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Bogie
2006-Sep-12, 11:53 PM
How do the following assumptions violate General Relativity?

Assumptions: The universe is infinite spatially and in energy content, i.e. a greater universe has always existed. Finite Big bangs are common place and are caused by big crunches. Each big bang sends out a particle horizon. Because of all of the partilce horizons from an infinite number of big bangs, over time space is permeated with the cosmic microwave radiation from all those big bangs, not just the CMBR from our own big bang.

Ken G
2006-Sep-13, 12:05 AM
Look up "Olbers' paradox" to find the violation, although the fact that a "horizon" means we cannot get CMBR from anywhere else should also suffice.

Bogie
2006-Sep-13, 12:30 AM
Look up "Olbers' paradox" to find the violation, although the fact that a "horizon" means we cannot get CMBR from anywhere else should also suffice.I am familiar with Olbers and the many solutions that don't quite work, but the solution that works to solve Olbers' is the finite life of stars, the fact that light is not instantaneous, and the universe is expanding. Also the outlook distance that would create a complete canopy is way beyond the age of the known universe. This is well covered in "Looking at the Invisible Universe" by James Jesperseon & Jane Fitz-Randolph. I have it.

It is quite possible that the horizon issue is the thing that GR can't go beyond.

Clarify that for me a little: I know that the standard cosmology tracks back to the instant after the big bang, and that the Big Bang with Inflation, goes as far back in time as the instant after the big bang, and describes the total content of the ‘known’ universe it that instant after the BB as being smaller than a pinhead, and hotter that Hades. In the second instant
(say 10^-30 seconds give or take) there was exponential expansion when the universe inflated 500,000,000,000 times in size, establishing an isotropic and homogeneous domain within which and from which the known universe "evolved" or unfolded.

Science cannot go back any farther that the instant after the BB because before that point our theories and the math that supports them lose their meaning in a confusion of infinites.

Is you statement that the horizon keeps us from getting CMBR from anywhere else based of the Big Bang Theory or on General Relativity? If it is GR, do you have a link that actually says so and that I could read to try to understand? What does GR say about CMBR? I know that things can pass into a black hole that has an event horizon. Isn't it possible under GR for something to enter the particle horizon that gives off our CMBR (http://space.mit.edu/home/tegmark/wmap/wiener_north.jpg)?

Or are you saying that the particle horizon that is causually connected to the big bang creates space-time as the universe expands. If that is it, then are you saying that is part of GR?

I'm not being difficult; I don't know GR well enough to know the answer and want help with the answer. I know you are trying to help, but I don't know how what you have told me relates to GR.

Nereid
2006-Sep-13, 01:28 AM
I am familiar with Olbers and the many solutions that don't quite work, but the solution that works to solve Olbers' is the finite life of stars, the fact that light is not instantaneous, and the universe is expanding. Also the outlook distance that would create a complete canopy is way beyond the age of the known universe. This is well covered in "Looking at the Invisible Universe" by James Jesperseon & Jane Fitz-Randolph. I have it.This seems a little confused (or perhaps too terse), but the minor part of the problem (per your OP).
It is quite possible that the horizon issue is the thing that GR can't go beyond.

Clarify that for me a little: I know that the standard cosmology tracks back to the instant after the big bang, and that the Big Bang with Inflation, goes as far back in time as the instant after the big bang, and describes the total content of the ‘known’ universe it that instant after the BB as being smaller than a pinhead, and hotter that Hades. In the second instant
(say 10^-30 seconds give or take) there was exponential expansion when the universe inflated 500,000,000,000 times in size, establishing an isotropic and homogeneous domain within which and from which the known universe "evolved" or unfolded.Substitute "observable" for "known" - we can only 'see' that part of the universe within our 'horizon'; the latter is (crudely) all parts of the universe from which light has been able to reach us.
Science cannot go back any farther that the instant after the BB because before that point our theories and the math that supports them lose their meaning in a confusion of infinites.I prefer a different way of describing the GR/QM incompatibility - there is a regime (the Planck) within which application of both GR and QM produces wild inconsistencies ("a confusion of infinites", if you will). However, the inconsistency is considerably deeper than the infinities - the very structures (of GR and QM) are incompatible. Or, if you prefer, there is no way to unite the two theories - we must abandon one, or both, and create a new theory (or theories) that have completely different structures (but which 'reduce to' GR and QM, respectively, in their limits).
Is you statement that the horizon keeps us from getting CMBR from anywhere else based of the Big Bang Theory or on General Relativity?The latter (the former is 'merely' an implemention of the former).
If it is GR, do you have a link that actually says so and that I could read to try to understand? What does GR say about CMBR?Google on "Ned Wright Cosmology Tutorial" or "Sean Carroll cosmology" (the former is perhaps more accessible; the latter has more math).
I know that things can pass into a black hole that has an event horizon. Isn't it possible under GR for something to enter the particle horizon that gives off our CMBR?I have no idea.

However, this 'something' would have to be pretty darn extraordinary - the CMB is the surface of last scattering; the last time, in the history of the universe, when (baryonic) matter and radiation were in equilibrium. What could this 'something' be possibly coupled to, that it left a footprint in the CMB, but didn't participate in the matter-radiation equilibrium?
Or are you saying that the particle horizon that is causually connected to the big bang creates space-time as the universe expands. If that is it, then are you saying that is part of GR?That may also be the case - but it is irrelevant, in terms of the CMB ... and your 'something'.
I'm not being difficult; I don't know GR well enough to know the answer and want help with the answer. I know you are trying to help, but I don't know how what you have told me relates to GR.Read Carroll, without paying attention to the math ... GR describes the universe and its evolution. If it's expanding, then, from some simply described properties of the matter we know a great deal about, and photons, the 'phases' of the universe are equally easy to state (in principle) - they are the times when (first) the strong, (next) the weak, and (last) the electromagnetic force dropped out of equilibrium - and thus baryosynthesis, nucleosynthesis, and the CMB. (this is, of course, a gross simplification).

Because it's the universe, there cannot be anything that comes in 'from outside'; the only way you can make things turn out differently is to have forces/fields we don't yet know about (e.g. inflation), or mass-energy components of the universe we can't yet model (e.g. dark matter), or something which replaces GR.

Ken G
2006-Sep-13, 02:54 AM
Is you statement that the horizon keeps us from getting CMBR from anywhere else based of the Big Bang Theory or on General Relativity?
I'm saying that's the definition of the horizon. It is as far as we can see in the age of the universe, just the point you raised in eliminating Olbers' paradox. My point was you can't have it both ways-- either it is all we can see, in which case the rest of those big bangs are pure speculation, or it isn't all we can see, in which case you reintroduce Olbers' paradox. If you are using general relativity and the Big Bang (which should be thought of as the initial constraint that general relativity needs as an input), then it's all we can see. But perhaps a better answer would simply be that it's kind of a moot point-- the Big Bang theory has no suggestion for "where the energy came from", it is merely part of the theory that it was there at some very very early time, in thermal equilibrium at some temperature. The interesting thing about thermal equilibrium is that it would erase any knowledge or information from any previous origin, even if it is even meaningful to ask about it.


I know that things can pass into a black hole that has an event horizon.
That's not the meaning of the term "horizon" in cosmology-- it's a different type of horizon. It has little to do with gravity, and everything to do with age.


Or are you saying that the particle horizon that is causually connected to the big bang creates space-time as the universe expands.
Spacetime appears, it's not clear it needs to be "created". It's equally possible that matter (like rulers) contracts.


If that is it, then are you saying that is part of GR?
Yes, GR describes how any coordinate description of the location of the matter would evolve in time, that's its purpose. How it is interpreted, like "creation of spacetime", is not part of GR, it's a pedagogy added to try and understand GR.


I don't know GR well enough to know the answer and want help with the answer. I know you are trying to help, but I don't know how what you have told me relates to GR.
It's very hard to really know GR unless you do it all the time, which I don't. But I can give you the basic idea. There's no substitute for really doing the calculations, however.

Bogie
2006-Sep-13, 03:23 AM
OK, thank you Nereid and Ken G.

Certainly I am speculating about "before and beyond" the Big Bang, and am not presenting alternative theory, so therefore I'm out of bounds of real science.

Your replies were helpful and instructive and I thank you.

LayMan
2006-Sep-13, 07:57 AM
OK, thank you Nereid and Ken G.

Certainly I am speculating about "before and beyond" the Big Bang, and am not presenting alternative theory, so therefore I'm out of bounds of real science.

Your replies were helpful and instructive and I thank you.

I always feel a bit I'm out of bounds of science completely, but I looked up Olbers paradox and I had already heard of it a long time ago, I think it was when I first read the book "Mr. Thompkins..." (I don't know the English title, I read a dutch copy of it, the dutch title would probably translate into something like "Mr. Thompkins and the throbbing/pulsating Universe").

Here's my question, I hope you can shed some light on it (pun intended): if I am to look at our Universe (and with that, I mean our visible Universe) as a big balloon that is expanding, with space, time, matter and energy strictly confined to its outer shell (that's to say, in the analogy with the balloon, I'm not allowed to say that the inside of the balloon were the air is, would also constitute space and time, am I correct in that?), is it then correct that - at least theoretically - I would see the Sun twice? Once when I was to stare at it directly (I know I should not do that!), and once when I was actually looking in the opposite direction? Kind of like I'm able to go from Europe to America in two opposite ways, via the Pacific and via Asia?

I know you will probably point out that the sphere of our known or visible Universe is so immensely large that the light of the Sun hasn't had the time yet to reach us from the opposing side, but if that sphere was much smaller a long time ago, it would also not need the amount of time it would require now, would it? Or is the Sun simply not old enough for that?

LayMan
2006-Sep-13, 10:45 AM
Actually, to follow up on my own question, the Sun spreads it light into every direction, so instead of asking whether I would see it twice, my question should be: why don't I see it infinitely? In other words, why do we see a spotted night sky instead of one big band of light? The reason I ask, is that when I tried reading about the paradox, the website started off by saying we needed to calculate the volume of space and gave the volume formula for a sphere, but if the inner part of the balloon should not be viewed as being part of the space/time continuum, then what's the point of calculating the volume of that balloon?

(P.S. the website was dutch, so I didn't include the link, I'll try to find an english version...).

Bogie
2006-Sep-13, 12:43 PM
Actually, to follow up on my own question, the Sun spreads it light into every direction, so instead of asking whether I would see it twice, my question should be: why don't I see it infinitely? In other words, why do we see a spotted night sky instead of one big band of light? The reason I ask, is that when I tried reading about the paradox, the website started off by saying we needed to calculate the volume of space and gave the volume formula for a sphere, but if the inner part of the balloon should not be viewed as being part of the space/time continuum, then what's the point of calculating the volume of that balloon?

(P.S. the website was dutch, so I didn't include the link, I'll try to find an english version...).
Space has volume and the shape of space in Euclidian geometry, assuming that space refers to the space occupied by our expanding big bang universe, is a sphere.

As the big bang universe expands the volume of the sphere increases.

The paradox is that if the sphere is increasing because of a big bang blast, we should be able to detect the direction of the center of the sphere by the vectors of the matter (galaxies) that we observe. In a blast everything moves away from the center and so all vectors would point back to that center.

This however is not the case. It makes no difference which direction we look, the universe appears homogeneous in that everything seems to be moving away from everything else at a pretty constant rate, i.e. no center can be detected. So thinking that the big bang was an explosion that set everything in motion on an outward path is not supported by the observational evidence of the homogeneous universe. The space between the galaxies seems to be stretching. If space is stretching instead of objects in space following the path of an explosion, you could explain the observational evidence.

Here comes the balloon. The space between the galaxies seems to be stretching and so scientists are hard pressed to describe the space of our universe in Euclidian geometry because in Euclidian space a big bang would appear to have a center and our universe does not reveal a center.

They then abandon the Euclidian space and try to describe the alternative space in terms that fits the evidence. The evidence shows everything expanding away from everything else as if each galaxy was painted on the surface of a balloon and the balloon was being inflated. They don’t mean the shape of the universe is literally a balloon. It is an analogy where the surface of the balloon represents the relative motion of the galaxies in the universe and demonstrates that space is stretching “like the surface a balloon”.

The problem of not being able to detect the center of the expansion has lead to the opinion by some that space-time was created by the big bang, i.e. no space or time existed before the big bang event. They surmise that as the big bang universe expands, space-time is being created evenly throughout the universe and therefore the galaxies seem to move away from each other evenly no matter which way you look.

This opinion fits the evidence but goes against the 3-D logic that we deal with in our everyday lives. Certainly the universe has some more surprises for us before everything will make sense.

Ken G
2006-Sep-13, 01:24 PM
Note also that current evidence suggests that if you take age as your time coordinate, and take space as co-moving with the matter in the universe, then the spatial part is Euclidean to within our ability to measure. So we don't know if straight lines bend around and form closed curves, like on a sphere, but there certainly isn't any evidence that they do. The simplest picture right now is that the universe is spatially infinite, although of course we only know as far as we can see.

Thus the balloon analogy is of limited value, and frankly I really don't like it at all. It suggests there "really is" a center, it's just outside of our 3D space, and it also suggests that the universe is finite in size. But if it really is Euclidean, then neither of those are true. So here's what I think is a better analogy. Take graph paper and draw x and y axes in the usual way. Imagine that there are galaxies every place the lines intersect. Now actually move your eyes closer to the paper. What happens? Space appears to expand. That's all that's happening. It will appear that there is a center, the point directly under your eyes, but you can see that this point is a result of your own choosing-- no matter where you put your head and do the same thing, the graph does the same thing in response-- the choice of the "center" is up to you, it is determined by your vantage point, just as our view of the Big Bang is determined by our vantage point.

LayMan
2006-Sep-13, 01:29 PM
...before everything will make sense.

If I'm not mistaking, according to Adam Douglas' "Hitchhikers Guide to the Galaxy", as soon as that happens, it will immediately be replaced with something else. Makes you wonder...

Anyway, thanks for the explanation.

However, I'm a bit confused about this part:


The paradox is that if the sphere is increasing because of a big bang blast, we should be able to detect the direction of the center of the sphere by the vectors of the matter (galaxies) that we observe

With direction, do you actually mean position (as in "which direction to look for it")? Because, if you imply movement with it, in relation to what would the center of the Universe be moving? Not out on a discussion about it, I'm just being carefull here: I'm already involved in a mind-bending discussion about something similar... :)

Bogie
2006-Sep-13, 02:03 PM
If I'm not mistaking, according to Adam Douglas' "Hitchhikers Guide to the Galaxy", as soon as that happens, it will immediately be replaced with something else. Makes you wonder...

Anyway, thanks for the explanation.

However, I'm a bit confused about this part:



With direction, do you actually mean position (as in "which direction to look for it")? Because, if you imply movement with it, in relation to what would the center of the Universe be moving? Not out on a discussion about it, I'm just being carefull here: I'm already involved in a mind-bending discussion about something similar... :)Let me rephrase that. The paradox is that if there was a big bang blast, we should be able to detect the center of the sphere by the vectors of the matter (galaxies) that we observe

Ken G
2006-Sep-13, 02:29 PM
And note, there is actually one type of blast where this is not true-- a blast where the speeds all change in the same way with time since the blast. In that case, the particles always arrange themselves such that their speeds are proportional to their distance from the center of the blast, with a proportionality "constant" that is the same for all particles (though not necessarily the same with time). In such a blast, there would still be a center, but every shard within the blast would also see receding velocities that are proportional to distance-- that is, every shard thinks it is the center of the blast, if it has no external references, and cannot see the "edge" of the blast wave. But... that's also the situation in the Big Bang, so you can't distinguish the presence of a center using velocities when they obey this rule! The real reason we don't think of it as an "explosion" (contrary to popular descriptions) is that an explosion has density and temperature variations with distance from the center, whereas the Big Bang is everywhere the same.

Bogie
2006-Sep-13, 03:35 PM
And note, there is actually one type of blast where this is not true-- a blast where the speeds all change in the same way with time since the blast. In that case, the particles always arrange themselves such that their speeds are proportional to their distance from the center of the blast, with a proportionality "constant" that is the same for all particles (though not necessarily the same with time). In such a blast, there would still be a center, but every shard within the blast would also see receding velocities that are proportional to distance-- that is, every shard thinks it is the center of the blast, if it has no external references, and cannot see the "edge" of the blast wave. But... that's also the situation in the Big Bang, so you can't distinguish the presence of a center using velocities when they obey this rule!
Let me follow up with you on this type of blast. It would seem reasonable that the pressure of the area that the blast is expanding into would determine the type of expansion we would observe. The expansion of a blast in water subsides quickly and the leading edge of the blast slows rapidly because the inertia is spent against the counter pressure of the liquid. But until the slowing, the center is detectible by measuring the vectors and relative velocity of the shards (as I understand it).

The same blast in air of course would expand more but would still allow an analysis of direction relative to the movement of the constituent shards, and would eventually slow as the inertia of the blast is spent against the air pressure.

If you explode an object in a vacuum it would expand even more but still relative movement would reveal the center, though the inertia would not be spent until it encountered some positive pressure or succumbed to its own gravity.

But now lets put the object we are blasting in a special chamber that is not just a vacuum, but has powerful vacuum compressors sucking away at the space in the chamber and as the particles from the blast expand from the blast, instead of their inertia being spent or overcome by their own gravity, they are then caught up in the suction of the compressors and they expand more rapidly. The shards leading the expansion would be accelerated as would all of the following shards but the leading shards would accelerated sooner and as the acceleration affected all of the shards, they would all be accelerating away from the ones behind.

Is this the kind of blast that would defy the ability to detect the center?


The real reason we don't think of it as an "explosion" (contrary to popular descriptions) is that an explosion has density and temperature variations with distance from the center, whereas the Big Bang is everywhere the same.
I have been wondering about the terms I use to describe the observed nature of our universe. I refer to homogeneity as that characteristic that no matter where you look, the structure looks the same on a large scale, i.e. the cosmological principle.

I have referred to the constant and very smooth temperature of the background radiation as being isotropic. Am I using these terms in properly?

Ken G
2006-Sep-13, 04:05 PM
The same blast in air of course would expand more but would still allow an analysis of direction relative to the movement of the constituent shards, and would eventually slow as the inertia of the blast is spent against the air pressure.
If the shard velocities all have the same dependence with time (staying the same being the simplest example of that), then any point will look like the center of the velocity structure, unless you can see an "edge". But even if you see an edge, it is the change in density/pressure/temperature that you would notice. Those are the parameters that will reveal the center of the blast, not the velocities (which will always increase in proportion to distance from every point in this type of expansion).


Is this the kind of blast that would defy the ability to detect the center?
Not necessarily. The key condition is that all the shards start out with different speeds in different directions, but their speeds all change with time in the same way, like perhaps all speeds fall or increase by a factor of 2 every second, that kind of thing (but the simplest case is-- don't change the speeds at all).


I have referred to the constant and very smooth temperature of the background radiation as being isotropic. Am I using these terms in properly?

That all sounds like fine usage to me.

LayMan
2006-Sep-15, 11:09 AM
Space has volume and the shape of space in Euclidian geometry, assuming that space refers to the space occupied by our expanding big bang universe, is a sphere.

As the big bang universe expands the volume of the sphere increases.

The paradox is that if the sphere is increasing because of a big bang blast, we should be able to detect the direction of the center of the sphere by the vectors of the matter (galaxies) that we observe. In a blast everything moves away from the center and so all vectors would point back to that center.

This however is not the case. It makes no difference which direction we look, the universe appears homogeneous in that everything seems to be moving away from everything else at a pretty constant rate, i.e. no center can be detected. So thinking that the big bang was an explosion that set everything in motion on an outward path is not supported by the observational evidence of the homogeneous universe. The space between the galaxies seems to be stretching. If space is stretching instead of objects in space following the path of an explosion, you could explain the observational evidence.

Here comes the balloon. The space between the galaxies seems to be stretching and so scientists are hard pressed to describe the space of our universe in Euclidian geometry because in Euclidian space a big bang would appear to have a center and our universe does not reveal a center.

They then abandon the Euclidian space and try to describe the alternative space in terms that fits the evidence. The evidence shows everything expanding away from everything else as if each galaxy was painted on the surface of a balloon and the balloon was being inflated. They don’t mean the shape of the universe is literally a balloon. It is an analogy where the surface of the balloon represents the relative motion of the galaxies in the universe and demonstrates that space is stretching “like the surface a balloon”.

The problem of not being able to detect the center of the expansion has lead to the opinion by some that space-time was created by the big bang, i.e. no space or time existed before the big bang event. They surmise that as the big bang universe expands, space-time is being created evenly throughout the universe and therefore the galaxies seem to move away from each other evenly no matter which way you look.

This opinion fits the evidence but goes against the 3-D logic that we deal with in our everyday lives. Certainly the universe has some more surprises for us before everything will make sense.

Would it then be ok to think of it like this: if the Big Bang (and the inflation of the 'analogical' balloon caused by it) started before galaxies formed, then the initial 'blob' of matter that was going to form the galaxies as we see them in our observable universe was going to 'dilute' as it expanded. So what we perceive as the center of our Universe should actually be considered as being located on the 'surface' of that sphere? Kind of like when you would draw a circle on a balloon and then inflate it some more: the circle would get bigger, which causes anybody within that circle to think that all points on its edge are moving away from the relative center of the circle (I mean, relative to the center of the sphere)? Or should I stop trying to visualize it, since GR can be said to be a strictly mathematical model and I should confine myself to asking it purely mathematical questions (which would be unfortunate since I lack the mathematical abilities to do that...)?

Ken G
2006-Sep-15, 02:09 PM
You understand the 'balloon analogy' now, and it's OK to use it in place of the mathematics, to a point anyway. Just don't take it too seriously, it is a 'closed' model and co-moving space does not appear to be.

LayMan
2006-Sep-15, 02:35 PM
You understand the 'balloon analogy' now, and it's OK to use it in place of the mathematics, to a point anyway.

Thank you, glad I got at least something right here!



Just don't take it too seriously, it is a 'closed' model and co-moving space does not appear to be.

Trust me, I won't... The words 'co-moving space' already make me feel slightly uncomfortable.