December 11th, 2011, 06:44 AM
I know that in cosmology it is not considered correct to speak of the centre of the universe, unless you are referring to our position at the centre of the observable universe.
Anyhow, something about this has always gotten me a bit muddled. It goes like this: when the universe was very small it does indeed have a centre (surely?), say when it was the size of a grapefruit. What happens to make the centre cease to be something we can speak about?
This is a very valid question that many people are confused about; one tends to think of a spherical universe with us sitting "at the centre" of a sphere. This is not correct, however, for the following reasons :Originally Posted by Zwirko
1. We do not really know the actual "shape" of the universe, because there are several possible configurations.
2. The universe is four-dimensional - the equivalent of the sphere in 4D is a hypersphere, or more generally, a spherical 3-manifold
3. The 3-manifold dynamically expands in all directions from each point, and has no boundary. As such it is generally not possible to define a "center" point, except for special cases ( see below ). If the universe was static we might have been able to do this, though.
The confusion arises when one tries to mentally picture the 4D equivalent of a sphere; the human mind is simply not able to visualize any body with more than three dimensions. Also one needs to take into account the metric expansion of spacetime.
References :
Spherical 3-manifold - Wikipedia, the free encyclopedia
Shape of the Universe - Wikipedia, the free encyclopedia
Just as a side note, you will notice in the above articles that it actually is possible to define a 4D spherical space with a center point - this is called the Milne Model. However, this model has been ruled out as a candidate for the global geometry of the universe through observational findings.
December 11th, 2011, 03:25 PM
Very tricky
The whole size of the universe thing gives me a headache.
If the universe is infinite now, was there ever a time when it was not?
If its size was always infinite how could it be smaller in the past?
Infinite is always the same size, even if it's expanding!
Does that help?
{Owwww}
What is it expanding into ?Infinite is always the same size, even if it's expanding!
Does that help?
{Owwww}
It isn't expanding into anything.
Nothing. That's the point.What is it expanding into ?Infinite is always the same size, even if it's expanding!
Does that help?
{Owwww}
Watch out - Genesis is the "nothing means something" guy.
The universe is not expanding into "nothing".
The universe is not expanding "into" anything.
This is a very valid question that many people are confused about; one tends to think of a spherical universe with us sitting "at the centre" of a sphere. This is not correct, however, for the following reasons :
1. We do not really know the actual "shape" of the universe, because there are several possible configurations.
2. The universe is four-dimensional - the equivalent of the sphere in 4D is a hypersphere, or more generally, a spherical 3-manifold
3. The 3-manifold dynamically expands in all directions from each point, and has no boundary. As such it is generally not possible to define a "center" point, except for special cases ( see below ). If the universe was static we might have been able to do this, though.
The confusion arises when one tries to mentally picture the 4D equivalent of a sphere; the human mind is simply not able to visualize any body with more than three dimensions. Also one needs to take into account the metric expansion of spacetime.
References :
Spherical 3-manifold - Wikipedia, the free encyclopedia
Shape of the Universe - Wikipedia, the free encyclopedia
Just as a side note, you will notice in the above articles that it actually is possible to define a 4D spherical space with a center point - this is called the Milne Model. However, this model has been ruled out as a candidate for the global geometry of the universe through observational findings.
Thanks for the detailed reply. I did kinda realise that there was some brain-melting geometry needed to understand such things.
What would be the correct way to comprehend the following crazy thought experiment: Imagine we went back in time to a point immediately just after the Big Bang, when the universe was very, very small. With us we took a measuring stick that was nearly the same size as the universe itself - say 4 m in length. Ignoring the exceedingly life-unfriendly conditions, what would we see? Would our measuring stick "bump" against the edge (I know there is no edge, but I don't know any other way to articulate this point), or would the measuring stick curve around the universe? Or something else?
Apologies for the silly question, but I'm just trying to visualise what a small spherical 3-manifold is without frying my brain with equations.
Think of it as denser, rather than smaller. (If that helps...)
Important point:
When cosmologists say that the universe was the size of a grapefruit after inflation, they are referring to the observable universe.
The universe as a whole could have been any size larger at that time - it might even have been infinite in extent.
If some thing is observable and you half it, time and and time again in existence. in existence when does it become none observable out of existence. ?
Zwirko, I am referring to your question in post #9. If the universe shrank by, say for example, a factor of 1000, then so would everything in it, including your measuring stick; in effect it would become shorter by some factor that depends on the exact geometry of the spacetime in question. You are right, the stick curves according to the curvature of the space time; it would not, however, bump on any boundary, because there is no boundary. Picture this as the surface of the earth - no matter which direction you walk in, you will never reach any edge. You just go round and round.This question is not silly at all, but quite valid.
Just a few things I want to make sure of:This is a very valid question that many people are confused about; one tends to think of a spherical universe with us sitting "at the centre" of a sphere. This is not correct, however, for the following reasons :
1. We do not really know the actual "shape" of the universe, because there are several possible configurations.
2. The universe is four-dimensional - the equivalent of the sphere in 4D is a hypersphere, or more generally, a spherical 3-manifold
3. The 3-manifold dynamically expands in all directions from each point, and has no boundary. As such it is generally not possible to define a "center" point, except for special cases ( see below ). If the universe was static we might have been able to do this, though.
The confusion arises when one tries to mentally picture the 4D equivalent of a sphere; the human mind is simply not able to visualize any body with more than three dimensions. Also one needs to take into account the metric expansion of spacetime.
References :
Spherical 3-manifold - Wikipedia, the free encyclopedia
Shape of the Universe - Wikipedia, the free encyclopedia
Just as a side note, you will notice in the above articles that it actually is possible to define a 4D spherical space with a center point - this is called the Milne Model. However, this model has been ruled out as a candidate for the global geometry of the universe through observational findings.
The universe is 4 dimensional according to general relativity, but one of them is time-like. The issue here is curvature. It is possible to describe the 3D (space-like) surface of a 4D (space-like) sphere. The analogy of the 2D (space-like) surface of a 3D (space-like) sphere is designed to help envision curvature in 3 space-like dimensions, where only the surface of this sphere forms part of the analogy. If you imagine what the universe would be like for 2D creatures living on the 2D surface of the balloon, you get somewhat of an intuitive idea of what is meant by curvature in 3D. For one, there would be no centre of their universe, as they would simply eventually end up back where they started. If the balloon was covered in dots and it inflated, you would see what we see; that things recede faster from us the further away they are.
So, for Zwirko's question, try and imagine how things would change for the 2D creatures if their universe deflated and you'll get an idea of what things was like in the early universe. For one, as the surface area decreases, eventually it will deflate all the way to a single dot. That is why we can say that there is no centre or outside; the "bang" happened everywhere in the universe and the whole of existence is contained on this 3D "surface", which is why it does not make sense to talk about an outside, as no such place exists, just like the seventh side of a standard die. The full 3D surface of our universe was once a single point, if in fact there was a singularity at t=0.
If at one point the universe was expanding slow enough and it was small enough (and our universe had a spherical shape), a laser pointed straight away from us would travel all the way "around" the universe and hit us in the back.
When it is smaller than a Planck length.
If some thing is observable and you half it, time and and time again in existence. in existence when does it become none observable out of existence. ?
All correct!
Although, when you say the issue here is curvature, we are referring to the global curvature - the topology or "shape", rather than the local curvature.
How does this global curvature fit in with the idea that universe is apparently flat? Does a flat universe still have a "hall-of-mirrors" effect? (re Kalster's laser spot(
Yes, we do indeed observe the universe to be flat to a high degree. This can be interpreted as follows :
1. The universe is indeed a flat one
2. The universe is much larger than the part we can observe; due to its sheer size it may appear flat locally ( its curvature may be too small to detect over short distances )
3. Curvature within the global structure of the universe varies, and we just happen to be in a region that is nearly flat
A flat universe would likely be of infinite size, so a laser beam sent in any direction will simply travel into infinity and never return to its point of origin. Even if the universe is hyper-spherical in some way, the path a laser beam travels would very much depend on the actual geometry of the space-time. It could conceivably intersect its original point of origin, but does not need to do so. It really depends on the global geometry.
Ok, thanks for your time Markus and everyone else.
I think I'm starting to get a clearer picture of this geometry/topology issue now.
You're welcome, glad to help
Bear in mind that that no human being is able to visualize a 4-dimensional object or space. It is simply not possible for us, because it is outside our realm of experience. Therefore the questions posed above are non-trivial, and many people have difficulty getting their heads around this. Even I sometime have to resort to the actual maths to see what is going on, because I just can't visualize a particular problem...
Don't forget the 3-Torus!
A flat universe can be finite but unbounded, and still have straight lines that "wrap" round and end up where they started!
http://www.etsu.edu/physics/etsuobs/starprty/120598bg/section6.htm
Last edited by SpeedFreek; December 13th, 2011 at 01:12 PM. Reason: added link
Interesting idea...strictly speaking though those lines have internal curvature, and appear straight in only one direction.Don't forget the 3-Torus!
A flat universe can be finite but unbounded, and still have straight lines that "wrap" round and end up where they started!
Bob Gardner's "Shape of Space" Talk, Section 6
Funny that you bring this up, though...I did this very problem for a final year assignment, and as it turned out a hypertoroidal metric is not a solution for Einstein's Field Equations. In other words, you cannot construct a universe with our observed laws of physics that has the shape of a hypertorus. This wasn't an easy calculation, I can tell you that
Hmmm. It seems there are a lot of cosmologists out there that think otherwise, as the 3-Torus is one of the 10 accepted topologies considered possible for the universe. I read about it in Joseph Silk's book "The Infinite Cosmos" (Silk is Savilian Professor of Astronomy at Oxford).
Here is a wiki article about it:
Doughnut theory of the universe - Wikipedia, the free encyclopedia
SpeedFreek, you are absolutely right, I rather unfortunately mis-worded my post 22. Here's why :
The calculation I did was very specific, in that I used a proper 3-torus ( perfect "doughnut" ) as a starting metric in 3+1 space to see if this geometry ( as opposed to the general topology ) would be a valid solution to the Einstein equations. I furthermore had to make the following assumptions to make the maths even remotely manageable :
1. Mass distribution is an ideal gas throughout the universe ( perfectly symmetrical )
2. Spacetime dimensions are strictly 3+1
3. The global geometry is a perfect 3-torus
4. There is no cosmological constant present
5. Dark matter and dark energy are not taken into account
From there I worked "backwards" to see if such a solution would be a valid one for the field equations. Well, it turned out that it wasn't. I suspect that's because within a 3-torus the Riemann curvature ( = gravity ) has different strength along different directions of space. This would in theory make it possible to define a preferred direction in space.
I agree with the articles though that it may well be possible to find a global topology with the characteristics of a 3-torus. Anything with exactly one hole in it has the same topology as a doughnut, though the metric can be very different from your usual "doughnut".
My argument was for a very specific geometry ( mathematically speaking a very specific metric tensor ), I cannot make any general claim concerning topology and all possible geometries. That's an interesting question, but way beyond me as I freely admit. For example, if string theory with its 11 dimensions turns out to be viable, the above metric might indeed be a valid solution - who knows ?? Even a non-vanishing cosmological constant - a very real possibility - might change everything. There is no way to know without actually performing the calculations, which I won't attempt because the presence of a cosmological constant makes the equations much harder to solve.
Makes me wonder, though, if it would be possible to locally distort spacetime into a 3-toroidal geometry, and what kind of energy configuration we'd need to do so ??
Last edited by Markus Hanke; December 15th, 2011 at 02:44 AM.
If i was in a spaceship that could travel through time and i parked that spaceship just above the earth, then if i pushed the full reverse button to send me and my spaceship heading back in time, when i looked out a window with a telescope, at first i would see that the observable universe was 14 billion light years away in every direction. As i traveled back in time i would see the universe appear 13, 12 ,11 all the way down to 1 billion light years away in every direction. If i was to keep going, the universe would continue closing in around me until eventually i was at the center of the universe. You see, the earth is at the center of the universe, right
But if you did the same thing from, 10 billion light years away today, you would get exactly the same result. That's the point. The center is everywhere in the Universe, so there is no real center.
Hehe, that was what i was trying to show but yes thank you for pointing it out more bluntly for me
I think this is an excellent question as others have pointed out here. According to at least one version of the BB model the beginning point/ entity had no relative dimensions to it. One or more Inflation proposals consider that from the beginning onward the universe curved around upon itself and had no center to it. In general one BB version of the present universe's form proposes a spheroid where all three physical dimensions are projected by Riemann geometry curving around to eventually meet. In this and other versions, the universe is closed by this positive curvature. This would mean that the center of the beginning of the universe expanded and everywhere now is equally a part of the expanded beginning entity.
Riemann geometry is a type of geometry in General Relativity where parallel lines can eventually meet. Many still think that reality probably does not work this way but General Relativity has had many successes concerning observational verification but requires dark matter at the galactic level to come close to observational conformance. If a Riemann geometry model does not sound logically appealing to you, be consoled that you are not alone
Many retort today be saying: who said the universe must be logical according to human ideas of logic? My reply: if the universe is a result of cause and effect there will always be logic to it whether we understand the logic or not. Of course in my opinion the understanding of everything in the universe could be presently taught in Junior high school if a totally valid perspective existed, if we understood the details well enough -- mathematics aside. Of course there will always be new frontiers of learning and things that we really don't understand, but think we do based upon theory. Hopefully in the next century we will be able to better distinguish theories like the kinetic theory of heat, the theory of plate tectonics, and natural selection, from theories/ hypothesis that are more speculative, like the idea of a non-centered universe, and in my opinion the entire BB model as well as many other of today's mainstream theories in physics.
Last edited by forrest noble; April 4th, 2012 at 11:23 AM.
Human brain is not so developed and will never be, that we could think in 4d or understand these things.
So no need to bother yourself with those questions.
Space accordingly curves in 3D according to General Relativity into a Psudo-Riemann 4D manifold. This curvature of space is presently contradicted by observations which seem to indicate that the universe is instead totally flat. But most believe that at a much larger but unobservable scale that the universe is still curved.
We will never seriously have to understand or conceive of 4D space if it does not exist in reality, such as in the present mainstream model(s). In my opinion every aspect of the universe is instead simple enough for the average person with an average education, to be able to understand in great detail, mathematics aside.
Last edited by forrest noble; April 4th, 2012 at 01:41 PM.
There is no contradiction here. The universe curves according to General Relativity and Reimann geometry. If the critical density of the universe is greater than the average density, that curvature is positive (a closed universe), whereas if the critical density is less than the average density, that curvature is negative (an open universe). If the critical density is equal to the average density, the universe is flat (also an open universe).
Our observations constrain the global curvature to being as close to flat as is currently measurable, but that does not preclude there being curvature (either positive or negative) on a scale much larger than the observable universe.
Your explanation is certainly correct according to the standard model. The seeming problem is that at the largest observable scale the universe appears to be flat and what would be the probability, according to the standard model, that .the critical density right now would be exactly, or very close to the average density?There is no contradiction here. The universe curves according to General Relativity and Riemann geometry. If the critical density of the universe is greater than the average density, that curvature is positive (a closed universe), whereas if the critical density is less than the average density, that curvature is negative (an open universe). If the critical density is equal to the average density, the universe is flat (also an open universe).
Our observations constrain the global curvature to being as close to flat as is currently measurable, but that does not preclude there being curvature (either positive or negative) on a scale much larger than the observable universe.
I think some of the contradictions of observations with theory are explained in the link below.
Flat Universe
Imo it's very simple, if it had a beginning with BB, then it must logically have a center and be sphere shaped, where imo most goes wrong, is they think of only 1 universe, our universe is somewhere in a greater hyperverse.
Logic need not apply. The center is everywhere, since it was not an explosion, but an expansion of space from every point everywhere all at the same time. I know it doesn't make intuitive sense. You have to make some serious effort to wrap your head around the concept. Without that, you will use your flawed intuitive misunderstanding of what it means.
Although I understand what you are saying, I think it may make intuitive sense to some concerning the beginning of the universe being everywhere, and that also now that the center of the universe continues to be everywhere. But I believe that such a universe according to the standard model, although certainly not illogical, is far from simple. As I said before, instead I think that everything in the universe is very simple so that a person of average intelligence could generally understand it if the explanations of it were generally accurate. But I think the standard model and its related explanations are not even close
Last edited by forrest noble; March 31st, 2012 at 09:14 PM.
Nature is not built around man; there is no requirement for things in the universe to be "simple". If we cannot understand the laws of the universe, than the failure lies entirely on our side. People do not generally like to hear this, but humankind does not occupy a special place in the universe, not even in terms of intellectual capacity. Things work just the way they work, and it is our job to make the effort and understand them, not the other way around !
I agree with the general idea of your comment, although I think that the universe is not that difficult to understand. Instead I think present theory has made understandings of it unnecessarily complicated. Such an example, I believe, is the idea that there is no center to the universe. Although the most accepted idea of it is that the center of the universe is everywhere due to the curving and expansion of space, the hypothesis that space is curving is based upon theory that has so far been contradicted by observation (instead the observable universe appears to be flat), and the expansion of space is simply based upon the assumption that the observed redshifts of galactic EM radiation is caused by a Doppler shift of the EM spectrum. If this single assumption is wrong then the entire BB model and most everything we presently think we know about cosmology, would also necessarily by wrong.Nature is not built around man; there is no requirement for things in the universe to be "simple". If we cannot understand the laws of the universe, than the failure lies entirely on our side. People do not generally like to hear this, but humankind does not occupy a special place in the universe, not even in terms of intellectual capacity. Things work just the way they work, and it is our job to make the effort and understand them, not the other way around !
Last edited by forrest noble; April 1st, 2012 at 11:38 AM.
That is not an idea - it is basic geometry.
Wrong. It is based on the field equations of General Relativity, which are experimentally very well verified.the hypothesis that space is curving is based upon theory that has so far been contradicted by observation
Any manifold will always appear to be flat locally. Where is the contradiction ? All that this means is that the universe is big. Really, really big.instead the observable universe appears to be flat
Besides, it is easy to construct cosmological models which have a globally flat topology, and these models are also solutions to the GR field equations.
That is not an assumption, it is a direct consequence of GR, which, as already mentioned, is experimentally well verified.and the expansion of space is simply based upon the assumption that the observed redshifts of galactic EM radiation is caused by a Doppler shift of the EM spectrum.
It's not wrong.If this single assumption is wrong then the entire BB model and most everything we presently think we know about cosmology, would also necessarily by wrong.
Riemann geometry is certainly not basic geometry.That is not an idea - it is basic geometry.
(my quote)The contradiction is that so far all observations seem to indicate that the observable universe has been measured to be flat and is not curved. Although space could be curved at a much larger scale but might never be observable; observations so far indicate that the observable universe is flat.the hypothesis that space is curving is based upon theory that has so far been contradicted by observation
Please provide references. What other "manifold(s)" are you referring to other than space? Your statement "Any monifold will always appear to be flat locally" I think will be a very difficult statement to justify. (underline added to quote)Any manifold will always appear to be flat locally. Where is the contradiction ?
If so such a model would not have the center of the universe as being everywhere at once unless space somehow curves and is not flat.All that this means is that the universe is big. Really, really big. Besides, it is easy to construct cosmological models which have a globally flat topology, and these models are also solutions to the GR field equations.
(my quote)....and the expansion of space is simply based upon the assumption that the observed redshifts of galactic EM radiation is caused by a Doppler shift of the EM spectrum.I disagree. The idea that space is expanding/ stretching is solely based upon an assumption as I have explained. If you believe GR supports the expansion of space please provide a reference with such a statement. One or more solutions to GR support an expanding universe, and one or more solutions to GR with the cosmological constant support a steady state universe whereby the universe or space would not be expanding.That is not an assumption, it is a direct consequence of GR, which, as already mentioned, is experimentally well verified.
There are also those that believe in the standard model but who do not adhere to the interpretation that space is expanding as in stretching.
http://arxiv.org/abs/0808.1081
(my quote)If this single assumption is wrong then the entire BB model and most everything we presently think we know about cosmology, would also necessarily by wrong.Whether right or wrong, it is still an assumption, premise, and/ or foundation pillar on which the entire BB model now rests as well as the OP's queryIt's not wrong.
Last edited by forrest noble; April 1st, 2012 at 11:15 PM.
To me it is. But maybe that's just me.
Yes, I agree with this of course so far as the universe globally is concerned. Locally though we can observe the effects of curvature around massive bodies.The contradiction is that so far all observations seem to indicate that the observable universe has been measured to be flat and is not curved. Although space could be curved at a much larger scale but might never be observable; observations so far indicate that the observable universe is flat.
I am just referring to Riemann manifolds in general, of which spacetime is of course a special case. If the ratio between curvature radius and observational radius is very large, the manifold will appear to be locally flat. Best example : surface of the Earth. Look out the window - your horizon appears approximately flat, even though in reality the surface of the Earth is of course curved. The apparent flatness is because your observable horizon is very small compared to the curvature radius of the Earth.Please provide references. What other "manifold(s)" are you referring to other than space? Your statement "Any monifold will always appear to be flat locally" I think will be a very difficult statement to justify. (underline added to quote)
Note that this is an approximation of course, and only valid locally. That is what I was trying to say.
The fact that the universe does not have a center is independent of whether the universe is flat or curved. It is only a consequence of homogeneity and isotropy, as explained here :If so such a model would not have the center of the universe as being everywhere at once unless space somehow curves and is not flat.
History of the Center of the Universe - Wikipedia, the free encyclopedia
So no, a flat universe would not have a center either.
Ok, no problem. Here is the general explanation, as well as summary of observational evidence :If you believe GR supports the expansion of space please provide a reference with such a statement.
Metric expansion of space - Wikipedia, the free encyclopedia
And here is the maths that goes with it - of course this is a solution of the GR field equations :
Friedmann
Yes, this is correct.One or more solutions to GR support an expanding universe, and one or more solutions to GR with the cosmological constant support a steady state universe whereby the universe or space would not be expanding.
This may well be, however, this assumption is in accordance with GR ( the currently accepted theory ), and also in good agreement with observational evidence.Whether right or wrong, it is still an assumption, premise, and/ or foundation pillar on which the entire BB model now rests as well as the OP's query
[QUOTE=forrest noble;317381]If there is no center. If the Big Bang theory is correct would there be a Starting point.?
And would the Big Bang be as equal as C.M.B.R shows right across the Universe. ?
Everywhere is the starting point.
I can't do the math but that is because I have never studied it. It seems pretty straightforward, conceptually, to me.
Even though I can't do the math, that seems obvious to me. I assume it is because it is differentiable - did I get that right Markus?Please provide references. What other "manifold(s)" are you referring to other than space? Your statement "Any monifold will always appear to be flat locally" I think will be a very difficult statement to justify. (underline added to quote)
Are you saying that there is specific IQ or education level that the universe was designed to match? Because however simple you make it, you will always be able to find someone who doesn't understand it. So by your argument, any possible explanation must be wrong.
On the other hand, the universe may be sufficiently complex that no one will ever be able to explain/understand it. Or maybe just three hyperdimensional white mice. Who knows.
There is no requirement for it to be as simple as you want it to be or think it ought to be.
Actually, thinking about it, the only argument I can think of in this regard is a theological one: if God made the universe then he would have made it simple enough to understand (so we could fully admire his work) but no simpler (so we would always be in awe of it.
I'm afraid it is not this simple since the universe is a 4-manifold. It is not possible to directly visualize this.
As an analog, image a balloon which starts off infinitely small ( all the balloon is concentrated into just one point ). Now the balloon gets blown up; on its surface all points suddenly move away from each other, but there is no center on the balloon's surface. Our universe corresponds to such an expanding surface, only in 4 dimensions.
Remember, the analog is the balloon's surface, not the balloon's interior - this is very important. It is thus immediately clear that there is no starting point, and no center point.
Sorry, I am not sure what you mean by this. Could you explain ?And would the Big Bang be as equal as C.M.B.R shows right across the Universe. ?
Well, time = 0 could be a starting point. But the big bang theory doesn't go back that far.
The CMB formed about 300,000 years after the big bang started, when it cooled enough for atoms to form. The reduced ionization meant that photons could move freely (without being scattered) and so become visible over great distances. The smoothness (isotropy) of the radiation reflects the state of the universe at that time; pretty much homogeneous.And would the Big Bang be as equal as C.M.B.R shows right across the Universe. ?
Not really, sorry. The differentiability of the manifold means that it is smooth, i.e. that all points are smoothly connected ( geodesics between points do not have "odd" shapes like corners, or discontinuities, or such like ).
Local flatness is a result of the ratio between curvature radius and radius of observation. If the area we observe is very small, and the curvature radius is very large, then spacetime will appear flat locally, i.e. the curvature only becomes apparent over larger distances. I am not sure about the formal mathematical proof, but I would think this can be done on any manifold, so long as the distances considered are small enough as compared to the curvature radii along that distance.
You are right though in saying that the manifold at hand should be differentiable, at least across the area which is considered; I don't know if the argument still holds if that isn't the case. I would think not.
So differentiability may be a necessary but not sufficient condition. OK.
As a concrete example for Forrest, if you are surveying your garden, yoiu can happily assume you triangles are Euclidean (ie. add up to 180º). If you are surveying the entire US, you probably can't. Similarly, on any manifold (roughly, a curved surface, possibly in more than 3 dimensions) there will be a scale at which it appears flat and can be approximated by Euclidean geometry.
Markus Hanke,
I generally agree with your statements up until these:
The fact that the universe does not have a center is independent of whether the universe is flat or curved. It is only a consequence of homogeneity and isotropy, as explained hereThese statements are just plain wrong. For the universe not to have a central geographic area it must curve around on itself either via Riemann geometry, some other non- linear geometry, or via extra dimensions. It is not a consequence of homogeneity and isotropy as you state. Please read your link again.....So no, a flat universe would not have a center either.
Again you have misinterpreted the link. GR was first proposed by Einstein to explain a steady state, static universe. This is what he believed when he formulated his equations and the reason he added the cosmological constant, to keep the universe from contracting under gravity. The only change Einstein made later to his equations after Freidmann, was to delete the cosmological constant. He never mentioned or proposed the expansion of space. It is only an assumption based upon the proposed idea of the Doppler shifting of the EM spectrum concerning distant galaxies.Ok, no problem. Here is the general explanation, as well as summary of observational evidence :
Metric expansion of space - Wikipedia, the free encyclopedia
And here is the maths that goes with it - of course this is a solution of the GR field equations :
Friedmann
Friedmann and a few others later found a solution to Einstein's equations that could justify an expanding universe. There were other solutions that led to a contracting or steady state universe. The metric expansion of space was an afterthought and explanation by others. For 20-30 years galaxies were believed to be moving away from each other instead of space expanding/ stretching, which was a much later idea.
(my quote, parenthesis added)Whether right or wrong (the expansion/ stretching of space) .... is still an assumption, premise, and/ or foundation pillar on which the entire BB model now rests as well as the OP's queryYou are correct in that this assumption does not contradict GR, but also there is no evidence for expanding space other than the supposed Doppler shifting of the EM spectrum concerning distant galaxies. I expect that you can recall that there have been a number of other explanations for galactic redshifts other than as a Doppler shift, albeit none of these explanations have been discussed much in print by mainstream cosmologists other than historically, since the Big Bang model has dominated cosmology.This may well be, however, this assumption is in accordance with GR ( the currently accepted theory ), and also in good agreement with observational evidence.
As far as Riemann Geometry being simple, it's not. Riemann Geometry requires both differential and integral calculus, plus matrices and tensors. The type of geometry used in GR is called Pseudo-Reinmannian geometry, a subclass of which contains Lorentzian manifolds which are the basis for GR. GR uses all of this plus a Ricci tensor (warping space) which is one of 10 partial differential equations of tensor calculus. In most cases one or more variables must be approximated for the equations to even be used.I can't do the math but that is because I have never studied it. It seems pretty straightforward, conceptually, to me.
Even though I can't do the math, that seems obvious to me. I assume it is because it is differentiable - did I get that right Markus?Please provide references. What other "manifold(s)" are you referring to other than space? Your statement "Any monifold will always appear to be flat locally" I think will be a very difficult statement to justify. (underline added to quote)
Are you saying that there is specific IQ or education level that the universe was designed to match? Because however simple you make it, you will always be able to find someone who doesn't understand it. So by your argument, any possible explanation must be wrong.
On the other hand, the universe may be sufficiently complex that no one will ever be able to explain/understand it. Or maybe just three hyperdimensional white mice. Who knows.
There is no requirement for it to be as simple as you want it to be or think it ought to be.
Actually, thinking about it, the only argument I can think of in this regard is a theological one: if God made the universe then he would have made it simple enough to understand (so we could fully admire his work) but no simpler (so we would always be in awe of it.
A principal assumption of GR is that space-time can be modeled as a 4-dimensional Lorentzian manifold, unlike Riemannian manifolds with their positive-definite metrics. This allows tangent vectors to be classified into time-like or space-like null or tensor matrices enabling the vector solutions of GR.
Pseudo-Riemannian manifold - Wikipedia, the free encyclopedia
Concerning my statement that "I think the universe is simple," applies to my model of it only since I am not aware of any other theory-of-everything that I think is simple. That does not mean there could not be other simple, valid models of the universe, in my opinion. That's why I prefaced the statement with "I think," and spent no time on the discussion of the statement.Are you saying that there is specific IQ or education level that the universe was designed to match? Because however simple you make it, you will always be able to find someone who doesn't understand it. So by your argument, any possible explanation must be wrong.
On the other hand, the universe may be sufficiently complex that no one will ever be able to explain/understand it. Or maybe just three hyperdimensional white mice. Who knows.
There is no requirement for it to be as simple as you want it to be or think it ought to be.
It is not simple to you. Why should the nature of the universe be defined by what you think is simple? Other people might think your idea is too complex. Does that prove it wrong? How "simple" does the universe have to be?
This is the trouble with this principle. It is not just anthropocentric, it is egocentric.
To quantify my statement I said: "In my opinion every aspect of the universe is instead simple enough for the average person (of average intelligence) with an average education, to be able to understand in great detail, mathematics aside" (words in parenthisis added). This can be further qualified by adding: "if the universe were explained properly (mathemitics aside, probably involving a different cosmological model). I also think this same problem relates to the statement that the center of the universe is everywhere. Such a statement of certainty involves too many assumptions: assumes Inflation, stretching (expanding) space, positively curved space, that Doppler shifts explain redshifts, a finite contiguous volume of matter, etc. Of course some of these assumptions could be valid, but all must be valid for a BB universe to exist without a central area to it.It is not simple to you. Why should the nature of the universe be defined by what you think is simple? Other people might think your idea is too complex. Does that prove it wrong? How "simple" does the universe have to be?
This is the trouble with this principle. It is not just anthropocentric, it is egocentric.
Last edited by forrest noble; April 2nd, 2012 at 02:47 PM.
The parts I bolded are not required for there to be no centre of the universe (or for everywhere to be the centre, as it were). Also, the assumption that "Doppler shifts" explain redshifts and that the universe is expanding are equivalent. And neither is required - the universe does not have to expand for it to have no centre. You are misrepresenting "too many" assumptions.
We do not need to assume inflation for there to be no centre of the universe (I'm not sure why one would think it is required - it only effects the flatness and horizon problems, neither of which has any bearing on whether the universe has a centre), nor do we require positively curved space (a flat universe has no centre, be it infinite or a 3-torus which are the only possible shapes for a flat universe), nor do we require the universe to be finite (an infinite universe has no centre), nor do we require expansion (expansion only changes the size of the universe, it does not change its shape).
The assumptions that are actually required for the universe to have no centre are that of homogeneity and isotropy.
Last edited by SpeedFreek; April 2nd, 2012 at 02:45 PM.
The parts I bolded are not required for there to be no centre of the universe (or for everywhere to be the centre, as it were). Also, the assumption that "Doppler shifts" explain redshifts and that the universe is expanding are equivalent. And neither is required - the universe does not have to expand for it to have no centre. You are misrepresenting "too many" assumptions.Concerning Inflation: The universe is thought by many that it would have collapsed on itself or looked very different without the Inflation hypothesis. This is why I said it is an assumption that provides for a universe as we see it, without a center, according to the related hypothesis. Expanding space is also assumed to explain an expanding universe with no center to it. Positively Curved space: For positive curvature I refer to any configuration whereby space bends inward such a spherical, torus, or other possible shapes without a center. For negatively bent space I refer to outward outward bending shapes like a saddle, or zero curvature as in Flat. According to my description of positive curvature I also referred to a torus. If my characterization was wrong concerning a torus then maybe a better description would have been an "inward bending" shape whereby I meant a spherical configuration, a torus, or any inward bending configuration that rejoins itself. If you think another geometry other than an inward bending configuration can result in a "no central area" universe, please explain. My contention is that any configuration other that flat is an assumption based upon theory and not observation. The Doppler shift does not necessarily explain expanding space since galaxies could be physically moving away from each other, so it is a separate assumption. A finite contiguous volume is an assumption of the standard BB model, justified by thoery.We do not need to assume inflation for there to be no centre of the universe (I'm not sure why one would think it is required - it only effects the flatness and horizon problems, neither of which has any bearing on whether the universe has a centre), nor do we require positively curved space (a flat universe has no centre, be it infinite or a 3-torus which are the only possible shapes for a flat universe), nor do we require the universe to be finite (an infinite universe has no centre), nor do we require expansion (expansion only changes the size of the universe, it does not change its shape).
Infinite matter or infinite multi-verses would have no center to them but these scenarios are not mainstream BB cosmology, and are not related to the OP query.
I agree with this statement and said nothing to contradict it, did I?Also, the assumption that "Doppler shifts" explain redshifts and that the universe is expanding are equivalent.
I agree that this is an assumption but in my opinion it is based upon observational evidence. What I contend is that the other assumptions embolden are not based upon observational evidence according to my explanations.The assumptions that are actually required for the universe to have no centre are that of homogeneity and isotropy.
Last edited by forrest noble; April 2nd, 2012 at 04:13 PM.
Don't you think it would be a rather odd coincidence if the laws that govern the universe just happened to match the average intelligence of a species around in the 21st century on a particular planet in this galaxy?
Why isn't it easily understood by dolphins?
Or only accessible to an alien of average intelligence and average education in another galaxy (said aliens being able to solve Fermat's last theorem at the age of 3. In their sleep)?
Do you really not see what an unlikely and pointless principle that is to base anything?
Even simple things that man has developed are not capable of being understood by an average person of average intelligence. Why the entire universe should be is beyond me.
But that is not exactly what you said. What you said is:I disagree with this statement. The universe is thought by many that it would have collapsed on itself or looked very different without the Inflation hypothesis. This is why I said it is an assumption to provide for a universe as we see it, without a center.
They are indeed all required for the Big-Bang universe to exist as we see it, but they are not related to the question as to whether the universe has a centre, or not, or whether it is everywhere.I also think this same problem relates to the statement that the center of the universe is everywhere. Such a statement of certainty involves too many assumptions: assumes Inflation, stretching (expanding) space, positively curved space, that Doppler shifts explain redshifts, a finite contiguous volume of matter, etc. Of course some of these assumptions could be valid, but all must be valid for a BB universe to exist without a central area to it.
That question is not dependent on inflation, expansion, positive curvature or finiteness. These are not assumptions required for there to be no centre to the universe. How can I make it more simple than that?
You listed them as separate assumptions required for the universe to have no centre, but when it comes to the shape of the universe they are one assumption, that of expansion, which has no bearing on the shape of the universe and whether it has a centre or not. You had two assumptions listed instead of one, when there should have been none!
I am not arguing that any of these are not assumptions, and I don't know where you got that from my post. I am arguing that these are not assumptions required for a universe to have no centre.
Is that clear now?
And, if you continue to mix up curvature with "inward bending", globally, it is no wonder you see an apparent contradiction between the flatness of the universe and the curvature of spacetime described by GR.
The question as to whether the universe has a centre is a question of topology (otherwise known as "the shape" of the universe), rather than curvature and although the two are related, they are not the same thing.
Last edited by SpeedFreek; April 2nd, 2012 at 04:41 PM.
Excellent point. Why anyone would expect the universe to be readily understood by the average person is beyond me. People who insist on this arbitrary condition are frequently the same people who struggled -- like everyone else -- through university classes that may have made sense to the professor, but almost no one else. But there's something about cosmology that makes people forget all those calibration points. I think it's another manifestation of the Dunning-Kruger effect, coupled with an unhealthy dose of narcissism ("the universe was designed for me!!!!!").Don't you think it would be a rather odd coincidence if the laws that govern the universe just happened to match the average intelligence of a species around in the 21st century on a particular planet in this galaxy?
Why isn't it easily understood by dolphins?
Or only accessible to an alien of average intelligence and average education in another galaxy (said aliens being able to solve Fermat's last theorem at the age of 3. In their sleep)?
Do you really not see what an unlikely and pointless principle that is to base anything?
Even simple things that man has developed are not capable of being understood by an average person of average intelligence. Why the entire universe should be is beyond me.
Strange, my friend, I think you are going into a little bit too much detail on this one point -- but if you insist.Don't you think it would be a rather odd coincidence if the laws that govern the universe just happened to match the average intelligence of a species around in the 21st century on a particular planet in this galaxy?
Why isn't it easily understood by dolphins?
Or only accessible to an alien of average intelligence and average education in another galaxy (said aliens being able to solve Fermat's last theorem at the age of 3. In their sleep)?
Do you really not see what an unlikely and pointless principle that is to base anything?
Even simple things that man has developed are not capable of being understood by an average person of average intelligence. Why the entire universe should be is beyond me.
Of course the level of understanding and details are dependent on one's intelligence and education. With GR, dark, matter dark energy, the question of this thread etc. , there are many aspects of the BB model that are not only not understood, but some think are illogical concerning a universe of changing expansion rates, the beginning Big Bang proposal, warping and stretching of space, causeless effects such as in QM, a priori force carrying particles, etc. etc. What I would consider a far better and simpler model of the universe, would be those also be based upon observation, but with a more logical basis for it. Whether right or wrong, my own model is such a model. The meaning of my related quotes asserts that theoretical models should ultimately be judged based upon observation, but I think the logic of a model is another necessity that is often overlooked.
I do not just fault the BB model, but nearly all models in physics today, as failing in logic. Whether right or wrong, Newton and Galileo's approach to science was logical based upon my readings. All the founders of todays theories were geniuses. Einstein for one, tried to logically justify his theories. On the other hand the founders of QM intent was to develop a mathematical theory of the quantum world, and then afterwards tried to justify the math the best that they could. Much of today's theories are formulated this way which is why I believe much of advanced science today does not make sense.Excellent point. Why anyone would expect the universe to be readily understood by the average person is beyond me. People who insist on this arbitrary condition are frequently the same people who struggled -- like everyone else -- through university classes that may have made sense to the professor, but almost no one else. But there's something about cosmology that makes people forget all those calibration points. I think it's another manifestation of the Dunning-Kruger effect, coupled with an unhealthy dose of narcissism ("the universe was designed for me!!!!!").Don't you think it would be a rather odd coincidence if the laws that govern the universe just happened to match the average intelligence of a species around in the 21st century on a particular planet in this galaxy?
Why isn't it easily understood by dolphins?
Or only accessible to an alien of average intelligence and average education in another galaxy (said aliens being able to solve Fermat's last theorem at the age of 3. In their sleep)?
Do you really not see what an unlikely and pointless principle that is to base anything?
Even simple things that man has developed are not capable of being understood by an average person of average intelligence. Why the entire universe should be is beyond me.
There are a number or exceptions in science that are based upon logic, such as natural selection, genetics, biology, medicine, geology, archeology, chemistry, etc. In physics Newtons laws and perspectives are a shining example of how I think physics should continue to be formulated, whether right or wrong. First should come the insight, then one should formulate the math. Never formulate math first from observation without strong insightful guiding principles.
Oddly enough I think that the "no center to the universe idea" (the OP here) has a logical appeal concerning the standard model, but I think it is not justified as being the only explanation by standard theory, or observation.
I did not say that I think that the universe should be readily understood by the average person. I said that I think that the universe if properly theorized and orginized, could be understood by the average person. There is a big difference between the two. I also believe no matter how complicated something is, that it can be organized and logically and correctly explained at a fundamental level to the average person, if it is well-enough understood in the first place.Excellent point. Why anyone would expect the universe to be readily understood by the average person is beyond me. People who insist on this arbitrary condition are frequently the same people who struggled -- like everyone else -- through university classes that may have made sense to the professor, but almost no one else. But there's something about cosmology that makes people forget all those calibration points. I think it's another manifestation of the Dunning-Kruger effect, coupled with an unhealthy dose of narcissism ("the universe was designed for me!!!!!").
SpeadFreek,
I am not arguing that any of these are not assumptions, and I don't know where you got that from my post. I am arguing that these are not assumptions required for a universe to have no centre.
Is that clear now?I like your approach. You are appealing to logic -- which is my own approach to discussion.The question as to whether the universe has a centre is a question of topology (otherwise known as "the shape" of the universe), rather than curvature and although the two are related, they are not the same thing.
You are correct in that Inflation does not cause a "no-center" universe, expanding space and/ or a Doppler shifts do not produce/ cause a no-center universe, a finite contiguous volume does not produce a no center universe, but curved space and its related topology is needed for the BB model to produce a no-center universe. All the rest (assumptions/hypothesis) are also seemingly needed by the BB model to explain observations if it were a no-center BB universe, without infinite matter or multi-verses.
I missed this earlier. Here it is.
No, expanding space is assumed to explain an expanding universe.
The no centre part comes from the topology. A static universe can also have no centre, as can a contracting universe, or even a steady-state universe!
Negative curvature can also lead to a universe with no centre. Did you not look at my link in post #21?
If the universe is only close to being flat, it might be positively or negatively curved. If negatively curved and finite, a solution is described by a Seifert-Weber manifold, and once again, there is no centre.
Our measurements only tell us the observable universe is close to being flat. Isn't it an assumption therefore to conclude it must be flat? Especially considering how much larger the whole universe might be in relation to our observable part of it.
But if we assume the universe IS flat, then it still has no centre! The simplest flat finite 3-manifold is the 3-torus. That is the simplest finite solution for a universe that is finite, homogeneous and isotropic. It is either that, or an infinite universe. Either way, there is no centre.
Well they couldn't be physically moving away from each other unless we are at the centre of the universe, that is. Are you suggesting that all the distant galaxies are moving physically through space, directly away from us, and that we are therefore at the centre of the universe? If not, then our observations tell us there is no centre to the expansion.
No, it isn't. In all the standard texts where these issues are discussed, it is acknowledged that the universe might be infinite in extent.
Multi-verses are a slightly different issue, but the possibility of an infinite universe remains part of the mainstream BB cosmology. So far there is no cosmological constraint on an upper limit to the size of the universe.
The mainstream view is that if it is flat, it is either infinite, or a 3-Torus. Which do you prefer?
No, it isn't. Flat space also produces a no-centre universe.
In reference to your earlier comments about mainstream theory and an infinite universe, here is a very good paper that is relevant to these issues:
http://arxiv.org/abs/astro-ph/0604616
Extending the WMAP Bound on the Size of the Universe
While it is certainly possible that the Universe extends infinitely in each spatial direction, many physicists and philosophers are uncomfortable with the notion of a universe that is infinite in extent. 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. For a short enough closed path, we expect to be able to detect an observational signature revealing the specific topology of our Universe.
Last edited by SpeedFreek; April 2nd, 2012 at 07:25 PM.
I think neither of us likes arguing semantics which I think we are doing. An unbounded flat universe concerning space projected by Euclidean geometry outward from a central starting point in all directions radially without bending -- has no center for an infinite amount of space, but the same unbounded universe in space with a finite amount of matter within it does have a center concerning its center of matter.No, it isn't. Flat space also produces a no-centre universe.
In reference to your earlier comments about mainstream theory and an infinite universe, here is a very good paper that is relevant to these issues:
http://arxiv.org/abs/astro-ph/0604616
Extending the WMAP Bound on the Size of the Universe
These studies are certainly comprehensive but I do not ascribe to the BB model or most of its implications such the cause of the CMBR being a beginning BB condition.
I too think the idea of matter, field or space, extending infinitely, is wrong. I believe space is solely defined as the volume that matter and field collectively occupies, and nothing more. Again if it's complicated at all I think the theory is wrongWhile it is certainly possible that the Universe extends infinitely in each spatial direction, many physicists and philosophers are uncomfortable with the notion of a universe that is infinite in extent. 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. For a short enough closed path, we expect to be able to detect an observational signature revealing the specific topology of our Universe.
My perspective of the mainstream model is explained in my posting #28.
Last edited by forrest noble; April 2nd, 2012 at 10:54 PM.
I missed this earlier. Here it is.The no centre part comes from the topology. A static universe can also have no centre, as can a contracting universe, or even a steady-state universe!Negative curvature can also lead to a universe with no centre. Did you not look at my link in post #21?If the universe is only close to being flat, it might be positively or negatively curved. If negatively curved and finite, a solution is described by a Seifert-Weber manifold, and once again, there is no centre.Our measurements only tell us the observable universe is close to being flat. Isn't it an assumption therefore to conclude it must be flat? Especially considering how much larger the whole universe might be in relation to our observable part of it.
But if we assume the universe IS flat, then it still has no centre! The simplest flat finite 3-manifold is the 3-torus. That is the simplest finite solution for a universe that is finite, homogeneous and isotropic. It is either that, or an infinite universe. Either way, there is no centre.Well they couldn't be physically moving away from each other unless we are at the centre of the universe, that is. Are you suggesting that all the distant galaxies are moving physically through space, directly away from us, and that we are therefore at the centre of the universe? If not, then our observations tell us there is no centre to the expansion.No, it isn't. In all the standard texts where these issues are discussed, it is acknowledged that the universe might be infinite in extent.Again we are discussing semantics and it's my faultMulti-verses are a slightly different issue, but the possibility of an infinite universe remains part of the mainstream BB cosmology. So far there is no cosmological constraint on an upper limit to the size of the universe.
The mainstream view is that if it is flat, it is either infinite, or a 3-Torus. Which do you prefer?
Shape of the Universe - Wikipedia, the free encyclopedia
Within such a finite flat universe as defined above and by a finite extention of contiguous matter and field, within the standard model or otherwise, there seemingly would always be a center or more central area to the matter and field of the universe.
Last edited by forrest noble; April 2nd, 2012 at 10:56 PM.
Then, as pointed out above, you by default contend that WE are the centre of the universe, since we observe everywhere moving away from us. Is that right? The problem that the galaxies are not simply moving away from each other, they are moving away as a result of expanding space, because their rate of recession is related to their distance from us. So, do you then content both that we are the centre of the universe and that space is expanding away from us?Within such a finite flat universe as defined above and by a finite extention of contiguous matter and field, within the standard model or otherwise, there seemingly would always be a center or more central area to the matter and field of the universe.
Besides this, what about all the different observational and experimental confirmations of curved space?
Of course not, which you should realize by reading my many postings above.
Of course not again, I do not even believe that space can warp or expand at all, or even that the universe is expanding. But that's just meThe problem that the galaxies are not simply moving away from each other, they are moving away as a result of expanding space, because their rate of recession is related to their distance from us. So, do you then content both that we are the centre of the universe and that space is expanding away from us?
I believe there isn't any. Instead GR has been successful accept at the quantum and galactic scales (hence dark matter) but this success is not evidence for curved space. As to the universe scale, experiments claim flat space. As to local bendings, they attribute such light bending/ lensing to dark matter, and rarely discuss warped/ curved space in such conclusions. As to the sun bending light, Newton also predicted the same bending of light by gravity based upon his gravity model, but with less accuracy than Einstein.Besides this, what about all the different observational and experimental confirmations of curved space?
Last edited by forrest noble; April 3rd, 2012 at 02:08 PM.
forrest noble, can you answer a simple question : on the surface of a sphere, where is the center point ?
While remaining on the surface of a sphere we would say that there is no center to the surface, or in the BB scenario we might say that there is no center to the universe -- as in my posting #28.
An unbounded finite space has no centre. Unbounded means it has no edge, or centre. You seem to be using standard terms in non-standard ways. There is no valid cosmological model with a centre for the universe, except for the Milne model, which doesn't match observation.
This is all wrong. You are at odds with the whole of cosmology. The mainstream view is that it is a universe with an edge that is the more complicated scenario - you only have to consider the boundary conditions to see why.I too think the idea of matter, field or space, extending infinitely, is wrong. I believe space is solely defined as the volume that matter and field collectively occupies, and nothing more. Again if it's complicated at all I think the theory is wrong
Your definition is completely non-standard. Good luck building a cosmology with it.
The link says otherwise.
SpeedFreek,
Unbounded in space but finite in matter and field does have a center to it, concerning the matter and field -- which was my point. In my own finite universe model, space is bounded by definition, the definition being: Space is the volume that matter and field occupies and would be a meaningless concept beyond the bounds of matter and field. Space accordingly is defined as to its size by the full extension of the matter and field within it.An unbounded finite space has no centre. Unbounded means it has no edge, or centre. You seem to be using standard terms in non-standard ways. There is no valid cosmological model with a centre for the universe, except for the Milne model, which doesn't match observation.
Space accordingly is the distance between matter, and the volume that matter and field collectively occupies.
The definition above is very simple. In this definition a finite universe would have a center. Not only space, but time and gravity should also be defined by matter and field.This is all wrong. You are at odds with the whole of cosmology. The mainstream view is that it is a universe with an edge that is the more complicated scenario - you only have to consider the boundary conditions to see why.
Einstein's famous quote was:later in his wrings he added the words "and field" to the end of this quote."When forced to summarize the general theory of relativity in one sentence: Time and space and gravitation have no separate existence from matter and field." - Albert Einstein
The point is that space, time, and gravity would not exist by definition, outside the confines of matter and field. To me this is the simplest possible concept and definition asserting that all space, time, and gravity, can be solely defined by matter and field whereby they accordingly would have no separate existence or meaning outside the bounds of the matter / field which the universe encompasses. The universe itself would have no greater boundaries than the full extension of the matter and field within it.
To me the above explanation of the boundaries of the universe, relating to Einstein's quote, is far simpler than anything the mainstream has to offer. Such a universe would accordingly have edges and a center. Again the principle that I follow is, if it complicated it probably does not exist in realityThis is all wrong. You are at odds with the whole of cosmology. The mainstream view is that it is a universe with an edge that is the more complicated scenario - you only have to consider the boundary conditions to see why.
Last edited by forrest noble; April 3rd, 2012 at 03:09 PM.
This doesn't make sense. Space implies, at the very least, the pressence of dimensions and so won't be meaningless. In your model, matter and fields would need that to expand into. It necessarily needs an infinite expanse of nothing. And you are wrong, again, about unbounded space implying a centre. Did you not read the link?Unbounded in space but finite in matter and field does have a center to it, concerning the matter and field. In my own finite universe model, space is bounded by definition, the defintion being: Space is the volume that matter and field occupies and would be a meaningless concept beyond the bounds of matter and field. Space accordingly is defined as to its size by the full extension of the matter and field within it
I can't see how it is even possible for an unbounded topology to have a center.
Unless you have your own personal definition of either "center" or "bounded" (or both).
KALSTER,
The question then would become: what would be the meaning of matter, field, space, time, and gravity, for a universe with absolutely nothing in it? My contention is that such a universe would be meaningless. And as in Einstein's quote that I posted, space, time, and gravity, must have field and matter to both create these entities as well as to define them -- as indicated by Einstein's quote.This doesn't make sense. Space implies, at the very least, the presence of dimensions and so won't be meaningless. In your model, matter and fields would need that to expand into.
This is not the only definition of space, and I think that it also is not the best definition of it.It necessarily needs an infinite expanse of nothing.
In my definition and discussion of space, I did not say that unbounded space has a center. Of course it doesn't. In my own model, for instance, space is finite and bounded by definition to the full extension of the matter and Field (The Zero Point Field) within it. Both matter and field have a finite extension in my own model. So for such a model the universe would have both boundaries and a center concerning the matter and field within it.And you are wrong, again, about unbounded space implying a centre. Did you not read the link?
What is beyond these boundaries in your model?
The topology of my own model is bounded by the definition of space that I use which is defined as: the distance between matter, and the volume which contains the full extension of both matter and field (the ZPF). Accordingly it is entirely Euclidean.I can't see how it is even possible for an unbounded topology to have a center.
Unless you have your own personal definition of either "center" or "bounded" (or both).
If one prefers and unbounded definition of space, then accordingly the center of our physical universe would be the physical center of the contiguous matter and field volume within the universe. Either way there would be a center based upon these definitions.
Other models of the universe could be quite different if one uses warped/ curved space with different definitions of space, as is the case of many versions of the standard model.
You confused things by saying it was unbounded previously. OK. It is bonded and has a center.The topology of my own model is bounded by the definition of space that I use which is defined as: the distance between matter, and the volume which contains the full extension of both matter and field (the ZPF). Accordingly it is entirely Euclidean.I can't see how it is even possible for an unbounded topology to have a center.
Unless you have your own personal definition of either "center" or "bounded" (or both).
I struggle to make sense of this. You are suggesting unbounded space (and therefore with no center) having an isolated and bounded "blob" of matter somewhere within it? Is that it? And the rest of space is completely empty?If one prefers and unbounded definition of space, then accordingly the center of our physical universe would be the physical center of the contiguous matter and field volume within the universe. Either way there would be a center based upon these definitions.
But you also suggest that the "field volume" is bounded. What does that mean; is that things like electric field, gravitational field, etc? If so what causes them to come to a sudden end? Surely they should extend to infinity (i.e. throughout the whole of this unbounded space)?
I suspect that all sorts of standard physics would no longer work if you say that fields of that sort have a "cut off" point.
This is a good question. Nothing would or could exist beyond these boundaries. In this model the ZPF is the pressure that holds matter together. Maybe only half way to these boundaries matter would disintegrate, first ionization, then molecular breakdown, and then atomic particles would spin out their looped existence becoming once again just another part of the ZPF. As the ZPF would thin out it would accordingly no longer be able to carry, radiate, or conduct, EM radiation so there would be no light in such areas, with temperature almost at absolute zero, much lower than the CMBR. Once far enough out even field particles would be too far apart to interact with each other. Even within these bounds there would be no possible light or possible measurement of anything within these volumes since no matter could even come within billions or trillions of light years from it.What is beyond these boundaries in your model?
In my own model the universe is vastly older than the 13.7G mainstream model -- but bottom line is that there still would accordingly be a physical central area to it, which could be denser in galaxies and matter, than our observable universe.
Come on, this doesn't makes sense. Space, as defined by anyone, including GR, is at least the presence of volume, of dimensions, with or without curvature. There doesn't need to be anything in it for the volume to exist. You just seem to, for some reason, want your model to be within a finite universe and at the same time be without curvature and are arbitrarily redefining empty space as meaningless in order to achieve that. You can't have it both ways. Either space is infinite, or it is finite with curvature. Do you have a problem with infinity for some reason?The question then would become: what would be the meaning of matter, field, space, time, and gravity, for a universe with absolutely nothing in it? My contention is that such a universe would be meaningless. And as in Einstein's quote that I posted, space, time, and gravity, must have field and matter to both create these entities as well as to define them -- as indicated by Einstein's quote
The topology of my own model is bounded by the definition of space that I use which is defined as: the distance between matter, and the volume which contains the full extension of both matter and field (the ZPF). Accordingly it is entirely Euclidean.I can't see how it is even possible for an unbounded topology to have a center.
Unless you have your own personal definition of either "center" or "bounded" (or both).
(my quote)You confused things by saying it was unbounded previously. OK. It is bonded and has a center.If one prefers an unbounded definition of space, then accordingly the center of our physical universe would be the physical center of the contiguous matter and field volume within the universe. Either way there would be a center based upon these definitions.I started this by saying "if one prefers." This is not my preferred picture or model. But even for such a model (not mine), if the matter and field were finite within an infinite space there would still be a physical center to the matter and field collectively. Some theorists have proposed that space and field are infinite and that just matter is finite in quantity. In such a model matter could have a physical central area to it but space and field would not.I struggle to make sense of this. You are suggesting unbounded space (and therefore with no center) having an isolated and bounded "blob" of matter somewhere within it? Is that it? And the rest of space is completely empty?
But of course I think none of above models are correct. Only defining space by the matter and field within it, and only if the matter and field is finite and generally contiguous, would my finite model apply. see my posting #71 above for details.
The volume is bounded by definition, see my posting #71But you also suggest that the "field volume" is bounded. What does that mean; is that things like electric field, gravitational field, etc? If so what causes them to come to a sudden end? Surely they should extend to infinity (i.e. throughout the whole of this unbounded space)?
I think it would not effect standard physics much since accordingly only the rarest existence of vastly spread out individual field particles could exist at these boundaries: no light or EM radiation, no electricity, magnetism, no matter or energy, etc. etc., solely field particles.I suspect that all sorts of standard physics would no longer work if you say that fields of that sort have a "cut off" point.
You have a finite volume containing a field, bounded by "something", with the matter of the universe somewhere within it, but not filling it.
You have a finite universe not only permeated by but also surrounded by a field, but that field has an edge!
This makes your model three times as complicated as the standard model.
Now you need to define boundary conditions between the edge of your finite matter universe and the empty space (or ZPF) around it, and then you need to define boundary conditions for the ZPF and whatever it is that bounds your universe!!
See posting #71. You might think this is a complicated model but I have easily explained it to high school kids.
My model of the universe is not bounded by anything except by its definition as I have explained. The matter in the universe certainly fills it but only field particles dominate at the boundaries where the field trickles to nothingness which one could call an edge or boundary if they liked.
The standard model required/ requires the Inflation of space; warped or curved space; expanding (stretching) space; and the accelerated expansion of space. These theories of space seem to be far more complicated than the simple Euclidean space of my model whereby space is simply the distance between matter. In curved space there are no boundaries to explain but there is no evidence to support a curved universe, even though it may still exist at a much larger unobservable scale.
Instead all the evidence of observations so far supports a flat universe that could be no different from Euclidean geometry, or simply explained by Minkowsky space with the inclusion of the coordinate of time. Therefore evidence so far seems to point in the direction whereby our universe could have a center, or a central area to it.
Last edited by forrest noble; April 3rd, 2012 at 06:13 PM.
We are going in circles here.
...in order to explain what we have observed - the redshift-distance relationship, time-dilation in supernova light curves etc etc. There is a very long list of evidence that supports the standard cosmological model.
So, how does your model explain all these observations?
Let's start with redshift. How does your Doppler interpretation account for the apparently superluminal recession velocities of galaxies we get when using the Special Relativistic Doppler formula?
My model is a diminution of matter model to explain galactic redshifts, and accordingly the universe is not expanding or superluminal in this regard. Time dilation is a prediction of my model concerning the longevity of the supernova events based upon the "appearance" that time was slower in the past. The formula for the dilation/ extension is simply (z+1) t, where t is the longevity of a Sn observation or any time interval within it that one is interested in -- such as the duration of peak luminosity. Time dilation does not apply to Quasar brightness variation cycles since in my model we are accordingly observing the rotation rate of the quasar. Although a quasars time of rotation would appear to have been slower/ taken longer, its size and distance around would appear to have been greater the further away it is -- therefore the speed of rotation per unit of time would appear identical (distance x time). since according to observations quasar light cycles remain consistent regardless of the distance, without time dilation. I have seen no mainstream explanations concerning the lack of time dilation of quasars....in order to explain what we have observed - the redshift-distance relationship, time-dilation in supernova light curves etc etc. There is a very long list of evidence that supports the standard cosmological model.
I adhere to the general redshift distance correlation which generally can be estimated by Luminosity Distance calculations as well as their angular size. To improve on the distance calculations for my model, I have re- formulated the Hubble formula to "more accurately" calculated the distances to galaxies and type 1a Sn, and to explain away the observations of type 1a Sn that claim the existence of dark energy. As to curved/ warped space, I have a different model of gravity including mathematically, which accordingly does not involve GR, require warped space or dark matter. It is a type of Modified Newtonian gravity that accordingly explains disc star rotation rates, galaxy rotation rates, generally with equal or better results to dark matter models using Newtonian gravity (or GR).So, how does your model explain all these observations?
Let's start with redshift. How does your Doppler interpretation account for the apparently superluminal recession velocities of galaxies we get when using the Special Relativistic Doppler formula?
Again I have re-formulated the SR based Hubble formula/ equation based upon the diminution of matter proposal, that you can see here in my technical papers.
As you can see, I adhere to the principle: if the explanation is overly complicated (prime examples Quantum Theory and GR) then what's being explained is probably not real, mathematics aside. Again I think observations indicate the possibility that the universe has a center, even concerning the standard model.
Last edited by forrest noble; April 3rd, 2012 at 11:31 PM.
Baganoff and Malkan (colleagues of Ned Wright at UCLA) offered a widely accepted explanation back in the mid-1990s. It is thus a mainstream explanation, and an old one, at that. The apparent lack of quasar time dilation appears to be just that -- apparent.
Last edited by tk421; April 3rd, 2012 at 10:03 PM.
Thank you. So you do understand.While remaining on the surface of a sphere we would say that there is no center to the surface, or in the BB scenario we might say that there is no center to the universe -- as in my posting #28.
Forrest, please stop wasting our time. This is a thread asking about how the universe can have no centre, and as the OP talks about what cosmologists say, we are talking here about the standard model in cosmology, or at least a valid alternative model.
Stop muddying the waters with your own invalid CRACKPOT theory of shrinking matter, and stop using standard terms like bounded and unbounded in non-standard ways. (I don't know how you managed to mangle the meaning of both terms, but you did!)
No cosmologist would talk of your model, so stop derailing a thread where the OP is asking what cosmologists mean when they say there is no centre to the universe.
What a waste of my time...
Last edited by SpeedFreek; April 4th, 2012 at 02:13 PM. Reason: edited whilst being quoted :)
I think you mis-characterized the OP question. The question was this:
(words in parenthesis added)....something about this (standard interpretation of no-centre to the universe) has always gotten me a bit muddled. It goes like this: when the universe was very small it does indeed have a centre (surely?), say when it was the size of a grapefruit. What happens to make the centre cease to be something we can speak about?
Your characterization of the OP question:--which is not what he was asking.....the OP is asking what cosmologists mean when they say there is no centre to the universe.
My primary point was and is simply this: Although many in the mainstream think there is no center to the universe as I explained in my posting #28, there is little or no evidence to support this mainstream proposal in my opinion, based upon my comments. Most all of my rhetoric beyond this has been in response to direct questions or commenting on others postings. For those that did not want to hear my answers, such leading questions should not have been asked. I think it is always a problem in discussion/ debate whereby one thing is related to another and therefore must be brought up to answer a question. This is especially true of models where everything concerning one part of the universe is directly related and in some ways involves everything else theoretically.
Last edited by forrest noble; April 4th, 2012 at 02:21 PM.
I think you missed out the first paragraph. Something about cosmology has him muddled.
I have already posted a link that shows the main evidence for the Big-Bang. There is ABSOLUTELY no evidence that the universe has a centre.
Fair enough, and I apologise for my earlier tone, but I did not start out asking you leading questions, I was simply correcting the statements you were making about the standard cosmology, for the benefit of everyone. It started in post #31, where your "contradiction" is based in your own misunderstandings of the theory you are arguing against. You were proposing a contradiction that doesn't actually exist, and my pointing that out was not a question.
You even acknowledged, in the next post, that I was correct in the context of the standard model, and then you posted a link to a web article that actually states that this supposed contradiction was cleared up when we discovered the universe was accelerating, and calculated how much energy would be required - it accounted for the difference between the visible mass and the mass required for critical density. Simple. A flat, open universe.
Next, in post #52 I had to correct you, once again, when you stated the assumptions required for a (Big-Bang) universe with no centre. None of those assumptions are required for a universe with no centre, whatever type of universe it is. Again, this was not a question, it was a statement. Yet again you were misrepresenting the theory you are arguing against.
In your reply to me, you completely went off topic, as all your arguments were against aspects of Big-Bang theory that are not a pre-requisite for the universe having no centre. You were just intent on having a go at the theory in general and seemed to have completely lost sight of the fact that the discussion is about the reason we think there is no centre to the universe. At the end of your post, you even agreed that the one assumption of the theory that is required for the universe to have no centre was the only part we have observational evidence for, homogeneity and isotropy!
From then on, it was a battle to get you to understand how the things you were saying were not the reason we think the universe has no centre, to stop you confusing other readers of this thread with your misconceived objections. You might have objections to the Big-Bang model, but they are not the reason why we think the universe has no centre.
The assumptions of homogeneity and isotropy are the reasons we think the universe has no centre. Your idea for a universe is neither homogeneous or isotropic, which is why you need two extra sets of boundary conditions to describe it, making it far more complicated than the standard cosmology.
Yes, I too apologize for any misunderstandings that I may have been a part of, but for my demeanor on this and all other threads, I always try to be pleasant, lightheartedI think you missed out the first paragraph. Something about cosmology has him muddled.
I have already posted a link that shows the main evidence for the Big-Bang. There is ABSOLUTELY no evidence that the universe has a centre.
Fair enough, and I apologise for my earlier tone, but I did not start out asking you leading questions, I was simply correcting the statements you were making about the standard cosmology, for the benefit of everyone. It started in post #31, where your "contradiction" is based in your own misunderstandings of the theory you are arguing against. You were proposing a contradiction that doesn't actually exist, and my pointing that out was not a question.
You even acknowledged, in the next post, that I was correct in the context of the standard model, and then you posted a link to a web article that actually states that this supposed contradiction was cleared up when we discovered the universe was accelerating, and calculated how much energy would be required - it accounted for the difference between the visible mass and the mass required for critical density. Simple. A flat, open universe.
Next, in post #52 I had to correct you, once again, when you stated the assumptions required for a (Big-Bang) universe with no centre. None of those assumptions are required for a universe with no centre, whatever type of universe it is. Again, this was not a question, it was a statement. Yet again you were misrepresenting the theory you are arguing against.
In your reply to me, you completely went off topic, as all your arguments were against aspects of Big-Bang theory that are not a pre-requisite for the universe having no centre. You were just intent on having a go at the theory in general and seemed to have completely lost sight of the fact that the discussion is about the reason we think there is no centre to the universe. At the end of your post, you even agreed that the one assumption of the theory that is required for the universe to have no centre was the only part we have observational evidence for, homogeneity and isotropy!
From then on, it was a battle to get you to understand how the things you were saying were not the reason we think the universe has no centre, to stop you confusing other readers of this thread with your misconceived objections. You might have objections to the Big-Bang model, but they are not the reason why we think the universe has no centre.
The assumptions of homogeneity and isotropy are the reasons we think the universe has no centre. Your idea for a universe is neither homogeneous or isotropic, which is why you need two extra sets of boundary conditions to describe it, making it far more complicated than the standard cosmology.
There certainly is some evidence to support the idea that the observable universe is homogeneous and isotropic but as you said, it is simply an assumption concerning the universe as a whole. If the over-all universe is say a 100 or more times larger than the observable universe then I believe this is not a good assumption. For the universe not to have a centre (or a more central area) it must curve in one or more dimension(s) or plain(s). There is no evidence for this.The assumptions of homogeneity and isotropy are the reasons we think the universe has no centre. Your idea for a universe is neither homogeneous or isotropic, which is why you need two extra sets of boundary conditions to describe it, making it far more complicated than the standard cosmology.
As to your quote:I agree with your statement but would add: There also is no evidence that the universe does not have a centre. I guess that's my bottom-line point on this topic.There is ABSOLUTELY no evidence that the universe has a centre.
best regards, Forrest
Last edited by forrest noble; April 4th, 2012 at 04:22 PM.
You keep saying this, but the topologists don't agree with you. A flat universe has no centre, and this statement is not tied to the current mainstream cosmology as you seem to think, it is tied to the fundamental concepts behind any cosmology, in the absence of any evidence of inhomogeneity or anisotropy.
And I guess my bottom line here is the cosmological principle. I think this means that "no centre" wins out, in the absence of any evidence to the contrary!
Last edited by SpeedFreek; April 4th, 2012 at 04:36 PM.
If it is untestable, then why make an unnecessary assumption? "Keep things simple" is an important guiding principle. And since you are already on record as aspiring to provide theories that are simple enough for the average person to understand, I'd have thought that you'd be on board with it. Since all observations are consistent with a basically homogeneous and isotropic universe with no center, then why invoke an untestable assumption of a universe so large that it could have a center somewhere? There could also be dragons beyond the observable universe, but why bother postulating such things?
I think it is just a matter of opinion whether a universe finite in field and matter, could have a center.You keep saying this, but the topologists don't agree with you. A flat universe has no centre, and this statement is not tied to the current mainstream cosmology as you seem to think, it is tied to the fundamental concepts behind any cosmology, in the absence of any evidence of inhomogeneity or anisotropy.
And I guess my bottom line here is the cosmological principle. I think this means that "no centre" wins out, in the absence of any evidence to the contrary!
In my opinion a centered universe, concerning the matter within it, is more likely since it does not require curved space in it at a universe scale and so far the universe appears to be flat and not curved.
In your opinion since most astronomers today believe the observable universe is homogeneous and isotropic based upon observations, it is a wise assumption that the entire universe is the same way, in the absence of evidence to the contrary. Therefore a non centered universe "wins out."
To quote you exactly:
And I guess my bottom line here is the cosmological principle. I think this means that "no centre" wins out, in the absence of any evidence to the contrary!
I'm not following you on this. What unnecessary assumption do you think that I have made? You are using the wrong terminology when you use the word "assumption." What I said concerning the cosmological principle was: if the over-all universe is say a 100 or more times larger than the observable universe then I believe this (the cosmological principle) is not a good assumption to make (parenthesis added). The meaning of this could also be phrased as a question: Since we have no idea how big the universe really is, do you think it is wise to assume that the whole universe must be like the part of it the we can observe?If it is untestable, then why make an unnecessary assumption? "Keep things simple" is an important guiding principle. And since you are already on record as aspiring to provide theories that are simple enough for the average person to understand, I'd have thought that you'd be on board with it. Since all observations are consistent with a basically homogeneous and isotropic universe with no center, then why invoke an untestable assumption of a universe so large that it could have a center somewhere? There could also be dragons beyond the observable universe, but why bother postulating such things?
On the other hand I believe two assumptions are needed for a finite universe not to have a center concerning contiguous matter. The first assumption is that space bends in some way which is not based upon observation, and the second assumption is that the entire universe must follow the cosmological principle of being homogeneous and isotropic. This could never be verified by observation.
The point is that it's a matter of intellectual economy. You know, Occam's (Ockham's) Razor and all that. And yes, I do think that, in the absence of observations that inform otherwise, it's a wise position to adopt. And we have no observational data that conflict with the cosmological principle, so it does keep things simple. Again, why complicate things by making more elaborate assumptions? I'm not getting your logic or taste, but I am getting accustomed to that.
To have a center, and also to reproduce our observations of homogeneity and isotropy (over suitable length scales) poses a rather challenging geometry problem! You seem unaware of the full implications of the observed remarkable isotropy of the CMB. Those measurements severely constrain our choices.On the other hand I believe two assumptions are needed for a finite universe not to have a center concerning contiguous matter. The first assumption is that space bends in some way which is not based upon observation, and the second assumption is that the entire universe must follow the cosmological principle of being homogeneous and isotropic. This could never be verified by observation.
How can you say something like this? It sounds exactly like the kind of claptrap creationists come up with when they claim evolution has never been observed. Again, you seem unaware of the large amounts of supporting evidence for it. Either that, or you are ignoring it with a wave of the hand. Why would GR make such precise predictions that get's verified by experiment if curvature didn't exist? You said light would bend under interpretations of Newtonian gravity as well, but does it produce the same results as that observed and predicted by GR? No it does not. To say curvature is unobserved and an assumption is dishonest imo.On the other hand I believe two assumptions are needed for a finite universe not to have a center concerning contiguous matter. The first assumption is that space bends in some way which is not based upon observation, and the second assumption is that the entire universe must follow the cosmological principle of being homogeneous and isotropic. This could never be verified by ob
Last edited by KALSTER; April 5th, 2012 at 02:08 AM.
In my opinion a non-curved space model of the universe is a much simpler and more justifiable model based upon observations, without assumptions. And a totally flat universe would have a central area to it.The point is that it's a matter of intellectual economy. You know, Occam's (Ockham's) Razor and all that. And yes, I do think that, in the absence of observations that inform otherwise, it's a wise position to adopt. And we have no observational data that conflict with the cosmological principle, so it does keep things simple. Again, why complicate things by making more elaborate assumptions? I'm not getting your logic or taste, but I am getting accustomed to that.
On the other hand I believe two assumptions are needed for a finite universe not to have a center concerning contiguous matter. The first assumption is that space bends in some way which is not based upon observation, and the second assumption is that the entire universe must follow the cosmological principle of being homogeneous and isotropic. This could never be verified by observation.Just because so far the universe appears to totally follow the cosmological principle, realize also that so far the universe also appears to be totally flat. Does that necessarily mean that the entire universe most likely follows the cosmological principle while being most likely totally flat. The answer is no. Regardless of whether the overall universe follows the cosmological principle or not, if it does not curve in any dimension or plain, it will have a central area to it.To have a center, and also to reproduce our observations of homogeneity and isotropy (over suitable length scales) poses a rather challenging geometry problem!
Those measurements and their interpretations of the CMB might constrain choices for some Big Bang proponents but they might mean less or little to those that believe that the Big Bang model is questionable, could be wrong, or is wrong in one or many ways.You seem unaware of the full implications of the observed remarkable isotropy of the CMB. Those measurements severely constrain our choices.
On one hand there is a mountain of evidence to support natural selection and evolution in general, but on the other hand there is no evidence that the overall universe has no center to it. For the universe not to have a center to it, it would seem that space must bend in one or more dimension or plain. There is no evidence for such bending since the universe is presently believed to be flat by mainstream astronomers based upon a number of different types of observations and numerous studies both from the ground and from satellites. Since there is no evidence for this curvature of space then it must be an assumption if it is believed to exist on a larger scale. Just because the equations of GR seem to work in our solar system or in parts of our galaxy does not mean that it works everywhere since dark matter is needed at the full galactic scale, and at the quantum scale QM prevails. Although GR predicts warped space and can predict curved space, it also can predict flat space. It does not matter whether GR is the correct model of gravity or not, the bottom line is that there is no evidence that the overall universe does not have a central area to it, other than by assumption, Is there?
Granted it is also equally true that there is no evidence that the overall universe does have a center to it other than that the observable universe appears to be flat, then to assume that the overall universe is most likely flat -- would also be faulty logic. For either judgement concerning whether the universe has a center to it or not cannot be determined because we really have no idea how big the universe really is concerning a finite amount of matter and field, and probability assessments concerning a center to the universe would likely vary depending upon who is being asked within the mainstream, and/or outside of it.
It is also granted that the majority of mainstream theorists today presently think that the universe does not have a center to it because of its geometry, and the majority of alternative theorists outside the mainstream also do not think the universe has a center to it because the majority of the models they ascribe to assert that the universe is infinite in volume and matter and therefore could have no center to it.
But there are some theorists that either believe the universe has a center to it, or could have one. So I realize that my views are in a small minority.
Last edited by forrest noble; April 5th, 2012 at 03:56 AM.
Yeah, for the umpteenth time, I get it: You plain don't like mainstream cosmology. I understood that many posts ago. I also understood many posts ago that you don't have a viable scientific alternative.
You are certainly entitled to your opinion, of course. But quit fantasizing that it's anything beyond that. You don't have a theory in the commonly accepted scientific definition of the term. And your notions certainly don't have anything even remotely resembling the vast observational support enjoyed by standard cosmology. You can't just "fix" one aspect you don't like without breaking a whole lot of other stuff that works really, really well. That's why coming up with an alternative theory is so challenging for everyone. The standard cosmology became mainstream because of a "survival of the fittest" contest among many competing ideas, all critically examined by everyone else. Most were so flawed that they failed to survive. Understand that each one of those failures sounded great to their proposers, seemed to fit enough data (available at the time) to merit publication, and seemed to repair whatever deficiencies of the previous mainstream that stimulated them to seek an alternative in the first place. The acid test is to see whether it survives the slings, arrows and outrageous critical attacks of everyone else.
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