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Author Topic:   The Big Bang Bamma
coffee_addict
Member (Idle past 477 days)
Posts: 3645
From: Indianapolis, IN
Joined: 03-29-2004


Message 31 of 80 (260136)
11-16-2005 5:47 AM
Reply to: Message 11 by Christian7
11-03-2005 4:31 PM


Re: Really starting to understand
guidosoft writes:
And loads of other vauge crap, that is useless to me, because it won't go into detail.
It's vague because most of these stuff cannot be told in layman's term.
For example, try to find stuff on how to calculate the lyapunov exponent on 1-D, 2-D, and 3-D systems and how it relates to chaotic behaviors.
Most of these stuff just can't be explained in a few short sentences for people to understand, damn it. Don't expect everything to be as simple as x+1=5 and find x. The world is much more complicated than your IRS forms.

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Ragged
Member (Idle past 3553 days)
Posts: 47
From: Purgatory
Joined: 10-26-2005


Message 32 of 80 (260156)
11-16-2005 7:43 AM


So what were they saying about radius haveing a curvature. Im still confused about that.
Also, if we can find the edge of the universe couldn't we calculate a center? An imaginary one?
Please read my previous post. I would like to get some insight on all this.

Replies to this message:
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Tony650
Member (Idle past 4033 days)
Posts: 450
From: Australia
Joined: 01-30-2004


Message 33 of 80 (260180)
11-16-2005 8:59 AM
Reply to: Message 23 by cavediver
11-15-2005 1:31 PM


Re: More questions.
cavediver writes:
There is no inside. The sphere can be defined without any reference to a 3d embedding space. The inside does not exist! There is no spoon...
This is something I've always had trouble getting my head around. I have no problem with the concept of our familiar space being curved back on itself within a four (or higher)-dimensional manifold. Well, that is to say, I can't picture it (despite many, many years of trying ) but I understand it.
What I don't understand is how that curvature can exist without a higher manifold within which to exist. In the same way that I don't see how a sphere can exist without three spatial dimensions to contain it, I don't see how our three dimensions of space can curve without, themselves, existing within a manifold of at least one dimension higher.
My problem with these things always seems to come back to relativity. In this case, what is the curvature relative to? I can only think of curvature in terms of spatial relationship, and always using more dimensions than the thing doing the curving. I can picture a line curving, but only by going through the second dimension. I can picture a plane curving, but only by going through the third dimension.
That's where I'm stuck when it comes to three-space. I can't picture curvature in any term but that of a higher embedding space. How exactly can something with dimension n curve without an embedding space of dimension > n through which to do the curving? How can it curve without... well... curving?
Sorry, for piling on another reply but you've touched on my favourite subject again.

This message is a reply to:
 Message 23 by cavediver, posted 11-15-2005 1:31 PM cavediver has replied

Replies to this message:
 Message 36 by cavediver, posted 11-16-2005 1:31 PM Tony650 has replied

  
Tony650
Member (Idle past 4033 days)
Posts: 450
From: Australia
Joined: 01-30-2004


Message 34 of 80 (260184)
11-16-2005 9:08 AM
Reply to: Message 32 by Ragged
11-16-2005 7:43 AM


Ragged writes:
Also, if we can find the edge of the universe couldn't we calculate a center? An imaginary one?
My understanding is that our three dimensions of space have no center (or edge), just as the surface of the balloon has none. As with the balloon, if our universe does have a center it will be along an axis that exists outside of our familiar three dimensions.
However, I think the balloon analogy falls a little short here. I may be wrong so don't quote me, but I believe the analogy is only meant to illustrate how our three-space can be curved, and not meant to indicate that our space actually does exist as a four-dimensionally curved geometric within a higher-dimensional manifold.
This is what I've never been able to wrap my mind around... how such curvature can exist when the only way I can think to define "curvature" is in terms of the axes it takes place within. I'm hoping cavediver can explain this to me because it's one of the things that has always driven me nuts.

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cavediver
Member (Idle past 3644 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 35 of 80 (260237)
11-16-2005 1:15 PM
Reply to: Message 25 by Ragged
11-15-2005 3:43 PM


Re: More questions.
I might be misunderstanding the concept of the term "radius".
Yes, I think you are. It is simply measure of how curved something is, it is not a distance in space as such. The bigger the radius of a circle or sphere, the less it is curved. Anything that is curved can have its curvature at a point described as the radius of a circle or sphere that would have the same curvature at that point. Check this out:
The piece you were reading was just a little confusing in the way it described the vast length of the radius of curvature as if it lay within the universe. It does not, it was simply making a comparison.
If there was a being so large, looking at the universe from the "outside", for that being our universe could be a perfect sphere and have a very definite and positive curvature.
Absolutely, or zero curvature if the universe is indeed perfectly flat, or negative curavture...
But I'm still not entirely clear about Hubble's law.
It's easy... it's just the observation that on our balloon, two points move away from each other much more quickly if they are far apart compared to if they are neighbouring.
quote:
Any two points which are moving away from the origin
The mention of origin is a very poor choice. There is no origin.
But, if we take a balloon and measure its circumference, or diameter, we could find its center, or really the center of the sphere of air that the balloon surounds. So could there be an imaginary center of the universe, or space within the universe?
No, it makes no sense to do so. The inside simply does not exist. You cannot point to it.
P.S: Those graphs don't make any sense to me. I don't even know what they are of.
They are electrom and photon interactions. Someone (madeofstarstuff?) was asking a while back about the significance of photon interactions to our understadnign of reality, and I always meant to get back to him. [If you're reading, do you still want to talk about this?]

This message is a reply to:
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Replies to this message:
 Message 72 by madeofstarstuff, posted 11-30-2005 5:13 PM cavediver has replied

  
cavediver
Member (Idle past 3644 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 36 of 80 (260242)
11-16-2005 1:31 PM
Reply to: Message 33 by Tony650
11-16-2005 8:59 AM


Re: More questions.
This is something I've always had trouble getting my head around.
Ok, you are getting confused over what we call intrinsic and extrinsic curvature.
Take a baked bean can, and cut off the top and bottom. Is it curved?
Take a football (sorry, soccer ball :rolleyes Is it curved?
Both are extrinsically curved... you can see that. But only one is intrinsically curved.
Cut both open and see if you can flatten them out.
The can will happily lie flat on the table. No matter how you cut the football, you cannot get any piece of it to lie flat.
So which is truely curved?
The 2d can was curved by using a higher dimension into which it rolled.
The football is by its very nature curved... the extra dimension just enables you to observe that curvature. There are several 2d surfaces that are curved, but 3d is not sufficient for viewing them: the klein bottle and RP2 are the two prototypes of this behaviour. Both are doughnut like surfaces, but with "mobius strip"-like twists. You cannot visualise them in 3d.
I can picture a line curving
But only extrinsically. The line can wind its way through a higher dimensional space, but intrinsically it is flat. It cannot posses curvature.
I should stress that curvature is a local property. You measure it by noting deficits in the circumference of cirlces or areas of surrounding spheres.
Strictly, we do it in mathematics by taking a vector around a little loop in space, keeping it as parallel as possible to its starting direction, and noting how its direction has changed by the time it gets back to its starting point. No change - flat space; change - curved space.
Put an arrow on the north pole pointing south (obviosuly ) towards London. Slide it down to the equator along the Greenwich meridian. Now slide it sideways until it is at New York's longitude, but still on the equator. Slide it back up to the pole. It is now pointing towards New York. Conclusion - the Earth's surface is curved. No need to mention a third dimension.

This message is a reply to:
 Message 33 by Tony650, posted 11-16-2005 8:59 AM Tony650 has replied

Replies to this message:
 Message 49 by Tony650, posted 11-18-2005 5:31 AM cavediver has replied

  
bkelly
Inactive Member


Message 37 of 80 (260339)
11-16-2005 7:37 PM
Reply to: Message 28 by cavediver
11-15-2005 9:00 PM


Re: No center?
cavediver writes:
Think of the balloon analogy. Every point on the balloon skin thinks that every other point is moving away radially as the balloon inflates, so concludes that it is the centre of expansion of the balloon. But we can see from our vantage that there is no centre on the balloon surface.
The surface of a baloon is two dimensional. Our universe is three dimensional. The balloon does indeed have a center, but obviously it is not on the surface.
As we look out across the galaxy we find the far away galaxies are indeed moving faster the closer galaxies. The galaxies are not moving at the same speed.
cavediver writes:
Then every point is the centre. Every point in space was "born" in the big bang. In a finite closed big bang scenario, all of those points were coincident.
What has been done to prove that every point in space was "born" in the big bang rather than the big bang occurring at a point in space. I certainly do not have knowledge but I suspect we have found neither the the edge of the universe nor evidence that there is no edge.
Going back to the baloon analogy, every molecule of air in the baloon "thinks" that every other molecules is moving away. This does seem to be true. However, the molecule at the center will find symetrical movement in all directions while I suspect that the ones near the edge will not.
Hmm, I don't know how I would approach this but it seems like a good module to simulate with a computer. But continuing to think, it can probably be calculated by hand much easier. Has anyone done that?

This message is a reply to:
 Message 28 by cavediver, posted 11-15-2005 9:00 PM cavediver has replied

Replies to this message:
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cavediver
Member (Idle past 3644 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 38 of 80 (260350)
11-16-2005 7:55 PM
Reply to: Message 37 by bkelly
11-16-2005 7:37 PM


Re: No center?
The surface of a baloon is two dimensional. Our universe is three dimensional. The balloon does indeed have a center, but obviously it is not on the surface.
Yes, this is why it is an anology The universe, although 3d spatially, behaves like the 2d skin of the balloon. There is only the surface. There is no "interior". There is no sensible concept of "centre" for the universe unlike the balloon. This is one place the analogy breaks down.
What has been done to prove that every point in space was "born" in the big bang rather than the big bang occurring at a point in space.
Nothing There is no need. This concept is included in the definition of the big bang. The big bang is a prediction of General Relativity, where every point in space IS "born" in the big bang. There is no other theory. You could invent one, but you can't call it a "big bang" 'cos we have the trademark
I certainly do not have knowledge but I suspect we have found neither the the edge of the universe nor evidence that there is no edge.
Well, an edge to the universe would be a curious thing, and in fact in these days of immensely speculative M-theory cosmology, such a concept isn't as daft as it was once thought wrt our 3d observable universe (but even then, the embedding space/multiverse/super-universe will not have an edge) HOWEVER, in the standard cosmology, no-one entertains the idea of an edge. It is not possible in General Relativity which is our only current theory of the universe. The universe is either infinite, and so no edge, or finite and topologically some compact object (like a hypersphere), so again no edge.
Going back to the baloon analogy, every molecule of air in the baloon "thinks" that every other molecules is moving away. This does seem to be true. However, the molecule at the center will find symetrical movement in all directions while I suspect that the ones near the edge will not.
The whole point of the balloon analogy is to take you AWAY from this kind of thinking! The interior is irrelevant. It is the nature of molecules/particles/points on the surface/skin of the balloon that is important. The interior has a centre and an edge, the universe has neither...

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Replies to this message:
 Message 39 by Funkaloyd, posted 11-16-2005 8:13 PM cavediver has replied

  
Funkaloyd
Inactive Member


Message 39 of 80 (260364)
11-16-2005 8:13 PM
Reply to: Message 38 by cavediver
11-16-2005 7:55 PM


Re: No center?
cavediver writes:
bkelly writes:
What has been done to prove that every point in space was "born" in the big bang rather than the big bang occurring at a point in space.
Nothing There is no need.
The observed uniformity of the Cosmic Microwave Background Radiation is pretty compelling, isn't it?

This message is a reply to:
 Message 38 by cavediver, posted 11-16-2005 7:55 PM cavediver has replied

Replies to this message:
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cavediver
Member (Idle past 3644 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 40 of 80 (260370)
11-16-2005 8:31 PM
Reply to: Message 39 by Funkaloyd
11-16-2005 8:13 PM


Re: No center?
The observed uniformity of the Cosmic Microwave Background Radiation is pretty compelling, isn't it?
To demonstrate that there is no edge and no centre? Yes, it is very compelling. Thanks for bringin it up.
Of course, it doesn't discount US being the centre, and the CMBR being some effect OF the edge!!! Hmmm, perhaps I shouldn't have mentioned this possibility...

This message is a reply to:
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bkelly
Inactive Member


Message 41 of 80 (260400)
11-16-2005 9:16 PM
Reply to: Message 39 by Funkaloyd
11-16-2005 8:13 PM


Re: No center?
re: The observed uniformity of the Cosmic Microwave Background Radiation is pretty compelling, isn't it?
Recognizing I am not up to your level, I don't see that it is compelling.
NASA and others have found that is it not completely uniform. I don't understand the implications but here is a link.
WMAP Cosmology 101: Cosmic Microwaves Fluctuations

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Replies to this message:
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cavediver
Member (Idle past 3644 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 42 of 80 (260488)
11-17-2005 5:25 AM
Reply to: Message 41 by bkelly
11-16-2005 9:16 PM


Re: No center?
The point is that apart from the exceptionally small fluctuations (which was our great discovery of the early 90s. I still remember when the COBE team arrived to present us their results. Great times ) the CMBR is identical in all directions (once you have removed the Sun's motion in the Galaxy). This is the same picture we get when we look at the distribution of galaxy velocities. There are two conclusions: either we (our Galaxy) is at the centre of the expansion of the universe, or there is no centre...

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Replies to this message:
 Message 43 by Ragged, posted 11-17-2005 2:49 PM cavediver has not replied
 Message 44 by New Cat's Eye, posted 11-17-2005 4:34 PM cavediver has replied

  
Ragged
Member (Idle past 3553 days)
Posts: 47
From: Purgatory
Joined: 10-26-2005


Message 43 of 80 (260619)
11-17-2005 2:49 PM
Reply to: Message 42 by cavediver
11-17-2005 5:25 AM


Re: No center?
[removed after rereading teh above posts]
OK, I think I got that part down. No center sounds good. . I'll post more questions as I do more research. Thanks for your help.
This message has been edited by Ragged, 11-17-2005 01:56 PM

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New Cat's Eye
Inactive Member


Message 44 of 80 (260644)
11-17-2005 4:34 PM
Reply to: Message 42 by cavediver
11-17-2005 5:25 AM


Cavediver,
First off I would like to thank you for putting time into writing these posts and offering information to others. I've read this whole thread (some messages multiple times) and feel that really am gaining knowledge.
Ok, I think this might be just a failure in the analogy but using the analogy of the globe for the universe. When I travel to the north pole and then look up, at what part of space-time am I looking, wrt the big bang? Or is this not a possible direction to 'look' towards?
If an electron is composed of photons and more electrons, then aren’t those more electrons also composed of photons and even more electrons, ad infinitum? Seems impossible to me. How can something be made of itself?
Is it nuclear force that holds the photons together? aren't they nuetral charged?
This message has been edited by Catholic Scientist, 11-17-2005 04:45 PM

This message is a reply to:
 Message 42 by cavediver, posted 11-17-2005 5:25 AM cavediver has replied

Replies to this message:
 Message 45 by cavediver, posted 11-17-2005 6:03 PM New Cat's Eye has replied

  
cavediver
Member (Idle past 3644 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 45 of 80 (260674)
11-17-2005 6:03 PM
Reply to: Message 44 by New Cat's Eye
11-17-2005 4:34 PM


Hi CS, glad I'm not just whistling in the wind!
I travel to the north pole and then look up, at what part of space-time am I looking, wrt the big bang? Or is this not a possible direction to 'look' towards?
You're quite correct, it is a failure of the analogy. There is no "up", there is only the surface of the globe. Each circle of latitude is a 1d analogy of our 3d spatial universe.
If an electron is composed of photons and more electrons, then aren’t those more electrons also composed of photons and even more electrons, ad infinitum?
No, what I am describing is the break-down of our understanding of matter as "things". There is actually no such thing as a single electron, as some sort of individual blob of stuff. It just looks that way when we observe from the intra-atomic scale upwards. If we try to zoom in on the electron, we no longer see "one" electron but rather a seething sea of virtual particles. If you sum over this observed volume, you will regain the charcteristics of the one electron (mass, charge, etc), but there is no one "object".
Assuming you are familiar with a little advanced maths... what we deal with at this scale are individual fourier modes of the quantum field. For the electron, the field is fermionic and the individual modes obey a Grassmanian algebra. This is the source of all the exclusion principle weirdness...
Is it strong nuclear force that holds the photons (and other electron) together?
No, absolutely not. It is the interaction of photons and electrons that give rise to what we call "force". For electrons and photons. the force is called electromagnetism, and the theory is called QED (Quantum ElectroDynamics)
Interactions of quarks and gluons give rise to what we call the strong force, and the theory is QCD (Qunatum ChromoDynamics). The quarks and gluons are totally analagous to the electrons and photons. Hwoever, QED is an Abelian gauge theory, where-as QCD is a non-Abelian gauge theory. This is beautiful mathematics, but the upshot is that photons cannot self-interact, whereas gluons can. This is immensely important for our lives, as this is the reason we can see! If photons self-interacted, there could be no vision as photons would be unable to follow free paths from the source to our eyes...

This message is a reply to:
 Message 44 by New Cat's Eye, posted 11-17-2005 4:34 PM New Cat's Eye has replied

Replies to this message:
 Message 46 by New Cat's Eye, posted 11-17-2005 6:16 PM cavediver has replied

  
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