Janek asks

I would be interested in a further post detailing roughly how we’ve calculated the size of the observable universe.

Okay. Actually I’m more than happy to answer this because the answer is relatively short and it’ll let me bunk off science posts for a week.

So once upon a time there was an astronomer called Edwin Hubble. Hubble’s career is notable for a number of firsts – such as the identification and use of the standard candles known as Cepheid variables found within the Andromeda and Triangulum galaxies to prove that these were indeed galaxies and not merely nebulae as had previously been assumed, thus incidentally proving that the universe extended beyond the bounds of the Milky Way – but the one that ended up getting his name attached to it was the discovery of something called the Hubble constant which basically defines our universe. Astronomers spend a lot of their time nailing down increasingly accurate values for the Hubble constant; part of the motivation for the whole CMB thing is to get better measurements of H_o.

So the Hubble constant is kind of a big deal, and what it is and how it works is best explained by telling the story of how Hubble found it in the first place. After having such success with the Cepheid variable approach to Andromeda and Triangulum (if you need Cepheid variables explained I go over them in one of my first posts here, and the Wikipedia article is here) Hubble decided to see just how many other galaxies he could find with Cepheid variables in them in order to build up a picture of what our universe really looked like. The Cepheids let him measure how far away these particular galaxies were, but while he was observing them he noticed something odd: the light from some of the more distant galaxies displayed a significant degree of redshift. It was already known that galactic redshift was related to their recession velocity thanks to work done by Vesto Slipher a few years earlier, and so Hubble was able to make a graph of galactic distance versus recession velocity that looked much like the following:

It’s a straight line relationship (albeit one with a fair amount of scatter), which is convincing evidence that the recession velocity of a particular galaxy is directly proportional to its distance away from . In other words,

where v is the recession velocity of the galaxy, d is its distance from us, and Ho is the Hubble constant. The expression above forms Hubble’s law, which states that the further away from us something is the faster it will be moving – and since that movement is caused by the expansion of space, Hubble’s law is effectively a relationship which governs that phenomenon. This means that what exactly the precise value of the Hubble constant is is going to have a profound impact on our views of how the universe is expanding, which is why scientists are so interested in obtaining increasingly accurate measurements of it. It also incidentally allows us to get a rough idea of galactic distance by measuring the redshift, converting it into a recession velocity, and plugging it into Hubble’s law along with the current value of the Hubble constant (67.80 ± 0.77 km s^-1 Mpc^-1 as of the most recent measurements obtained by the Planck probe).

So in theory when we look at things we have a fairly good way of figuring out how far away they are from us. All we have to do is find the thing that’s furthest away, plug its redshift into Hubble’s law, and from that calculate the approximate radius of our observable universe, right? Unfortunately — as with most things in astronomy – the reality is nowhere near that simple. Whenever you read an article reporting the discovery of the most distant astronomical object yet discovered, that article will likely quote two things: the object’s redshift, which is a thing that can be directly measured via observation, and its age, which can be reliably calculated from its redshift. What it won’t quote, unless it’s been written by an idiot, is its distance from us. This is due to several factors which complicate Hubble’s law immensely, most notably:

• That the simplified version of the law I described above – which incidentally is the one we teach to reasonably intelligent people up to and including undergraduate level¹    – assumes that the redshifted light we see from galaxies moving away from us is caused by a simple Doppler effect; that is, that the galaxies are moving away from us through space, like a boat sailing on the ocean. What’s actually happening is that the space itself is expanding and carrying that boat away from us on a tidal wave, which requires a far more complex treatment of the redshift.
• That the rate of galactic expansion has been constant and unchanging throughout its entire history. This is not true, as we now think that the universe is accelerating in its expansion. You know that value of Hubble’s constant we calculated just this year using the Planck probe? That’s the value of Hubble’s constant now. We have little to no idea what the value of Hubble’s constant was ten billion years ago, and the various cosmological models that attempt to establish this differ wildly in their predictions of how it’s changed over time.

These two factors together not only make the use of galactic redshift to calculate distance a rather iffy proposition at the best of times, but that second one also makes it effectively impossible to gauge the distance of the really old stuff we find. And if we can’t put an accurate number on those distances, this means it’s impossible to directly measure the volume of our observable universe.

If that’s the case, though, then why do astronomers throw around a precise number for the radius of the observable universe (currently about 46 billion light years)? It’s because they’re not using the term observable in the same way that you (or I) might. To them, “observable” does not mean “Can we see it right now?” Instead, the observable universe is simply the radius inside which light emitted from objects at some point over the entire history of the universe could theoretically reach us here on Earth. It doesn’t matter if the light actually does get here or not, or whether somebody manages to detect it, or whether we can make sense of what we eventually see; if the light has the potential ability to reach us, then the part of the universe that would hypothetically emit it falls within the bounds of the observable universe.

This simplifies the calculation of the radius of the observable universe immensely; instead of trying to establish actual physical boundaries you simply dial things back all the way to the oldest thing that could possibly exist and be observed and try to derive a distance measurement to that. In the case of our universe this happens to be the cosmic microwave background radiation, which is a collection of extremely redshifted particles released at the moment of photon decoupling². That 46 billion light-year number is derived from our observations of the surface of last scattering, a collection of points in the sky where photons from the CMB are only just now reaching us here on Earth. The great advantage of using the CMB to calculate this radius is that it isn’t just one object; since it exists over the entire sky it provides an awful lot of data which allows astronomers to average out those huge uncertainties in using redshift to gauge distance I described above. This means that it’s a reasonably solid number, although there’s no reason a more detailed observation of the CMB wouldn’t cause it to change in future.

So that’s how we arrived at a definition for our observable universe. There’s stuff inside it that we haven’t seen — and likely never will – because our instruments aren’t good enough, but that doesn’t change the fact that we could see it with sufficiently advanced equipment. It’s possible that the boundaries of the observable universe could move outwards if we figure out a way to see stuff without relying on electromagnetic radiation (observations of neutrino emissions and gravity waves could allow us to look back beyond the moment of photon decoupling, for example) but I wouldn’t hold your breath; that stuff is very definitely future science.

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The post The Hubble Bubble. appeared first on The Scientific Gamer.

In which I tackle one of the things that for a long time seemed like a colossal fudge to me, but which has an ever-increasing weight of evidence supporting it: inflation theory.

How big is the universe, really? Nobody knows, and it’s entirely probable that nobody will ever know. We’re limited in our measurements to observations of the bits of it we can actually see; all we have access to are the stars and galaxies which are close enough to have their light crawl slowly, painfully across the ever-expanding fabric of spacetime to be received by our telescopes within the 13.7 billion year lifetime of the universe. Anything emitting radiation which takes more than 13.7 billion years to get here will forever be locked behind a causal event horizon that we’re unlikely to ever penetrate, and not having access to an unknown proportion of the universe makes it pretty difficult to estimate the overall size of the thing. However, even the bits of it we can see raise some pretty interesting questions.

For starters, the  universe — everything we can see — appears to be about 93 billion light years across. A common misconception is that since the universe is 13.7 billion years old, and light travels one light year per year, then the observable universe must have a 13.7 billion light year radius. This is not true; the fact that the fabric of spacetime is stretching and expanding underneath the light as it wends its way through the cosmos means that by the time it reaches us the distance between us and the source has grown to several times what it was when the light set out on its journey. This also has the effect of stretching the light itself, spreading it out into longer wavelengths and shifting it into the red part of the spectrum; this redshifted light is what tells us space is expanding in the first place, and is distinct from the Doppler effect caused by a simple moving body which is used to explain shifting wavelengths to schoolchildren.

So that’s why the observable universe is so big. Thinking about it, though, this just presents us with more problems. Consider the case of two galaxies situated a long way away from us, one on each side of the Milky Way at opposite ends of the universe, whose light is only just now starting to be detected by our telescopes. Logic dictates that since the speed of light is an absolute limit and since the light has twice as far to go until it reaches the other galaxy, neither galaxy can see the other, and that the only reason we can see both is that we happen to be conveniently situated at the midpoint between the two. From the perspective of each of these galaxies the other is locked behind that causal event horizon I mentioned earlier. No information can travel faster than light, and so these galaxies are effectively out of causal contact — they cannot influence each other in any way, and never have been able to influence each other.

(Everyone with me so far?)

This gives rise to something called the horizon problem: if these two galaxies lie beyond each other’s cosmic horizons, and are completely isolated from each other and unable communicate information to each other in any way whatsoever, then why are they so similar? Everywhere we look in the universe we see two things: homogeneity, and isotropy. This is a fancy way of saying that forces act uniformly throughout the universe, and that when viewed on a large scale the distribution of matter and energy is astonishingly even (this is one of the reasons the increasingly accurate measurements of the cosmic microwave background are such a big deal, which we’ll get to later). Which would be fine, except the fact that large portions of the universe are (apparently) out of casual contact with each other means this should be impossible. Think about molecules of gas that have been pumped into a container; initially different parts of the gas will have different kinetic energies, and thus different temperatures, but eventually the gas will reach thermal equilibrium as the gas molecules bounce off of each other and communicate their energy to all the other gas molecules in the container. If two parts of the gas were isolated from each other in the same way that the portions of the universe containing these galaxies are, though, we would expect them to have different thermal energies and different temperatures since there’s no way for one part of the gas to communicate its thermal energy to the other. So it is with the universe in general: if these two galaxies are out of causal contact then they should have evolved along dissimilar lines and look at least broadly different to us, and each different region of space should have its own unique character. Instead, the whole damn thing is the same to us no matter which direction we look in.

This should be impossible — hence our calling it the horizon problem rather than the horizon curiosity or the horizon discrepancy or whatever — but obviously it’s happened somehow, and so we’ve had to come up with a mechanism by which different regions of the universe which have been out of communication with each other since the dawn of time have somehow acquired such similar physical properties. The theory goes that very shortly after the beginning of the universe — we’re talking 10^-36 seconds here — it underwent a phase of rapid and massive expansion, growing to 10^78 times the size in just 10^-33 seconds. Much like a scrunched up sheet suddenly being stretched out to its full flat length this period inflation had the effect of smoothing out irregularities in the structure of the universe, removing nearly all of the inhomogeneity and (eventually) resulting in the uniform structure we observe around us today. This explains why those two galaxies have evolved like the regions of space that contained them were once in causal contact with each other: they were, since the entire universe originates from this one small causally connected part of space. After this period of dramatic inflation the expansion of the universe slows down¹, achieving its current, relatively sedate character.

Inflation theory explains why the universe is homogenous, why it is flat (see the sheet analogy above) and why there are no magnetic monopoles when particle physics says there should be (too complicated to go into here). However it always seemed to me like a classic case of post hoc ergo propter hoc; writing the theory solely to fit observed phenomena without making any falsifiable predictions is bad science (hello string theory). It’s a good thing the cosmic microwave background is a thing that exists, then, since it provides actual experimental evidence that inflation theory might have something concrete to it. The CMB is residual thermal radiation left over from the formation of the universe, and it is very nearly uniform throughout the entire sky. When the CMB was first observed by the COBE satellite back in 1993, though, it was observed to contain tiny irregularities on the scale of one part in  10⁴; these irregularities just happen to match those we’d expect to see if you took a relatively small region of hot gas and suddenly expanded it to the size of a universe. Quantum fluctuations in the hot gas would suddenly be magnified to the point where they have a significant effect on the macro scale of things, and despite their tiny scale the resulting irregularities were sufficient to provide a starting point for the clumping together of matter to form dust clouds, to form stars, to form galaxies. This is one of the reasons the CMB is such an intense target of study for astrophysicists, with the far more accurate WMAP probe being launched in 2001 and the Planck spacecraft following that up in 2009; it basically explains why we even have a universe in the first place, and better measurements of those irregularities (called anisotropies) give us a much improved understanding of how things all began, and incidentally provide a compelling reason why inflation theory might not be such a bit of flim-flam after all.

(Of course exactly how and why inflation happened is still a bit of a mystery. But then science wouldn’t be any fun if we knew everything, would it?)

The post Inflation Theory. appeared first on The Scientific Gamer.