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"I'm not convinced this explanation-by-analogy style is really all that helpful, particularly with regards to "the big bang is an expanding balloon". What makes it such a confusing analogy is that most people were already picturing something like an expanding sphere anyway, just one filled uniformly with matter moving away from a central point as it expands. And it doesn't reinforce that the Universe has no center, since most people can easily imagine what the center of a balloon is."

The key to the balloon analogy is that it only applies to the surface. The interior of the balloon is to be ignored. You say you can easily find the center of the balloon, so I think you don't get this, because I suspect your "center" is the 3D center of the balloon. But that doesn't exist. Only the surface does. What's the central surface point of a sphere? There isn't one. That's the universe, only the surface is 3D, not 2D.

I'm fairly sure that even a large number of people using the "expanding ballon" metaphor don't get that, let alone the poor readers. I tend to be surprised when I see it explained correctly.

Also, in the classic picture of the wormhole, like you might find here: http://casa.colorado.edu/~ajsh/schwm.html , the wormhole is not the tunnel itself. If you see someone drawing an arrow that goes down the middle of the tunnel as the path of travel, they don't know what they are talking about. (That's the best picture I could find quickly, they're actually showing something else with that arrow, so I do not accuse them.) The wormhole is the sides; the image is two 2D chunks of space being connected through a 3rd dimension. (Incidentally you can tell Hollywood doesn't know either, because they always actually "draw" the wormhole.) The curvature of the 2D planes corresponds to gravity in these displays.

This is also true of the classic "rubber sheet" gravity analogy; the rubber sheet applies only to 2D, and the 3D "things" usually drawn should be understood to be merely labels explaining where the curvature comes from. You really shouldn't see a "rolling ball" on the surface, you should see it in the surface. Again, this is done incorrectly far more often than it is done correctly.

I get the intention behind the analogy, but I know from experience that nobody ever comes away from it understanding what they're meant to. I don't think I've ever mentioned to a friend without them pointing out that balloons do have centers, or asking what's outside of the balloon. I've had much better luck just telling people why what they think is happening can't possibly be right, so they stop defending it or trying to reconcile it with reality, and then building up.

But, I'm not a physics professor. Your mileage may vary.

Ah, you do get it, I apologize for suggesting otherwise. Statistically, my odds were good, because you're right, and virtually nobody does it right. (I claim a Bayesian defense!)

Unfortunately, I don't know how to do any better. There's a leap to even abstractly understanding 4+ dimensions and a lot of people simply won't make it. Without that you've "already lost" regardless of how clever your metaphor is.

With my limited cosmological understanding, it seems like much of what you're saying is also key to, in part, understanding that the expansion or shift isn't a movement THROUGH spacetime, but the expansion OF spacetime.

I have a question. Our current cosmological understanding indicates that no matter where you are in the universe, you'd see this recession, correct? If so, bizarre thought experiment: If I could somehow magically teleport from here to the very edge of observable spacetime, wouldn't I see, broadly, the same stuff as I see from earth? A whole bunch of receding galaxies?

Yes. That's what makes metric expansion of spacetime elegant: it doesn't require you to suppose there's anything special about our location in the Universe. If the recession of galaxies were intertial, the only explanation would be that the Big Bang happened exactly where Earth is now, and we're at the exact center of the Universe and everything is moving away from us. It's the key absurdity that needed to be explained away.

Further, we know from more recent evidence that the Universe is homogenous on scales larger than galactic clusters. On the scales of stars and galaxies, the Universe has large expanses of empty space sprinkled with massive galaxies. Zooming out, you can see "clusters" of up to about a thousand galaxies separated by larger areas that have fewer galaxies. But once you get above that level, on the order of 10^24 to 10^25 meters, there's simply no more structure to be found. As far as we can tell, if you take a spherical region with a diameter 10^25 meters from anywhere in the Universe, it will have roughly the same amount of mass regardless of where you take it from, and the Universe is of roughly uniform density.

So then, and this is where the crazy starts to happen: when people talk about the size of the universe, I start to get really confused. While there's an observable limit from our reference point, isn't that functionally a consequence of the null cone? That is: doesn't the homogeneity irrespective of location mean that if I were on the edge of the spacetime 'bubble' from Earth's point of view, there would be a completely different spacetime bubble with different 'stuff' in it? That is, different galaxies alltogether?

Maybe the question is too absurd, since we can't teleport in the way I described, but it's...I don't know...interesting.

Thanks!

You're right: the "Observable Universe" is defined only relative to a point of observation. For any spot in the Universe, there's a 93-billion-light-year-wide sphere centered about that point that constitutes the OU for that point. What exactly this sphere means it somewhat complicated. The simplest way I can think to say is this: The radius of the OU is the current distance of the farthest point in space such that if a radio signal were emitted from that point 13.7 billion years ago, immediately after the Big Bang, it would be possible in principle (but by no means in practice) for us to receive that signal. Anything that is outside of the OU is causally disconnected from us as a matter of fundamental principle, and nothing that has ever happened or ever will happen at any point outside the OU can ever affect us in any way, ever.

It was previously (up until a decade or so ago) an open question as to whether the Universe itself might be smaller than the OU. This sounds absurd, but consider the example of a hypothetical jet that could circle the Earth ten times without refueling. While normally the "range" of a jet plane is a circle about some point, the range of this jet exceeds the size of the Earth itself. Similarly, if the Universe were smaller than the OU, some of the distant galaxies we see would actually be repetitions of closer galaxies from an earlier time and a different angle, since the light had been "looping around" the Universe once or more before reaching us. Or, as Modest Mouse put it in one of their better songs: "The Universe is shaped exactly like the Earth / If you go straight long enough, you end up were you were." Recent evidence from the Cosmic Microwave Background has made this idea very unlikely, but it's a useful example to clear up misconceptions about the OU.

So, however big the Universe actually is, it's bigger than the OU, which means that the stuff cosmologists are debating about is space that cannot, even in principle, ever be observed. It's an important question, though, since whether the Universe loops back on itself on the large scale or just keeps going forever has implications for whether gravity will win out over Hubble Expansion in the long run, determining the eventual fate of the Universe.

I'm really curious about how CBR observations solved the question related to universe size.

Also, then, for me this makes me wonder: is then the big bang simply the origin of the null cone over whose event horizon we can't see? Clearly this is a Minkowski spacetime paradigm, and I have no idea where that stands in terms of general favor.

Also: further reading? I'm guessing "The large scale structure of space-time" is a bit dated ;)

The WMAP space probe allowed better measurements of the CMBR, from which the relative composition of matter at the time of the CMBR's emission could be determined (using methods I don't fully understand). Once it was known that the Universe was X% atomic nuclei, Y% photons, Z% dark matter, etc., this information implied certain bounds on how quickly the Universe was expanding during the inflationary epoch (10^-36 to 10^-32 sec after the Big Bang), since high rates of expansion can overpower the nuclear forces and prevent quarks from bonding to form protons/neutrons. The math for all of this is, unfortunately, far over my head. Sorry I can't be of more help.

I'm not fully understanding your next question. The origin of our light cone is here and now. Minkowski spacetime is an approximation that (almost) works in the absence of gravitating bodies. Once general relativity gets involved, certain features of Minkowski spaces start failing, like the fact that you can always reorient light cones so that they're parallel. This fails even in intergalactic space, where there is still a non-vanishing Weyl tensor effect due to Hubble Expansion. So, without getting too much into the detail, in the real world light cones are (forgive me) uncannily un-coney. Our past light "cone" collapses back in on itself in the distant past and converges on the Big Bang, but so do light cones everywhere in the Universe, even outside of our observable universe. Though, whether a light cone even has meaning before the inflationary epoch is a question of Grand Unification Theory, which is very much over my head.

As for further reading, Dodelson's "Modern Cosmology" is great if you're not afraid of learning the math behind General Relativity: http://amzn.com/0122191412 The text doesn't assume very much familiarity with GR, but it does assume enough mathematical sophistication that you can fill in any gaps in your knowledge on your own.

(And if you don't like the idea of learning about tensors, you're SOL. Sorry. There's a very low ceiling of how much one can know about cosmology without tensor calculus.)

Whoa, I praise your deep knowledge of cosmology, anyway, to my question:

> "So, however big the Universe actually is, it's bigger than the OU, which means that the stuff cosmologists are debating about is space that cannot, even in principle, ever be observed"

What if we learn how to make better neutrino telescopes, them how much of the Unobservable Universe could we see? Can you recommend a paper about this?

The stuff outside the OU cannot be seen in principle. Its size is fully independent of our current level of technology, and no advancement of technology will let you see beyond it. (Seeing beyond it would mean you can send signals faster than light, which implies you can build a time machine, in which case all bets are off.) In practice, we cannot see anywhere near as far as the radius of the OU, since after a certain distance you're looking so far into the past that space is opaque to microwave radiation. If you can somehow see neutrinos you get to see more, but that's still all inside the boundary of the OU.

Yes, I know that they cannot move faster than the speed of the light, and that the universe was opaque to visible light before the decoupling of radiation.

But there're a group of neutrinos that decoupled before the decoupling of radiation, even before this gravitational waves were at large in the universe, they could in principle say something about regions that are outside the Observable Universe, this ignoring the fact that they must be absolutely difficult to observe and that both neutrinos and gravitation waves are generated by new events and that we can in fact extract some information about these regions from them in the same way we can from light.

This was what I found from a paper, "Detection of gravitational waves with resonant antennas" from Francesco Ronga, earlier today:

"Gravitational wave and neutrino astronomy will increase the amount of observable universe, because they will investigate places that are completely inaccessible to the electromagnetic radiation and probably will change our knowledge of the universe evolution"

I think you're confusing two very different points in the history of the Universe. The CMBR was emitted after the decoupling of matter and radiation, as you mentioned, but this event was over 300,000 years after the Big Bang. And you are correct that there could, in principle, be observable signals emitted before this event in the form of neutrinos or gravitational waves. The observable universe, however, is defined not by reference to the signals emitted at the decoupling event, but rather the start of the inflationary epoch, which was merely 10^-36 seconds after the Big Bang. So, the OU is big enough that it encompasses all of the space from which any signal, even neutrino or gravitational, that might have been emitted 13.75 billion years earlier that could eventually reach us.

But, terminology aside, this still leaves your question: How much farther could we see if we could pick up neutrinos or gravity waves? Not a whole lot, unfortunately. Most of the expansion of the early Universe occurred during the (aptly named) inflationary epoch, and that lasted less than a tiny fraction of a second, leaving very little time for a neutrino or gravitational wave to travel before the Universe became very large. The expansion that occured in the following 300,000 years is negligible by comparison to that first tiny moment, so you won't get a whole lot more than 300,000 light years out of those neutrinos. I'm too tired and lazy to do the math to find the radius of the surface of last scattering, so I'll run a quick Google search, and...

The final answer is that the visible universe, or that which is not obscured by the opaque matter that dominated in the first 300K years, is a sphere with radius of 45.35 billion light years, while the observable universe, which is everything that can observed in principle, is just a bit further at a radius of 46.5 billion light years. So, yeah, we've got most of it covered.

You are correct. There's more to the universe than we can see, but what we can't see should be basically the same as what we can. By analogy, from any place on the earth, you can only see as far as the horizon[1]. If you were to teleport (or travel) to the edge of your horizon, you would see more earth that you couldn't see before, but that new stuff would basically be similar to the earth you're seeing now.

Just for kicks, let's add in that the earth is expanding like the universe. You're at point A, there's a tree at point B, and the horizon past the tree in that direction is point C. If the earth is expanding, then point B will be receding from both point A and point C, in part because point C is receding twice as fast.

[1] The reason for the boundary of the observable earth is totally different, but that doesn't change the point.

Yes, the basic ideas underlying cosmology are the assumptions of isotropy (it looks the same in every direction) and homogeneity (it is the same everywhere). These two assumptions combine to tell you that it looks the same in every direction from wherever you are sitting.

Edit: grammar

Plus, we still aren't 100% sure if the red shift is due to the Doppler effect, or something else and then the Universe is not expanding at all. I always found it strange that there is such a simple and straightforward correlation between distance and speed. It should have been more complicated than that, shoudln't it?

No. We're sure. We can observe that the universe was hotter and denser in the past because light takes time to get here, so when you look far enough into space you see older things. Also, there are tons of incidental facts about the doppler shift that can only be explained by Hubble Expansion. The best one that comes to mind is the "Finger of God" effect where galaxies are stretched out in doppler phase with an axis pointed toward the observer. This isn't caused by Hubble Expansion directly, but by the peculiar velocity (velocity within spacetime rather than metric expansion) caused by gravitation bonding acting against the Hubble Expansion. That is, when Hubble Expansion tries to pull a galaxy apart, the gravity of the stars keeps it together, and there are effects from that which we can calculate very precisely, and we see exactly what we would expect to.

The existence and relative long-term stability of Hubble Expansion is, frankly, one of the most certain things anyone knows about physics. If you can replace it with something else, it has to be something that reduces to the exact phenomenon of Hubble Expansion under the normal conditions our Universe is currently in.

I'm not quite sure I understand the effect with galaxies. So let's say from two opposite parts of a galaxy we would expect certain difference in red shifts because of the distance (one part is farther than the other), but what we observe is not that?

Suppose you could make a galaxy out of stars that have no mass. They're just big, bright balloons arranged in the pattern of a galaxy. If you looked at the balloon galaxy from far away, you'd expect that the part of the galaxy that's far from you would be red-shifted more than the part that's closer to you, due to Hubble Expansion. Also, as time goes on, you'd expect the balloons to drift away from each other, since the expansion causes everything to become farther away from everything else.

But because real galaxies are made of massive stars, they pull on each other and maintain the shape of the galaxy against the effect of the metric expansion. In addition to the doppler shift you see in the balloon galaxy, you get an added effect from the "peculiar velocity" of the stars perpetually falling toward each other within the expanding space time--but, of course, never actually getting any closer, since the effects cancel out. The parts that are closer to you have peculiar velocity away from you (because they're falling to the center of the galaxy, which is further away) and the parts that are farthest from you have peculiar velocity toward you (since the center of the galaxy is closer to you).

So, the red-shift from the distant parts is reduced by the blue-shift caused by their peculiar velocity in the direction of the observer, and the lesser red-shift of the closer parts is exacerbated by the peculiar velocity away from the direction of the observer. If we were to naively suppose that this "Finger of God" effect weren't happening, and that red-shift and distance behave as they normally do in accordance with Hubble's Law, we would be forced to conclude that all galaxies are somewhat "pancake-shaped" with every pancake facing toward Earth. This doesn't seem quite right, and fortunately the effect of peculiar velocity shows us that it doesn't have to be, and conveniently verifies the truth of Hubble Expansion.

Your question reads like you think there's an expansion from something to somewhere else. Like, as though people were periodically allowed to run in opposite directions from a 50 yard line, and we're observing them from the 35 yard line as we slowly run in one direction or the other. But that's not what's going on, given the near-uniformity of cosmic microwave background radiation.

"Right now, everything is moving away from us in proportion to its distance from us."

From us? So does that mean that we are at the center of this expansion?

If it were inertial expansion, in the sense of movement in the usual sense through space, yes it would. That's obviously a big problem, and confused a lot of people in the early parts of the 20th century. Metric expansion fixes this absurdity, since when spacetime itself is expanding it is everything that moves away from everything else. No matter where you stand, you appear to be the center that everything is running away from.