Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: JohnDuffield on 21/09/2014 17:18:30

This came up on a thread about infinity (http://www.thenakedscientists.com/forum/index.php?topic=52368.0) started by jeffreyH, and I thought it deserved a thread of its own.
If you ask around about the size of the universe, some people will tell you about the size of the observable universe (http://en.wikipedia.org/wiki/Observable_universe). The radius of this is thought to be 46 billion light years. I don't think there's much of an issue with that.
If you then ask about the size of the whole universe, some people will say we don't know. I think that's fair enough myself. However some people will say it's infinite. And on seemingly good authority too. See for example this NASA article (http://map.gsfc.nasa.gov/universe/uni_shape.html) where you can read this:
"Recent measurements (c. 2001) by a number of groundbased and balloonbased experiments, including MAT/TOCO, Boomerang, Maxima, and DASI, have shown that the brightest spots are about 1 degree across. Thus the universe was known to be flat to within about 15% accuracy prior to the WMAP results. WMAP has confirmed this result with very high accuracy and precision. We now know (as of 2013) that the universe is flat with only a 0.4% margin of error. This suggests that the Universe is infinite in extent; however, since the Universe has a finite age, we can only observe a finite volume of the Universe. All we can truly conclude is that the Universe is much larger than the volume we can directly observe."
I have no issue with the universe being flat. But I take exception to the inference that a flat universe is an infinite universe. It's a nonsequitur. It just doesn't follow. This thinking is a bit like measuring the curvature of the Earth, and when you can't detect it, declaring that the Earth is infinite. You just can't make this claim, especially since it's at odds with Big Bang cosmology. The universe can't have grown from a small size to an infinite size in a finite time, and I do not accept that the early universe was already infinite. Particularly since I don't see how an infinite universe can expand  the "pressure" of space would be counterbalanced at all locations. I also think that we can't "truly conclude that the universe is much larger than the volume we can directly observe".
What do you think?

The universe can't have grown from a small size to an infinite size in a finite time,
What do you think?
I think you're confusing the term "universe", referencing the material locality we presently reside within with the socalled "Bulk Universe" that our currently observable one is only a part of. What scientists refer to as the "Bulk" can be, and in my opinion is truly infinite. Our present existence within our observable and material locality is, of a truth, only a finite portion of the infinite "Bulk".

Well this is ignoring the curvature of spacetime in the whole universe. Where gravitation and mass density become infinitesimally low does the curvature then flatten out? Can it ever completely flatten without being at an infinite distance from any source? A system that curves can be likened to a hyperbolic space. What about negative curvature? Does such a thing exist? Can something that appears to be expanding in actual fact be contracting? Is this a consequence of the curvature and what bearing does this have on a universe with infinite extent?

"Flat within 15%" sounds to me like rolling hills, or maybe Scotland. But then I live in East Anglia, and round 'ere we knows what flat looks like, boy.

How would you define gravity Jeffrey? Can there exist a vacuum of where gravity is not a property? I don't know but my view is that even when 'flat', the property of it should be there? and the definition of a universe as infinite, homogeneous and isotropic, with conservation laws and physics being the same wherever I go, demands its 'bulk' to present itself the same, a equivalent 'universe', no matter from where you stand looking out. That tells me that if I could go to the limit of what we can see today, what we from here might define as the Big Bang looking at light reaching us from there. It should be the same view as I have from here, although there is a weak anisotropy measured, as I remember. The universe may not be perfectly 'even' but it seems very close to it. And if it doesn't I would expect physics to be in trouble.

How would you define gravity Jeffrey? Can there exist a vacuum of where gravity is not a property? I don't know but my view is that even when 'flat', the property of it should be there? and the definition of a universe as infinite, homogeneous and isotropic, with conservation laws and physics being the same wherever I go, demands its 'bulk' to present itself the same, a equivalent 'universe', no matter from where you stand looking out. That tells me that if I could go to the limit of what we can see today, what we from here might define as the Big Bang looking at light reaching us from there. It should be the same view as I have from here, although there is a weak anisotropy measured, as I remember. The universe may not be perfectly 'even' but it seems very close to it. And if it doesn't I would expect physics to be in trouble.
Think of this. An observer watches his companion from a safe distance approach an event horizon. He decides to calculate his friends speed using the gravitational constant. He determines he is traveling at near light speed and yet he sees his companion slowing down. The companion determines his own speed and does in fact get the right answer. Whose gravitational constant is wrong? It is like one person wading through water while a distant person wades through treacle. The observer in water would see the other person slowing down because of the density of the medium. So what is getting denser to slow down the astronaut at the event horizon? If he is in vacuum then it has to be spacetime. If the gravitational constant varies in a varying gravitational field then the Planck dimensions must too. This is the easy part. The hard part is the mechanism that alters the path of a particle and why it only attracts. This does not sit well with electromagnetism.

I think you're confusing the term "universe", referencing the material locality we presently reside within with the socalled "Bulk Universe" that our currently observable one is only a part of. What scientists refer to as the "Bulk" can be, and in my opinion is truly infinite. Our present existence within our observable and material locality is, of a truth, only a finite portion of the infinite "Bulk".
That's what they say, but I don't buy it.
Well this is ignoring the curvature of spacetime in the whole universe. Where gravitation and mass density become infinitesimally low does the curvature then flatten out?
Let's just simplify things by setting aside the expansion of the universe. If you have an energy density that's homogeneous, you will find that your light beam goes straight.
Can it ever completely flatten without being at an infinite distance from any source?
If you shine a light beam between two massive stars, it will go straight.
A system that curves can be likened to a hyperbolic space. What about negative curvature? Does such a thing exist? Can something that appears to be expanding in actual fact be contracting? Is this a consequence of the curvature and what bearing does this have on a universe with infinite extent?
I don't think the universe has a negative curvature.
How would you define gravity Jeffrey? Can there exist a vacuum of where gravity is not a property?
Yes. If the energy density is uniform light goes straight.
I don't know but my view is that even when 'flat', the property of it should be there?
If it's flat there's no overall gravity. Note that the early universe didn't contract when it was small and dense.
and the definition of a universe as infinite, homogeneous and isotropic, with conservation laws and physics being the same wherever I go, demands its 'bulk' to present itself the same, a equivalent 'universe', no matter from where you stand looking out.
The isotropy is an assumption. For all you know, there may be some people somewhere who look up to the night sky, and half of it is black.
That tells me that if I could go to the limit of what we can see today, what we from here might define as the Big Bang looking at light reaching us from there. It should be the same view as I have from here, although there is a weak anisotropy measured, as I remember. The universe may not be perfectly 'even' but it seems very close to it. And if it doesn't I would expect physics to be in trouble.
It's just an assumption. If I could snap my magic fingers such that you were instantly relocated to a planet 46 billion light years away, you might see something very different to what we see.

Think of this. An observer watches his companion from a safe distance approach an event horizon. He decides to calculate his friends speed using the gravitational constant. He determines he is traveling at near light speed and yet he sees his companion slowing down. The companion determines his own speed and does in fact get the right answer. Whose gravitational constant is wrong? It is like one person wading through water while a distant person wades through treacle. The observer in water would see the other person slowing down because of the density of the medium. So what is getting denser to slow down the astronaut at the event horizon? If he is in vacuum then it has to be spacetime. If the gravitational constant varies in a varying gravitational field then the Planck dimensions must too. This is the easy part. The hard part is the mechanism that alters the path of a particle and why it only attracts. This does not sit well with electromagnetism.
It does actually. And it goes all the way back to Newton's Opticks: "Doth not this aethereal medium in passing out of water, glass, crystal, and other compact and dense bodies in empty spaces, grow denser and denser by degrees, and by that means refract the rays of light not in a point, but by bending them gradually in curve lines?" Newton was really interested in light. And light is all to do with electromagnetism. Why don't you start a new thread on this, and I'll tell you what I can.

That's not a easy part Jeffrey, that's questioning constants. If you do you also need to redefine everything that rest on constants. Both you and John seem to be wondering in those terms. The point is that I don't think it should simplify anything, it should just complicate the definitions we use.
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For example, we have this definition of a isotropic and homogeneous universe. That one will no longer be true. We have another stating that physics should be the same wherever you go to measure, that one will no longer be true. Then you have the definitions of a light quanta, and further definitions going out from that, no longer true. I suspect one would need to rewrite physics to make it work. (and symmetries will be very difficult to define)

That's not a easy part Jeffrey, that's questioning constants. If you do you also need to redefine everything that rest on constants. Both you and John seem to be wondering in those terms. The point is that I don't think it should simplify anything, it should just complicate the definitions we use.
It doesn't complicate anything, it clears up some "fine tuned" multiverse myths. See for example this (http://physics.nist.gov/cuu/Constants/alpha.html) and this (http://physicsworld.com/cws/article/news/2007/mar/23/probeseekschangesinfinestructureconstant) about the fine structure constant. It's a "running" constant. Which means it isn't constant. And see this Baez article (http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html):
"Einstein talked about the speed of light changing in his new theory. In his 1920 book "Relativity: the special and general theory" he wrote: "... according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity [...] cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity [Einstein means speed here] of propagation of light varies with position." This difference in speeds is precisely that referred to above by ceiling and floor observers."
People think the speed of light is constant, but that's the locallymeasured speed of light. The "coordinate" speed of light varies with gravitational potential, hence this (http://en.wikipedia.org/wiki/Shapiro_delay) Shapiro quote:
"The proposed experiment was designed to verify the prediction that the speed of propagation of a light ray decreases as it passes through a region of decreasing gravitational potential".
For example, we have this definition of a isotropic and homogeneous universe.
IMHO it is homogeneous on the largest scale, but the isotropy is just an assumption. It isn't based on anything scientific.
That one will no longer be true. We have another stating that physics should be the same wherever you go to measure, that one will no longer be true.
It's no big deal. People are always looking into tests of Lorentz invariance (https://www.google.co.uk/?gws_rd=ssl#q=test+of+lorentz+invariance).
Then you have the definitions of a light quanta, and further definitions going out from that, no longer true. I suspect one would need to rewrite physics to make it work. (and symmetries will be very difficult to define).
IMHO it's just a tweak here and there for physics. The popscience is what gets the rewrite.

"It doesn't complicate anything, it clears up some "fine tuned" multiverse myths."
That would then be your interpretation John. Don't think you will find many scientists agreeing with it.

"It doesn't complicate anything, it clears up some "fine tuned" multiverse myths."
That would then be your interpretation John. Don't think you will find many scientists agreeing with it.
Honestly, you will. A lot of scientists really dislike the multiverse. Here's George Ellis (http://www.scientificamerican.com/article/whythemultiversemaybethemostdangerousideainphysics/) writing in Scientific American about it. Google on multiverse pseudoscience (https://www.google.co.uk/?gws_rd=ssl#q=multiverse+pseudoscience).

It's not about multiverses to me. That one, to my mind, belongs more to the subsequent interpretations you might do from a 'Copenhagen model', or any of the others existing. What I wrote about was constants, and what I expect physics needing to do, redefining them. I also mentioned the isotropic and homogeneous universe we see, as a example of what we need to redefine if so. The problem isn't as simple as you think, a lot of logic assumptions build on each other, so reducing constants to variables you would find it extremely hard to 'correct' it all. I actually looked into that at one time, and even though I didn't collect all data I proved to my own satisfaction that it would create a really messed up situation. The ones we have work, and are, all considered, remarkably simple.
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It doesn't really matter whether the universe prefer a complicated or a simple solution. It works any way. But if I have two theories, where one gives me a really hard time comprehending it, whereas the other is simple and so easier for me to understand, I will go for that one. Presuming that both theories cover the experiments and universe we observe/measure.

and yes, a multiverse do change our ideas about what physics is about. But so did relativity, and Newton, and Maxwell. And your weak experiments can be seen as a try to get back to a universe as it once was thought to be. Some sort of container in where we find causality, action and reaction, and limits, but as a linear proposition. The universe though seems trickier than that, it seems as if it uses both, non linear as well as linear physics, 'simultaneously' depending on experiment made, what you search for. This duality we see is not only limited to light it seems.
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I'll add this one, it's from here but older, relatively speaking :)
There is a nonlinearity to all of the universe we know, macroscopically as well as at the quantum level. But there is also a strange linearity surrounding and infusing it, as the Feigenbaum constant shows us, both macroscopically and on a quantum level as I understand it.
Now for what’s called ‘scars’ in chaos theory.
“According to Michael Berry, a leading theorist in the study of quantum chaos at the University of Bristol, this issue of linearity is a red herring. "This is one of the biggest misconceptions in the business," he says. His critique rests on the fact that it is possible to recast nonlinear classical equations in a linear form and linear quantum equations in nonlinear form.
Berry's preferred explanation for the difference between what happens in classical and quantum systems as they edge towards chaos is that quantum uncertainty imposes a fundamental limit on the sharpness of the dynamics. The amount of uncertainty in a quantum system is quantified in Heisenberg's uncertainty principle by a fixed value known as Planck's constant. In classical mechanics, objects can move along infinitely many trajectories," says Berry. This makes it easy to set up complicated dynamics in which an object will never retrace its paththe sort of behaviour that leads to chaos. But in quantum mechanics, Planck's constant blurs out the fine detail, smoothing away the chaos."
This raises some interesting questions. What happens if you scale down a classically chaotic system to atomic size? Do you still get chaos or does quantum regularity suddenly prevail? Or does something entirely new happen? And why is it that macroscopic systems can be chaotic given that everything is ultimately built out of atoms and therefore quantum in nature? These questions have been the subject of intense debate for more than a decade. But now a number of experimental approaches have begun to offer answers. …
Quantum billiards
More recently, signs of quantum suppression of chaos have come from another experimental approach to quantum chaos: quantum billiards. On a conventional rectangular table, it is quite common for a player to pot a ball by bouncing the cue ball off the cushion first In the hands of a skilled player, such shots are often quite repeatable. But if you were to try the same shot on a rounded, stadiumshaped table, the results are far less predictable : the slightest change in starting position alters the ball's trajectory drastically. So what you get if you play stadium billiards is chaos. In 1992, at Boston's Northeastern University, Srinivas Sridhar and colleagues substituted microwaves for billiard balls and a shallow stadiumshaped copper cavity for the table. Sridhar's team then observed how the microwaves settled down inside the cavity. Although their apparatus is not of atomic proportions (a cavity typically measures several millimetres across) , the experiment exploits a precise mathematical similarity between the wave equations of quantum mechanics and the equations of the electromagnetic waves in this two dimensional situation. If microwaves behaved like billiard balls , you would not expect to see any regular patterns. The experiments, however, reveal structures known as "scars" that suggest the waves concentrate along particular paths.
But where do these paths come from? One answer is provided by theoretical work carried out back in the 1970s by Martin Gutzwiller of the IBM Thomas J. Watson Research Center in Yorktown Heights near New York. He produced a key formula that showed how classical chaos might relate to quantum chaos. Basically, this indicates that the quantum regularities are related to a very limited range of classical orbits. These orbits are ones that are periodic in the classical system. If for example , you placed a ball on the stadium table and hit it along exactly the right path, you could get it to retrace its path ,after only a few bounces off the cushions.However, because the system is chaotic, these paths are unstable. You only need a minuscule error and the ball will move off course within a few bounces. So classically you would not expect to see these orbits stand out. But thanks to the uncertainty in quantum mechanics, which "fuzzes" the trajectories of the balls, tiny errors become less significant and the periodic orbits are reinforced in some strange way so that they predominate.
Sridhar's millimetresized stadium was a good analogy for quantum behaviour, but would the same effects occur in a truly quantumsized system? This question was answered recently by Laurence Eaves from the University of Nottingham, and his colleagues at Nottingham and at Tokyo University. Eaves conducted his game of quantum billiards inside an elaborate semiconductor "sandwich" . He used electrons for balls, and for cushions, he used a combination of quantum barriers and magnetic fields. The quantum barriers are formed by the outer layers of the sandwich, which gives the electrons a couple of straight edges to bounce back and forth between. The other edges of the table are created by the restraining effect of the magnetic field, which curves the electron motion in a complicated way. As in Sridhar's stadium cavity, the resulting dynamics ought to be chaotic.
Number Crunching
To do the experiments, Eaves needed ultraintense magnetic fields, so he took his device to the High Magnetic Field Laboratory at University of Tokyo; which is equipped with some of the most powerful sources of pulsed magnetic fields in the world. Meanwhile his colleagues in Nottingham, Paul Wilkinson, Mark Fromhold, Fred Sheard, squared up to a heroic series of calculations, deducing from purely quantum mechanical principles what the results should look like.In a spectacular paper that made the cover of Nature last month, the team produced the first definitive evidence for quantum scarring, and precisely confirmed the quantum mechanical predictions. Sure enough, the current flowing through the device was predominantly carried by electrons moving along certain "scarred" paths. Quantum regularity was lingering in the chaos rather like the fading smile of the Cheshire Cat in Alice's Adventures in Wonderland. “
So, now we have a little more evidence for it’s not being nonlinearity alone ruling, but rather like a intricate mosaic of both ‘linearity’ and ‘nonlinearity’ constituting the ‘laws’ creating ‘SpaceTime’. And with it we’re starting to get an idea of what ‘free will’ might be seen as, something actually able to vary in itself, but still falling prey to statistics and probability theory. And with it our universe becoming weirder than ever :).
Now what would that have to do with my thoughts on light not moving? Well, if the universe is becoming a mosaic, as I see it, then ‘moving parts’ just complicates it. But, we see the universe moving, don’t we? Well, maybe we do? But, if it moves, how do ‘shadows’ correspond to a barrier?
Institut d'Optique reported on the direct observation of Anderson localization of matterwaves in a controlled disorder. “From the quantum theory of conduction, in which electrons are described as matter waves, we can draw a naïve picture based on the idea that electrons with certain momenta can travel freely through the crystal, while others cannot as they diffract from the periodic structure played by the lattice. “
Fifty years ago, Philip Anderson, 1977 Physics Nobel Prize winner, worked out that tiny modifications of the lattice, such as the introduction of impurities or defects, can dramatically modify this behavior : the electron that would move freely inside the solid does not simply diffuse on the defects as expected for classical particles but they can be completely stopped.
On a macroscopic scale, that would be like saying that a few blades of grass scattered haphazardly over a golf course could completely stop a fullspeed golf ball in its tracks : this would be a surprising situation, since we all know that small perturbations can only slow the movement of material objects, but can never stop them. In the light of fundamental discoveries made in the 1930s about semiconductors that led to the invention of the transistor and then to integrated circuits, this phenomenon called 'Anderson Localization' created and is still creating strong interests among physicists.”
Did you notice “electrons are described as matter waves” I must admit that I like that, it’s kind of ‘hard’ imagining a golf ball being superimposed in two places simultaneously, on the other hand, it’s almost as hard imagining a wave being it, so?
“In our experiment, ultracold atoms play the role of electrons. They are chilled to a temperature close to absolute zero (459.67 degrees Fahrenheit) to generate a BoseEinstein condensate (BEC), in which all the atoms can be described as a single wave function. We allowed these BECs to expand from a small starting spot along a single direction imposed by a laserinduced atomic waveguide. To “simulate” the disordered environment, we created a perfectly controlled disorder by shining laser light through finely ground glass onto the expanding atoms — creating then a random distribution of light and dark regions. Without disorder, the atoms propagate freely, but when disorder is present, all atomic movement stop within a fraction of a second. We then observed the atomic density profile. Its exponential form, characteristic of Anderson Localization is the awaited direct proof that random diffusion of matter can hinder the diffusion process.”

But then I live in East Anglia, and round 'ere we knows what flat looks like, boy.
Should that have been "bor", or are you too far from Norfolk for that? [:)]

Particularly since I don't see how an infinite universe can expand  the "pressure" of space would be counterbalanced at all locations. I also think that we can't "truly conclude that the universe is much larger than the volume we can directly observe".
What do you think?
First, I agree that we have to be very careful about drawing conclusions about that which cannot be observed directly or indirectly.
Second,an infinite plane (or space) can expand. The questions regarding "Hilbert's Hotel" (http://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel) show this.
I don't think pressure, as you have defined it, is the best way of thinking about this. Perhaps instead think of an infinite (and stretchy) plane that has a perpendicular pressure applied. The plane would stretch and distort, ultimately having a greater (but still infinite) area. This isn't a perfect analogy, because it requires changing the curvature of the plane, but it is more easily pictured than just dilating the whole thing (without changing the curvature, or anything other than distances).

my answer is the universe is infinity.
based on charged particle has infinity force range.
it is easy to think the universe is infinity.
if it has boundary, what's out side?

I have no issue with the universe being flat. But I take exception to the inference that a flat universe is an infinite universe. It's a nonsequitur. It just doesn't follow.
If someone, like JohnDuffield, rejects contemporary cosmology (and especially rejects learning the relevant mathematics), then that person can't follow the reasoning. This does not mean that there isn't reasoning.
This thinking is a bit like measuring the curvature of the Earth, and when you can't detect it, declaring that the Earth is infinite.
It is, actually, quite similar. If one has good theoretical reasoning to suppose that the Earth was either an infinite flat plain or a sphere, but the best attempts to measure the curvature of the Earth came up to 0, then the proper inference would be that the Earth was an infinite flat plain.
There are good theoretical reasons to suppose things about the geometry of the universe. Einstein laid this reasoning out. If someone wants to read all of Einstein instead of cherrypick very specific sentences from him, one will find that Einstein is part of laying out this reasoning.
You just can't make this claim, especially since it's at odds with Big Bang cosmology. The universe can't have grown from a small size to an infinite size in a finite time, and I do not accept that the early universe was already infinite.
OK, so here we see that JohnDuffield would rather stick to his own dogma instead of learn about the contents of "Big Bang cosmology". What we learn from this is not something about physics, but about JohnDuffield's abilities and character. This is relevant when deciding how to evaluate claims that JohnDuffield makes about physics.

Don't know about you guys but this sentence tickle my imagination. "So classically you would not expect to see these orbits stand out. But thanks to the uncertainty in quantum mechanics, which "fuzzes" the trajectories of the balls, tiny errors become less significant and the periodic orbits are reinforced in some strange way so that they predominate." As if there was some sort of Mach principle hiding microscopically perhaps? If it now can be broken down to relations? there are so many presumptions we do measuring, using local definitions, as everything taking a 'time' for example, forgetting that this is a observer dependency hinging on our use of a ideal local clock and ruler. That makes any observation a relation.
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Defining a local clock to 'c' doesn't change this situation. It still is a 'observer dependency' by which we measure something else. Our 'tools of the trade' as they say. If we now presumed that at some scale 'time' (strictly locally) disappear, dissolve, whatever. We still wouldn't be able to prove it other than indirectly, as our local 'clock and ruler' never cease to work for us. It's easy to see thinking of a clock, and, to me, has nothing to do with time dilations unless you want to call the local macroscopic interpretation of your wrist watch a time dilation too. It's much harder to imagine what happens to the ruler at that scale. Defining it as a 'stopped clock' locally at/under that scale though it shouldn't matter. The local ruler should cease too as I think.
But if you assume there to be a limit for a discreteness then you also need a reason for particles, and a macroscopic universe, coming into existence. And that? Mach principle should have to do with it, in some way, as well as the Pauli exclusion principle does. Maybe not its old form? (Mach) but in some variation of it.

This came up on a thread about infinity (http://www.thenakedscientists.com/forum/index.php?topic=52368.0) started by jeffreyH, and I thought it deserved a thread of its own.
If you ask around about the size of the universe, some people will tell you about the size of the observable universe (http://en.wikipedia.org/wiki/Observable_universe). The radius of this is thought to be 46 billion light years. I don't think there's much of an issue with that.
If you then ask about the size of the whole universe, some people will say we don't know. I think that's fair enough myself. However some people will say it's infinite. And on seemingly good authority too. See for example this NASA article (http://map.gsfc.nasa.gov/universe/uni_shape.html) where you can read this:
"Recent measurements (c. 2001) by a number of groundbased and balloonbased experiments, including MAT/TOCO, Boomerang, Maxima, and DASI, have shown that the brightest spots are about 1 degree across. Thus the universe was known to be flat to within about 15% accuracy prior to the WMAP results. WMAP has confirmed this result with very high accuracy and precision. We now know (as of 2013) that the universe is flat with only a 0.4% margin of error. This suggests that the Universe is infinite in extent; however, since the Universe has a finite age, we can only observe a finite volume of the Universe. All we can truly conclude is that the Universe is much larger than the volume we can directly observe."
I have no issue with the universe being flat. But I take exception to the inference that a flat universe is an infinite universe. It's a nonsequitur. It just doesn't follow. This thinking is a bit like measuring the curvature of the Earth, and when you can't detect it, declaring that the Earth is infinite. You just can't make this claim, especially since it's at odds with Big Bang cosmology. The universe can't have grown from a small size to an infinite size in a finite time, and I do not accept that the early universe was already infinite. Particularly since I don't see how an infinite universe can expand  the "pressure" of space would be counterbalanced at all locations. I also think that we can't "truly conclude that the universe is much larger than the volume we can directly observe".
What do you think?
The answer is an axiom of yes, because placing a smaller box into a larger box.
Ask yourself how many times you can do this?
The only answer is an infinite amount of times.
There is only two logical choices that lead to one conclusion.
Analogy  I and you are standing in a cave, we are within a space within a box within an outer space.
You are either in a space within a space or a space within a box, if you were in a box like the cave you know outside of that box is a space.
Only infinite can it be, a space within a solid or a space within a space.
There is no third option,

There is a alternative John, you could also think of it through connections. Connections makes the 'paths' (degrees of freedom) we can take, and find, creating the dimensions we see. It's like a Möbius ring, without a outside and without any possibility of finding yourself doing a 'circuit' in it. There are several ways to define why that is impossible, the simplest is using time as one parameter for defining when you have returned. As the arrow has only one path it takes us on measurably, there never becomes a way to 'return' to anything. A Möbius ring imply a constriction though, but those should then be the constants, rules, laws and properties defining the connections to my mind. And it has to be a 'intrinsic' thing, as if this universe keeps together not by 'premade dimensions' but by its equivalence of laws rules etc. Those then becoming the 'dimensions' we define to it.
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Defining it through connections, as when calling a thought up 'isolated system' two dimensional in its degrees of freedom, it becomes quite correct. You can have a 'two dimensional system' inside a three dimensional, defined through its behavior. In the exact same way we usually define our three (four) dimensional room by testing our degrees of freedom in it.

I think there has no evidence can prove that the universe is infinity.

First, I agree that we have to be very careful about drawing conclusions about that which cannot be observed directly or indirectly.
Me too. The early universe is a subject where we don't have a lot to go on. I prefer to hear people saying "we don't know" rather than drawing conclusions.
Second,an infinite plane (or space) can expand. The questions regarding "Hilbert's Hotel" (http://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel) show this.
I don't think that's a great analogy because it's very abstract, and it doesn't refer to space and the universe.
I don't think pressure, as you have defined it, is the best way of thinking about this.
Maybe not, but I referred to "pressure" because it features I the stressenergymomentum tensor (http://en.wikipedia.org/wiki/Stress%E2%80%93energy_tensor). The analogy is to think of space as a squeezeddown stressball, then you open your fist.
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fwww.thenakedscientists.com%2Fforum%2Findex.php%3Faction%3Ddlattach%3Btopic%3D52406.0%3Battach%3D19517%3Bimage&hash=85040bff314cdb3c7191cb33032694ef)
Perhaps instead think of an infinite (and stretchy) plane that has a perpendicular pressure applied. The plane would stretch and distort, ultimately having a greater (but still infinite) area. This isn't a perfect analogy, because it requires changing the curvature of the plane, but it is more easily pictured than just dilating the whole thing (without changing the curvature, or anything other than distances).
I don't like this analogy. IMHO a much better analogy involves a 3D bulk.
There is a alternative John, you could also think of it through connections. Connections makes the 'paths' (degrees of freedom) we can take, and find, creating the dimensions we see. It's like a Möbius ring, without a outside...
There's no evidence of any kind of toroidal universe. The Planck collaboration wrote a paper on this, see http://arxiv.org/abs/1303.5086.
If someone, like JohnDuffield, rejects contemporary cosmology (and especially rejects learning the relevant mathematics), then that person can't follow the reasoning. This does not mean that there isn't reasoning.
There is no mathematics that supports the infinite universe, and no evidence either. It's a nonsequitur, and it's at odds with bigbang cosmology.

I don't think pressure, as you have defined it, is the best way of thinking about this.
Maybe not, but I referred to "pressure" because it features I the stressenergymomentum tensor (http://en.wikipedia.org/wiki/Stress%E2%80%93energy_tensor). The analogy is to think of space as a squeezeddown stressball, then you open your fist.
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fwww.thenakedscientists.com%2Fforum%2Findex.php%3Faction%3Ddlattach%3Btopic%3D52406.0%3Battach%3D19517%3Bimage&hash=85040bff314cdb3c7191cb33032694ef)
Mr. Duffield has posted this pseudoexplanation in many places. He also refuses to answer questions that he demonstrate how his idea works, given the mathematical object he is using here.
One can also find the same mathematical object in standard cosmology textbooks, where no author makes an analogy to a "squeezeddown stressball", but where they present clear argument and show the evidential support for their use of mathematical objects. Note that contemporary cosmology has a wealth of evidential support in the form of specific theory that can compare to measurement results (as opposed to qualitative claims and vague analogies).
If someone, like JohnDuffield, rejects contemporary cosmology (and especially rejects learning the relevant mathematics), then that person can't follow the reasoning. This does not mean that there isn't reasoning.
There is no mathematics that supports the infinite universe, and no evidence either. It's a nonsequitur, and it's at odds with bigbang cosmology.
Again, Mr. Duffield decides to stick with his own dogma and refusal to learn mathematics (even though he will cherrypick mathematical equations as he did above). I urge the reader to consult any cosmology textbook to find the mathematical reasoning behind the inference that the universe might be infinite. (One can even look at the infinite cosmological models investigated by Einstein, though this would require reading more of Einstein that the two small passages that Mr. Duffield wishes one to focus on.) This behavior is something that one should consider when evaluating the truth values of his claims.

I wasn't referring to any shape John. I only used it as a analogy, and a pretty bad one too considering your response. The 'shape' of this universe is the one defined from a inside. I knew I should have avoided it, but I just wanted to point out one way infinity can be reached. In my idea of it you have to start with how things connect, and there we have a lot of contenders, strings and loops among them. It can't be anything else than infinite in my thoughts if what decides a universe is how it connects. And it fits all evidence I know of too.
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What I used to get stuck on was the idea of 'sizes', that one has to go, and so has infinity actually :)
They becomes meaningless terms if one keep thinking of it from a observer position 'outside a universe', and yep, that möbius ring was a dumb thing to lift forward considering the associations one gets from it. Both terms are meaningful from a inside though.
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Maybe this will help to see my point. Instead of using dimensions as the building blocks, exchange it for a mathematical space. Then each point of this universe we're inside is defined by the number three, length width and height. Those are properties in my eyes, to that you then add a fourth being the local arrow, locally equivalent in each point. And you use scaling to define where it all 'ends' (discreteness). Passing that you should find a similarity to Einsteins 'fifth dimension', but, you won't be able to observe from it. The physics we use, and find are directly measurable things, if possible. Indirect evidence is not as simple to prove. But you have one in entanglements, which is a very strong contender for how 'things work microscopically'. Another is the idea of 'all paths taken'.
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You can connect both to the lack of a arrow. A entanglement is instantaneous, distance have no meaning for it. 'All paths taken' is a state outside of a arrow. Both seems to be used by nature to find 'shortest paths' and probable outcomes. Both belong to QM.
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The idea of 'all paths taken' demands this scaled up 'dimension', lacking a arrow, either to have 'all paths' available at its finger tops, or that it in some way 'know' what the macroscopic system (our universe) situation is in each (SpaceTime) point. Which to me relates to Mach principle. To assume it to take all paths 'simultaneously', they must all be realizable and 'known', one way or another. That should be the 'rules', properties and constants giving guidelines. Most probably you need both to be able to define each outcome, at each position. Especially if you add observer dependencies. Meaning that there need to be a connection between the systems arrangement in 'time', macroscopically and this 'Planck state' without a arrow. But we know there is one, otherwise QM wouldn't exist.

...Note that contemporary cosmology has a wealth of evidential support in the form of specific theory that can compare to measurement results (as opposed to qualitative claims and vague analogies).
Contemporary cosmology is bigbang cosmology. We have good evidence for this, and that the universe has been expanding for a finite time. But we have no evidence whatsoever that the universe expanded from a small size to an infinite size in a finite time, and we have no evidence whatsoever that the universe was already infinite when the big bang occurred.
If someone, like JohnDuffield, rejects contemporary cosmology (and especially rejects learning the relevant mathematics), then that person can't follow the reasoning. This does not mean that there isn't reasoning.
I don't reject contemporary cosmology. I'm happy with big bang cosmology. What I reject is the fairy tale notion that the universe was already infinite when the big bang occurred.
Again, Mr. Duffield decides to stick with his own dogma
It isn't dogma to point out that there no evidence for the infinite universe and that it's at odds with big bang cosmology.

I wasn't referring to any shape John. I only used it as a analogy, and a pretty bad one too considering your response. The 'shape' of this universe is the one defined from a inside.
I don't see how. If the universe is "flat", then expansion apart, light goes straight. I take my cue here from cosmologist Neil Cornish (http://www.cnn.com/2004/TECH/space/05/24/universe.wide/) who said he thought the universe was at least 156 billion light years wide, and that this "can be thought of as a spherical diameter is the usual sense".
I knew I should have avoided it, but I just wanted to point out one way infinity can be reached. In my idea of it you have to start with how things connect, and there we have a lot of contenders, strings and loops among them. It can't be anything else than infinite in my thoughts if what decides a universe is how it connects. And it fits all evidence I know of too.
But that's just the thing. There's no evidence for anything fancy. And yet it seems that people can't conceive of the mundane universe where space doesn't curve back round on itself, and doesn't go on forever.
What I used to get stuck on was the idea of 'sizes', that one has to go, and so has infinity actually :) They becomes meaningless terms if one keep thinking of it from a observer position 'outside a universe'...
I don't get stuck with this. I think of the wave nature of matter and waves inside a droplet of water. They can't go beyond the droplet, they undergo total internal reflection instead. Meanwhile the droplet is spherical, with a finite size. OK it isn't a perfect analogy because there's space beyond this droplet, but IMHO it's better than most.

...Note that contemporary cosmology has a wealth of evidential support in the form of specific theory that can compare to measurement results (as opposed to qualitative claims and vague analogies).
Contemporary cosmology is bigbang cosmology. We have good evidence for this, and that the universe has been expanding for a finite time. But we have no evidence whatsoever that the universe expanded from a small size to an infinite size in a finite time, and we have no evidence whatsoever that the universe was already infinite when the big bang occurred.
Except, of course, the evidence that is in every major cosmological paper since 1999.
I know that Mr. Duffield doesn't like this evidence and that it contradicts the contents of his selfpublished book, but that isn't a good reason for other people to ignore the contents of cosmology papers and textbooks and the reasoning found therein.
If someone, like JohnDuffield, rejects contemporary cosmology (and especially rejects learning the relevant mathematics), then that person can't follow the reasoning. This does not mean that there isn't reasoning.
I don't reject contemporary cosmology. I'm happy with big bang cosmology. What I reject is the fairy tale notion that the universe was already infinite when the big bang occurred.
Mr. Duffield clearly has a dogmatic position that he wants to stick to that leads him to refuse to acknowledge the contents of the scientific theories he supposedly accepts. People should judge him accordingly.
Again, Mr. Duffield decides to stick with his own dogma
It isn't dogma to point out that there no evidence for the infinite universe and that it's at odds with big bang cosmology.
Here we see Mr. Duffield doing the rhetorical equivalent of sticking his fingers in his ears. One may speculate on whether it is ability or character that prompts his actions, but that is beyond the scope of this forum.

I wasn't referring to any shape John. I only used it as a analogy, and a pretty bad one too considering your response. The 'shape' of this universe is the one defined from a inside.
I don't see how. If the universe is "flat", then expansion apart, light goes straight. I take my cue here from cosmologist Neil Cornish (http://www.cnn.com/2004/TECH/space/05/24/universe.wide/) who said he thought the universe was at least 156 billion light years wide, and that this "can be thought of as a spherical diameter is the usual sense".
Cornish is correct in identifying that the visible universe is a finite spherical volume. That does not mean that the entire universe is a finite spherical volume. In the standard cosmological models used today, this is true regardless of the overall curvature of the universe, flat or not.
As Cornish correctly points out, results that set a minimum size of the universe do not set a maximum or necessarily imply that the universe is infinite in size. The standard argument that the universe is, and always has been, infinite does not rely on one kind of observation or on determinations of minimum size. To claim that it does is to offer a straw man argument.
And yet it seems that people can't conceive of the mundane universe where space doesn't curve back round on itself, and doesn't go on forever.
Indeed, it is difficult to reconcile such a universe with general relativity. Mr. Duffield refuses to offer a cosmological model of his own, with sufficient detail that it can be compared to empirical results, so one can safely ignore the idea that he has a real alternative to offer.

I don't know John, you lose me there. "I don't see how. If the universe is "flat", then expansion apart, light goes straight. I take my cue here from cosmologist Neil Cornish who said he thought the universe was at least 156 billion light years wide, and that this "can be thought of as a spherical diameter is the usual sense"."
That one should be defined from Earth, presuming our visionary to have spherical vision :) And then he will find this 'light sphere' all around him. It doesn't define the universe in any other way to me? Now, if this guy Neil on the other hand had stated that going to one 'edge' of his 'light sphere' would give our spherical visionary a radically new view, with some 'barrier' cutting of space outside that edge, then he would need to prove it.
"The density of the universe also determines its geometry. If the density of the universe exceeds the critical density, then the geometry of space is closed and positively curved like the surface of a sphere. This implies that initially parallel photon paths converge slowly, eventually cross, and return back to their starting point (if the universe lasts long enough). If the density of the universe is less than the critical density, then the geometry of space is open (infinite), and negatively curved like the surface of a saddle. If the density of the universe exactly equals the critical density, then the geometry of the universe is flat like a sheet of paper, and infinite in extent.
The simplest version of the inflationary theory, an extension of the Big Bang theory, predicts that the density of the universe is very close to the critical density, and that the geometry of the universe is flat, like a sheet of paper. The WMAP spacecraft can measure the basic parameters of the Big Bang theory including the geometry of the universe. If the universe were flat, the brightest microwave background fluctuations (or "spots") would be about one degree across. If the universe were open, the spots would be less than one degree across. If the universe were closed, the brightest spots would be greater than one degree across.
Recent measurements (c. 2001) by a number of groundbased and balloonbased experiments, including MAT/TOCO, Boomerang, Maxima, and DASI, have shown that the brightest spots are about 1 degree across. Thus the universe was known to be flat to within about 15% accuracy prior to the WMAP results. WMAP has confirmed this result with very high accuracy and precision. We now know (as of 2013) that the universe is flat with only a 0.4% margin of error. This suggests that the Universe is infinite in extent; however, since the Universe has a finite age, we can only observe a finite volume of the Universe. All we can truly conclude is that the Universe is much larger than the volume we can directly observe." http://map.gsfc.nasa.gov/universe/uni_shape.html
This one might be interesting too. http://www.scientificamerican.com/article/darkenergycosmicdistances/
And "If you have an accurate galactic ruler, it then becomes fairly easy to work out whether the universe is flat or curved, and whether the universe is static, expanding, or contracting" http://arxiv.org/abs/1312.4877
Which then means that I won't agree to your statement that "There's no evidence for anything fancy. And yet it seems that people can't conceive of the mundane universe where space doesn't curve back round on itself, and doesn't go on forever."
That doesn't mean that you can't propose other ideas, but you will have to adapt it to those experiments that exist, or prove them wrong.

I don't know John, you lose me there. "I don't see how. If the universe is "flat", then expansion apart, light goes straight. I take my cue here from cosmologist Neil Cornish who said he thought the universe was at least 156 billion light years wide, and that this "can be thought of as a spherical diameter is the usual sense"."
I fear that you have been mislead by the way that Mr. Duffield placed that particular quotation. Cornish does not believe that the universe is a finite sphere, he was speaking only of the shape of the set of all points that have sent light to the Earth. That is, in every standard cosmology, a finite sphere. Cornish does not seem to believe that there is any boundary to the universe, as much as Mr. Duffield would like to quote him in support of such an idea.

Ahh, thanks PB. Wondered a little there.
There are other ways to consider it too. Think of the statement that physics should be the same throughout a universe. That makes a lot of sense to me, but assuming a bubble I now create a situation in where one have to consider what's outside that bubble? And what 'membrane' I should presume to exist inbetween those regions. There the physics can't be the same any more, you could also see it as some sort of 'regime' splitting this universe from some other. It gives way to all sorts of complications for me when we start to define the universe as something with a boundary. We have no evidence for that sort of thinking that I know of. the simplest way around it using a 'container model' is then something alike a möbius strip, but it doesn't simplify anything.
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what I think one need to be clear on is that the definition of 'astronomic time' we find for this universe isn't about the scale of it. Not if we use a Big Bang and inflation. Because there is no singular defined point of origin for that Big Bang, it happened 'everywhere', just as I understand expansion to do. You can pick any position you want in this observable portion of a universe, just to find all other galaxies move away from you. Doesn't matter where you place yourself.
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To see how that works think of our spherical observer. He actually sees the origin of the universe 'everywhere', simultaneously, well, sort of :) as the 'earliest light' reaching him comes from all directions, inside that 'observable light sphere' he finds around him. If there was one point of origin we should also find a direction for the infalling light, but we don't. And that's the definition of that Big Bang, the earliest light we can observe, now put that together with a accelerating expansion, in where our spherical observer can pick any position she like, just to see the same happening, all other galaxies moving away from her. (As well as once again finding the earliest light to reach her, from all over the light sphere)

Now, if this guy Neil on the other hand had stated that going to one 'edge' of his 'light sphere' would give our spherical visionary a radically new view, with some 'barrier' cutting of space outside that edge, then he would need to prove it.
He was trying. Read the article (http://www.cnn.com/2004/TECH/space/05/24/universe.wide/) and note the mention of the "hall of mirrors". They didn't find any evidence of it, but note stuff like this:
...All the pieces add up to 78 billionlightyears. The light has not travelled that far, but "the starting point of a photon reaching us today after traveling for 13.7 billion years is now 78 billion lightyears away," Cornish said. That would be the radius of the universe, and twice that  156 billion lightyears  is the diameter...
He's saying the universe is some kind of spherical thing that's at least 156 billion light years in diameter. Let's say you're in the middle of it. The obvious question is what's 78 billion light years away? Some kind of edge?
"The density of the universe also determines its geometry. If the density of the universe exceeds the critical density, then the geometry of space is closed and positively curved like the surface of a sphere. This implies that initially parallel photon paths converge slowly, eventually cross, and return back to their starting point (if the universe lasts long enough). If the density of the universe is less than the critical density, then the geometry of space is open (infinite), and negatively curved like the surface of a saddle. If the density of the universe exactly equals the critical density, then the geometry of the universe is flat like a sheet of paper, and infinite in extent.
That's from the NASA WMAP article about the shape of the universe (http://map.gsfc.nasa.gov/universe/uni_shape.html), and it's misleading. It doesn't follow that a flat universe is an infinite universe. It's a nonsequitur, and it's at odds with big bang cosmology.
The simplest version of the inflationary theory, an extension of the Big Bang theory
You need to be a bit wary about inflation. Not the big bang, inflation. See John Horgan's SciAm blog where you can read Physicist Paul Steinhardt Slams Inflation, Cosmic Theory He Helped Conceive (http://blogs.scientificamerican.com/crosscheck/2014/12/01/physicistpaulsteinhardtslamsinflationcosmictheoryhehelpedconceive/).
Recent measurements (c. 2001) by a number of groundbased and balloonbased experiments, including MAT/TOCO, Boomerang, Maxima, and DASI, have shown that the brightest spots are about 1 degree across. Thus the universe was known to be flat to within about 15% accuracy prior to the WMAP results. WMAP has confirmed this result with very high accuracy and precision. We now know (as of 2013) that the universe is flat with only a 0.4% margin of error
I'm confident that the universe is flat because of what I know about general relativity and gravity. However...
This suggests that the Universe is infinite in extent
No it doesn't.
however, since the Universe has a finite age
It can't be infinite, can it? Not unless it was already infinite when it began.
we can only observe a finite volume of the Universe. All we can truly conclude is that the Universe is much larger than the volume we can directly observe."
No we can't.
This one might be interesting too. http://www.scientificamerican.com/article/darkenergycosmicdistances/
I read it. It seems reasonable.
And "If you have an accurate galactic ruler, it then becomes fairly easy to work out whether the universe is flat or curved, and whether the universe is static, expanding, or contracting" http://arxiv.org/abs/1312.4877
I didn't read the whole paper, I just searched on infinite and flat. It doesn't say anything about an infinite universe, but it says plenty about a flat universe, which is fine by me.
Which then means that I won't agree to your statement that "There's no evidence for anything fancy. And yet it seems that people can't conceive of the mundane universe where space doesn't curve back round on itself, and doesn't go on forever."
Show me the evidence for an infinite universe. There isn't any.
That doesn't mean that you can't propose other ideas, but you will have to adapt it to those experiments that exist, or prove them wrong.
I'm not saying the experiments are wrong. What I'm saying is that the idea that the universe was already infinite when it began is wrong, and that there's no evidence to support this notion.

As for PhysBang saying stuff like this:
Cornish is correct in identifying that the visible universe is a finite spherical volume.
Neil Cornish was talking about the universe, not the visible universe. The article (http://www.cnn.com/2004/TECH/space/05/24/universe.wide/) includes sentences like this:
But the universe has been expanding ever since the beginning of time, when theorists believe it all sprang forth from an infinitely dense point in a Big Bang...
"Our results don't rule out a hallofmirrors effect, but they make the possibility far less likely," Cornish said, adding that the findings have shown "no sign that the universe is finite, but that doesn't prove that it is infinite."
So we come back to the central issue, which is this: if the universe started off pointlike or small 13.8 billion years ago, how can it be infinite now? It can't. So it must be finite. And if it's finite and flat, it has to have some kind of edge.

Now, if this guy Neil on the other hand had stated that going to one 'edge' of his 'light sphere' would give our spherical visionary a radically new view, with some 'barrier' cutting of space outside that edge, then he would need to prove it.
He was trying.
This is the problem with Mr. Duffield's dogmabased approach: he doesn't want to understand the actual science, so he misreads all the things that he comes across and then says things that are untrue about the statements of scientists. While it is always a really, really bad idea to ignore science textbooks and empirical evidence and try to establish a scientific point through a website run by a television station, even here Mr. Duffield misrepresents the views of Cornish because he so desperately wants to find some scientists saying one thing that seems to match his own dogma.
[quoteRead the article (http://www.cnn.com/2004/TECH/space/05/24/universe.wide/) and note the mention of the "hall of mirrors".[/quote]
The scientific investigation that Cornish is commenting upon did not search for reflections, but for light that went in a direction away from the Earth but that ended up coming in towards the Earth because it effectively wrapped around the universe. This is something that can happen in a finite universe with no boundary.
One can read about this in the actual scientific paper, here: http://arxiv.org/abs/astroph/0604616
You'll find the authors, including Cornish, writing, "It is possible instead that our three dimensional Universe has a finite volume without having an edge, just as the two dimensional surface of the Earth is finite but has no edge. In such a universe, it is possible that a straight path in one direction could eventually lead back to where it started."
This is the basis for the discussion Cornish is making. Someone who is interested in responsibly representing a scientific claim would look at the actual science discussed, not a website for a television station. Someone interested in only their own dogma would grab whatever cherrypicked statement they could that they imagined matched their own fantasy.
He's saying the universe is some kind of spherical thing that's at least 156 billion light years in diameter. Let's say you're in the middle of it. The obvious question is what's 78 billion light years away? Some kind of edge?
Except that this isn't what he's saying, he is saying that all the points from which light was sent to the Earth are up to that distance away. There is no edge there, that's just how far away some of those points have reached, if we are using the time coordinates normally used to represent cosmological eras.
That's from the NASA WMAP article about the shape of the universe (http://map.gsfc.nasa.gov/universe/uni_shape.html), and it's misleading. It doesn't follow that a flat universe is an infinite universe. It's a nonsequitur, and it's at odds with big bang cosmology.
SO here one has a choice to make: trust that Mr. Duffield, with his selfpublished book for sale and a history of misrepresenting the claims of scientists, is correct about the contents of the "Big Bang theory" or trust that NASA's page for a greater than seven year cosmology project with dozens of scientists and published papers is correct. Having read the relevant papers and reviewed them, I don't have to trust in this case, but I know what I would do.
Recent measurements (c. 2001) by a number of groundbased and balloonbased experiments, including MAT/TOCO, Boomerang, Maxima, and DASI, have shown that the brightest spots are about 1 degree across. Thus the universe was known to be flat to within about 15% accuracy prior to the WMAP results. WMAP has confirmed this result with very high accuracy and precision. We now know (as of 2013) that the universe is flat with only a 0.4% margin of error
I'm confident that the universe is flat because of what I know about general relativity and gravity.
Note that Mr. Duffield does not care for the evidence, he only cares about his personal knowledge, gleaned from his personal, perhaps mystical, understanding of the writings (but not the mathematics) of Einstein.
And "If you have an accurate galactic ruler, it then becomes fairly easy to work out whether the universe is flat or curved, and whether the universe is static, expanding, or contracting" http://arxiv.org/abs/1312.4877
I didn't read the whole paper, I just searched on infinite and flat. It doesn't say anything about an infinite universe, but it says plenty about a flat universe, which is fine by me.
If one is ignorant of the science, then one can miss that the paper does, in fact, discuss infinite universes. This is because the idea is so ubiquitous now, all the authors of the paper have to do is say that they are using a "minimal [Lambda]CDM model" (pg. 30) and the educated reader knows that they are discussing the FriedmannLemaitreRobertsonWalker familiy of models, which can be infinitely in size. If one bothers to read the most basic textbooks on cosmology, this is laid out clearly along with the relevant reasoning. If one, dogmatically, works to ignore the basics in the field and make claims on the basis of this willful ignorance, then one is likely to say a number of falsehoods.

As for PhysBang saying stuff like this:
Cornish is correct in identifying that the visible universe is a finite spherical volume.
Neil Cornish was talking about the universe, not the visible universe.
As usual, Mr. Duffield doubles down on his, to be charitable, mistakes. I know that Mr. Duffield has a difficult time reading an entire piece and that he prefers that he and his readers only read the parts that he has cherrypicked, but, unfortunately for him, I have to read the entire article.
Here is the passage from the article explaining that Cornish is discussing the visible universe:
'All the pieces add up to 78 billionlightyears. The light has not traveled that far, but "the starting point of a photon reaching us today after traveling for 13.7 billion years is now 78 billion lightyears away," Cornish said. That would be the radius of the universe, and twice that  156 billion lightyears  is the diameter. That's based on a view going 90 percent of the way back in time, so it might be slightly larger.'
As always, one can believe the dogmatic position of Mr. Duffield, or one can believe the words of the scientist himself.
So we come back to the central issue, which is this: if the universe started off pointlike or small 13.8 billion years ago, how can it be infinite now? It can't.
I'm sure that in the mind of Mr. Duffield, this is a great argument. However, that this argument can be taken seriously has been effectively abandoned since the 1920s, if not earlier.
Indeed, this issue is settled and Mr. Duffield seems to know this, given his original post in this thread. As such, this thread seems little more than a deceitful attempt for Mr. Duffield to present his own "New Theories" without having to follow the forum rules on where to post such theories. Again, this is an important factor to use in a consideration of the truth value of any statement made by Mr. Duffield.

...As always, one can believe the dogmatic position of Mr. Duffield, or one can believe the words of the scientist himself.So we come back to the central issue, which is this: if the universe started off pointlike or small 13.8 billion years ago, how can it be infinite now? It can't.
I'm sure that in the mind of Mr. Duffield, this is a great argument. However, that this argument can be taken seriously has been effectively abandoned since the 1920s, if not earlier. Indeed, this issue is settled...
No, it isn't settled, and it definitely isn't dogma to point out that a universe that was small 13.8 billion years ago cannot be infinite now.

My understanding is that, by tracing back all that makes up our current observable universe, it can be concluded that very near the time of the big bang it all must have been in a very small space (high density), but that this argument does not necessarily mean that the *entire universe* was that small.
One could imagine an infinite universe with an initially high density that expanded into the density that we observe today while remaining infinite in scope from inception onward.
If, in fact, the zeroenergy universe theory is correct, then I think it would be just as possible to for an infinite amount of matter to "come into being" as it would for any finite amount.
On the other hand, I am not convinced that the universe "must be" infinite, merely because it is the simplest solution that fits with our observations. However, this is mostly a philosophic point (for now), as we can model the universe as infinite or just arbitrarily large and reach most of the same conclusions. Certainly we cannot perform any experiment that proves that the universe is finite. We could show that the universe is flat here, there, and everywhere we we can observe, but that doesn't ultimately prove that there isn't either a point beyond which the universe does curve, or a point beyond which there is some kind of "edge."
At this point, I am satisfied knowing that we don't know the answer, and hypothesizing that it is possible that we cannot know the answer. But that's just me.

...As always, one can believe the dogmatic position of Mr. Duffield, or one can believe the words of the scientist himself.So we come back to the central issue, which is this: if the universe started off pointlike or small 13.8 billion years ago, how can it be infinite now? It can't.
I'm sure that in the mind of Mr. Duffield, this is a great argument. However, that this argument can be taken seriously has been effectively abandoned since the 1920s, if not earlier. Indeed, this issue is settled...
No, it isn't settled, and it definitely isn't dogma to point out that a universe that was small 13.8 billion years ago cannot be infinite now.
It is nice to see Mr. Duffield attempting to misrepresent the issue in such a hamfisted manner that readers can clearly see his character. Rather than apologize for misrepresenting the words of Neil Cornish, he instead attempts to present a moreorless correct inference (a small universe cannot become infinite) while neglecting to bring up his main points (the universe cannot in principle be infinite and contemporary cosmology cannot include an infinite universe). These main points are so demonstrably false that it is amazing that one can claim them and claim to have read anything on this topic without lying.

Now John, this is a single malt day, so you have to take what I write with a pinch of salt. My view ok?
Time is a construction. Which 'ticks' macroscopically.
Life is indeed a mystery, but it make us look around and think.
Why does it exist?
Most of the things we've believed in as a species has been proved wrong. And the ones proving it wrong is us.
That makes me rather proud over us :)
Although, at no time the transition has been easy.
And yes, the universe is indeed weird. Einstein didn't expect 'black holes', they were a expression of the mathematics he defined, but he didn't expect it. We're all explorers John, you and me both :) And we have our own views. The logic is there if you want to explore it.

PB, reading you I get a distinct impression of Neil Cornish et al defining a universe from what I define as a 'container perspective' ?
If that is so? Then it's a outdated perspective in my view.
The thing is, there is a complementary principle involved, but stretch it too long and it will break.

And John "No, it isn't settled, and it definitely isn't dogma to point out that a universe that was small 13.8 billion years ago cannot be infinite now."
You really need to look up the logic used there. what it will tell you is that there is no 'origin', or that everywhere is the 'origin'.
Both of those statements should tell you the same. There is no origin, the universe is indeed infinite, no expansion needed. and what that should tell you is that there are different types of logic, some fitting this universe, others won't, that doesn't discuss the mathematics 'reality', just where we exist.

PB, reading you I get a distinct impression of Neil Cornish et al defining a universe from what I define as a 'container perspective' ?
If that is so? Then it's a outdated perspective in my view.
The thing is, there is a complementary principle involved, but stretch it too long and it will break.
I'm not sure what you mean. There are a number of ways of defining regions within the universe. One is to identify the region at a given time that can possibly send light to Earth. One is to identify a region that has once sent light to Earth. In both cases, these are not the entirety of the universe unless the universe is finite and, in one sense, small.
The CNN article was reporting on the failure of some observations to detect a signal that the universe was so small that the entire universe is within the visible universe in the second sense above.

My understanding is that, by tracing back all that makes up our current observable universe, it can be concluded that very near the time of the big bang it all must have been in a very small space (high density), but that this argument does not necessarily mean that the *entire universe* was that small.
That's what people used to say. Google on big bang singularity (https://www.google.co.uk/?gws_rd=ssl#q=big+bang+singularity). Somehow we've gone from the universe used to be small to the observable universe used to be small and that nonsequitur that a flat universe must be an infinite universe. Like I was saying, Neil Cornish was talking about the universe, not just the visible universe.
One could imagine an infinite universe with an initially high density that expanded into the density that we observe today while remaining infinite in scope from inception onward.
I can't. Because from what I know of relativity, an infinite universe can't expand. IMHO the very expansion of the universe is hard scientific evidence that the universe is not infinite.
If, in fact, the zeroenergy universe theory is correct
It isn't. That's a myth that arises on the mistaken idea that gravitational field energy is negative. It isn't, it's positive. See The Foundation of the General Theory of Relativity (http://einsteinpapers.press.princeton.edu/vol6trans/197?highlightText=gravitatively) where Einstein said the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy. The people who propose the zeroenergy universe cannot have read this.
I think it would be just as possible to for an infinite amount of matter to "come into being" as it would for any finite amount.
I don't know how or why the big bang occurred, but I know of no infinities in nature, and I'm not comfortable with some infinite amount of space and matter and energy just popping into existence.
On the other hand, I am not convinced that the universe "must be" infinite, merely because it is the simplest solution that fits with our observations.
That's the thing  I don't think it is the simplest solution.
However, this is mostly a philosophic point (for now), as we can model the universe as infinite or just arbitrarily large and reach most of the same conclusions. Certainly we cannot perform any experiment that proves that the universe is finite.
Neil Cornish et al had a go, WMAP looked at flatness as did Planck which also looked for the toroidal topology. So never say never.
We could show that the universe is flat here, there, and everywhere we we can observe, but that doesn't ultimately prove that there isn't either a point beyond which the universe does curve, or a point beyond which there is some kind of "edge."
Agreed.
At this point, I am satisfied knowing that we don't know the answer, and hypothesizing that it is possible that we cannot know the answer. But that's just me.
Me too. Only I reject "the universe is infinite" as a nonanswer that runs counter to big bang cosmology.

You really need to look up the logic used there. what it will tell you is that there is no 'origin', or that everywhere is the 'origin'.
I take no issue with that. Space itself is expanding.
Both of those statements should tell you the same. There is no origin, the universe is indeed infinite, no expansion needed.
Sorry yoron, but expanding space doesn't mean infinite space. And we have good evidence that space is expanding. Not only that, but look at Einstein's stressenergymomentum tensor. See that energypressure diagonal? Einstein should have predicted that space had an innate "pressure" and just had to expand. He didn't, and it was his greatest blunder.
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fwww.thenakedscientists.com%2Fforum%2Findex.php%3Faction%3Ddlattach%3Btopic%3D52406.0%3Battach%3D19517%3Bimage&hash=85040bff314cdb3c7191cb33032694ef)

Ok PB, I see how you define it. It doesn't answer the definitions I'm wondering about though. That means that I need a link, to see for myself I suspect :)
A 'containetr' in my view is a try for something that will 'hold it all'. And I don't expect that, what I expect are rules, and 'properties' scaling.
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Actually PhysBang, what I really expect is a symmetry.

Ouch, I told you that a expansion isn't needed, if you use the logic, or premises, defining a Big Bang. You don't really need it, as long as you understand that our 'spherical observer' find the origin of light coming to him wherever he goes, and at a exact same 'time scale'. If that logic is correct then there is no defined origin in the usual sense, as with some force expressing itself normally (Explosion). And I better point out that I don't see your arguments as being 'less' in any way. You and me both want to discuss, And we both want to use our imagination :) Not such a bad thing in my view. Too few that dare.
=
I told you John, I'm on a single malt diet today, have nothing to do with logic, just life.

I'm sorry yor_on, I don't know what you mean. We have what looks like good evidence that the universe is expanding, and from what I know of the nature of space, it just has to expand. See the stressenergymomentum tensor above? It "describes the density and flux of energy and momentum in spacetime". See the energypressure diagonal? See the sheer stress? It's like space is this ginclear ghostly elastic that can curve and wave. I kid ye not, google it (https://www.google.co.uk/?gws_rd=ssl#q=%22elastic+space%22+einstein). And Einstein's greatest blunder is that he talked about gravitational fields being everywhere, but he didn't think of space has having a pressure everywhere. For some reason he didn't follow his theory to its logical conclusion, and instead was convinced that the universe was static. So he didn't predict the expanding universe.

Ok John. different definitions :)
I don't like 'shear stress' when applied on a vacuum. Doesn't state that it must be wrong. Same as the idea of a vacuum, a vacuum according to old views is complementary. Yin and Yang. That's a very naive interpretation naturally, doesn't mean it hasn't a logic though. I'm questioning a vacuum, as I do most everything.

Like I was saying, Neil Cornish was talking about the universe, not just the visible universe.
This really is all that needs to be pointed out about Mr. Duffield: he cherrypicks statements, he then uses this selective quotation to mislead his readers, then he ignores all the evidence that shows that he is misleading his reader, finally, he returns to the cherrypicked quotation.
Did Cornish discuss the universe as a whole? Yes. Did Cornish claim that the universe as a whole was a sphere of a certain size? No, he explicitly said something about the visible universe (given a certain definition).
This is essentially the only technique that Mr. Duffield has to attempt to harness scientific results.

The idea that the shearstress component of the field equation play a role in cosmology at the largest scales is a relic of the electric universe or plasma universe theories. These theories do not currently have serious and sane proponents.
The standard cosmological model sets these components to 0, because the ideal particles of the model (galaxy clusters) do not interact except for with gravity.

PhysBang, you're one of the clearest minds here, as far as I know it at least. And John, the difference is the one between expecting 'measurable force' and mathematics. Using mathematics is one thing, it's 'ideal', defining a relation. Expecting the universe to be a 'force' is another.

The point is that you don't need 'elastics' to define reality. You do need logics though. When those take you into paths not seen you have you to ask yourself what is most correct, the mathematics, or my preconceptions of how 'it is'? I will go for the mathematics, as long as they make sense :) That means that they need to fit what we already know. It doesn't guarantee that you can translate them into 'measurable forces' though, as with the Einstein stress energy tensor. That's actually a challenge I think you're trying to answer John. But you're still stuck with 'forces', as far as I can see?

This is reminiscent of that song by The Fortunes: “Here it Comes Again”. I suppose discussions about infinity will always be with us, and frequently they will be about the question as to whether or not the universe is infinite.
Why will they never go away, or reach any reasonable conclusion?
The answer, I believe, is that different people mean different things by “infinite” and “universe”. It seems that, in general scientists avoid trouble by treating “infinite” as though it were synonymous with “unbounded”; and if that works so well and good. If your ladder reaches the roof, why grumble that it is not 6ft longer?
John Gribbin’s suggested usage of “Universe”, “universe” and “cosmos”, to avoid confusion, has not caught on in the almost 20 years since he published it. Could this be because scientists always specify exactly what they mean when they talk of the universe? I’m not hazarding any guesses about that.

John, I have spent a lot of time on forums trying to come to grips with what seemed logical and inevitable to me, and comparing it with what seemed logical and inevitable to others. Most often, these viewpoints were very different when infinity was involved. What was the outcome?
On the basic issues, I would say: no real change. However, what was really important to me was not so much trying to establish who was right, and who wrong, as trying to understand why those other people thought as they did. I like to think I have made some progress on that front.
Have you tried looking at answers to a few questions while varying your terminology?
Consider, for example:
Can something finite become infinite? No.
Can something small and expanding always have been infinite? No.
Can something finite become boundless? Yes.
Can something small and expanding always have been boundless? Yes.
If you regard “infinite” and “unbounded as synonymous, do the answers to those questions remain the same? No: all the answers can become “Yes”.

Did Cornish discuss the universe as a whole? Yes. Did Cornish claim that the universe as a whole was a sphere of a certain size? No, he explicitly said something about the visible universe (given a certain definition).
No, he didn't explicitly say something about the visible universe. Here's the article again:
http://www.cnn.com/2004/TECH/space/05/24/universe.wide/
He was talking about the universe, not the visible universe. I'm not cherrypicking, I'm giving the reference, and you're trying to claim the cosmologist said something he didn't.
The point is that you don't need 'elastics' to define reality...
No, but when we're talking about space, it's good to look at things like the stressenergymomentum tensor.
...It seems that, in general scientists avoid trouble by treating “infinite” as though it were synonymous with “unbounded”; and if that works so well and good.
It isn't true Bill. The Planck mission found no evidence of the toroidal universe that is finite but unbounded. That's like the old asteroids game, where you go thataway and end up coming back thisaway. In that scenario there's no edge to the universe, it is unbounded, but it has a finite size. The infinite universe is very different. Again there's no edge and it is unbounded, but it goes on and on. From your latest post:
Can something finite become infinite? No.
Can something small and expanding always have been infinite? No.
That's my point.
Can something finite become boundless? Yes.
Can something small and expanding always have been boundless? Yes.
Agreed. Again this is the toroidal universe akin to the asteroids game. But there's no evidence for it, or for any kind of intrinsic curvature in wherein you go thataway and end up coming thisaway.
If you regard “infinite” and “unbounded as synonymous, do the answers to those questions remain the same? No: all the answers can become “Yes”.
But they aren't synonymous. The surface of a sphere is boundless but not infinite. And if the universe started small 13.8 billion years ago, it can't be infinite. It could be boundless, but we have no evidence for it. So we surely have to consider that it might be bounded.

This is reminiscent of that song by The Fortunes: “Here it Comes Again”. I suppose discussions about infinity will always be with us, and frequently they will be about the question as to whether or not the universe is infinite.
Why will they never go away, or reach any reasonable conclusion?
I might suggest that they don't go away because; like the universe, opinions have an infinite character.

John, you missed the point I was trying to make.
When I said: It seems that, in general scientists avoid trouble by treating “infinite” as though it were synonymous with “unbounded”
I was not referring to the toroidal universe or the asteroids game. I was simply saying that by treating the two (incorrectly, in my view) as though they were synonymous, one could make claims about infinity that you and I might take issue with.
Similarly, when I said: If you regard “infinite” and “unbounded as synonymous, do the answers to those questions remain the same? No: all the answers can become “Yes”.
I was not advocating considering them as synonymous; just pointing out that holding that view could be considered to “justify” answering any of those questions: “Yes”.

Ethos, you're one of the most emphatic minds I've meet. Go for it.

As well as I would hate TNS to be a place where we color people to our purpose, I want it to be a place where we have room to breath, all of us.

An interesting thought, Ethos. I'm not going to be drawn into considering infinite thoughts in a finite population. [:)]

John, you missed the point I was trying to make.
Sorry Bill.
When I said: It seems that, in general scientists avoid trouble by treating “infinite” as though it were synonymous with “unbounded”
I was not referring to the toroidal universe or the asteroids game. I was simply saying that by treating the two (incorrectly, in my view) as though they were synonymous, one could make claims about infinity that you and I might take issue with.
Agreed.
Similarly, when I said: If you regard “infinite” and “unbounded as synonymous, do the answers to those questions remain the same? No: all the answers can become “Yes”.
I was not advocating considering them as synonymous; just pointing out that holding that view could be considered to “justify” answering any of those questions: “Yes”.
OK noted. The thing with all this is that you can read articles like this: Is the universe infinite, or finite? How big is the universe? (http://www.skyandtelescope.com/astronomyresources/universeinfinitebiguniverse/) Only they totally duck the issue. Here's an excerpt:
"But a spatially flat universe can be characteristic of either a finite or an infinite universe. When we say that space is “flat,” we mean it obeys Euclidean geometry: parallel lines never intersect, and the angles of a triangle always add up to 180 degrees. We can imagine the universe in two dimensions as a plane, which is flat and infinite (like an infinite piece of paper). But we can also imagine taking that paper and rolling it into a cylinder, then rolling it again into a torus (doughnut shape). The surface of the torus is spatially flat, like the piece of paper, but finite."
Get a piece of paper. Grab hold of it. Hold it out flat. What's it got? An edge. But it just doesn't feature in articles like the above. See the interview with Joe Silk? (http://www.esa.int/Our_Activities/Space_Science/People/Is_the_Universe_finite_or_infinite_An_interview_with_Joseph_Silk) See this bit?
"So you have two possibilities for a flat Universe: one infinite, like a plane, and one finite, like a torus, which is also flat."
What about a third possibility?

Not bad Billl, it seems we all think in different terms, some brave souls actually working in the field we try to explore. I will need to read you later.

As I'm on a 'discovery' tonight, and furthermore, I'm sure we've all been there, one time or another. Let me tell you that I think that we all, no matter how kooky someone might find thoughts. It's what makes TNS a special place. a place where wee will try to understand, and answer to the best of our abilities. It does not guarantee that the answers will be made into stone though, and sometimes we will argue. Ok, most times :) But, it is a place to breath.

Ethos, you're one of the most emphatic minds I've meet. Go for it.
Thank you sir, and as for going for it, like many others here I resist being drawn into the debate about infinities. However, I will offer one personal comment about this issue.
Because the pros and cons concerning universal infinity balance so very closely on the scale of likelihoods, I feel reasonably free to choose the one that offers me the greatest degree of cerebral comfort.
For that reason, I choose infinity. When thinking about the concept of space, the word finite demands limitations. And if science continues to deem space as flat, I find it irrational to set limits on it.

:)
Quite so Sir.

Did Cornish discuss the universe as a whole? Yes. Did Cornish claim that the universe as a whole was a sphere of a certain size? No, he explicitly said something about the visible universe (given a certain definition).
No, he didn't explicitly say something about the visible universe.
Mr. Duffield has a pattern of writing the same falsehoods about the articles that he cites over and over again, even when the truth of the matter is explicitly quoted in response to his claims.
This could be, sadly, because he is simply incapable of recognizing his errors for some reason.
Here's the article again:
http://www.cnn.com/2004/TECH/space/05/24/universe.wide/
He was talking about the universe, not the visible universe. I'm not cherrypicking, I'm giving the reference, and you're trying to claim the cosmologist said something he didn't.
Sadly, I will direct the reader once again to the passage in that article where Neil Cornish is explicitly talking about the visible universe.
"All the distance covered by the light in the early universe gets increased by the expansion of the universe," explains Neil Cornish, an astrophysicist at Montana State University. "Think of it like compound interest."
Need a visual? Imagine the universe just a million years after it was born, Cornish suggests. A batch of light travels for a year, covering one lightyear. "At that time, the universe was about 1,000 times smaller than it is today," he said. "Thus, that one lightyear has now stretched to become 1,000 lightyears."
All the pieces add up to 78 billionlightyears. The light has not traveled that far, but "the starting point of a photon reaching us today after traveling for 13.7 billion years is now 78 billion lightyears away," Cornish said. That would be the radius of the universe, and twice that  156 billion lightyears  is the diameter. That's based on a view going 90 percent of the way back in time, so it might be slightly larger.
Note that here the radius being discussed is the radius of the points in the early universe that sent light that could have reached the Earth. I do not expect Mr. Duffield to recognize his mistake, at least not explicitly, though he may attempt to mislead his readers by switching to another source that he feels he can cherrypick a quotation from with better results.
Additionally, rather than simply telling you to "google" for more information (information that never supports Mr. Duffield's position, in my past experience), I will direct you to a copy of the paper Neil Cornish is discussing, so that you can read more clearly that Cornish is discussing the visible universe. http://arxiv.org/abs/1312.4877
Can something finite become infinite? No.
Can something small and expanding always have been infinite? No.
That's my point.
Indeed, that is Mr. Duffield's point. He creates a strawman argument of the scientific papers he criticizes, none of which claim that a finite space became infinite. Then, because of his dogma, he merely declares that the standard cosmological model does not include the possibility of a universe that was always infinite.
I cannot accept the religion of Mr. Duffield and will not join his particular cult of the worship of two sentences from Albert Einstein.

"So you have two possibilities for a flat Universe: one infinite, like a plane, and one finite, like a torus, which is also flat."
What about a third possibility?
I would be interested in seeing this third possibility, but I know that Mr. Duffield will never commit to providing the details of such a possibility, since it is doubtful that these details could match the available observations. As such, his discussion remains interesting fantasy when it does not involve insulting practicing scientists and attempting to foster his particular religion.

...I would be interested in seeing this third possibility...
The relevant paragraph is where Joe Silk gives a 2D analogy:
"No. We do not know whether the Universe is finite or not. To give you an example, imagine the geometry of the Universe in two dimensions as a plane. It is flat, and a plane is normally infinite. But you can take a sheet of paper [an 'infinite' sheet of paper] and you can roll it up and make a cylinder, and you can roll the cylinder again and make a torus [like the shape of a doughnut]. The surface of the torus is also spatially flat, but it is finite. So you have two possibilities for a flat Universe: one infinite, like a plane, and one finite, like a torus, which is also flat."
See the bit that says you can take a sheet of paper. A piece of paper isn't infinite. All the way around, it has an edge. The third possibility is that the universe is finite but doesn't wrap around on itself. Because it has an edge.

...I would be interested in seeing this third possibility...
The relevant paragraph is where Joe Silk gives a 2D analogy:
"No. We do not know whether the Universe is finite or not. To give you an example, imagine the geometry of the Universe in two dimensions as a plane. It is flat, and a plane is normally infinite. But you can take a sheet of paper [an 'infinite' sheet of paper] and you can roll it up and make a cylinder, and you can roll the cylinder again and make a torus [like the shape of a doughnut]. The surface of the torus is also spatially flat, but it is finite. So you have two possibilities for a flat Universe: one infinite, like a plane, and one finite, like a torus, which is also flat."
See the bit that says you can take a sheet of paper. A piece of paper isn't infinite. All the way around, it has an edge. The third possibility is that the universe is finite but doesn't wrap around on itself. Because it has an edge.
This reply is one that makes me wonder if there is some mental block that Mr. Duffield has or whether he is deliberately deceptive. In a post where I note that Mr. Duffield never gives details, he cherrypicks one sentence of my post and then proceeds to give a very vague answer, avoiding once again giving details.
Perhaps Mr. Duffield is simply a very sophisticated trolling bot.

Thnks Phybang, that citation made Neils idea understandable in simple way. And yes, that's how I imagine a inflation too, and a expansion.