Is the Universe Expanding?

[harrycostas]

G'day

The following link is complicated but it mentions some interesting issues
supersymmetric spinning particle models
Kaehler manifolds
Dirac operator
Hilbert space
etc
In search to explain how manifolds form. I thought is was interesting to share the reading.

http://arxiv.org/abs/1003.2234
Quaternionic Kaehler Detour Complexes & N=2 Supersymmetric Black Holes

Authors: David Cherney, Emanuele Latini, Andrew Waldron
(Submitted on 11 Mar 2010)

Abstract: We study a class of supersymmetric spinning particle models derived from the radial quantization of stationary, spherically symmetric black holes of four dimensional N= 2 supergravities. By virtue of the c-map, these spinning particles move in quaternionic Kaehler manifolds. Their spinning degrees of freedom describe mini-superspace-reduced supergravity fermions. We quantize these models using BRST detour complex technology. The construction of a nilpotent BRST charge is achieved by using local (worldline) supersymmetry ghosts to generating special holonomy transformations. (An interesting byproduct of the construction is a novel Dirac operator on the superghost extended Hilbert space.) The resulting quantized models are gauge invariant field theories with fields equaling sections of special quaternionic vector bundles. They underly and generalize the quaternionic version of Dolbeault cohomology discovered by Baston. In fact, Baston's complex is related to the BPS sector of the models we write down. Our results rely on a calculus of operators on quaternionic Kaehler manifolds that follows from BRST machinery, and although directly motivated by black hole physics, can be broadly applied to any model relying on quaternionic geometry.

 

[csmyth3025]

G'day

The following link is complicated but it mentions some interesting issues
supersymmetric spinning particle models
Kaehler manifolds
Dirac operator
Hilbert space
etc
In search to explain how manifolds form. I thought is was interesting to share the reading.

http://arxiv.org/abs/1003.2234
Quaternionic Kaehler Detour Complexes & N=2 Supersymmetric Black Holes

Authors: David Cherney, Emanuele Latini, Andrew Waldron
(Submitted on 11 Mar 2010)

Abstract: We study a class of supersymmetric spinning particle models derived from the radial quantization of stationary, spherically symmetric black holes of four dimensional N= 2 supergravities. By virtue of the c-map, these spinning particles move in quaternionic Kaehler manifolds. Their spinning degrees of freedom describe mini-superspace-reduced supergravity fermions. We quantize these models using BRST detour complex technology. The construction of a nilpotent BRST charge is achieved by using local (worldline) supersymmetry ghosts to generating special holonomy transformations. (An interesting byproduct of the construction is a novel Dirac operator on the superghost extended Hilbert space.) The resulting quantized models are gauge invariant field theories with fields equaling sections of special quaternionic vector bundles. They underly and generalize the quaternionic version of Dolbeault cohomology discovered by Baston. In fact, Baston's complex is related to the BPS sector of the models we write down. Our results rely on a calculus of operators on quaternionic Kaehler manifolds that follows from BRST machinery, and although directly motivated by black hole physics, can be broadly applied to any model relying on quaternionic geometry.

Harry, if you can explain to me in plain english what that abstract says you'll certainly have my attention. To make it easier (on me), just start with the first sentence and then we'll go on from there.

Chris

 

[MeteorWayne]

Mod Hat on**

Juts a reminder, the subject of this discussion is Is the Universe Expanding?, not Black Holes. Off topic posts will be moved.

MW

 

[MeteorWayne]

Re: Re:Is the Universe Expanding?

Hello,
I am a new member of space.com I don't know how to add a post but I like to give you some important information which is some what related to "BIG BANG THEORY" but is related to black holes.

Welcome to Space.com. If your post is related to Black Holes, please place it is a dicussion about black holes. There are dozens.

First: Actually what you think black hole is? I will to mention you the true answer: "There is nothing like black holes generally what every body knows a dead star. The star after burning most of the fuel from its outer surface and after the supernova the surface of the star cooled down and it becomes a planet which liberate energy but that energy is so less that it is not visible from light years distance compare it as a planet like Venus or mercury say.

This is factually inaccurate. A black Hole results when the mass remaining after a stars death is too great to be supported without the heating provided by the thermonuclear reactions during it's life. The gravity forces it to collapse.

Now I will like to mention one new thing that also our planet Earth is also a star but it is not having so much high surface temperature because due to the presence of surrounded water.

That is preposterous. The earth, which is most definately NOT a star, has a lower temperature because it's heat is derived from 3 sources. Leftover heat from it's original gravitational compression, radioactive decay in the core and mantle, and heating from the sun. On the other hand, the sun, being a star get's it's heat from the fusion of elements in it's core.

Second: we think that our planet is been protected by the large gravitational force of planet Jupiter from numerous asteroids: It may be true from our common thinking. Tell me brother what happen if a big asteroid strike a surface or let say you bombard a hard stone or metal to a surface with a high velocity and momentum that portion of surface will heat up. Same thing is happening there and also to planets like sun, Venus, Mercury, Jupiter, Natural satellites etc.

There will be time when all those planet will become so hot that they will become a star like object and start heating our planet and after may be 200-300 years later our planet will also become a star as all the water will be vaporized and all the life will extinct from our planet.

Sorry, again more ridiculous non physics. First, the sun is not a planet, it is a star. Currently large impacts are rare in the objects of the solar system so any heating is quickly dissapated.

For example let say the nuclear weapons ,fuels ,reactors which we are getting from our own earth and also I like to mention that all the 9 planets were born from our main star sun that means all planets have that source to develop the energy more the planet will heat up more there chances of converting into stars.

Indecipherable gibberish

Next thing the water which exists in our planet are protecting our planet convert into star & due to green house effect they are vaporizing and thus our planet is heating up thus we must have to cut the green house emigration, fossil fuel burning, destruction of forest, nuclear warheads testing and also the war upto to 0%. Still there is danger.

Every planet when they are converting into star after thousands of year later will become cool not like the 9th planet but surface temperature will be some what cool. Like this "cycles will be repeated" explained below.

More indecipherable gibberish. Try again.

Third: Another thing I like to say that there will be no planetary collision like "nebula" or some think like that not may be now, but when after thousands or billion of years I can't say the exact date after, when all the solar system will collide together i.e. all the universe, stars, planets that will again will make a "Primeval Atom" and again new "Big bang will start" for that I think there is long time.

But what I had mentioned above is due to my long time study & imagination in science and technology field.

Thank you.

[/quote][/quote]

Yeah, well certainly there's a lot of imagination involved!! :roll:

 

[ramparts]

Unfortunately, since the world we live in is very nearly Euclidean and thus our intuition is entirely Euclidean, there's really no analogy that entirely gets at intrinsic curvature. The blanket in your example is still embedded in a higher (three-dimensional) Euclidean space. The best we can do is use examples like the balloon or that blanket and just add at the end "oh, and they can exist on their own without a higher dimensional space to be 'in.'" It's the concept of every space which isn't flat needing to be 'in' a higher-dimensional flat space which is in our experience but is not necessary in the universe as a whole.

I think I have a glimpse of what your talking about - which I believe is the concept of "manifolds" and their properties. I have only a very vague idea how mathematicians and cosmologists actually use manifolds except to say that they are very heavily mathematical. Wikipedia has a very good article on manifolds - most of it is too advanced for me, though.

The following paragraph from the Wikipedia article sort of encapsulates both the usefulness and complexity of manifolds:

"...The concept of manifolds is central to many parts of geometry and modern mathematical physics because it allows more complicated structures to be expressed and understood in terms of the relatively well-understood properties of simpler spaces. For example, a manifold is typically endowed with a differentiable structure that allows one to do calculus and a Riemannian metric that allows one to measure distances and angles. Symplectic manifolds serve as the phase spaces in the Hamiltonian formalism of classical mechanics, while four-dimensional Lorentzian manifolds model space-time in general relativity..."

Chris

Yep, the spaces I was talking about are exactly manifolds. That's the technical term. I mean, I think intuiting the concept is more useful than just having an idea of the mathematics. A manifold is any space, of any dimension and curvature. So the surface of a sphere is a two-dimensional closed manifold, the Euclidean world we think we live in is a three-dimensional flat manifold, the surface of a curled-up blanket is some crazy complicated manifold, etc. The universe at large is very nearly a four-dimensional manifold that is flat in the three spatial dimensions but expanding.

So the concept of a manifold (in particular, a Riemannian manifold is the type you see in relativity) is like the blanket or the balloon or the sphere surface but with two generalizations: first, it can have any curvature without being embedded in a flat space, and second, it can have any dimension (obviously we can't visualize >4-dimensional spaces, and the only three-dimensional space we can visualize is the flat one).

 

[ramparts]

Harry, as you certainly know, since you are an expert in all things physical, we're talking about classical general relativity, where things like Kaehler manifolds (which come into play in string theory), and Dirac operators and Hilbert spaces (which are important in quantum mechanics) are not entirely relevant. Thanks for posting, though I really would suggest you tone down the high level of your discourse so as not to confuse the newbies. Not everyone here knows as much as you and you need to come down to our level sometimes!

 

[harrycostas]

G'day

In a nut shell

Subatomic particles have a spin property and are able to be compacted.
Neutron matter 10^15
Quark matter 10^15 to 10^25
Axion and other similar particles over 10^25
Compact matter (such as Black holes or Dark stars) have be noted to contain as high as 18 billion Sun masses

This spin property generates dipole electromagnetic fields, similar to a dual torch that shines at the speed of light. Small, large or monster dipoles have the similar origin. As per the BB Nucleosynthesis manifolds were created ejecting matter that reformed into normal matter. Since the BBT states that these manifolds popped up through out the universe (timing is a big question mark) than these manifolds are important in trying to understand the theory of expanding universe of time and space and not actual matter. Observations show us that matter clusters into stars, clusters of stars, galaxy, galaxy clusters, clusters of clusters of galaxies that form super monster clusters. NASA estimates that the observable universe has over 300 billion galaxies all clustering, merging and doing their evolutionary form from spiral to elliptical etc as per Hubbles tuning fork.

Expansion of the Universe is in reference to the observable universe and can be explained by a giant manifold. Giant manifolds are found in the centre of giant galaxies centred in the cetre of the cluster. But! I do not think it is that simple and further research in this field is needed.
NASA hubble site has images . A simple search.

 

[origin]

What are you talking about??

G'day

In a nut shell

Subatomic particles have a spin property and are able to be compacted.
Neutron matter 10^15
Quark matter 10^15 to 10^25
Axion and other similar particles over 10^25
Compact matter (such as Black holes or Dark stars) have be noted to contain as high as 18 billion Sun masses

Some units would be nice... Are these numbers densities?

This spin property generates dipole electromagnetic fields, similar to a dual torch that shines at the speed of light.

Magnetic fields are like a torch (flashlight) shining light at the speed of light?

Small, large or monster dipoles have the similar origin.

Are you saying the spin of the subatomic particles in a neutron star are responsible for the magnetic field? If that is what you are saying, my question is, 'why are all the dipoles lined up with the same orientation?'

As per the BB Nucleosynthesis manifolds were created ejecting matter that reformed into normal matter.

The BB says matter was ejected that formed matter? Huh?

Since the BBT states that these manifolds popped up through out the universe (timing is a big question mark) than these manifolds are important in trying to understand the theory of expanding universe of time and space and not actual matter.

Could you cite some evidence for this rather strange idea as it relates to the big bang. If you are going to post a 400 page article with out citing the page number or you are going to post 15 individual papers - please don't bother. A specific reference would be nice.

Observations show us that matter clusters into stars, clusters of stars, galaxy, galaxy clusters, clusters of clusters of galaxies that form super monster clusters. NASA estimates that the observable universe has over 300 billion galaxies all clustering, merging and doing their evolutionary form from spiral to elliptical etc as per Hubbles tuning fork.

Galaxies do not evolve per Hubbles Tuning Fork. It is still used as a classification method but it is now realized that the galaxies do not evolve along the lines of the tuning fork.

Expansion of the Universe is in reference to the observable universe and can be explained by a giant manifold.

Then by all means explain it!

Giant manifolds are found in the centre of giant galaxies centred in the cetre of the cluster. But! I do not think it is that simple and further research in this field is needed.

Do you have any evidence for this? Again I am not looking for 20 or 30 papers that have the word manifold in them, I am asking for some specific evidence that "Giant manifolds are found in the centre of giant galaxies", or is this your 'theory'.

 

[csmyth3025]

...Expansion of the Universe is in reference to the observable universe and can be explained by a giant manifold...

I'll agree that the expansion of the universe is in reference to the observable universe. The cosmological principle states, in general, that we don't occupy a privileged or special place in the universe and "...that the part of the universe which we can see is a fair sample, and that the same physical laws apply throughout..."(William Keel, Astronomer - as quoted by Wikipedia in their article on the cosmological principle). Most scientists (if not all) agree with this principle.

Applying this principle to the expansion we see in our observable universe implies that the parts of the universe which we can't see are also experiencing the same expansion. I'm not a scientist, so please feel free to correct me if my interpretation of the cosmological principle in this context is off the mark.

I haven't heard how the expansion of the universe "...can be explained by a giant manifold...". If you can elaborate on this point (in plain english, please) it would be very helpful.

Chris

 

[ramparts]

Chris, sadly no such thing is possible as Harry isn't even speaking in scientific jargon, but rather in a strange pseudo-language called Harry-ese.*

*Note: This is different from Australian English, although only slightly.

 

[harrycostas]

G'day

I do not speak with a fork tongue.

What I have stated can be searched.

Go to the hubble site for giant jets. There you will find the giant jets that go for millions of light years.

Search for BB nucleosynthesis.

Ramparts said

no such thing is possible as Harry isn't even speaking in scientific jargon, but rather in a strange pseudo-language called Harry-ese.*

The sad thing is that you do not know. Question it, yes, but to close your eyes to it and not research, that is the sad thing.

Right now I'm moving house so when I'm settled in, I will give you the reference links.

In the mean time look up arXiv

Select search: Manifolds Cosmology 2010 or what ever year or no year at all, that may give you a gist of the scope, but not limited to it.

As for Harry-ese, I have dislexia, so sometimes my letters and words are out of balance. Thats life.

 

[csmyth3025]

Right now I'm moving house so when I'm settled in, I will give you the reference links.

In the mean time look up arXiv

Select search: Manifolds Cosmology 2010 or what ever year or no year at all, that may give you a gist of the scope, but not limited to it.

Harry, I'm afraid your reference links will be as confusing to me as the last abstract you posted. It would help me understand your view of the relationship between manifolds and the expansion of the universe if you would just explain it in your own words.

Chris

 

[MeteorWayne]

Trust me, he won't be able to. It appears he has no enlightening words of his own.

 

[csmyth3025]

I've been reading some of the first posts in this thread from July of last year. I take it that the discussion started as a debate on whether the expansion of the universe could be attributed to the motion of galaxies, etc. through a static, non-expanding space or whether space itself was expanding. At the beginning of this thread the expansion of the Universe was considered a given. The posts seem to be related to how that expansion is explained.

At this point is there still any serious scientific debate about whether space itself is expanding?

Chris

 

[ramparts]

No.

 

[csmyth3025]

Ramparts,

In another thread you commented on the momentum of photons. This got me thinking about the net momentum of the Universe. Since everything (on large scales) is moving away equally from every other thing, I'm guessing that the net momentum of the Universe remains (as far as we know) zero.

This line of thought leads me to wonder if the expansion of space itself results in a net increase in the kinetic energy of the matter contained in the universe. I'm thinking that, although a "local" group of matter is relatively staionary in its own local space, it's moving at an accelerating speed relative to distant groups of matter.

Am I mistaken about this?

Chris

 

[ramparts]

Well, first of all momentum is a relative thing. What something's momentum is depends on your frame of reference just as its velocity does. In special relativity we talk about the four-momentum:

http://en.wikipedia.org/wiki/Four-momentum

A four-dimensional vector which contains a three-dimensional momentum vector (think of it as momentum in all three spatial directions) and the 1-dimensional energy (think of it as momentum in the time direction). What is invariant in all reference frames is the length of that vector. The length squared is given by:

E^2/c^2 - p^2

where E is energy, c is the speed of light, and p is momentum. That's the same in all frames. What is this quantity equal to? (mc)^2, of course, so that if you set p=0 (that is, an object at rest) then you get good ol' E=mc^2.

Point is, it's difficult to talk about the net momentum of the Universe. Anyway, as far as I know (I could be missing something here), a bunch of particles just expanding with space have no momentum since they're locally stationary. Their "movement" caused by the expansion of the Universe gives no momentum. Momentum does, however, come from all the small-scale gravitational and other interactions which go on locally. For example, you're not expanding with the Universe - lots of momentum there. So the net momentum, however you define it, wouldn't be zero.

 

[alphachapmtl]

Universe expanding or Matter contracting ?
Maybe those point of view are equivalent, but maybe thay are not.
In any case, a different point of view may lead to new insights.
I don't know why this formulation is never considered.

Going back to the expanding universe formulation, why is space expanding but not objects?
Where (and why) is the expansion limit?
Space is expanding. Is our galaxy expanding (why?, why not?).
What about the solar system, the earth-moon system, the earth itself? What about a bacteria, a molecule, an atom, a proton?
How can big thing expands, but not small things?
To me something does not logically make sense.
If space between galaxy clusters is expanding, why not space between earth and moon?
Comments welcome.

 

[Couerl]

To me something does not logically make sense.
If space between galaxy clusters is expanding, why not space between earth and moon?
Comments welcome.

Well on the local level gravity by itself may still present enough influence to check the expansion. It's purely speculatory on my part, but let's assume for a moment that the big bang is in essence still "banging", but at a much lower energy. Whichever forces split apart to allow inflation to begin with may simply never have equalized enough to contain or stop it.. I envision a sort of battle between the 4 forces much like that of matter and anti-matter in the first plank moments where expansion won out slightly over gravity. Mind you it is just a guess. I hope we find out one of these days what is actually happening.

 

[SpeedFreek]

Universe expanding or Matter contracting ?
Maybe those point of view are equivalent, but maybe thay are not.
In any case, a different point of view may lead to new insights.
I don't know why this formulation is never considered.

It has been considered, and it is indeed equivalent. The difference between the views is simply how we choose to "coordinatize" the situation. In a nutshells, certain variables become constant and certain constants become variable. As it is equivalent the only insights gained are a better understanding of the different ways General Relativity can be used to describe the same thing.

The answers to all the other questions in your post are contained in the PDF file linked in my signature below.

 

[csmyth3025]

How can big thing expands, but not small things?
To me something does not logically make sense.
If space between galaxy clusters is expanding, why not space between earth and moon?
Comments welcome.

I've been doing some "back-of-the-envelope" calculations regarding the the expansion of the Universe using very approximate numbers. This may help to answer your question.


In round numbers, the Hubble Constant (the rate at which things are moving away from each other as a result of the expansion of space) is currently pegged at about (70 km/sec)/Mpc (megaparsec). A megaparsec is a very large distance. For example, the Andromeda Galaxy is about 0.77 Mpc away from us. This distance is about 2,500,000 light years away from us.

To bring this rate of expansion down to a scale that's more possible to imagine, consider that this rate is equal to (7cm/sec)/parsec. The closest star to our sun (Alpha Centauri) is about 1.34 parsec away. Using the Hubble Constant alone, Alpha Centauri would have a velocity of about 9.4 cm/sec away from us. The observed motion of Alpha Centauri is about 21.6 km/sec towards us, however. In short, the observed motion of Alpha Centauri completely drowns out any possible effect we could hope to attribute to the expansion of space.

Now consider that Alpha Centauri is about 4 x 10^13 km from Earth and the Moon is (roughly) 4 x 10^5 km away from Earth. The motion of the Moon away from the Earth attributable to the expansion of space would be about 9.4 x 10^-10 m/sec. This distance (9.4 x 10^-10 m) is roughly the width of a sucrose molecule.

In short, the space between the Earth, the Moon, and the stars in our galaxy may be expanding, but their actual movement through the space around them is many, many times greater.

Chris

 

[ramparts]

Good calculations Chris! The other thing to consider, though, is the effect of local gravity. Since the Moon is gravitationally bound to the Earth, it wouldn't even feel that tiny expansion you mentioned. The number we have for the Hubble constant is for distant galaxies, assuming that the distribution of matter in the Universe is more or less the same everywhere. Since that breaks down on smaller scales - like those of the solar system - the Hubble constant is not really meaningful to talk about in the first place.

 

[csmyth3025]

Good calculations Chris! The other thing to consider, though, is the effect of local gravity. Since the Moon is gravitationally bound to the Earth, it wouldn't even feel that tiny expansion you mentioned. The number we have for the Hubble constant is for distant galaxies, assuming that the distribution of matter in the Universe is more or less the same everywhere. Since that breaks down on smaller scales - like those of the solar system - the Hubble constant is not really meaningful to talk about in the first place.

I think the original question remains, though - does space expand more-or-less uniformly throughout the Universe (Einstein's cosmological constant, perhaps?) or only in the vast "empty" reaches between galaxies and clusters?

Perhaps a better way to phrase the question would be: Is the expansion of space uniform, but measurable only when objects separated by vast distances (such as galaxies and galaxy clusters) are considered?

Chris

 

[ramparts]

The expansion of the Universe is crucially dependent on where the matter in the Universe is; that's the stuff that gravitates and affects the expansion. So the expansion is only uniform when the distribution of matter is uniform. That's believed to be true on very large scales, but it's obviously not true on e.g. galactic scales.

 

[csmyth3025]

The expansion of the Universe is crucially dependent on where the matter in the Universe is; that's the stuff that gravitates and affects the expansion. So the expansion is only uniform when the distribution of matter is uniform. That's believed to be true on very large scales, but it's obviously not true on e.g. galactic scales.

As I understand the Standard Model, the very early Universe underwent a period of exponential expansion (inflation) which provides a theoretical explanation for the homogeneous and isotropic universe we see on large scales today. Is the mechanism by which this early inflationary period occurred the same mechanism believed responsible for the more recently discovered accelerated expansion of the universe? Specifically, is dark energy responsible for both? Also, do the terms "cosmological constant" and "dark energy" describe the same thing or are they two different concepts?

Chris