Physics for my Mom

Update on my job

2010-10-17T14:45:00.000-07:00

I'm still trying to decide what my next topic should be, but I figured I'd tell everyone a little about what I've been doing in my new job. As we might recall, I started a postdoc in July at Fermilab outside of Chicago. In my new experiment, COUPP, I'm still looking for dark matter, but the way we go about it is very different. It's probably worth reiterating how the whole dark matter search works, or you can also read over some of the summary posts on the side bar. To recap a portion of those entries, we are pretty sure that dark matter of some kind exists, and we know this gravitationally; I've described in detail rotation curves and the CMB in prior posts, and there are other observations that support the conclusion that there is some form of matter out there that we can't see.

There are certain classes of theories that predict dark matter might be a new type of particle, one that only interacts weakly. These particles would theoretically be all around us, just like neutrinos produced in the atmosphere and the sun (the villains in the ridiculous, apocalyptic movie 2012 from two years ago from whence comes the picture to the right, that I was quite happy to find my father had rented when I went home for a weekend. A friend of mine at Fermilab, Dave Schmitz, blogged about the physics behind the premise to 2012 back when it came out) that constantly stream through. Every once in a while, we expect these hypothetical particles to hit something on earth, and so we build detectors to catch those hits. At this point, we know that dark matter can't interact more than a handful of times per year in the most sensitive detectors we know how to build. Unfortunately, these detectors are also sensitive to any other radiation that's flying around - say at a rate of about 100 times per second. Or 4 billion times per year. And we are looking for a handful of events.

This is the problem with backgrounds that I went into in detail in those early posts. I said there that the majority of those backgrounds are "electronic recoils," where the radiation has hit an electron in the detector. My new experiment is something called a bubble chamber, which was used a great deal in the heady days of high energy particle physics in the 60s and 70s. They aren't used for high energy work anymore, but we've repurposed the technology for our experiment. In our bubble chambers (and I think I will have to talk about the physics a little at some point), we can set it up so that electronic recoils don't do anything in the detector - we are effectively blind to the main background to dark matter searches!

That's probably a bit more setup than I wanted. Because what I really wanted to say (in one paragraph only) was that I spent all day Friday in a jumpsuit (I do love the jumpsuits) with a full face mask respirator (requiring me to shave the beard I had grown while writing my thesis) trying to shove a 1/2" steel pipe down the neck of an incredibly expensive, delicate, and very clean (for radioactivity purposes) glass bell jar surrounded by a stainless steel vessel (making it rather difficult). And failing. Physics isn't all math and equations and brilliance. In fact, for me, most of the time, it's working down in a tunnel doing plumbing, rebooting computers ("wait, it's not working? Have you tried rebooting it yet?"), or trying to carefully put a steel tube in a pressurized glass jar filled with red fluid that might or might not contain HF acid and a poison gas used in WW1. So all in all, pretty fun, even when it doesn't work.

My experiment

Angular scales from the CMB

2010-09-06T08:20:00.000-07:00

The physics of the CMB is extremely rich, and I won't do it justice in this series of entries. However, I do want to give one example of how the spectrum of the CMB fluctuations and in particular the location and size of the peaks gives us information about the universe. Let's look at the results from analyzing the CMB maps using the spherical harmonic functions one more time:

As I said last time, this plot tells us about the correlations between different regions of the sky. What exactly does that mean? Well, to the naked eye, the CMB map looks fairly random - some parts are blue, some parts are green, but there's no obvious pattern. What the above graph tells us is that regions of the map separated by 1 degree are actually related to each other. The amplitude of the spherical harmonic with a "frequency" of 1 degree is very high compared to other frequencies, just as the amplitude of the sine curve with the same frequency as the A note was very high when I was decomposing the A chord using Fourier analysis.

The next question to be asked is, "so what?" And the answer relates to stuff I was talking about a while ago in the posts on Gravitational Potential Wells. There, I talked about how early fluctuations in the gravitational potential created oscillations, like balls rolling in and out of a divot. In the early universe, small gravitational fluctuations of all shapes and sizes were created. These fluctuations expanded and contracted, interacting with photons to make hot and cold photons, up until the moment of last scatter when the universe became neutral and no longer interacted with photons at all, creating the CMB. What the large peak at 1 degree in the CMB spectrum tells us is precisely the size of the fluctuation that oscillated one time before the moment of last scatter.

Let me see if I can come up with an analogy for how that works that makes sense. Imagine watching a swimming race where the swimmers do laps in the pool. Let's suppose this race includes swimmers of all abilities, so some are very slow and some are like Michael Phelps. The race starts with all swimmers along the starting line, but as time passes, the swimmers spread out according to their abilities. However, because they have to swim laps, the absolute distance between the swimmers and the starting distance is always less than or equal to the length of the pool - in other words, you can't tell the fast and slow swimmers by how far they are from the start, since there will be times when the fast swimmer is heading back to the start line while the slow swimmer is still at the far end of the pool and vice versa.

From Ironman blogger, Chad Holderbaum

Now let's stop the race and have each swimmer stop exactly where they are. They will be spread out all over the pool. But, a few of them will be near the far end of the pool. And some of them, the ones whose pace was exactly right will be exactly at the far end of the pool. If we measure the maximum fluctuation in the position of the swimmers, we find that all the swimmers who exactly swam the full length of the pool have that maximum fluctuation - they are farthest from the start. The CMB measurement is making a similar type of measurement. It measures the size of the gravitational potential well that was maximally expanded when we stopped the race, or when the CMB decoupled from the universe. Therefore, we can calculate the size of the pool - or the size of the universe at the time of last scatter. The location of the first peak in the CMB is like a ruler for the early universe. And that ruler helps us find all that other information I've been talking about.

As usual, I fear I have not fully done the physics justice in this rather slow developing and superficial treatment of the problem. However, I think I'm done with the CMB for now. If you want to learn more about it, I do recommend Professor Wayne Hu's excellent website at http://background.uchicago.edu/~whu/ which explains the CMB much better than I could hope to.

Understanding the CMB

2010-08-30T15:03:00.000-07:00

How do scientists understand the CMB? At this stage, I think we can try to outline the whole process. Over a year ago, I described the CMB as a sea of photons streaming through the universe, not interacting with anything until they reach us on earth. These photons are microwaves and can be picked up by radio antennas; at one point in time, the snow that people saw on their old television sets with bunny-ear antennas contained a component of the CMB. As I described here, the first group to observe the CMB initially interpreted it as an unexplained source of noise in their state of the art radio equipment.

To make the very sensitive measurements necessary to understand this today, we need to measure the CMB in space, where there is less interference from man-made radio backgrounds and the atmosphere. Therefore, in the 1990s, a group of scientists developed the WMAP satellite, which was flown by NASA at the beginning of the 2000s and has been collecting great data ever since.

(Personal aside: the WMAP satellite was originally the MAP satellite. The W was added in honor of Prof. David Wilkinson of Princeton University who passed away in 2002. I had the good fortune of being taught by Dave as a sophomore in college when I didn't know the first thing about experimental physics, and I also worked with him for a summer on the Search For Extraterrestrial Intelligence project [a topic for another time, perhaps]. He was a really great teacher, a wonderful man and one of the reasons I am a physicist today. It's nice that his work has had such a profound influence on physics research today.)

The WMAP satellite detects the CMB as it streams in from all directions, and the data can be used to produce the lovely CMB map that I keep showing. But what is this map? Essentially, it's sort of the inverse of a world map. As we know, the earth is a sphere and flat world maps are projections of that sphere onto a flat surface, as in this nice illustration taken from www.nationalatlas.gov:

The CMB map is very similar. If you look out into the sky the same distance in every direction, you would map out the inside of a spherical surface. Then you could project what you saw onto a flat surface just like the globe projects onto a flat world map. The result is the CMB map.

Ok, now what? We have a map of all the little temperature fluctuations in the CMB photons coming from all directions of the sky. Well, the CMB scientists use a version of Fourier analysis to find correlations in these temperature fluctuations. For those who want more mathematical detail, in the series on Fourier analysis, I stated that any function could be obtained by summing sine functions of different frequencies. Well, there are a class of functions similar to the sine function called Spherical Harmonics that can in most cases recreate any two dimensional function, and the spherical harmonics have many of the same properties as the sine function when it comes to integration. Therefore, one can multiply the two-dimensional signal by a spherical harmonic of a given "frequency" and integrate just as one would in Fourier analysis to find the amount of the signal described by that particular frequency. And the result is something that looks like the following:

Courtesy WMAP/NASA Science Team

This is analogous to the breakdown of the A chord into frequencies, with the difference that "l" or the "multipole moment" refers to the way frequencies are understood in spherical harmonics. Just as the Fourier transform shows us how much of a signal is contained in different frequencies, this plot shows us how much of the CMB are correlated over different angular scales (the lower x-axis in the plot). For example, much of the CMB signal is contained around an angular scale of between 2 and 0.5 degrees. What does that mean? It means that the map is not just a random collection of fluctuations, but that regions separated by about 1 degree are related to each other.

This is a fairly dense post, so I'll leave it at that for now and come back later if I get questions. Next, we'll talk about how the angular correlations tell us about the universe.

Back to the CMB

2010-08-20T15:51:00.001-07:00

Over a year ago now (I have been really delinquent), I started talking about the CMB. If you recall, the CMB was like a picture of the universe as it was very early on after the Big Bang. And in this post, I said the following: "using the [noise in the] CMB, we can understand the age of the universe (13 and a half billion years), the geometry of the universe (flat), the amount of energy and density in the universe (the pie charts in the first post of this blog, including the 23% accounted for by dark matter [there is a connection between this and what I have been talking about until now, after all]), the rate of expansion of the universe, and other things."

Now that we've been through the whole sequence on Fourier analysis, we can start to understand how we extract that kind of information from a map that looks completely random to the eye. The key is that by applying a variation of Fourier analysis to the map in the picture, we can look for correlations between the fluctuations in the noise. As I explained it, Fourier analysis was able to extract how much of an apparently noisy and random signal was contained in different frequencies - for example, it could pull the individual notes out of the idealized A chord.

An artificially noisy A-chord.

The Fourier transform of the A-chord, with constituent frequencies easily visible.

In that example, the Fourier analysis effectively looks for correlations in time. Because the signal was made up of discrete frequencies, different parts of the signal were related to each other. For example, the A note has a root frequency of 440 Hz, or 440 cycles per second. What that means, although it can be hard to see by eye, is that two parts of the signal separated by 1/440 seconds are related in the way they appear, and the Fourier transform picks up on that. The premise of the CMB analysis is that two areas on the CMB map are also related in the way they appear (just not by eye). Instead of looking for time correlations, they look for spatial correlations in the map using a similar algorithm to the Fourier transform described above. In the next post, I'll show how they decompose the map shown above into its underlying angular or spatial frequencies.

A little more about me and the blog

2010-08-20T15:22:00.000-07:00

I've talked to a few people in the last few weeks who asked me to write a bit more of an introduction to both me and what I'm trying to do with this blog, so here goes:

My parents are both extremely intelligent people. Before he retired, my father was in academic publishing as an editor for several years before running the Princeton University Press for the last 20 years of his career. My mother is a writer, author of several books on a rather wide-ranging list of subjects including gardening, architecture, biographies of several people and two novels. I grew up surrounded by books on history, literature, politics, etc. Despite this rather literary background, however, all through school I somehow found myself doing my best work in math and science. I graduated college with a physics degree, but I did not then know what I wanted to do (nor did I have a job). Fortunately, my thesis advisor in college, Dan McKinsey, was hired as a professor at Yale University that summer and asked me to come work for him while I figured things out. Seven years later, I left Yale with a PhD in physics and I think it's pretty safe to say that I am now trying to make a career as a practicing physicist.

Although my family has gotten used to this idea during the (many) years spent lost in graduate school without a real job, I think it's still a bit of a mystery to them how I ended up as a scientist. And perhaps more importantly, I've often felt that they (and in particular, my mom) really don't know what I do nor how I do it. While the question of how I ended up here is sometimes a mystery to me (as far as I can tell, I like doing the physics I do and figure I should keep at it as long as people let me), the second mystery is something I should be able to do something about, especially if I want to be a good physicist. Hence this blog.

I truly do want to try to explain my work so that my family, and my mom in particular, understands. As I said before, my mom is a very intelligent woman, but she tends to be a touch skittish around mathematical ideas. And if I can explain things like dark matter in an understandable way to her, it will mean that I myself understand what I'm doing. More generally, I've found over the years that people I meet really have a lot of interest in physics, but they always say, “I was no good at it” or even worse, “my teacher was terrible.” In the blog, therefore, I'm trying to write about what I'm doing and why it's interesting in a way that does not require any background while simultaneously not underestimating the audience.

Once I started writing, I quickly discovered the particular format I wanted the blog to take, which I outlined at the bottom of this post: Update and future plans. So that's the summary.

Also, here's a picture of me at my sister's wedding. I'm trying to be funny here.

Update and future plans

2010-07-29T08:01:00.000-07:00

To all three regular readers of this blog,
I apologize for not having posted in several months. By way of explanation, I will say that since April 2, I finished and defended my dissertation, spent a month out of the country, moved to a new city, started a new job and finished it off by watching my sister get married in a beautiful ceremony in Maine. That said, I'm now back and I plan to post more regularly for the foreseeable future.

A giant sun dial in Jaipur, India

To give a little more detail about my new job, I have moved to Chicago to work as a postdoctoral associate at Fermilab, which is the location of the second largest particle accelerator in the world now that the new LHC has turned on at CERN in Switzerland. To a large degree, Fermilab has been the focus of high energy particle physics over the last twenty years, and I'm really excited to be here. Fortunately for all of us, I still plan to work on a dark matter experiment, so I won't have to start on a completely new thread in the blog but instead can pick up where I left off in April.

Let me restate the way I imagine this blog looking - to me, the study of physics builds upon the huge amount of effort and thought that humanity has put into the subject for several hundreds of years (with emphasis on the 20th century). Nothing that we do is a completely new idea, but instead we must draw on all the experiments, theories and results that have gone before. My goal in this blog was to illustrate that idea by starting with a very modern, exciting topic of research like dark matter and showing how each argument that leads us to believe both in its existence and that we might be able to detect it depends on other, more established observations. And then I hoped to explain all of those observations in a more or less simple to understand fashion.

"Standing on the shoulders of giants (taken from mushon)."

As an example, I started with the argument that galaxy rotation curves prove that we are missing something, which of necessity led me to the Doppler effect, light as a wave, Newtonian gravity and back to dark matter. I'm currently trying to explain the Cosmic Microwave Background, which led me to a discussion of thermal equilibrium and then Fourier Analysis, and I'm not quite finished yet.

That is the image I have for this blog, but I'm open to suggestions if I'm failing somewhere or otherwise losing your interest, so please do not hesitate to let me know what you think. And in the next post, I'll get back to physics.

Hugh

Fourier analysis - Sines and integrals (part 3)

2010-04-02T13:33:00.001-07:00

We're almost there. Let's talk about two more features of integrals and sine curves. First, (and mom, remember the symbol for "integral" is an s-shaped thing):

∫sin

²(x)dx > 0

The integral of the square of the sine function is always positive. This makes sense sort of by definition, because anything squared is always positive, so the negative parts of the sine curve become positive when squared. To illustrate this graphically, I'll show the integral of the sine function:

followed by the integral of the sine squared:

So the integral of the sine times itself is always greater than 0.

Now, the key: the integral of the sine times a sine with a different frequency over an entire period is always equal to 0. Let's slow down and read that one more time, since it's hard to say in a small number of words. The integral of two sine functions with different periods is always 0. To take a specific example, let the second sine function be sin(3x), or one with 3 times the frequency like the green curve here:

The statement I'm making can be expressed symbolically,

∫sin(x)*sin(3x)dx = 0

(integrated over a full period)

How about graphically? Well, here is a plot of sin(x)*sin(3x), and if you look, the green regions are equal in area to the yellow regions, for a total integral of 0.

How about if I show another example, with a sine of four times the frequency.

∫sin(x)*sin(4x)dx = 0

(integrated over a full period)

Again, the areas of the green and yellow regions are equal, and the total integral is 0. Now I haven't proven this is true for all frequencies, but it can be done rigorously (or rigourously); I suppose you might have to take my word on it, but it clearly works for the two examples given.

There's one more theorem that I need to state before finally explaining Fourier analysis, although I hope it won't be too difficult to understand. This is an associative statement, that the integral of the sum of two functions (any functions, let's just call them f(x) and g(x); for example, they could be sin(x) and sin(3x)) is equal to the sum of the integrals done separately:

∫ (f(x) + g(x) )dx = ∫ f(x)dx + ∫ g(x)dx

Let me know if that is not clear, because I'm so excited about the punch line, I'm inclined to skip past some of this stuff.

Finally...

To recap, so far we know the following things:

1. Any periodic shape can be expressed as the sum of sine functions with different frequencies.

2. The integral of a curve is the area under the curve.

3. The integral of a sine times itself is greater than 0.

4. The integral of a sine times a sine with a different frequency is equal to 0.

5. The integral of a sum of functions is equal to the sum of the integrals done independently.

Who can guess what the next step is?

Suppose I have an unknown function (like the A chord from the November post).

By Rule 1, I know that this function can be expressed as the sum of many sine curves of different frequencies. Now, suppose I want to understand what the signal actually is - I want to break it down into the frequencies that went into its construction.

What if I multiplied the unknown function by a sine curve of a given frequency that I know and integrated the result over an entire period? From Rule 4 above, if the frequency I control does not match one of the frequencies that make up the unknown function, the integral will be 0. But if I do find a match, all of a sudden, the integral is positive (by Rule 3) and I've identified one of the component frequencies in my unknown function!

Now, I scan my known frequency over all frequencies, and at the end of the scan, I've found all of the elements that went into making the unknown signal, producing a plot like this:

In this graph, I'm basically plotting the value I get when I integrate the product of the A chord function times a sine with a frequency given by the value on the x-axis. In most situations, I get 0, but when I find a match, the integral (or "power") is positive and I see a spike!

Isn't this exciting? And I'm being completely serious here, none of the vaguely self-mocking tone you might find elsewhere in this blog - I find Fourier analysis completely awesome and elegant and beautiful. Simply using mathematical formalism, we can completely deconstruct a complicated and unknown signal into its individual constituents and understand exactly what is going on. It's stuff like this that makes me love physics and math. If I didn't quite manage to get the beauty and simplicity across in the last few posts, let me know and I'll do what I can to fix it.

Fourier analysis - Sines and Integrals (part 2)

2010-04-02T13:12:00.000-07:00

In the last post, I attempted to remind the reader of the definition of a sine curve. I particularly wanted to highlight that the sine function is the mathematical representation of a wave, and since waves are representations of musical notes, a sine curve is also a mathematical representation of a musical note. Those who are familiar with music (or perhaps with my post on the guitar back in November) will be aware that different musical notes are simply waves with different frequencies. That is easily related to the sine curve by multiplying the variable by some number. For example, I've been showing plots of just the basic sine function, y = sin(x) or y = sin(θ). If, however, I decided to plot y = sin(3x), then all of a sudden the frequency of the wave would be tripled, as in this figure:

It is pretty clear that during the time it takes the standard sine function (the red curve) to undergo a full oscillation, the higher frequency curve (the green curve) represented by y = sin(3x) has undergone three full oscillations. Thus, I can represent any of the musical notes using the sine function, simply by changing the multiplication factor. This is essentially what I did in the graphical representations from the November post, by just adding different functions together to produce the sounds I wanted.

We are now ready to talk about the two fundamental keys to Fourier analysis. The first is that any periodic signal can be obtained simply by adding sine curves of different frequencies. To illustrate this, I'm going to draw on everyone's friend, Wikipedia, which has a great entry on Fourier analysis and Fourier series (which does raise the question, "why am I bothering to do this when so many other people have already done it before?" but then this is my blog and I can do it again if I want to. In general, for those who are interested, Wikipedia is really good at mathematical concepts, and I use it as a reference all the time). In the Fourier series article, the unnamed Wikipedia author is exactly illustrating the point I'm making here, that any periodic function can be expressed as the sum of sine curves with different frequencies.

The first example is the square wave. This is a wave that alternates between two values, for example either 1 or -1, so that it looks like a box. The sine function is very smooth, so it may seem hard to believe that you can get a square wave from sines. But, as in the following picture, it doesn't take very many iterations before the sines do a pretty good job at imitating the square wave:

A second example, featuring our favorite gimmick animation, is the the sawtooth wave. Assuming I get this to work right, the animation should show a sawtooth wave along with the sum of sines as each additional sine is added to the total. As with the square wave, the approximation gets pretty good without too many steps:

From here, it should be easy to imagine creating the shapes from my guitar post simply by adding different notes together. The second key will be the subject of the next post.

Fourier analysis - Sines and integrals

2010-02-26T16:04:00.000-08:00

In case anyone is still reading this, now that it is being updated so sporadically, I'm finally managing another post on Fourier analysis. In this post, I'll try to set up a little bit of the math behind the theory. To do so, I'm going to first remind everyone about the sine function, which I wrote about when talking about the Double Slit Experiment. In that post, I said that the sine function was a mathematical representation of a wave. Here is a plot of y = sin(θ):
Now, that looks an awful lot like the sound waves I was looking at with my guitar back in November. Because they are the same. In fact, when I wanted to depict the sound waves graphically, I used the sine and its partner, the cosine to do it. Going back to the post on the double slit experiment, I believed I compared these functions to a part of speech; by using them, I can now describe a whole host of different phenomena that were previously inaccessible. Including sound waves.

Next, I want to talk about integrals. My mother never took calculus and says she has no idea what an integral is, which means I'm going to try to give a brief introduction (without going into details, alas). The first thing I was taught about integrals is that they represent the "area under the curve," and I think that's really all we need to know about them. If I draw a curve on a coordinate system, for example, like the sine curve above, then the integral is the area between the curve and the x-axis. Therefore, we need to know one other thing to define it, and that is the range of the integral. For example, I am going to zoom in slightly on that sine curve, and then I'll take the integral from x = 0.5 to x = 2.5, which is just the area below the curve between those limits, or the region shaded green.

Now, things can get a bit trickier conceptually when the curve crosses the x-axis and becomes negative-valued. In this case, the integral is still the area under the curve, except that it is now negative. This is represented by the yellow shading.

Finally, if you look carefully, you'll notice that the sine function appears to be symmetric. This will be really important for Fourier analysis. If you integrate the sign function over an entire period, the positive part and the negative part cancel each other out, and we're left with a total integral of 0.

I want to make two final comments about integrals. The key to calculus is finding out that you can generally solve for these areas if you know the functional form of the curve (in this case, for example, we know the curve is a sine curve, so I could write down the function representing the area from calculus). And because I know this is the kind of thing that might interest my mom, in math, we represent an integral with a symbol that looks a little bit like an "S". For example, the integral of sin(x) is written like this:

∫sin(x)dx

The "dx" is there partly to let the reader know that the integral is being performed over the x variable.

Carl Wieman and learning science

2010-01-22T12:29:00.000-08:00

This will be the second non-Fourier post I will write, and again I apologize. Who knew that writing a thesis and applying for jobs was so demanding? The subject of this post is learning and teaching science. This week, we had Nobel Laureate Carl Wieman visiting Yale, and he gave two great talks on research people have done on how students actually learn science. Professor Wieman has been applying scientific methods to scientific learning for some time now, and among other things, he writes a blog about it.

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...)

The CDMS result

2009-12-24T07:25:00.001-08:00

Merry Christmas, everyone. I know I promised more on Fourier analysis, and I'll get to it, but I want to take a slight detour to mention some exciting results announced last week by the Cryogenic Dark Matter Search (CDMS), a dark matter experiment based on a different technology than my own. For the last decade, CDMS has been the leading experiment in the field, and their new result is no different. A week ago, CDMS released the results of their most recent analysis, and lo and behold! they had some events. This is exciting.

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.

Fourier analysis 2 - More complicated sound waves

2009-11-07T16:58:00.000-08:00

I imagine the discussion in the previous entry seems pretty boring. It was really easy to tell apart the A note from the white noise, both by sound and by looking at the graphical representation. Things get more complicated however when we add more notes to make a chord or a complicated piece of music. For example, a simple A chord consists of three notes - A, C# and E. The nearest C# to the standard A has a frequency of 523.25 Hz while the nearest E has a frequency of 659.26. Here's what that sounds like on my guitar (it's sort of fun posting videos of my guitar online), followed by the graphical image:

One can still see the oscillatory behavior, but things aren't quite as clean as they were when I was plotting just the simple A note.

Now, what happens if I play a full A chord by adding A notes from the next two octaves up and another C# as well?

You can still see a few clear features, but overall it doesn't look nearly as obvious that this is an actual chord. In reality, no sound wave is perfectly free of noise either. We are all familiar with static in our speakers and acoustic reflections tend to add noise to the wave as well. In general, external sources of static add white noise on top of the underlying wave. In such a situation, it can be impossible to see the wave underneath the noise just by eye.

This is where Fourier analysis comes in. Fourier analysis is a mathematical method that can decompose signals like the ones shown in the various pictures into their constituent waves. By Fourier analyzing a pulse, we can find out how much of each pulse is contributed by a wave of a particular frequency. For example, returning to the simple A note, the entire pulse is a wave of 440 Hz. Therefore, the Fourier transform of that plot should provide us with a peak at 440 Hz, and nothing else. Here's what the Fourier transform of the A note looks like:

The Fourier transform has picked out the signal at 440 Hz, and shown that it is the only component there. What about white noise, where there is no dominant frequency component? Fourier analysis can find that as well.

And finally, where Fourier analysis really shines is when the signal is so complicated that one couldn't possibly tell apart all its constituents by eye. For example, look at the Fourier decomposition of the full A chord - all of the 6 notes are clearly broken out in the decomposition and we can understand exactly what went into the making of that sound.

I have one last example, just because I think this is so cool. I made a signal of 12 semi-random frequencies, with a little white noise added. The first plot is what they look like in the time domain (i.e. when you plot the amplitude of the sound as a function of time). There's no real pattern there that I can see. But when I plot the Fourier transform, there they all are. It's like magic. But it's not, it's just math, and I'll try to explain it qualitatively in the next post.

Fourier analysis 1 - Sound waves

2009-11-07T16:13:00.000-08:00

First, I need to apologize for the lack of activity on this blog, and regretfully state that the relative dearth of new posts will likely continue for another few months. I'm at the point of my career when I try to graduate and get a job for next year, and between these two activities I don't have much time for posting to this blog. I do plan on continuing it, but it will of necessity be sporadic for a few more months.

Now that that is out of the way, I want to discuss Fourier analysis, which I mentioned at the end of the last post (over two months ago). One theme that may have come through to someone reading this blog since the beginning is the ubiquity of "waves" in physics. When discussing the Doppler effect back in March, I used sound as an example (the police siren) before moving to light. I want to do the same thing now. Sound is a pressure wave that moves through the air and is interpreted by our ears. Just as the color of light is determined by its frequency, the pitch of sound is also determined by the frequency of the sound wave. People who play music will be very familiar with this - the root A note, for example, is a sound wave with a frequency of 440 Hz (if I haven't used this unit before, a Hz is just inverse seconds. So 440 Hz means that the wave oscillates 440 times per second). Let's use the power of modern computers to show a video of me playing the A on my guitar:

The idea here is fairly simple. The guitar is tuned so that plucking the string makes it oscillate at 440 Hz, creating the note that we hear.

On the opposite end of the spectrum from a perfectly pitched musical note is "white noise." We all know what white noise is, it's static, something with no discernable pattern. It's called white because the color white is a combination of all colors. White noise is a combination of all frequencies. For a lovely example of white noise, one can go to http://simplynoise.com/.

The point of this is that waves are very well understood mathematically. Therefore, we can very easily represent these sounds with a mathematical expression. For example, the A note I played in the video can be represented as an oscillating wave with frequency 440 Hz, and it would look something like the drawing to the right. There's clearly a pattern in there of the appropriate frequency (I also added an overall envelope to describe the starting and stopping of the pulse, but that's not really important for this discussion).

White noise looks like the next plot, and there is no pattern there.

In part 2, I'll talk about what happens when you add more tones to form a chord (or an orchestra) or what happens when you add noise to a tone.

Gravitational potential wells (final)

2009-08-26T13:51:00.000-07:00

In the last post, I compared the early universe to a mattress with a number of bowling balls on it, creating divots for matter to fall in and out of. I have to admit that it isn't the best analogy; the behavior I'm trying to describe is relatively universal, however. Imagine a really great vacation spot - initially, people will be attracted to this spot. As more and more people visit it, the pressure of all those people mean that it's no longer an attractive location and they stop coming. Also not a good analogy.

In the end, the point is that local density fluctuations created sources of oscillation. Matter was attracted to regions of high density and fell into the well, before photon pressure became too great and pushed it back out. The final piece of information we need before we can finish this particular section is that regions of high density are hotter than regions of low density. And as we already know, the temperature or energy of a photon is related to its wavelength. Therefore, a photon coming from a region of high density is "hotter" or has a higher frequency than a photon coming from a region of low density. This is how the CMB tells us about the early universe. By looking at the temperature fluctuations of the CMB, we can understand the density fluctuations in the early universe.

To once again plagiarize Wayne Hu's website, he has an expanded version of the movie in the previous post. Here, there are two potential wells with a hill in the middle. When the balls are at the bottom of the well, the temperature is hotter and photons departing at that time are correspondingly hotter. When the balls are not in the well, things are colder and the photons reflect it accordingly (I believe in this movie, hotter is represented by blue and colder by red, since blue light has more energy than red light). By detecting these photons we now know about how uniform the early universe was and we can make conclusions about the distribution of matter and energy. In the next post, I'll start talking about how we decode these photons using Fourier analysis.

Gravitational potential wells (part 2)

2009-08-08T15:21:00.000-07:00

In the last post I described gravity as the curvature of space, creating little wells for other masses to fall into. This is the image we want to think about as we imagine the early universe. At that time, the structure we see in the universe today hadn't formed yet - there were no planets, galaxies or clusters of galaxies. Instead, there were small perturbations, small potential wells that contained the seeds of future galaxies. Returning to the image of a bowling ball on a mattress, we can imagine a giant mattress with many small little bowling balls on it. These bowling balls were placed at random, simply because nothing is perfectly smooth. In addition to the bowling balls, there are countless smaller marbles moving at random across the surface of the mattress. None of the bowling balls was very large, but they did create small little divots for the little marbles to fall into or orbit around or bounce in and out.

This isn't the whole picture though. Over a month ago, I described the thermal equilibrium of the early universe, where everything was reacting with everything else, atoms were ionized and electrons were constantly interacting with photons. There was a lot of energy involved in those reactions. In particular, this energy was enough to keep the marbles from settling down in the divots. If too many marbles gathered in a particular place, the pressure caused by all the photons bouncing around tended to push the marbles apart. In this way, a situation very much like the pendulum on the spring was created. The marbles were attracted to the wells created by the bowling balls, but when they tried to reach the center, there was enough energy to push them back out. Once out, they were again attracted to the bottom of the well, and therefore we have an oscillation.

I've taken a nice illustration from University of Chicago Professor Wayne Hu's website. In this movie, the well is caused by the random gravitational fluctuations, or the bowling balls. The marbles are represented by the yellow balls, and the pressure caused by all the photons is represented by the springs, pushing the marbles apart when they get too close to the bottom of the well.

Gravitational potential wells

2009-08-08T14:30:00.000-07:00

I've changed my mind on how I want to proceed with the CMB. I had a post starting to talk about general relativity, but I've decided that it is too much for this particular sequence. I'd want to really talk about special relativity and general relativity to really do it justice, therefore I've decided to skip it for now. However, that still leaves us needing to understand just what is the information encoded in the Cosmic Microwave Background, so I'll try to do a slightly different description.

Imagine a pendulum - like this one!

The pendulum oscillates back and forth, and as it does so, it traces out a well. The pendulum wants to rest at the bottom of the well, but it has too much energy, and so it continuously overshoots the bottom. The well looks like the line drawn in the still picture to the right. In physics, something like this is known as a potential well - the force of gravity is pulling the weight downward, towards the bottom of the well, but because of the string, the pendulum just bobs up and down in the well.

There are a surprising number of situations like this, and most gravitational interactions can be described in terms of potential wells. For example, the motion of the Earth around the Sun is an orbit that follows the same path as a pendulum in two dimensions. The Earth wants to go straight to the center of the Sun, just like the ball wants to rest at the bottom of the well; instead, the Earth goes around the Sun forever, unable to reach the middle (thankfully).

General relativity is a theory of gravity. Why does gravity create these potential wells? The answer can be thought of in terms of curvature. Large masses tend to curve the space around them, so that other masses will fall in towards the large one. In this framework, one can imagine the Sun as a giant bowling ball on a very smooth mattress. The mattress dips because of the mass of the Sun, and so the space around the Sun curves. Now, one can imagine rolling a bunch of marbles around the divot left by the Sun; if there were no friction, those marbles could roll around the Sun forever in an orbit, just like the planets.

In this sense, then, mass will curve the space around it to attract other masses. But those masses won't necessarily just fall straight in (although that can happen), but can oscillate, much as the Earth oscillates around the Sun, or as the pendulum above keeps going back and forth.

CMB Anisotropies (part 2)

2009-07-12T18:03:00.000-07:00

The Dipole
The above picture is an image of the temperature variation in the CMB with the contrast turned up to 1 part in 1000. Therefore, there is about 0.1% difference between the left side and the right side. This particular pattern appears fairly often in physics and is known as a dipole (there are two "poles" where the temperature is hotter or colder and the rest of the distribution stems from those two centers). Why is there such a distinct pattern in the temperature distribution?

The answer lies in the Doppler effect, which we've talked about at length before. In fact, we've talked about everything we need to explain this pattern. I've mentioned that the temperature is similar to the energy, so that we're effectively showing the energy of the CMB photons as a function of where they are coming from. And we know that the energy of a photon is related to its frequency. Therefore, the above picture shows the change in frequency of photons coming from one direction or another. We know that galaxies rotate, including our own. And finally, we know from the Doppler effect that the relative velocities of a source and an observer can change the observed frequency of light.

Mom, can you now guess why this pattern looks the way it does (I'm not sure how I feel about directly addressing anyone in this blog, since there's clearly no possibility of a direct response, but I'll leave it for now)? If you guessed that the Earth's motion through the galaxy resulted in a Doppler shift of the CMB photons depending on whether they are coming from in front of us or behind us, you would be exactly right. In effect, the Earth (and the Sun and the entire solar system) is moving towards one of those poles and away from the other, and thus we see the Doppler shifted dipole pattern shown above.

That is pretty interesting, but not revolutionary. We understand the Doppler effect and we know our galaxy is rotating, so if that were the only thing in the CMB anisotropy, it wouldn't be that big a deal. The real excitement (I keep pushing it forward, don't I?) arrives when we subtract the dipole effect (it's fully understood, so we can do that), leaving the smaller part in one hundred thousand variations.

Tiny variations
Finally (finally!), I will talk about what the CMB is showing us. The above is a map with the contrast turned up to that part in 100,000. And now there's no obvious pattern, which is good, because the universe is supposed to look the same in all directions. Basically, these little fluctuations are the imprint of noise in the very early universe (remember, at one point I described the CMB as a snapshot of the universe at 400,000 years old). And by studying the distribution of this noise, we can infer things about the properties of the universe.

I plan on going into this in more detail (with a detour through something called Fourier analysis), but using the CMB, we can understand the age of the universe (13 and a half billion years), the geometry of the universe (flat), the amount of energy and density in the universe (the pie charts in the first post of this blog, including the 23% accounted for by dark matter [there is a connection between this and what I have been talking about until now, after all]), the rate of expansion of the universe, and other things. I think (and I hope you agree with me) that this is really impressive - this one measurement has answered several deeply fundamental cosmological questions about how the universe works all in one go, just by carefully studying the snow picked up by the rabbit ears on my mom's now useless analog television set.

CMB Anisotropies (part 1: tricks with figures)

2009-07-05T17:14:00.000-07:00

Now that we've had a week since the last post for us all to calm down about how exciting we found the giant map of pink representing the CMB and the implications that single color had for our understanding of the universe, I want to start talking about "anisotropy." Last week, I defined isotropy as meaning that everything looks the same in all directions. My mother, being a woman of letters, will immediately recognize that anisotropy must be the opposite - everything is not the same in all directions. In the last twenty years, it's been the anisotropy of the CMB that has really changed the physics world.

First, let's talk about the pink map one more time. What is actually being shown in that map is the temperature of the photons coming from that particular region of the sky (the map is elliptical because we are projecting a spherical surface [the sky around the earth] onto a flat space, much like flat maps of the globe are elliptical). The temperature is in this case a proxy for energy, and recall that the energy of a photon is related to its wavelength. Therefore, we can think of the pink map as showing the wavelengths of photons coming from different parts of the sky, and they all have about the same wavelength or temperature (about -270 degrees Celsius if you're interested).

Now, there's a subtlety here regarding contrast, because I never told you what the color actually represents in terms of temperature. If pink means any temperature between 0 and 4000 C, then no wonder the universe looks the same everywhere! To illustrate what I mean, I'm going to once again draw some of my own really high quality images. I have a gas stove in my apartment with 4 burners. When I turn those burners on, there are four hot spots on my stove. Let's assume the main part of the stove always stays at room temperature (70 degrees Fahrenheit or 21 C). Let's further assume that the temperature in the flame of my burners is 3500 F or 2500 C. I can represent this graphically in two different ways:

In the plot to the left, I've used a reasonable contrast, and we can clearly see the white that represents the room temperature part of the stove and the red that represents the hot part. But in the plot to the right, I've used such a big scale (or a small contrast), that the stove looks the same color, just like the map of the CMB.

Hopefully, you're now all asking the question, "so just how isotropic is the CMB?" since I can apparently make a plot that looks uniform just by changing the scale. The answer is that it is very isotropic, but not perfectly. The pink map is accurate up to 1 part in 1000. Basically, all the photons have the same temperature to within 0.1%. Which is pretty uniform. But, suppose we turned up the contrast, so that colors varied with that 0.1% (this would be analogous to switching from the right plot to the left). Now the CMB looks like this:

What about if we went even further, to a contrast of 1 part in 100,000 (this would be like looking for the difference between adding or subtracting a penny from 1,000 dollars)? Here is where the excitement really enters, but I'll talk about that in the next post (CMB plots courtesy of the WMAP homepage, as usual).

The Cosmological Principle

2009-06-28T08:24:00.000-07:00

The definition of cosmology is the study of the structure and evolution of the universe. In modern physics, cosmology begins with the application of Einstein's theory of gravity, or General Relativity (recall this post), to the universe. This is a difficult task and would probably not be possible without a basic assumption about the universe - that it is spatially homogeneous and isotropic on large scales. Isotropy is a statement that the universe is the same in all directions (the universe looks the same whether you are looking directly outward from the North Pole or the South Pole). Homogeneity contends that the universe is the same at all points. These two hypotheses are together known as the "cosmological principle," without which much of our presumed understanding of the workings of the universe would be invalid.

Over short scales, this is obviously not true. Looking at the Milky Way is clearly different from looking at other parts of the sky. This makes it hard to test the hypotheses, as we need to go to larger and larger length scales to really see this principle in action, by averaging large volumes (using painting again as an example, imagine a canvas entirely of one color. Up close, you can see individual brush strokes with a great variation from place to place. From far away, though, one section of the canvas looks much like any other section, as they are all one color. Our universe is like that, if you believe the cosmological principle) .

Viewed in that context (I originally wrote "viewed in that light" but didn't want anyone to think I was making a pun), this rather boring picture of the CMB (taken from the COBE satellite in the early 1990s) becomes much more exciting - as already discussed, the CMB photons are coming from all corners of the universe. And they all look exactly alike (to 1 part in 100,000)! The first measurement of the very smooth spectrum of the CMB provided strong supporting evidence to the foundational hypothesis of cosmology, as the universe truly does look the same in all directions (it's slightly harder to convince yourself of homogeneity, that the universe looks the same at every point, but Copernicus can help here - if we proceed under the conservative assumption [although perhaps contentious from a religious point of view] that we do not live in a particularly special place in the universe [the "Copernican principle"], we can conclude that since the universe is isotropic around us, it should be isotropic everywhere. This implies homogeneity).

The Horizon Problem
Of course, that is not the entire story. I will briefly discuss the "horizon problem" here, before talking about the "anisotropies" in the CMB in later posts (these are the 1 part in 100,000 fluctuations that you can't see in the above picture because they are too small). We've decided the universe looks the same in all directions (the left side of the picture is the same color pink as the right side of the picture). But is the entire universe in causal contact?

My mom might ask, "what does causal contact mean?" If two events in space and time can be caused by the same preceding event, they are in causal contact. Here on earth, this is generally understood in terms of time. If something happens after something else (say, for example, I get a book out of the library because my mother recommended it), there can be a causal relationship (I got the book because my mom recommended it). On the other hand, if things are happening at the same time, they can't be causal (if my mom's recommendation comes at the exact moment I'm getting the book [or after I do so], she clearly can't be the cause of my literary enjoyment).

On universal scales, things are slightly complicated by the finite speed of light which adds a dimension of distance to the picture. We all know that the speed of light is constant, but for most of us, this doesn't really mean anything. We turn on a light switch, and the light turns on immediately. That is because the speed of light is so fast that we don't notice the time it took for the information to travel down the wire to the light bulb and back to our eyes. In space, however, this is not the case. For example, it takes about 8 minutes for light from the Sun to reach us. That means that an event in the Sun can only cause a response on Earth 8 minutes later. Suppose there were explosion in the Sun followed by an explosion on Earth 4 minutes later. The Sun's explosion cannot be the cause of the one on Earth, because any information from the Sun cannot reach us in less than 8 minutes (of course, both explosions could have been caused by some event happening in between, but hopefully the idea is clear).

This gives rise to the horizon problem. We know roughly how old the universe is and we know the speed of light. That means we know how far light can have traveled since the "epoch of last scattering." The problem is that the far right side of the pink ellipse is too far away from the far left side of the pink ellipse to have been in causal contact. Imagine running time backwards and following a photon emitted from both edges directed towards the center. At the time of last scattering, those photons would not have reached the center yet. In other words, what is happening on the left side and what is happening on the right side could not possibly have been caused by the same thing. Yet, they clearly look the same. How is this possible, when they could not have been influenced by the same initial conditions? This is the horizon problem, because the two extremes are outside of each other's causality horizon.

There are some theories on how to solve the horizon problem (with the leading candidate being "inflation") but they are probably beyond the scope of this blog (an argument can be made that the CMB is beyond the scope of this blog, but I hope my loyal reader(s) ignores that argument).

Some history

2009-06-16T18:20:00.001-07:00

In the 1940s and 50s, a few scientists (George Gamow, Ralph Alpher and Robert Herman among others) predicted the continued existence of the photons that last scattered in the very early universe. Theoretically, those photons had continued to travel through the universe, cooling as the universe expanded. The early theorists tried to predict what the temperature of these photons would now be (with varying degrees of success). These photons should be all over the place and hence providing a constant "background" to any antenna on earth. In addition, they should have cooled enough that now their wavelength would be in the microwave range. Thus, these photons came to be called the cosmic microwave background.

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 http://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.

Thermal equilibrium recap

2009-06-16T17:48:00.000-07:00

The last post is rather long and involved, so I will try and recap in briefer terms. The early universe was very hot, so that everything was in thermal equilibrium. In particular, because reactions were constantly taking place, the universe was strongly "ionized" or charged. Therefore, photons were constantly scattering off the charged particles.

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).

Thermal equilibrium

2009-06-07T19:36:00.000-07:00

Last week was graduation at Yale, and a few of my closest friends here were getting their degrees. As such, some celebrating ensued. One of my friends is now doing post-doctoral work at UCLA, while another is working for a financial firm outside of New York. One night we spent some time in the early morning hours discussing the economy and the stock market. In that discussion, I came up with a somewhat stilted metaphor that I'm now going to invert to describe the concept of thermal equilibrium, which is where I want to begin the series on the CMB. In physics, temperature plays a similar role to that of money (or liquidity) in the markets.

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.

Introduction to the Cosmic Microwave Background

2009-06-01T19:11:00.000-07:00

The first series of posts contained one argument for the existence of dark matter. The response from my mother among others was tentatively positive, although most comments seemed to agree that I was perhaps going a bit too fast with the math and trying to pack too much in (my beloved sister has weighed in with a somewhat more negative opinion for which I thank her with all the fraternal feeling I can muster). I take the point that this blog may need more romance and less dry insistence, and I will attempt to respond accordingly.

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.

Baby blues

2009-06-01T17:54:00.000-07:00

The aforementioned picture of me (narcissism being a commonly found flaw among physicists).

At the mine

2009-05-22T10:13:00.000-07:00

I'm writing this entry from 6800 feet below ground. I am wearing a baby blue jumpsuit (pictures to come, hopefully), safety glasses, steel toed boots, a hair net and a hard hat. At some point, my mom commented that hearing about working in the mine might be more interesting than posts on physics, and so I am going to give the human interest piece a try.

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).