is pretty constant.

[otseng]

Despite the huge mass of nearby Galaxies like Andromeda we see negligible amounts of redshift in escaping light and the large-scale structure of the universe is isotropic at all ranges so galaxies are not packed closer and closer the further we look out -- which is what you would need for apparent recession velocities at or beyond light-speed in your geocentric model. Here's how astronomers tell the difference between the different kinds of redshifts.

Objects would not be closer packed the farther out we go. If the universe "exploded", objects at the boundary would be spaced farther apart.

The article assumes that the gravitational field is only from the object itself. In the geocentric model, the gravitational field would also be from all the other objects in the universe. It would not simply be a result of a single or group of objects, but from every object in the universe.

Let me illustrate what I'm thinking this way. Suppose we have a circle with a bunch of dots representing objects randomly sprinkled inside the circle. Each dot has the same mass. The center of the circle would have a net gravitational force of zero. A point on the circumference would have a net gravitational force towards the center of the circle as a result of all the dots in the circle.

Would it be true that the universe is metrically expanding at every single point in the universe at the exact same rate?

Yes, the Hubble flow is the same on average everywhere. There is some talk of a local variation but as far as constants go, Hubble's is pretty constant.

OK, next questions.

What is causing the metric expansion?
How is it able to cause every single point in the universe to expand at the same rate?
What is causing objects to hold together if every single point is expanding?
How exactly does the expansion of space-time affect light?
How does the expansion explain the time dilation of distant objects?

[QED]

Despite the huge mass of nearby Galaxies like Andromeda we see negligible amounts of redshift in escaping light and the large-scale structure of the universe is isotropic at all ranges so galaxies are not packed closer and closer the further we look out -- which is what you would need for apparent recession velocities at or beyond light-speed in your geocentric model. Here's how astronomers tell the difference between the different kinds of redshifts.

Objects would not be closer packed the farther out we go. If the universe "exploded", objects at the boundary would be spaced farther apart.

The article assumes that the gravitational field is only from the object itself. In the geocentric model, the gravitational field would also be from all the other objects in the universe. It would not simply be a result of a single or group of objects, but from every object in the universe.

Let me illustrate what I'm thinking this way. Suppose we have a circle with a bunch of dots representing objects randomly sprinkled inside the circle. Each dot has the same mass. The center of the circle would have a net gravitational force of zero. A point on the circumference would have a net gravitational force towards the center of the circle as a result of all the dots in the circle.

According to your model, then if anything, photons will be blue-shifted not red-shifted!

OK, next questions.

What is causing the metric expansion?
How is it able to cause every single point in the universe to expand at the same rate?
What is causing objects to hold together if every single point is expanding?
How exactly does the expansion of space-time affect light?
How does the expansion explain the time dilation of distant objects?

OK, you'll probably think I'm "fobbing you off", but I think the best way for you to understand the answers to your questions is to follow Ned Wright's Cosmology Tutorial. Most of your questions are answered in the FAQ and there is a liberal use of diagrams. I already started drafting my own reply to each question but soon realised the number of additional questions each answer would provoke. This made my heart sink. I've yet to see anything vaguely resonant in your model, except in ways that W.H.Auden captures in After Reading a Child's Guide to Modern Physics (See the link for all verses)

Our eyes prefer to suppose
That a habitable place
Has a geocentric view,
That architects enclose
A quiet Euclidian space:
Exploded myths - but who
Could feel at home astraddle
An ever expanding saddle?

(It's his centenary this year so pardon me for inserting a minor homage)