Archive for the '[PhysicalScience]' category

The Minimum Size of the Whole Universe

The Observable Universe

When we talk about our Universe, we make a distinction between "the Universe" and "the Observable Universe". The latter includes only what we can see. By "can see", I don't mean what we have the technology to detect. Rather, I mean all objects out there from which light has had time to reach us given the age of the Universe, the speed of light, and the history and future of the expansion of the Universe. The age of the Unvierse is 13.8 billion years. Because the speed of light is finite, we can't see anything that is so far away that light would have taken longer than that from us to reach us. This isn't a technological limitation; this is a limitation on whether or not there is light, even in principle, for us to see given as much technological prowess as you could want.

Indeed, as we look towards the edge of the Observable Universe, we're looking back in time. If light took us 13.7 billion years to reach us, then we're seeing the Universe out there as it was 13.7 billion years ago, not as it is now.

The Universe as a whole, however, is probably infinite. This is easy enough to say, but it's a rather difficult concept to wrap your brain around when you really start thinking about it. One solution is not to think too hard about it. If you find yourself asking questions like "if it's already infinite, how can it expand?", you're not thinking properly about infinity. Infinity is a concept, not a number.

However, the Universe doesn't have to be infinite. According to General Relativity, there are other possibilities. I'm going to lump those possibilities into two categories, but only really talk about the latter.

Interesting Topologies

It's possible that our Universe has an interesting topology. Topology is different from geometry. Geometry includes things like lengths of lines, radii of curvature, sums of angles inside polygons, and so forth. Topology talks about how different parts of space are connected.

As an example, consider the classic video game asteroids:

[Asteroids!]

This game takes place in a (very small) two-dimensional universe. The geometry of the Asteroids Universe is Euclidean— that is, parallel lines will never cross, the ratio of the circumference to the diameter of a circle is π, the sum of the three interior angles of a triangle is 180°, and so forth. However, if you ever played this game, you know that if you go off of the left of the screen, you come back on the right side of the screen. Likewise, if you go off of the top of the screen, you come back on the top. This universe is unbounded; you never hit a boundary, or an edge. However, it is also finite. Its topology is toroidal; it has the same topology as the surface doughnut, although it does not have the same geometry of a doughnut. (The surface of a doughnut has curvature.)

It's possible that our Universe is similar. It may have a flat geometry, but a topology that means that if you kept going in one direction, you came back where you started. If it does have this topology, it's on spatial scales larger than the Observable Universe. Otherwise, we would have seen the signature of this topology (i.e., the fact that parts of space are effectively repeats of each other if you keep going far enough in one direction) on the Cosmic Microwave Background.

For the rest of this post, I shall assume that the Universe does not have any interesting topologies like this. Either it's just infinite space, or it's finite space that is the 3d equivalent of the surface of a sphere.

Possible Geometries of the Universe

The geometry of our Universe doesn't have to be Euclidean. Depending on the total energy density (including the density of regular matter, dark matter, and dark energy), there are three possibilities for the curvature of our Universe.

[Possible Shapes of the Universe
Two-dimensional visualizations of the possible shape of the Universe. Our Universe would be the three-dimensional equivalent of one of these, depending on the total energy density of the Universe.

The parameter Ω is a convenient way of talking about the density of the Universe. There is a critical density, which depends on the current expansion rate of the Universe. That critical density is about 9×10-30 g/cm. That doesn't sound like a lot, but remember that the Universe is mostly empty space! Where we live, on Earth, is an extremely high-density place compared to most of the Universe. The parameter Ω is defined as the ratio of the density of the Universe to the critical density. If Ω=1, then the Universe has a flat geometry. Note that "flat" here doesn't mean "two-dimensional", the way you may used to be talking about flat. Rather, it means that the geometry of space is Euclidean, just like the geometry you probably learned about in high school.

On the other hand, if Ω>1, the Universe has a "closed" geometry. In this case, the geometry of the Universe is the same as the three-dimensional surface of a four-dimensional hypersphere. If that sounds like gobbledygook, think of it as the 3d equivalent to the surface of a sphere. Note that there doesn't need to really be a fourth spatial dimension or a 4d hypersphere out there. It's just that the geometry of the Universe— how parallel lines will behave when extended, how the angles of triangles will add up, what the ratio of the circumference to the diameter of a circle will be— is the same as the geometry of the surface of a sphere. It's possible to describe the mathematics of this geometry entirely using only three spatial dimensions, so there's no need for a higher spatial dimension in which to embed our Universe. However, for purposes of our visualization, it's worth thinking about the surface of a sphere, as that helps us get some idea about what sorts of things would be true in such a universe. The surface of a sphere is a two-dimensional closed universe. Remember, that the universe is the surface. There is no center to this universe, not within the universe— for everything within the universe is on the surface of the sphere, and no point there is any different from any other point.

If Ω<1, the Universe has an "open" geometry. This is harder to visualize. It turns out that you can't embed a slice of an open 3d universe into three dimensions to visualize it, the way you can with a closed universe (in which case you get the surface of a sphere, as described above). However, the closest two-dimensional equivalent would be a saddle or a potato chip (each of which is a hyperboloid or hyperbolic paraboloid). This is an unbounded and infinite universe. It keeps on going forever. However, it's also clearly not flat, and so will have an interesting geomoetry.

The Geometry of Our Universe

You can figure out the geometry of your universe several ways. One way is to create a triangle by drawing three straight lines through space. Then, measure the angle between each of those pairs of lines. If the three interior angles add up to 180°, you're in a flat universe. If they're more than 180°, then you're in a closed universe; if they're less than 180°, you're in an open universe. The problem is the precision needed for this measurement. In order to be able to tell whether or not the angles add up to 180°, you either need to measure them mind-bogglingly precisely, or you need to draw huge triangles, such that the length of one side of the triangle approaches the radius of curvature of your universe. (How close it approaches it depends on how precisely you can measure angles.)

Effectively, we have done this. Measurements of the Cosmic Microwave Background (CMB) give us triangles. One leg of the triangle is given by the characteristic size of fluctuations in the CMB. We know the physical size of those fluctuations. The other legs of the triangle are given by the path of light travelling from either side of one of those fluctuations. By measuring the angle between the light coming from either side of a fluctuation, we can figure out what the geometry of this isosceles triangle is. We did this. The answer: our Universe is flat. However, as with all physical measurements, there is uncertainty on this measurement. The latest form of this measurement tells us that Ω must be between 0.9916 and 1.0133, to 95% confidence (see "Reference" at the end for the source of these numbers). That means that there still is the possibility that our Universe is either infinite (in the case of Ω≤1) or finite (in the case of Ω>1).

The Minimum Size of Our Universe

The Universe is big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist's, but that's just peanuts to the Universe.

With all due apologies to Douglas Adams, let's quantify how big our Universe is.

First, the age of the Universe is 13.8 billion years. That is a long time compared to you and I, but as compared to the age of the Universe, it's just about right. The edge of the observable Universe, right now, is 48 billion light-years away. "Wait!" you may cry. "How can light from something 48 billion light-years away have reached us in a mere 13.8 billion years!" Remember that while that light was working its way towards us, the Universe was expanding. The light, in a sense, had to try to "catch up" with that expansion. This is imperfect language, and indeed if you know Special Relativity you should object to it. However, it does (sort of) make sense in the context of General Relativity.

How does this size compare to the size of the Universe as a whole? If we make the assumption that Ω=1.0133— the highest total energy density consistent with our current data, and thus the smallest closed universe consistent with our data— it's possible to calculate how big the Universe is. The result looks something like the following:

[Observable Universe in the Minimum Total Universe]
Click for a bigger version

In this picture, the surface of the sphere is meant to represent the whole Ω=1.0133 Universe. The parts that are "greyed out" are outside our Observable Universe; the patch at the top that you fully see is the Observable Universe. The radius of curvature of this universe is 120 billion light years. Its circumference is 760 billion light years. That means that the diameter of our Observable Universe is just 1/8 of the full length of a line you'd have to draw through space if you wanted it to connect back go yourself. The volume of the whole Universe is about 100 times the volume of our observable Universe. (If you object to the fact that 83 is not equal to 100, remember that we're not talking Euclidean space here, so your intuition for how radii and volumes of spheres relate doesn't entirely apply.)

Remember, though, that this is the minimum size of the Universe given our current data. Most of us suspect that the Universe is really a whole hell of a lot bigger than that, and indeed may well be infinite.

Size and Fate Are Separate

If you read almost any cosmology book written more than 12 or so years ago, and some written since, you will probably read something about a closed universe being one that recollapses, and an open universe one that expands forever. This is true only if the dark energy density of the universe is zero! Implicitly, those texts assumed that our Universe was matter dominated, and as such the geometry and fate of the Universe were linked. In a universe such as ours, where there is dark energy, the fate and geometry are not so tightly linked. Dark matter and dark energy both affect both the shape of the Universe and its ultimate fate, but they affect it differently. Exactly what will happen to our Universe depends on the details of what dark energy really turns out to be. However, for what most of us consider to be the most likely versions of dark energy, the Universe will keep expanding forever, with clusters of galaxies getting ever more and more separated. This is true whether the geometry of the Universe is flat, open, or closed.

References

The numbers for the current expansion rate of the Universe (used to derive the critical density) and for the limits on the curvature of the Universe come from the cosmological implications of the WMAP 7-year data as described in Komatsu et al., 2011, ApJS, 192, 18. The image used to wrap the universe sphere is the Hubble Ultra-Deep Field.

3 responses so far

"Whence Supernovae?" : Online public astronomy talk Saturday Sep. 11

The summer is over, and that means that MICA is resuming its activities. MICA is currently undergoing internal evaluation and evolution, but one thing that we're going to keep doing is our regular public astronomy outreach talks. This Saturday, I'll be talking about where supernovae come from:

There are two types of supernovae: thermonuclear and core-collapse supernovae. Both signal the deaths of stars as best we understand them. Thermonuclear supernovae in particular have been important as tools to tell us about the Universe. It was observations of such events out to great distances that told us the expansion of the Universe is accelerating. Yet, supernova science has a dirty secret: our model for how these events occur hasn't been observationally confirmed. In the last year, X-ray observations have called into question what many of us believed to be the primary mechanism for the production of such stellar explosions. In this talk, I'll give an overview of what we do know about these thermonuclear supernovae, and what the current state of knowledge is in figuring out just where they came from.

The talk is at 10AM pacific time in Second Life. Remember that Second Life accounts are free! Follow the link to sign up. Once you're in Second Life, follow this link to find the MICA Public Amphitheater, which is where the talk will be.

For more information, look at the MICA Events web page, and follow the links to see slides from previous talks, and announcements of upcoming talks.

(As for why I've been so quiet in the last couple of weeks: soon I will make a post about what it's like to teach on the block plan!)

Comments are off for this post

Radioactive decay rates... decreasing... because of... the Sun????

When I see something like this on Slashdot, I figure it's the usual crap science that somebody picked up. Only the press release it links to is from Stanford, which is normally what we think of as a respectable institution.

The basic idea is that tiny decreases in the radioactive decay rates of some isotopes have been observed. Presumably, these were statistically significant decreases, although I don't have details. One case of this seemed to correlate in time with a solar flare, and other cases seem to vary annually in ways that suggest that maybe, somehow, Solar neutrinos are interacting with these isotopes and influencing the decay rates.

I'm not going to believe this until I see strong evidence for it and until multiple groups have confirmed it. It would be cool if it were true, for it would tell us that neutrinos are interacting with other matter in ways that we didn't expect. But, for now, all I've been able to find are two papers (here and here). One is from a conference proceedings (and I've only seen the abstract); the other is a sort of response that has only been uploaded to the preprint server. In other words, as best I can tell, neither of these papers has yet been through any kind of peer review.

The latter paper— by Parkhomov, on the preprint server— has the full text available, although I have to admit I haven't read it. The abstract suggests, however, that he does not observe the effect mentioned in the conference proceedings.

So, we've got two papers: a conference proceedings, and a paper only uploaded to a preprint server, the latter contradicting the former. As such, I'm not going to get all excited about this until the paper trail gets a little bit more solid.

My prediction: this is going to go away and not turn out to be a real effect. But, I guess we should keep our eyes open in case it does turn out to be real. It would surprise the heck out of me if it were real, though.

6 responses so far

The Astronomy Decadal Survey

Every 10 years, a committee of astronomers gets together to solicit input from astronomers across the United States. This committee then sets forth a set of recommendations for the priorities in funding astronomy programs for the next ten years. By and large, the USA astronomy community buys into this effort, and accepts as a group the committee's recommendations as the recommendations of the consensus of the whole astronomy community.

Today (2010 Aug 13), the report for the 2010 decadal survey was released. Places to find information about it:

If you scroll down on the first page linked above, you can find the full text of the survey online for free. (I have just glanced at it, and it appears to be scanned images, at perhaps not sufficient resolution.)

So far, I've only looked at the presentation. There's not a lot surprising in here. It lists the primary driving science goals, which are things that are already the current "holy grails" of astronomy. It includes detection of gravitational waves (which is strictly a physics issue, but which can hopefully then be harnessed for astronomy), understanding the first generation of stars that caused the reionization of the Universe, understanding the Big Bang and also the present epoch of cosmic acceleration, and finding Earthlike planets outside our Solar System (but still within our Galaxy).

The funding recommendations are specific, at least for large projects. On the space side, the top priority is WFIRST, a wide-field infrared survey telescope, which would be used both for signatures of probing cosmic acceleration and for finding exoplanets (as well has being a "general use" infrared telescope that would complement the JWST-- the JWST already being under construction.)

The second priority is one I applaud: reinvigorating a previously existing NASA program of "explorer class" missions. These are small and mid-size space missions which don't have the cost of something like HST, JWST, Spitzer, Chandra, or WFIRST. Some of these missions have been extremely productive, and I'm glad to see the report listing these. I haven't read the full text for the justification of it, but I suspect the the flexibility for responding to new opportunities that come with new discoveries, together with the Explorer track record, are key.

After that are LISA, a space mission that will detect gravitational waves and really make gravitational wave astronomy possible, and then a powerful international X-ray telescope.

On the ground based side, the budget scenario is more depressing. While the presentation linked above seems to believe there is a decent chance that NASA will be able to fund the top priorities, the ground based large intiatives are more sketchy. There is this ominous statement: "In event NSF budget is as predicted by agency, there can be no new starts without closure of major facilities following senior review."

What are the new starts? Two things are listed. The first is LSST, which has been the bandwagon of astronomy for several years already. It's going to be an impressive project, an 8m telescope in Chile that will survey the entire night sky in four different colors once every four days. This is going to produce an utterly mind-bogglingly huge amount of public data-- and indeed, some of the technical challenges of LSST involve effectively dealing with all of that data. This is going to be an impressive data set that will be able to do a whole lot.

It won't however, be able to do everything. I have heard some astronomers say "the LSST will do everything". Sometimes they're theorists, but often they ought to know better. Yes, the LSST is going to be an amazing dataset that will "just do" some of what people do in special targeted projects right now. But there's a whole lot that it's not going to do by itself. I already know that there are astronomers out there (like, say, me) who are worried that bread-and-butter facilities used by lots of astronomers, especially astronomers who aren't at a Caltech or a Harvard (i.e. an institution with their own private telescopes), will be sacrificed on the altar of the LSST. (The key players in which you can be sure are going to come predominantly from institutions that also have their own private mid-size telescopes.) I really hope this doesn't have to happen. There is something called the "MREFC" -- Major Research Equipment and Facilities Construction -- an NSF budget thingy, the politics and economics of which I am clueless about. Ideally, LSST (and the other major projects) are going to be at least partially funded out of this, so that they don't have to eat up the entire NSF astronomy budget (leaving people who aren't key players on those huge projects completely in the cold).

The second major project mentioned is participating in one of the efforts to build a thirty-meter class "segmented mirror" telescope. This is a telescope like the Keck telescope, only with three times the diameter. Whereas the LSST will be surveying the entire night sky every four days, this giant telescope will be used for targeted observations of the most difficult targets requiring the best light-gathering power possible.

I've left out quite a number of projects in this brief driveby. Take a look at the presentation... and if you have a whole lot of time to blow, you can always read the entire report.

As astronomers always say with great optimism when one of these things come out, "it's going to be an exciting decade for astronomy." I have to admit, though, that with ongoing financial crises that don't seem to be recovering as fast as we'd hoped, coupled with the sure knowledge that in coming decades there's going to be ever more economic, political, and humanitarian turmoil as a result of anthropogenic climate change, that I won't be surprised if over the the public starts to lose patience with pure science in the face of increasingly urgent crises (that are upon us because we spent so much time ignoring science).

Update: for a more thorough summary, see what Julianne has written at Cosmic Variance here, here, and here.

Comments are off for this post

Why Our Universe is Almost Certainly Somebody's Simulation

Despite the title, this blog post is really here as a warning to others about trying to reason from first principles about the nature of our Universe...

We have already done sophisticated simulations ourselves that do the large scale simulation of structure in our Universe. Yes, this is for a small fraction of the total Universe, and, yes, it only simulates down to galaxy size. (That is, it doesn't simulate small enough areas to model the formation of stars or anything like that.) But the point remains that we're simulating the Universe.

We've also done "artificial life" simulations, in which we've shown that computer programs evolve. One of the most interesting physics colloquia I heard as a grad student at Caltech in the first half of the 1990's was about the Tierra project, that created an "environment" in which small computer programs competed for resources. It had a mechanism for random mutation, and over time the programs evolved to become more efficient.

Take these simulations, and allow for computer power to continue to improve as we've seen it improving in recent decades, and it really doesn't seem too much of a stretch to imagine that we could create a simulation of the local area of a galaxy that has the computer power necessary to evolve very complex "organisms"-- simulated organisms, that is. Code in the basic laws of physics, and give them enough space and computer power to evolve, and it could just happen.

Now, consider our Universe as we've observed it to be. We only know of one life-bearing planet, but we do know that there are lots of other planets in our Galaxy. And, looking out there, within the observable Universe (not even considering things so far away that light hasn't had time to reach us since the Big Bang), there are something like 100 billion galaxies like ours. Given how tenacious life is on this planet once it got started, even if it's rare for it to get started (say even only one or a few instances in our own Galaxy), there are certainly other planets out there with life on them.

If we use our statistical sample size of one, so far we see that a few hundred years out of a few billion years of evolution includes a technological civilization. That's a small fraction... but given the number of stars in our Galaxy, and the number of galaxies in the observable Universe, it means that there are other technological civilizations out there, somewhere. Let's assume that an appreciable fraction (i.e. anything more than an infinitesimal fraction) of these civilizations eventually are able to produce computation able to make the kinds of simulations I'm talking about above. It's been for the last 7 billion years or so that it's reasonable to suppose that life could arise on planets like our own. During those 7 billion years, there have almost certainly been lots of these simulations run. (What does "lots" mean? Well, the numbers going into this are very uncertain, of course, but it's probably somewhere between hundreds and billions.)

In other words: for one observable Universe like our own, in which intelligent creatures could arise, there are many simulations in which intelligent creatures could arise. Thus, any given civilization of intelligent creatures is by far more likely to be within one of the simulations rather than in the real Universe.

So, we're probably all part of somebody's simulation.

Right. Do I really believe that? No. I mean, maybe, but if so, so what?. If the simulation were done well enough, though, we'd have no way to tell the difference. So, at some level, trying to decide if we're somebody's civilization or if we're in a real Universe is mental masturbation. We see a Universe out there which has physical laws that are Universally obeyed. The process of science has a great track record in explaining how this Universe works and predicting what we will observe. Hence, it makes the most sense to go with the simplest explanation, that there is a real Universe and we are working on understanding it. If certain things about our Universe seem improbable from first principles-- for instance, why are the densities of Dark Matter and Dark Energy so close?-- it's worth thinking about whether that's a pointer to something deeper. But, at some level, the Universe is what it is, and it's worth trying to understand it without getting hung up on fundamental probabilistic arguments that lead us to thinking that none of it means anything anyway.

13 responses so far

The History of the Universe

You're going to read a lot about science on Scientopia. This post is to help you put it all in context. I'm not going to go into great depth, because that would take, well, the effort of humanity over many lifetimes. This is just a drive-by overview.

The slide below is one that I show in a substantial fraction of the talks that I give:

A History of the Universe

The first thing to notice about it is that it's a logarithmic scale. In the top line, at each tic-mark the universe is about 10 billion times older than it was a the previous tic-mark. That sounds like a lot, until you look at the labels on the tic-marks... the last mark on the top line is 109 seconds, or about 30 years.

Since the Universe is only about 14 billion years old, another factor of 10 billion past that step would take the Universe past the present day. Thus, the black circled region on the right of the top line is expanded into the bottom line, where each step is only typically a factor of 30 in age. This isn't exactly right, because really it's a step of a factor of 10 of redshift. That's what the variable "z" is in the figure, and it's very important, but I'm going to have to save it for another post. Likewise, the variable "T" along the timeline is the ambient temperature of the Universe, which also requires a lot of additional exposition, and so I will put that off to a future post. Continue Reading »

9 responses so far