One of the more interesting conclusions is that the standard lecture format of undergraduate courses is poorly matched to the way people actually learn and retain scientific understanding - in fact, often students come out of these classes thinking more like a "novice" scientist than when they started. By novice, I mean the following: there are certain ways that an expert in a scientific field thinks about that field that are very different from the way a novice thinks about that field. For example, a novice believes that scientific content consists of isolated pieces of information that have been handed down by some authority and require memorization. An expert believes that scientific content consists of a coherent structure of concepts that build on each other, being accurate descriptions of nature and established by experiment. Sad to say, but students coming out of intro science classes are even more likely to believe that science is bits of memorization based on nothing more than faith, as opposed to a coherent argument based on reality.

These results resonated with me, because in this blog, I've tried to emphasize how one builds to a conclusion (like "dark matter exists") from a variety of physical observations and theories (like the 20 posts that followed my original three). I'm sure that sometimes (often?) I fail in communicating this key point about the way I look at physics, but that is ultimately the goal of this blog. And when I start writing it again regularly, I'll try not to forget that.

Finally, Wieman and his group have developed a series of simulations for students to play with that really demonstrate key concepts of physics. One example that caught my eye is something that I tried to explain in a post a few months ago, the photoelectric effect. If a reader really wants to understand what I was trying to say in that post, I highly recommend trying out Wieman's simulation, located here. Especially you, mom (although she's currently in India right now, and therefore not reading this blog at all. By the time she gets back, I'll be writing more regularly...)

Eventually the universe began expanding and cooling.* As it did so, the ions and free electrons "recombined" (during the time romantically referred to as the era or epoch of recombination) to form neutral atoms, after which photons no longer scattered (romantically referred to as the "surface of last scattering," a phrase that always puts me in mind [for whatever reason] of the "Last Homely House" in the Lord of the Rings [yes, I am a physicist and I love Tolkein and I write a blog for my mom]). Those photons remain unmolested since that time.

*Aside: my mom asks in a comment "why did the universe cool?" The short answer to that is because it expanded. Temperature is in some sense a measure of how many collisions occur in a space [recall my analogy about money in the last post] - at high temperature, there are lots of collisions. Suppose we expanded the space, but kept the number of particles the same. All of a sudden, the number of collisions would go down, because the particles wouldn't be able to find each other to collide. Therefore the temperature drops. Many [if not all] refrigerators operate this way, by allowing a compressed gas to expand rapidly and thereby drop in temperature. A follow-up question is then "why did the universe expand?" and I have a less satisfactory answer to that. My best explanation is that there was a lot of energy released in the big bang, and it was that energy that drove the expansion. We may have more to say on this subject at later times).

In the mid 1960s, a group at Princeton led by Robert Dicke began building a radiometer to detect the CMB. At the same time, Arno Penzias and Robert Wilson at Bell Labs observed some noise in a sensitive antenna they were planning to use for radio observation. After careful work, they decided that this noise had to be external and coming from all directions in the sky. Eventually they made contact with the Princeton group, and this background noise was interpreted as being the CMB (after first talking to Penzias and Wilson, Dicke supposedly got off the phone and told his collaborators, "Boys, we've been scooped"). The two groups published companion papers on the observation and the interpretation, and in 1978 Penzias and Wilson received the Nobel Prize.

Although important, that first observation is not on its face all that exciting. The CMB is remarkably smooth or isotropic (meaning it looks the same in all directions). The picture below shows what Penzias and Wilson might have seen if they'd been able to observe the CMB in all directions (courtesy www.map.gsfc.nasa.gov), and it's hard to see what all the fuss is about. But I'll leave that for the next post.

Before going forward, I'll just mention the methodology at work here. With some notable exceptions (like DAMA, for example), most dark matter experiments work by pushing down the backgrounds as much as possible to reveal the dark matter signal that may or may not be there. Therefore, the majority of work goes into understanding exactly how much background might be left over, with the goal to have "zero" background during the time the experiment is looking for WIMPs. It is generally impossible to have "zero" background - what is possible is a very small fractional expectation of a background. For example, CDMS expected 0.6 background events in their data set. What that means is they studied all possible sources of background using calibration sources and simulations and estimated that in the amount of time they looked for dark matter, on average they would see 0.6 background events.

When they looked at their data, they found 2 events. One can calculate the probability of having 2 background events given an expectation of 0.6, and CDMS has done this; they determined that there was about a 25% chance that the two events could be a fluctuation on the background, leaving a 75% chance that the 2 events were something new, like a dark matter interaction. This is not enough significance to claim a discovery (most physics experiments require a measurement with over a 99.999% chance of being something new before a discovery can be claimed), but it is exciting. Up until now, most experiments have never claimed to see something over background, so these results are a sign that there might actually be something to the last five years of my life. Of course, it's always possible CDMS underestimated their backgrounds.

As mentioned in the NYTimes article, we'll now wait with bated breath for the results from XENON100 in Italy, which should be the next experiment to get results. If the 2 events in the CDMS data are real dark matter events, XENON100 should be able to find out. And then my experiment should follow that up with our own search in a year or two. It's a good time to be involved in dark matter - who knows, maybe we'll figure out one of the biggest mysteries in physics from the last 70 years before the next presidential election.

First, I'm going to define "ionization" by referring briefly to the Bohr model I described here. Ionization is the process by which an atom loses (or gains) an electron and becomes charged. In the old post, I compared an atom to a building with an elevator which could transfer people (or electrons) between discrete levels. Using that image, ionization would occur if the elevator dropped you off on the roof, at which point you could leave the building entirely. As long as you were within the building, you remained trapped, just as an electron remains trapped by the electric field of the protons at the center of the atom (or as the Earth is trapped by the gravitational field of the Sun). On the roof, however, you have gained enough energy that you can leave the building; if an electron gains enough energy, it can escape from the electric field and be free, leaving the atom positively charged. This positively (or negatively, if it picks up an electron) charged nucleus is referred to as an ion.

One more thing that we should keep in mind about charged particles is that they interact rather strongly with light (or photons, as faithful readers will remember that light is a particle called a photon). A photon traveling through a cloud of charged particles will scatter many times, so that the photon that appears on the other side of the cloud will have very little to do with the one that entered it.

I'll now switch gears completely to describe the relationship between temperature and money. Suppose my mother in her younger days was living in a rather small apartment in London. My mom is a rather accomplished amateur interior decorator, and we'll assume she had those skills in her flat in London. I'm going to go one step further and ascribe a fickle nature to my mother which I would like to emphasize for posterity that she does not in actuality possess; in my hypothetical situation, this invented nature of hers combined with her penchant for interior design led her to continually change her mind on how she wanted to decorate her small house.

Ok, now we'll add money. If my mom had a lot of money, she could indulge her ever-changing whims. One week she could go for ultra modern and the next for antiques. Basically, the furniture would be coming and going, styles would be in and out, her little flat would be in a constant state of flux. Suppose, however, that she suddenly lost all her money; my mother would be forced to pick the cheapest option with which to decorate her house and stick with it. While she may still desire a change, she would have to settle for the most practical option.

In the physics of chemical reactions, temperature is like money. If my mom has money, she can change her flat at will - she can bring in new stuff, get rid of the old stuff easily whenever she wants. If the temperature is very high, a chemical reaction can occur easily and can go in both directions. Specifically for the purposes of the CMB, at high temperatures atoms can easily lose electrons and become ionized, before quickly finding other electrons freed from other atoms to become neutral again. In the early universe, the temperature was very hot and this was happening all the time; the universe was a soup of charged particles and photons bouncing off each other constantly. In particular, the photons never went very far before hitting another charged particle.

However, when my mom no longer had any money, she was forced to pick the cheapest option and stick with it. Similarly, after the big bang the universe began expanding and cooling. As the temperature dropped, it was no longer so easy to ionize atoms. Eventually, the universe cooled enough that it dropped out of thermal equilibrium. That meant that all the atoms had to neutralize, because a neutral atom requires less energy than an ionized atom and free electron, and nature prefers to minimize the amount of energy in any system (just as my mom had to settle for the cheapest decor). Once the atoms were all neutral, any photons that were bouncing around no longer had to travel through a soup of charged particles. In effect, the photons that were produced just as the universe become neutral did not scatter again. These photons are still traveling through the universe and we can detect them now; they are the CMB. They still contain information from the last time they interacted with matter, which was 13 billion years ago, right when the universe became neutral.

Therefore, my next topic will be another argument for the existence of dark matter, and in my opinion one of the cooler phenomena in physics (I understand that my stating something is "cool" is not necessarily sufficient evidence, but I will try to explain) - the Cosmic Microwave Background or CMB for short (another good name, by the way).

In very broad strokes, the CMB is an echo or an image of the universe as it was 13 billion years ago (when it was only four hundred thousand years old - relative to the human lifespan, it's like we have a baby picture from when the universe was 1 day old). Much as archaeologists can learn about prehistoric epochs from fossils (or mosquitos trapped in amber) and geologists can infer the climate from ice cores that have been frozen for thousands of years, physicists can discover information about the contemporary contents and future evolution of the universe by studying the CMB.

So what is the CMB? It's a sea of light streaming across the universe in all directions that was produced 13 billion years ago and has not touched anything since that time. This light isn't visible to us, because its wavelength (remember these posts) is in the microwave band (i.e. too long to be visible by our eyes, but with enough intensity [thankfully not present in the actual CMB or else we'd all be in trouble], perfect for heating up instant hot chocolate [too quaint?]). It's always there though, and like a photograph, each individual photon contains an image of the universe shortly after the big bang.

The illustration (click for a bigger view) shows the history of the universe from the Big Bang to the present. The CMB is produced at the green and blue ellipse during the very early universe and detected in the present by the satellite labeled "WMAP."

I'll stop there for now, but hopefully the reader will want to know more. I'll probably refer to two web sites a great deal in the coming posts. The best existing CMB experiment is the Wilkinson Microwave Anisotropy Probe, or WMAP, and they have a great resource at http://map.gsfc.nasa.gov/ from which I've taken the illustration. The second web site is where I learned most of what I'll be talking about, the homepage of Professor Wayne Hu of the University of Chicago. He's done a great job explaining all the details and implications of the CMB in simple terms, and I hope to do half as good a job.

This is the goal of this blog - to try and describe all the pieces that go into a physics argument in a way that's understandable. My hope is that interested readers will see that while specific parts of physics may be esoteric or complicated (i.e. high level math), in a general sense we're making deductions in a way that is very similar to those made in almost any other field of study.

We know the equation of circular motion, F=mv²/r. And by hypothesis, the only force acting on the object in orbit is the force of gravity, F=G*m₁*m₂/r². In this case, m₁ is the mass of the galaxy, and m₂ is the mass of the object. We equate the forces, so mv2/r = G*m₁*m₂/r². Now, the mass from the circular motion equation is just the mass of the object in orbit, so m₂ will cancel. All that remains is to solve for the velocity, since that's what we measure using the Doppler effect and red shift.

m₂*v²/r = G*m₁*m₂/r²

First, divide both sides by m₂

v²/r = G*m₁/r²

Next, multiply through by r

v² = G*m₁/r

Now, take the square root of both sides

v = Sqrt(G*m₁/r)

And that's it. We have derived that the velocity of an object in orbit about a galaxy should be proportional to the square root of the mass of the galaxy divided by the orbital radius. There is one more thing we should be aware of, which is that I haven't made any assumptions yet about the size of the mass of the galaxy. A galaxy is a very large thing, and what happens if you're inside part of it? For example, the Sun and the Earth are somewhere inside the Milky Way galaxy. We do orbit the Milky Way center, but part of the Milky Way is outside our orbit. The answer is that in this case, m₁ refers the total mass inside the orbit. It doesn't matter how spatially extended it is in space, as long as the object in which we're interested is outside of the galaxy, the equations are fine. And since I'm particularly interested in the mass of the bright part of the galaxy, it's easy to know when we're outside that part, so everything holds.

Now, let's look at a plot. If all the mass were in the bright part of the galaxy, then outside the bright part (say a radius of 100, just to make the plot look right), from the last equation, we would expect the velocity to fall like 1/Sqrt(r) (G and m₁ would be constant). That would look like this:

Instead, we measure a flat line, like this:

Therefore, by deduction, we know that either Newtonian gravity is wrong (a possibility, I'll admit), or that there is more mass than we thought, mass that is not contained in the bright part of the galaxy. In fact, we know the distribution of that mass, as it has to increase like 1/Sqrt(r) or else the the velocity would not be flat.

This is what some of the actual data looks like:

These are measurements of galaxy rotation curves (Begeman, Broeils and Sanders, Mon. Not. R. astr. Soc., 1991, 249, 523). I apologize for the image quality, but velocity is on the y-axis and radius is on the x-axis, and all the black points are actual measurements. You can see at small radius the velocity increases. This is where the bright part of the galaxy is, and as the radius increases, we are containing more mass in the orbit. At larger radius, we would expect to see the velocity drop. But instead, it stays constant. The dashed and dotted lines are the the components of the mass, the bright part and the dark part. This data provides evidence that there is matter that we are not seeing, that is not interacting with light, but is dark matter.

I think I would like to know what the consequences are of discovering or measuring dark matter. Also, does what you are doing have any relation whatsoever to things like the Hubble telescope or general space travel that people seem to be doing more and more of? Might your discoveries, for instance, give us an idea of the future of the universe as we know it?
xox MOM

These are good questions. What would be the consequences of discovering dark matter? When people ask me this question, one of the first things that I have to emphasize is that there are no foreseeable applications to my research. Nothing obviously useful will come out of it, unlike, for example, research in quantum computing or more applied fields. Now, there's always the chance that something we develop in trying to detect dark matter could be useful to society (for example, there are a number of ideas to use technologies developed in this field for detecting nuclear weapons at border crossings), but I believe that justifying this research by appealing to possible applications is dishonest.

The only reason I have for searching for dark matter is to increase our ("Mankind's" with a capital M) understanding of the universe. 23% of the universe is dark matter, and 85% of all the matter is dark. There are two aspects to this. The first is humanity's standard musings over "why are we here? how did we get here?" Dark matter is a key component to the evolution of the universe, influencing the expansion rate of the universe and the way matter first clustered to form stars and then planets. If it didn't exist in the way that it does, the Earth would probably not exist and neither would this blog. I'm touching up on religion again, here, which interestingly enough seems to happen quite a lot in this blog.

The second aspect that interests me is that I just think it's cool to know more about the way the universe works. Why is there more matter than antimatter in the universe (another great physics question, as naively we might expect identical amounts in which case we would have all disappeared in a puff of energy a long long time ago)? What was the big bang? Does dark matter really take the form we think it does (I sort of like the fact that we can predict the existence of a particle and then go out and find it, which has happened many times in the past)?

To answer my mom's other questions, this is very closely related to the Hubble telescope in the sense that a lot of the evidence for dark matter comes from telescopes like Hubble, and that telescopes have a chance to detect dark matter in a completely different way from us. Not so much space travel, which in my mind isn't so interesting.

The picture is a simulation of structure formation in the universe. All the filaments and bright sports are made of dark matter (Courtesy http://www.casca.ca/ecass/issues/1997-DS/West/ and interestingly enough titled "hugh.gif")

I have been working up in Sudbury, Ontario for the past two and a half weeks at the underground lab I mentioned in the overview posts (linked from the right of this blog). What is it like? Well, it's pretty cool, I have to admit. Life at the lab is in many ways defined by the cage schedule of the mine, as I'll explain. I get up before 7, because I have to catch the 7:30 cage underground. If I miss that cage, I'm pretty sure that I won't be able to go under on that day. So, I'm up at 7 (I don't have to shower, as you'll soon see), drive to the mine, go to my locker. I take off the civvies, and put on a mining jumpsuit (lots of reflective tape), hardhat, glasses, wellington boots. I get my head lamp (there's a slot on the hard hat for the head lamp to slide into), tag in (the mine has a lot of safety rules, but the main one is the tag-in and tag-out system. If you go underground, you have to be tagged in, and then when you come back up you tag out. That way, when the company wants to do some blasting, they can make sure no one is underground. If you forget to tag out, or tag out the wrong person, they are not allowed to blast. People do get calls at 4 in the morning about being tagged in, you do not want to be the person who forgets) and wait for the cage. When it arrives, we all pile in. The cage is very cage-like. It's maybe 5 ft wide and 15 ft deep, made all of beat-up metal, and the miners and lab workers pile in in rows of 4. Sometimes, when it's full, we'll be squeezed all the way in, and I hear stories that "in the old days, we used to put 5 in a row." Then we drop. A couple of people will put their lights on at this point, otherwise we'd just be going down in the dark. We stop at a few places along the way for people to get off at various levels (if we stop too many times, that's known as a "milk run"), and then finally, we arrive at the 6800 ft level.

Next, we have to hike about 1.5 km down a drift. The drift is 10 ft wide maybe, with screen or "shotcrete" helping to support the walls. We'll hike half the way down, and then we call ahead to the lab where someone has advanced ahead of us with an air monitor (the modern version of a canary) to make sure it's safe to proceed. Sometimes there will be water on the ground to tramp through, and there's evidence of mining all over the place. Eventually we arrive at the lab. At this point, we take off our clothes, and take the garbage bags off anything we've brought down with us. We shower (there's a built in shower every morning, which is nice when you're getting up so early [at least for a grad student]) and put on a clean jumpsuit and hair net, etc. The entire lab is a "clean room," which means that considerable effort has gone into making sure that all the dirt and dust picked up on the walk through the drift is cleaned off before we enter the lab. Hence the cleaning precautions.

So now we're in the lab. The walls are all whitewashed (but not straight, since it's a cave, essentially), and most of the ventilation and wiring is visible. It looks like the set of a sci-fi movie. So off I go to my experiment where I do the day's work (fiddling with high voltage power supplies, making sure the detector stays cold, that there is enough liquid nitrogen, doing various radioactive source calibrations, etc). Then, 45 minutes before the cage up time (again, there's a fixed schedule. I can't just come in and out whenever I want), we go through the reverse process, take off the lab clothes, put back on the mining gear, hike back out through the drift, etc. And you'd better make that cage.

So up we go back to the surface (there's a signal system for the cage, and you always know that when they signal 2 short pulses twice, the next stop is the surface), take off the mining gear, shower again (I love that the day is bracketed by showers), and voila, life underground at the lab.

It's a good thing I'm done this little summary, because a liquid nitrogen fill just completed so today's tasks are all done and the detector will survive the weekend, and I have to start cleaning up to catch the next cage out (I'm taking the early cage today).

I have not posted (I can't quite bring myself to use "blogged" as a verb in the past tense, but I should probably get over such squeamishness) in almost a month now, for which I apologize. My excuses are standard - my work intruded. In the last month I have started looking at data from a new run and been to a conference (I've also been to my 10th high school reunion), and I am now visiting the mine in Canada I mentioned in one of the original posts to help run an experiment underground. Enough about my current activities, however, as it's time that I finally finished off the series on galactic rotation curves and Newtonian gravity. Unfortunately, I've realized that I still can't finish this in one post, but we'll get there eventually.

Mother, I'm sorry to say that we're going to need equations, but hopefully it won't be so bad. We'll start with Newton's Second Law of Motion, which says that F=ma. That's it. Force equals mass times acceleration. This law governs almost all macroscopic kinematics (a fancy word for the physics of motion). When you apply a force to something (say by pushing a book across a table), the book will accelerate with a particular acceleration depending on its mass. As with a lot of physics, this is intuitive, especially if we rewrite the equation as a=F/m. If I push a very light object, I can accelerate it rapidly (m is small, so the acceleration is big). If I try to push a heavy object like a car, I can barely move it at all (m is very large, so the acceleration is small). Likewise, the harder I push (more force), the faster it will accelerate.

Ok, next we'll look at circular motion where I'm presented with a pedagogical dilemma. Ultimately, I only really want the equation of circular motion (F=mv²/r), but I can't very well just state the equation without trying to explain it. I condescendingly fear, however, that any attempts at explaining it with a single paragraph in this blog will only result in confusion (which raises a question concerning the wisdom of the entire endeavor, but I'll ignore that). But here goes. In a circle, there are two important directions: the radial direction, which points from the center of the circle to a point on the circle itself, and the tangential direction, which is perpendicular to the radial direction. At any point on the circle, these directions have the same relationship to each other.

The key to circular motion (i.e. when an object just travels in a perfect circle forever and ever) is that the instantaneous velocity is always tangential to the circle while the acceleration is always radially inward. Imagine that my mother is on a ferris wheel. At point "A" on the ferris wheel, she is travelling straight to the left. At point "B" on the wheel, she is travelling straight down (for example, if she were to jump off the ferris wheel at that point, she would drop straight down). Likewise at points "C" and "D," she is travelling to the right and straight up, respectively. The point being that she is always moving tangentially and never radially.

The strange thing is that the force she experiences (the "centripetal force") is always radially inward. At this point, I think I may just have to revert to a "trust me." It's a matter of mathematical fact that to keep her motion circular, she must experience only radial forces. And if you work out the math, the necessary force is F=mv²/r; in other words, the force required to keep her in circular motion is proportional to the square of her velocity divided by the radius. This does make sense intuitively. The faster she is moving, the more force is required to get her to go around the circle. And, the larger the circle, the less change is required to keep her in orbit.

I'm very unsatisfied with that explanation, but I'll leave it for now. The final equation we need is Newton's equation of gravity. This is an empirical law (keeping in mind the discussion in the prior post). Newton discovered that two masses (call them m1 and m2) separated by a distance (call it r) will exert an attractive force on each other, F=G*m₁*m₂/r², where G is a constant that is experimentally determined and set by nature. Every mass in the universe exerts such a force on every other mass and vice versa. However, the value of G is very small, so it takes either an extraordinarily large mass (like the Earth or the Sun) or an extremely small separation to observe this force. But that's all there is to Newtonian gravity.

I fear that I got a bit ahead of myself at the end of the last post on the spectral lines of hydrogen. To fully close the circle between dark matter and everything I've been talking about in the last few entries, we do need to cover Newton's theory of gravity. Therefore, I will try to do so now, so that we can put this particularly sequence to rest.

First, on talking with a friend earlier today, I was asked, "I always hear the term "Newtonian gravity: is there any other kind?" This is exactly the kind of question I need to be asked, because otherwise I forget that I've been studying this stuff for 10 years. The answer is yes, there is another kind of gravity; more precisely, the answer is that there is a more complete form of gravity, namely Einstein's Theory of General Relativity (and possible string theory is a yet more complete form, although I'll leave that argument to Brian Greene's The Elegant Universe). Newton observed the effects of gravity and described those effects using math. However, he didn't describe how gravity works. To borrow an analogy directly from Greene's book, when my mom (and no, Greene didn't refer explicitly to my mom in his book [he did address himself directly to "you," but I don't think my mom has read it]) uses her computer, she doesn't know how it actually works (i.e. little electrical signals flashing through a chip). She only knows how to use it to write an article or to read this blog (sometimes she is unsure even how to do those tasks, at which times, coincidentally enough, she often checks in with her favorite son). Newton gave us a personal computer (gravity) and told us how to use it to write articles and check email (the equations), but he didn't tell us how it actually works (how is gravity transmitted, or how does the apple "know" it has to fall to the ground?).

In addition, Newton's formulation was only an approximation that was incorrect on certain scales (which are largely inaccessible to us and unobservable in our day to day lives). For example, I'll poach another commonly used illustration; from far away, a Seurat painting looks like a smooth picture. Newton's theory of gravity is accurate when viewed "from far away," which more or less is the point from which we all experience gravity. Up close, however, and all the dots become clear. While Newton got the big picture right, he did not describe the dots. General relativity can handle both the smooth "far away" view, but also the rough "up close" view.

That's why we can talk about "Newtonian gravity." For all intents and purposes, we could just talk about gravity and we'd all be referring to Newton, but since this is a physics blog, I figure I should try to be more precise in my language. In the next post, I'll actually use Newton's equations to look at the rotation of galaxies.

The image of Seurat's Sunday Afternoon on the Island of La Grande Jatte was scanned by Mark Harden

We are now talking about "spectral analysis." The OED (do you like the use of the OED, mom?) defines spectrum in a couple of ways, but I'll print two of them here. First, a general definition for physicists: "An actual or notional arrangement of the component parts of any phenomenon according to frequency, energy, mass, or the like." Physicists often talk about an energy spectrum, a frequency spectrum, etc., and what we mean is exactly the definition given by the OED - breaking up some group or data set into its components.

A second definition is this: "The coloured band into which a beam of light is decomposed by means of a prism or diffraction grating. Also, a dark band containing bright lines produced similarly; such a (coloured or dark) band, or the pattern of lines in it, as characteristic of the light source; hence, the pattern of absorption or emission of light or other electromagnetic radiation over any range of wavelengths exhibited by a body or substance." Now this is exactly what I'm talking about. The general idea is familiar - anyone who has seen a rainbow has seen light broken up into its various colors. When applied to the hydrogen atom, the spectrum is the characteristic colors of light that can be emitted or absorbed. Using the Bohr model, we can predict which wavelengths can interact with hydrogen (this may be the subject of another quantitative post).

At right is an image of a tube filled with hydrogen that is being excited by high voltage (taken from here). The light passes through grating to separate the spectral lines, with the result being the smaller lines shown to the right. All hydrogen, anywhere in the universe, will emit these colors when excited.

And now we finally get back to dark matter. In the first post, I talked about how we can tell how fast the galaxies are spinning using redshift or the Doppler effect. That's because any hydrogen in those distant galaxies will have the same spectrum as hydrogen on Earth, which means the hydrogen in the distant galaxy is emitting the same wavelengths of light that we can measure here on Earth. As discussed in the Doppler effect posts, since light is a wave, its wavelength will be shifted via the Doppler effect depending on the speed of the source. Because we can measure the relationship between the different lines, we can use the observed shifts to deduce the rotational speed of the source galaxy (one side spins away from us, one side spins towards us). And voila, now we know that the galaxies are spinning too fast and that there must be matter we aren't seeing (well, we would see that if we understood Newtonian gravity, which will be the topic a future post, I'm sure).

The above plot taken from the website of an MIT experiment, FIRE, shows the redshift for three real objects. Why is it called "redshift?" Most objects in the universe are moving away from us, and when the source of light is moving away, the light shifts towards the red end of the spectrum (or towards lower energy).