Don't even know which question to ask first

[GreatBigBore]

I've been trying to understand some basic stuff about cosmology for years, and I still can't quite get there. I'm not even sure which part of it I'm misunderstanding, and don't know what questions to ask, so I'll just start blasting out the questions and see if anyone can help me make sense out of it.

So, first question has to do with geometry and topology I think, but I'm not sure how. Let's say that I can stop time completely right now, and I travel four billion light years in a straight line, in any direction (please, don't confuse me by asking me what I mean by "straight line"). Can anyone help me to understand what significant differences I'd see in the sky? Obviously different stars, but what I'm trying to get a handle on is this idea that nowhere is the center, but the universe isn't infinite. I understand the "open/flat/closed" geometry issue, or at least I think I do. I've heard our closed, finite space made analogous to the surface of a sphere. But I've also heard cosmologists assert that our universe is as flat as we can measure, so the sphere analogy doesn't work, I think. It seems to me that if I went four billion light years in some direction, I'd perceive that I'm getting close to the "edge" of something, that I'd see less in some direction: fewer galaxies? Ok, that's enough of a dumb question for now. If I can make sense out of that one, maybe I'll know what question to ask next.

Twofish-quant, feel free to wait on answering until everyone else has weighed in. When I read your responses before everyone else's, my head explodes, and then there's a mess, and my mom gets mad.

 

[Chalnoth]

So, first question has to do with geometry and topology I think, but I'm not sure how. Let's say that I can stop time completely right now, and I travel four billion light years in a straight line, in any direction (please, don't confuse me by asking me what I mean by "straight line"). Can anyone help me to understand what significant differences I'd see in the sky? Obviously different stars, but what I'm trying to get a handle on is this idea that nowhere is the center, but the universe isn't infinite.

Everything would remain more or less the same. I mean, yes, there would be different stars, and different galaxies. But any sort of statistic that describes the visible universe as a whole would remain unchanged (to within some small random variance). For instance, the average matter density would be the same, the average dark matter density would be the same, the average dark energy density would be the same, the typical separation between galaxies would be the same, the CMB temperature would be the same, the distance to the CMB would remain the same, etc.

This is known as the cosmological principle: the universe is (on average) the same everywhere and in all directions. For a long time the cosmological principle was merely assumed, not because there was really any compelling reason to do so, but rather because it was the easiest thing to consider. But as more and more experimental data has come in, every observation has held up the cosmological principle as being valid, at least for a ways out (I don't think anybody expects it to be valid for infinite distances, but it definitely appears to be valid for some distance beyond what we can see).

I understand the "open/flat/closed" geometry issue, or at least I think I do. I've heard our closed, finite space made analogous to the surface of a sphere. But I've also heard cosmologists assert that our universe is as flat as we can measure, so the sphere analogy doesn't work, I think.

In the flat case, you'd just pick a different topology, such as a torus. The same principle applies though.

In any case, we don't necessarily know how big our universe actually is, or whether or not it wraps back on itself. Even if we detected that it was locally closed or open, we still couldn't say whether or not it wraps back on itself (because it certainly doesn't do so within our visible region, as we've looked for this). We just know that it is very, very big: much bigger than the small piece of it we can observe.

 

[GreatBigBore]

Everything would remain more or less the same.

Yeah, I've heard that answer before too, and I still don't get it. Maybe I need to ask the question differently. How about this: if I stop time and just start traveling in a straight line, will I ever arrive back at my starting point? And, if I stop time and travel in a straight line to the location where we currently see the last scattering surface, what would I see there? (In general, obviously. I know that I won't find Elvis.)

...the distance to the CMB would remain the same, etc.

Umm, yikes. Maybe I need to go to the "for Dummies" forum. *Distance* to the CMB? I thought that the CMB is everywhere. I'm hoping that you mean the distance to the last scattering surface. But now that I think of it, I can't make sense of that either.

In the flat case, you'd just pick a different topology, such as a torus.

Unfortunately, from within my confusion, a torus looks the same as a sphere: the only relevant characteristic I can see is that the surface curves back on itself, just like that of a sphere.

 

[bapowell]

Right, the torus does look like a sphere, that is, when it's embedded in a 3D space so that we humans can visualize it. But a torus is indeed flat (you can make one by identifying opposites sides of a flat rectangle.) However, the benefit of that pesky embedding is that it reveals that a torus is closed, just like a sphere, in the sense that if you walk far enough in a given direction, you'll eventually loop back on yourself.

Also, the CMB is everywhere. By "distance to the CMB" Chalnoth does mean distance to the last scattering surface. This surface does not have a physical location -- if you stop time and go out far enough you won't eventually run into it. This surface is best understood using the following setup:

Draw the Earth at the center of giant sphere. This giant sphere is the last scattering surface. Each CMB photon that reaches Earth today was on this sphere when the CMB was generated 14 billion years ago (ignoring incidental rescatterings and effects from reionization). If you stop time and move out across the universe, you remain at the center of this sphere!

Lastly, while the universe does appear to be rather flat, this measurement only describes our observable universe. Our observable universe could be a tiny patch on a giant sphere, in which case the observable universe would look to us the way the Earth looks to us -- flat. But again, the topology of the universe really is key here, and the local geometry does not necessarily tell us anything about the global topology.

 

[GreatBigBore]

Right, the torus does look like a sphere, that is, when it's embedded in a 3D space so that we humans can visualize it.

Sounds like I don't really know what a torus is. Is it easy to explain to me how something can be flat and closed? Or will it just degenerate such that I'd be better off getting a book? Or maybe a URL that has a good primer on topology?

If you stop time and move out across the universe, you remain at the center of this sphere!

Yeah, I understand that the last scattering surface isn't an object. I just was trying to visualize what I would see if I could go to that location. I'm trying to educate my faulty intuition, which keeps telling me that if I went there, I'd see some indication in the sky that I'm nearer the edge of something, or back within view of Earth in front of me, or at least I'd see something that would be consistent with one or the other of those possibilities.

 

[Ich]

Sounds like I don't really know what a torus is. Is it easy to explain to me how something can be flat and closed?

That's quite easy, in one dimension: a cylinder surface has no intrinsic curvature, so it is flat in the GR sense.
It's more difficult with the torus, which isn't actually flat. You can't embed a 2D surface with no edges in 3D space while keeping it flat. So it's definitely not easy to explain or imagine, but mathematically rather simple, as you don't have to embed it in higher dimensions.

I'm trying to educate my faulty intuition, which keeps telling me that if I went there, I'd see some indication in the sky that I'm nearer the edge of something,

If the "edge" were much farther away, you would see no indication. Current consensus is that we'll see no change as far out as we can get information from. What's behind that boundary isn't important, we can't know anyway.

or back within view of Earth in front of me,

Maybe this is true. All we can say for sure is that we found no evidence for such a periodicity on scales of ~50 Gly.

 

[bapowell]

Sounds like I don't really know what a torus is. Is it easy to explain to me how something can be flat and closed? Or will it just degenerate such that I'd be better off getting a book? Or maybe a URL that has a good primer on topology?

Sorry, I shouldn't have said looks like a sphere. I meant looks curved like a sphere. A torus is a donut, as you know. Don't mean to confuse. The closed part comes from the topology, which for the sake of discussion, is just a set of rules for how to glue the edges of a rectangle together. The famous example is the old Atari game Asteroids -- it's a 2D world with rules that say "when you exit screen left, appear from screen right", and same for up and down. This is toroidal topology. You don't need a 3rd dimension (or curvature) to make a torus. It's the rules (topology) that close the surface. I don't know of any good primers.

Yeah, I understand that the last scattering surface isn't an object. I just was trying to visualize what I would see if I could go to that location. I'm trying to educate my faulty intuition, which keeps telling me that if I went there, I'd see some indication in the sky that I'm nearer the edge of something, or back within view of Earth in front of me, or at least I'd see something that would be consistent with one or the other of those possibilities.

I was trying to explain that the LSS is not a present-day location that you could go visit. It's the collection of points from which CMB photons reaching Earth today were emitted 14 billion years ago.

 

[GreatBigBore]

...a cylinder surface has no intrinsic curvature...

Oh boy. Sounds like I need to do some studying. I'm like, wait a second, spheres have curvature but cylinders don't? I'll bone up and come back!

...evidence for such a periodicity on scales of ~50 Gly.

Whoa, what do we use for testing such huge periodicity? Is it strictly theoretical or is there a physical basis for it? And that leads to another of my zillion questions: Krauss says that we know how many particles there are in the universe. I recall a calculus professor saying something about 10^85 as an estimate, but Krauss insisted that we *know*, and we use the knowledge to convince ourselves that dark matter isn't just ordinary, non-luminous matter. I would love to know how we reached a firm conclusion about the particle count (or it may have been proton count).

Current consensus is that we'll see no change as far out as we can get information from. What's behind that boundary isn't important, we can't know anyway.

Ah, but this goes right to the heart of my compulsion to get my head around this and get involved in the discussion. I've had a religious experience recently. When I first heard Sagan say, all those years ago, that we are the cosmos recognizing itself (or something like that), I thought that he was a kook. But I suddenly get it: we *are* the mind of the universe! No, that doesn't put it in perspective. Nobody says, "I am the mind of this body." We just say, "I am me." (Ok, we don't say it, but it's implicit.) We *are* the universe.

Whoa.

Even if we're not entirely alone, consciousness has got to be pretty darned rare. We have to figure out how to get around these boundaries, to take control of the very fabric of things, so we can figure out what we are, who we are. I can't be the only one here who often finds himself sitting there considering everything we know and don't know about how we find ourselves here, and then, almost like waking up with a shock, look around and go, "What the hell?" We have to answer that question.

Maybe all our religious visions had a grain of truth to them: maybe the universe itself (you and I!), becoming conscious, gaining control over its body like a living thing, is a sort of god. We have to get out there, find our siblings (if there are any), and become something undreamable. We owe this to ourselves.

It's fun to be all cynical and say that the reason no aliens have visited us is that they're too smart. But think about it. What do you do when your kid brother is acting like an idiot and getting himself into serious trouble? You don't let him get himself killed. What that tells me is that we're the first to wake up, or among the first, or perhaps--and this gives me chills--the only ones. We've got to figure out a way not to blow ourselves up.

Anyway, I want to be part of this craziness, even if it can't even be dreamed of by engineers for another 500 years, or 5000. *sniff* I made myself cry.

 

[Chalnoth]

Yeah, I've heard that answer before too, and I still don't get it. Maybe I need to ask the question differently. How about this: if I stop time and just start traveling in a straight line, will I ever arrive back at my starting point? And, if I stop time and travel in a straight line to the location where we currently see the last scattering surface, what would I see there? (In general, obviously. I know that I won't find Elvis.)

1. We don't know, because we don't know the overall topology of the universe yet.
2. You'd see a different region whose properties are the exact same as ours. You see, the light that we see from the last scattering surface was emitted 13.7 billion years ago. The stuff that emitted that light has been doing stuff this entire time, and is now a region of the universe that, statistically, looks just like the stuff we see around us.

Umm, yikes. Maybe I need to go to the "for Dummies" forum. *Distance* to the CMB? I thought that the CMB is everywhere. I'm hoping that you mean the distance to the last scattering surface. But now that I think of it, I can't make sense of that either.

Yes, I do mean the distance to the last scattering surface, which is the distance to the stuff that emitted the photons that we are seeing today. Tomorrow, we'll be seeing photons that came from just a little bit further away. Next year we'll be seeing photons that came from just a little bit further away than that, and so on and so forth. So the distance to the surface of last scattering increases with time, not because it is physically increasing, but because we're seeing that part of it whose photons took a little bit longer to get to us.

Unfortunately, from within my confusion, a torus looks the same as a sphere: the only relevant characteristic I can see is that the surface curves back on itself, just like that of a sphere.

Except that the curvature of a torus is flat. This may not be completely obvious, but basically a flat surface is any surface that you can make out of a flat piece of paper without stretching or tearing. For example, you can make a cylinder out of a flat piece of paper without any stretching. But you can't make a sphere.

A torus requires a little bit of explaining, because if you make a torus in three dimensions, it does require some stretching. On average, the curvature is still flat (there's some positive curvature on the outer bits, some negative curvature in the inner bits). But you can mathematically write down a torus that is perfectly flat. In fact, in four dimensions, you can even make a 3-dimensional torus that is perfectly flat.

One way of visualizing this mathematical construct is to just look at the game of asteroids: when you travel out one side of the screen, you appear at the other. This is toroidal topology: it's flat in every direction, and yet still wraps back on itself.

 

[George Jones]

That's quite easy, in one dimension: a cylinder surface has no intrinsic curvature, so it is flat in the GR sense.

Oh boy. Sounds like I need to do some studying. I'm like, wait a second, spheres have curvature but cylinders don't? I'll bone up and come back!

Intrinsic curvature is a measure of how much geodesics deviate form each other. Take a sheet of graph paper and roll it up into a cylinder. The lines on the graph paper deviate no more from each other when the graph paper forms a cylinder than when the graph paper lies flat on a desk. The is true even for a set of parallel "inclined" lines drawn on the graph paper.

 

[Phyisab****]

"That's quite easy, in one dimension: a cylinder surface has no intrinsic curvature, so it is flat in the GR sense."

lol I'm about to get a degree in physics and I was still like "wait, what?" This is the perfect way to confuse the crap out anyone without prior education in geometry.

 

[bapowell]

It might be good for responders to read the posts given before them so as not repeat things.

 

[Ich]

I'm like, wait a second, spheres have curvature but cylinders don't?

Yes, you can roll a sheet of paper without doing harm. That's called no intrinsic curvature, the kind of curvature some "flatlanders" could measure. It has "extrinsic" curvature, however, but that's irrelevant.

Whoa, what do we use for testing such huge periodicity?

They're looking at http://arxiv.org/abs/astro-ph/0310233" .

Krauss says that we know how many particles there are in the universe.

Yeah, Krauss.
There's always one pitfall: when people are talking about "the universe" and it size, mass, particle number and so on, they usually mean the observable universe, but forget to mention that. We don't know how big the universe is, we don't know how many particles there are. We just can make an educated guess at how many particles there are in the part of the universe that we can know about today.

We *are* the universe.

I can't speak for you, but I'm just a physicist.

Maybe all our religious visions had a grain of truth to them: maybe the universe itself (you and I!), becoming conscious, gaining control over its body like a living thing, is a sort of god. We have to get out there, find our siblings (if there are any), and become something undreamable. We owe this to ourselves.

Um, will half an universe and a physicist do also? Or just half an universe, me staying here, conscious most of the time anyway?

 

[Chalnoth]

Whoa, what do we use for testing such huge periodicity?

50Gly is approximately the current distance to the surface of last scattering.

 

[GreatBigBore]

Yeah, Krauss.
There's always one pitfall: when people are talking about "the universe" and it size, mass, particle number and so on, they usually mean the observable universe, but forget to mention that. We don't know how big the universe is, we don't know how many particles there are. We just can make an educated guess at how many particles there are in the part of the universe that we can know about today.

Ok, I can live with the caveat about observability. But still, how do we arrive at this guess, and what is the basis for our confidence that it rules out normal, non-luminous matter as dark matter?

Um, will half an universe and a physicist do also? Or just half an universe, me staying here, conscious most of the time anyway?

I'm not sure what you mean, but given the loftiness of my speech, it's probably safe to assume that you're teasing me. You can stay here. I'll send pictures. Of me. Doing green chicks.

 

[GreatBigBore]

50Gly is approximately the current distance to the surface of last scattering.

One major *click* sound just happened in my head. Thanks! But of course, now more questions come up. Now I can possibly give a useful formulation to my first question: if I could stop time right now and travel in a straight line 25Gly minus 15 feet, what might I expect to see? Or might I even expect to be unable to travel that far because I'd bump into something before that? I'll just let it be believed that I think there's something to bump into, because I truly have no better alternative to imagine.

Twofish-quant, feel free to respond now, because my head just now did explode.

 

[bapowell]

Ok, I can live with the caveat about observability. But still, how do we arrive at this guess, and what is the basis for our confidence that it rules out normal, non-luminous matter as dark matter?

The acoustic peaks in the spectral decomposition of the cosmic microwave background offer tons of information about the observable universe. They give the frequencies with which the plasma of the early universe was sloshing about. You can pinpoint the density of baryonic matter because baryons increase the effective mass of the plasma (think harmonic oscillator). The bottom line is that you can determine the baryon density by carefully measuring the amplitudes of the peaks of the CMB spectrum. The peaks also give information on the dark matter content of the universe.

Other data, like that from Large Scale Structure surveys, give additional evidence for nonbaryonic dark matter. Without dark matter, galaxies form later and it's difficult to get a universe that resembles ours. I can talk about that more if you're interested.

 

[Chalnoth]

One major *click* sound just happened in my head. Thanks! But of course, now more questions come up. Now I can possibly give a useful formulation to my first question: if I could stop time right now and travel in a straight line 25Gly minus 15 feet, what might I expect to see? Or might I even expect to be unable to travel that far because I'd bump into something before that? I'll just let it be believed that I think there's something to bump into, because I truly have no better alternative to imagine.

So yeah, this doesn't change things much. Obviously the further you go, the less confident we can be that the cosmological principle will hold, that everything you see will be the same (on average) as it is here. But the fact that our universe is so uniform out to the surface of last scattering (we only see deviations of one part in 100,000 on the CMB itself), we can be pretty confident that the cosmological principle holds for at least a factor of a few times the size of the bubble we can observe.

That said, let me point out that it may well hold for an absurdly larger region. Due to the exponential nature of its expansion, if inflation only lasted twice as long as required to explain the flatness and homogeneity of just the region we observe, then it would have generated a region that is 10^30 times larger on a side than the part we observe.

 

[GreatBigBore]

Without dark matter, galaxies form later and it's difficult to get a universe that resembles ours.

Naturally I couldn't keep up with all of your details, but I understood enough of the broad concepts to be satisfied for the moment. But then I tripped on this last thing. We weren't talking about a no-dark-matter universe before, so I'm guessing that maybe there's a typo somewhere? Or that I'm missing your meaning, anyway. Did you mean that if dark matter were baryonic then galaxies would form later?

 

[Chalnoth]

I'd just like to add a bit about intrinsic curvature, because I'm not sure it's been adequately explained yet.

As George Jones mentioned, intrinsic curvature is a measure of how much geodesics deviate from one another. But what does this mean?

First, what is a geodesic? For this, we have to go back to Euclid, and his definition of parallel lines. One of the perhaps perplexing things about Euclidean geometry is that Euclid never was able to prove that parallel lines never meet: he had to put that into his geometry as an axiom. This may seem a little strange. You'd think that it's something that could be proven rather easily, because it's just so obviously true.

But the problem is that it's not true. At least not all the time: it's only true for flat space. In order to prove that parallel lines never meet, you have to allow for the possibility of curved space. But then there's a problem: what is a straight line in curved space? After all, if space itself is curved, then aren't straight lines impossible? In a sense yes, this is true. However, you can generalize a straight line, and there are a few ways to do this.

One way to generalize a straight line is to take a particular property of straight lines in flat space: in flat space, a straight line is the shortest distance between two points. In curved space, the shortest distance between two points is called a geodesic. A geodesic also has the interesting feature that if, for example, you are sitting on the Earth and decide to move in one direction without deviating at all, you will end up walking along a geodesic. So this seems to be a very natural generalization of a straight line.

So when we are talking about geodesic deviation, we are going all the way back to Euclid and his axiom that parallel lines never meet: by measuring how far away parallel lines (geodesics) actually do meet (or get further from one another), we get a measure of how far we deviate from flat space.

To take a perhaps familiar example, take the Earth. A geodesic on the Earth is called a great circle: it's the circle you would make if you were able to walk in one direction without deviating. Some examples of great circles are the equator and lines of longitude (not lines of latitude besides the equator, however). If you take two different lines of longitude, for instance, these are perfectly parallel at the equator. But as you move towards the poles, they get closer and closer together. This is because the Earth is curved.

This definition of curvature is also why any shape you can make out of a flat piece of paper without stretching or tearing is a flat surface. Imagine drawing a grid on this flat piece of paper: any change you make to the paper that leaves the distances between grid points unchanged doesn't change the curvature. And only if you stretch or tear the paper do you change the distances between grid points.

 

[bapowell]

Naturally I couldn't keep up with all of your details, but I understood enough of the broad concepts to be satisfied for the moment. But then I tripped on this last thing. We weren't talking about a no-dark-matter universe before, so I'm guessing that maybe there's a typo somewhere? Or that I'm missing your meaning, anyway. Did you mean that if dark matter were baryonic then galaxies would form later?

Oops! Yup. I meant that if there was no (or less) non-baryonic dark matter then we'd see differences in large scale structure.

 

[GreatBigBore]

...we can be pretty confident that the cosmological principle holds for at least a factor of a few times the size of the bubble we can observe.

Right, but I'm still trying to figure out if there's anything that could be thought of as an edge, or an indication that an edge exists. I get it if the answer is that we just don't freaking know, but I just wonder what is being considered plausible by the current community.

That said, let me point out that it may well hold for an absurdly larger region.

Ha ha. I heard "50Gly" today, for the first time ever. If I'd heard it anywhere other than here, I would have considered it absurd. My head hurts trying to realize that "all the matter in the universe" is, what, 360 billion times what I thought it was yesterday. If I were to, unadvisedly, think of the universe as a sphere.

 

[Chalnoth]

Right, but I'm still trying to figure out if there's anything that could be thought of as an edge, or an indication that an edge exists.

Not within the observable universe. It is quite smooth out to the limits of our vision.

Ha ha. I heard "50Gly" today, for the first time ever. If I'd heard it anywhere other than here, I would have considered it absurd. My head hurts trying to realize that "all the matter in the universe" is, what, 360 billion times what I thought it was yesterday. If I were to, unadvisedly, think of the universe as a sphere.

Hehe :)

 

[twofish-quant]

One thing that you have to realize is that a lot of things that we are talking about are metaphors. When someone says that "space is curved", what they are saying is that when you measure angles and calculate volumes, the numbers come out in a certain way.

Also this is how you tell if you are on a "flat" surface. Take a pencil on the surface and point it in a certain direction, Walk in a circle keeping the pencil pointing in the same direction, when you get back to your starting point, is the pencil pointing in the same direction or not? If it is, then you are on a "flat" surface. If it isn't, you are on a "curved" surface. By seeing how much the pencil changes direction, you can tell how "curved" the surface is.

 

[twofish-quant]

Ok, I can live with the caveat about observability. But still, how do we arrive at this guess, and what is the basis for our confidence that it rules out normal, non-luminous matter as dark matter?

Two main things (there may be more)

1) An all baryon universe would be lumpier than we observe. Throw two bricks at each other. You get a pile of bricks. Throw two lasers at each and you don't get a pile of light. You can calculate a "lumpiness factor" for baryonic matter and non baryonic-matter, and the universe is a lot less lumpy than it would be if it was all baryons.

2) Deuterium abundances. There is a lot of deuterium in the universe. If the universe were all baryons then you'd have more nuclear reactions right after the big bang, and the deuterium gets burned up. People have tried to deal with this by proposing ways of creating deuterium post-big bang. No one has come up with anything that works. (However, in the process of trying to make deuterium, people ended up figuring out how to make lithium and beryllium).

 

[twofish-quant]

One other thing. Sound goes through baryons. If you have a room full of baryonic gas, you end up with sound waves. You make a noise, it compresses the gas, the gas bounces back, and you get a sound wave. If have a room filled with light, you don't get sound waves. You can see the "ripples" caused by the sound waves in the cosmic microwave background.

So to summarize. We know that baryons form lumps, have nuclear reactions, and propagate sound. Whatever the dark stuff is, it doesn't seem to do any of that.

 

[bapowell]

Two main things (there may be more)

1) An all baryon universe would be lumpier than we observe. Throw two bricks at each other. You get a pile of bricks. Throw two lasers at each and you don't get a pile of light. You can calculate a "lumpiness factor" for baryonic matter and non baryonic-matter, and the universe is a lot less lumpy than it would be if it was all baryons.

We should be a little careful here. Structures in the universe started out as tiny perturbations in the cosmological fluid. Before decoupling, these perturbations caused the baryon-photon plasma to oscillate -- as the plasma fell into the gravitational potential wells caused by these perturbations, radiation pressure pushed back and we get the well known standing wave acoustic oscillations. However, non-baryonic dark matter is decoupled, and has no problem settling into these wells. As these perturbations accrete more and more dark matter, we begin to form structure. Later, when the baryons decouple from the photons, they join the party. So, as simulations show, without non-baryonic dark matter, structures are less formed by today because baryons can only form structure after they decouple.

So, I guess it boils down to what we mean by lumpy.

 

[bapowell]

We know that baryons form lumps, have nuclear reactions, and propagate sound. Whatever the dark stuff is, it doesn't seem to do any of that.

Non-baryonic dark matter most certainly does form clumps. That's why it was suggested in the first place. Non-baryonic dark matter is not like light -- in it's simplest form it merely needs to be weakly interacting, not bosonic. It can (and does) form gravitationally bound structures.

 

[GreatBigBore]

Not within the observable universe. It is quite smooth out to the limits of our vision.

Ok, but "out to the limits of our vision" brings me back to the question: what do we think might be there, or what might I experience if I tried to get "there"? I don't mean unicorns. I mean what are the things being considered plausible by the larger community?

 

[GreatBigBore]

One thing that you have to realize is that a lot of things that we are talking about are metaphors. When someone says that "space is curved", what they are saying is that when you measure angles and calculate volumes, the numbers come out in a certain way.

That doesn't sound like a metaphor to me. If I were able to measure that the angles in a triangle of my arbitrary choosing were not equal to 180 degrees, then I would easily believe that space is quite literally curved. Hmm, maybe that's not the point. Maybe the real point is that I don't think that "curvature of space" is a metaphor. I am pretty sure that we're really checking for the literal curve of space.

Also this is how you tell if you are on a "flat" surface. Take a pencil on the surface and point it in a certain direction, Walk in a circle keeping the pencil pointing in the same direction, when you get back to your starting point, is the pencil pointing in the same direction or not? If it is, then you are on a "flat" surface. If it isn't, you are on a "curved" surface. By seeing how much the pencil changes direction, you can tell how "curved" the surface is.

I like this idea, but I'm too stoned right now to tell whether it gives me the same answer as the triangle would. Feel free to tell me the answer. If it doesn't, then yeah, maybe I need to reexamine my ideas about curvature. Not that they're heartfelt ideas; I'll take anything that works as well or better.

Speaking of underlying philosophy, I have a feeling that you and I differ in our underlying philosophies about consensus. I've been around the fundamentalist block enough times to smell the difference between consensus and conspiracy, and I don't smell anything fishy about the consensus in the physics community at large, or on this board in particular. I mention this as an explanation as to why I might expect a bit more substantiation of any of your claims (philosophical or physical or whatever) than I might from other members of this forum. I don't mean this as an attack; just an explanation. If I've offended you then I apologize, and I won't respond if you flame me.

 

[DaveC426913]

Ok, but "out to the limits of our vision" brings me back to the question: what do we think might be there, or what might I experience if I tried to get "there"?

We would arrive back at our departure point.

 

[Chalnoth]

Ok, but "out to the limits of our vision" brings me back to the question: what do we think might be there, or what might I experience if I tried to get "there"? I don't mean unicorns. I mean what are the things being considered plausible by the larger community?

Different low-energy laws of physics.

Let's see if I can explain this. Basically, in our current physical theories, there are certain symmetries that are respected at high energies, but at low energies are broken.

One way that this is often illustrated is this: imagine that you have a large field of pencils, all evenly spaced. Once end of each pencil is anchored in the ground, and the pencil is free to move around. Now, we're also going to connected the other ends of the pencils with springs to one another, so the nearby pencils will tend to want to be in the same direction.

What happens at high temperatures for such a configuration is that these springs have a lot of random energy, so the pencils are bouncing around every which direction: the system as a whole has no preferred direction.

But as you lower the temperature, the pencils start to fall. And when they do start to fall, the neighboring pencils all want to fall in the same direction. So the pencils in one region may fall and point east. The pencils in another region may fall and point northwest. And so on. The size of the regions of the pencils pointing in anyone direction will depend upon how rapidly they froze.

We expect that with our current theories, there are direct analogs of this process that went on: fields that want to take on the same value at neighboring points in space, but don't care (much) what value that is. And things like the strengths of forces and masses of fundamental particles may depend critically upon the particular value of this field.

 

[GreatBigBore]

We would arrive back at our departure point.

And your basis for this is?

And the sign said / Anybody caught trespassin' / Will be shot on sight.
So I jumped on the fence / And I yelled at the house / "Hey! What gives y* -=>BLAM<=-
*thud*
(Dude! Didn't you see the sign? Jeez!)

Oh. Dude. I can't stop laughing.

 

[GreatBigBore]

Let's see if I can explain this.

You have a fan. Thanks. Could you name a book or two along these lines? Or a URL?

 

[Chalnoth]

You have a fan. Thanks. Could you name a book or two along these lines? Or a URL?

Well, this is mostly information I remember from classes, and I'm not entirely sure I want to suggest our textbook. But the phenomenon I described is known as "spontaneous symmetry breaking." The linked Wikipedia article will get you some more in-depth information. This sort of phenomenon is seen in all sorts of physical systems here on Earth, and seems to be an integral component of the standard model of particle physics (for electroweak symmetry breaking).

Also, spontaneous symmetry breaking has another interesting aspect: depending upon the dimensionality of the space, you tend to get what are called defects. For the pencil example above, for instance, a stable configuration is one where one pencil is standing up on end, and the neighboring pencils are all pointing away from that one. This "defect" would manifest itself as a point of very high energy.

For three dimensional space, a similar thing happens, but due to the extra dimension, instead of a point, you have a string: a long region where the field takes on a high-energy value and isn't allowed to "fall" due to the neighboring field values. These are called cosmic strings, and so far we haven't yet detected any. We know now that they must be quite rare, but the search for such direct signatures of spontaneous symmetry breaking is ongoing.