PFE015: Mirage

This was inspired by driving down the highway (I've been driving around a lot lately).

If you have ever been on a long road trip on a sunny day and you've looked ahead on the highway, you may have noticed a shimmer or a reflection. It sort of looks like there is water on the road, but even as you're driving 70 miles per hour, you can't seem to reach it. Where does this phenomenon come from?

It turns out to be a trick of the eyes.

Before we can discuss this, let's talk about the way light and our minds behave. First, imagine you are seeing something both in a mirror and normally. We know that the light from the same object hits your eyes twice, after traveling along two different paths. Since I assume that light travels in a straight line it looks like there is a second object behind the mirror. Luckily, I (along with most people and some chimps) have experience with mirrors and know that the light is really bouncing off it.

There is another fascinating property of light, and that is that it bends as it passes through different substances. Consider a (straight) straw in a glass of water. The straw actually looks bent at the point where it enters the water even though we know it is actually straight. This is because the speed of light actually changes in the water creating a bending effect. "But, I thought the speed of light was always constant?" you protest. Once again, your teachers have lied misinformed you. The speed of light is constant in a vacuum, but is slower in other things like glass, water, even air a little bit. And as light changes speed, it bends.

Now we know all of the physics to understand the glimmer at the edge of vision. On a sunny day (it doesn't necessarily have to be warm) the sun will heat up the pavement which will in turn heat up the air. But this effect has a limit in that only the air up to about a foot or two will be significantly warmer than the rest of the air. This difference in temperature, you guessed it, causes the light to bend. But unlike with the water where there's a kink, the bend is smoother and curvier because the temperature of the air changes smoothly.

(I think I have one of those awards coming for my graphic artistry.)

So there appear to be two images of the car, the normal one, straight ahead, and another one from below. But since we naturally assume that light travels in a straight line, our eyes see the second image as a reflection.

Desert mirages are actually the same thing, but they should be differentiated from hallucinations. Mirages are actual images (they show up on a camera) that remind us of water. You don't have to be crazy to see them. The other kind, the hallucinations, does require some loss of sanity.

That's a mirage.

PFE014: LHC Part 2 - The Big Picture

Now that you know how the LHC works, I can talk a little bit about some of things happening there and explain some things you may have read in the media.

The LHC is at CERN. CERN is the European Organization for Nuclear Research and is in Geneva on the border between France and Switzerland (hence the misleading acronym). It has been a center for high energy physics research for some time. Recently the began work on the LHC, the large hadron collide. The fact that it's 17 miles should explain the large part. A hadron is a type of particle. There are so many different particles and so many classifications that it is often referred to as a particle zoo. Protons are hadrons (and the primary particle collided at the LHC). Collider should also be pretty clear, although it is interesting to note that there are 4 collision points in the LHC and that only a small fraction of the particles in the beams actually collide at these points.

On to the media. Google news gives 150 news stories for "god particle" in the last year alone including another one picked up by all the major news outlets just yesterday. This one irks me the most because it is entirely a media construction. The particle in question is the Higgs boson. The Higgs hasn't been seen even though it was first predicted some 45 years ago. The Higgs is supposed to be a way to describe how gravity works (yeah, we still don't really know how gravity works. I know, lame, right?) and since everything feels the gravity of everything else it is said, in some sense to be everywhere. So not only is the particle a sort of holy grail, a way to complete a nearly complete model that has been sitting for decades, but would also, in some sense, exists everywhere. Somewhere along the way a journalist misinterpreted a physicist comments and dubbed the particle the "god particle". Since the name is edgy in an article about science the media seems to love it, but it should be clear that the particle has nothing to do with any god of any sort. My main fear here is that if the LHC sees the Higgs, the papers are going to scream that physicists have proven god's existence with sections poorly explaining the actual physics.

The next media fiasco tied to the LHC is the fear that it will destroy the world (see here and here). There were several attempts to sue the United States government to shut down the LHC before it turned on (one such opinion can be found here (pdf)). Needless to say such claims are preposterous and baseless (you don't have to worry about the world ending from the LHC. 2012 is up to you though). Essentially the fears stem from a particularly bizarre theory taking off in a really unfortunate way (things like microscopic black holes or strange matter). On the one hand, there's no a priori reason to believe that these things can't happen. The Tevatron has been running for decades and nothing has happened. Not only has nothing happened, they haven't even glimpsed anything to suggest that something unheard of might occur. Maybe because the LHC will collide particles with 7 times as much energy these new phenomena will show up? Again, maybe. But particles with these energies (and higher) have been striking the earth's atmosphere forever and the earth is still here. While the frequencies are significantly lower than in a particle accelerator, these collisions do happen very regularly all the time and all around us.

Is this proof that the LHC won't destroy the world? No. It is very hard to prove that something won't happen. We can show that something has happened, or that something won't happen up to a certain probability. This is incredibly unsettling to some people. But our lives are ruled by random events. A random solar flare in just the right place can knock out half our satellites. No GPS, no satellite communications, in an instant. Or on a highway. The driver next to you can lose concentration and swerve into your car. These events, and their effects on us are probabilistic. We can plan for some eventualities, and put in place measures to limit these probabilities, but this doesn't mean that we shouldn't use cars or take advantage of satellites.

To be more precise on topics like these is impossible simply because no one understands them. If we did, we wouldn't need huge machines like the LHC to sort them all out.

That's the LHC.

PFE013: LHC Part 1 - The Basics

Over the last several years, the LHC has been in the news a lot. Enough to hit critical mass in the media. Apparently, when it comes to science that no one understands, this means that it's okay to write stories based on a bizarre theory someone came up with, write about it as though it's widely accepted, and then include a sentence at the end explaining that it hasn't been proven yet.

Before I talk about these things, I think an understanding of how such a monstrous machine works is helpful to keeping up with a large portion of physics in the news.

A particle accelerator may be used for a variety of different things. Accelerators like the LHC, the Tevatron, or SLAC are used to study basic physics. But accelerators like this account for a very small percentage of all accelerators. There are accelerators for manufacturing electronics, medical research, and medical treatment. Most of this post will focus on the higher energy physics based accelerators, but it all applies to medical, manufacturing accelerators too.

But we have all seen particle accelerators in our everyday lives. A battery is a device that accelerates electrons. It is doing essentially the same thing as the LHC! Just on a scale about nine trillion times smaller. So an accelerator is any mechanism that creates a stream of particles going very quickly (or, more usefully, with more energy).

Particle accelerators can be classified into two main types: circular accelerators, and linear accelerators. Each with its own advantages and disadvantages.

Circular accelerators have three main parts: magnets, rf-cavities, and detectors. Since the particles that are accelerated are charged, magnets are used to bend them in a circle. In fact, there are typically two beams of particles moving in opposite directions. A simple relation can be used to show that how strong the magnets need to be increases as the speed and energy of the particles increases and decreases as the size of the circle increases. Since more new physics can be seen at higher energies, and the limiting factor is often the size of the magnets, these machines can end up being as large as 17 miles around.

The next important part is the rf-cavities. The first thing to know is that magnets can't be used to make particles go faster, they can only change their direction. To get the particles going this fast, you need something else to accelerate them. And the methods used are similar to how microwaves work. The best way to imagine how an rf-cavity works is to think of surfing. The cavity creates waves of energy moving through a chamber, and, if the particles enter the cavity at just the right point on the wave, it will be pushed through the cavity and will get a touch more energy. The major advantage of circular accelerators is that  one rf-cavity can be used many times to accelerate a particle. So particles can gain as much energy as we want, up to infinity, right? Sadly, no. As the particles are bent around the circle, energy is lost. The more energy the particles have and the sharper the curve, the more energy is lost. So eventually the amount of energy lost will equal the amount of energy the cavity can add and the particle has reached its maximum energy.

The final part is the detector. There are a number of monitoring devices to keep track of where everything is. Now they use all kinds of fancy equipment, but a story passed down to me from the early days of accelerators was that to check if the particles were in the pipe, they would stick their head in and actually look. The particles would create a blue light inside their eyeball and they would know that the machine was working properly. The main detectors are where the particles collide. At these points on the ring, the magnets bend the two beams into each other and a bunch of massive collisions (hopefully) happen. Particles are sprayed out in all directions and huge detector measures what happens to all of them, before the next particles collide, an instant later. Then, computer software figures out what happened at the collision point.

A linear accelerator operates in largely the same fashion as a circular accelerator. As it turns out, the energy lost as particles are bent around in a circle is much more for some particles than others (it goes by m^-4 for those interested). So for these sorts of particles (typically electrons) it is more efficient to line a bunch of rf-cavities and either smash two such beams or hit a stationary target. This takes more rf-cavities, but you don't need huge magnets to bend it in a circle and energy isn't lost from doing so.

I should emphasize that as much as I have covered here is only a small portion of the actual mechanics of particle accelerators. There are a number of topics that I glossed over (or simply ignored), so please ask to expand on anything that's confusing or unclear.

That's accelerators.

PFE012: $E=mc^2$

Einstein's most well known formula

is most certainly $E=mc^2$. It gets tossed around as a symbol of intelligence, but what is it really about?

First, briefly, in case you don't recall from you grad-school science, there are two principles crucial to experiments and are fundamental rules to science. The first is that mass is conserved. That is, that you can't create more matter than you have and you can't destroy the stuff. If you're doing an experiment and your mass seems to change from the beginning to the end, that means you either lost some stuff or something else was added.

The second fundamental rule is that energy is conserved. The total amount of energy in the universe is a constant and all we can do is change it's form. For example, coal in the ground has chemical potential energy that we can use to turn into electricity and then into light.

These two rules will get us a long ways. In the early 20th century, however, a number of physicists were trying to find ways to relate mass and energy directly. After a few wrong turns, the famous $E=mc^2$ equation was settled upon. What this says is that energy can be converted into mass and mass into energy.

Unfortunately, this looks like another one of those times when our grade school teachers lied to us because "they didn't think we could handle the truth" or something. So energy isn't really conserved, and neither is mass, but they can be converted back and forth from one another. So then why did it take until 1905 or so to figure all of this out? Why doesn't sunlight hitting the ground just turn into a house?

It turns out that the scale of the conversion is very uneven, at least in terms of things that we're used to. For example, if we could convert a penny entirely into energy, it would cost merely $6.40 in pennies to power New York city... for a year (extra credit (pdf)).

So on the one hand if we have matter and we want energy we're totally in luck. Then again, if we suddenly need to create matter: good luck.

But of course, I've got probably nearly 640 pennies in my car, and yet we're still struggling to meet our power needs. The problem is that this conversion is quite difficult to do. It typically requires a monstrous amount of energy to happen. The initial energy isn't gone, but if it isn't there, it won't happen. The best example of something that converts mass into giant amounts of energy is our friend the sun. The sun works so well because it is so hot, and it is so hot because it works so well. Researchers have been trying to make a sustainable version of the sun for many years now unsuccessfully. News articles puts the technology as about "20 years away". As a professor of mine joked, "it has been 20 years away for about 30 years now - and is still 20 years away". Maybe this time they'll be right, maybe not.

There is another way to turn mass into energy, and that is by using different, generally rarer materials such as uranium or plutonium. They are much more willing to give up some of their mass for energy. Such a mass conversion can yield huge amounts of energy, but is also very dangerous if proper precautions aren't taken.

What does all of this mean for all of those horrible lies our K-12 teachers filled our innocent, eager brains with? Since energy and mass are both conserved anytime there isn't anything going "nuclear", and whenever something does go nuclear, there is a strict conversion ration, we can say that "mass-energy" is conserved. That is, we can add up all of the mass and the energy at any point (by converting using the handy $E=mc^2$) and it will never change.

So I guess we can all forgive our teachers on this one because, in most cases (excepted by stars, nuclear bombs, and nuclear power plants) energy and mass are each separately conserved.

That's $E=mc^2$.

PFE011: Music

This post takes us down a slightly different direction. I have always been involved in music (hence the url), and decided to take some time to discuss it a bit.

Specifically, I'm going to talk about intervals. For some this may be old hat, but I didn't fully understand this until recently even after taking lessons for years, so I hope it is at least a little new. I should note that I am going to stick with intervals as developed in western music. There are two main reasons for this. The first is that most music that you hear on the radio, at the symphony, or that you might play, will use theory developed in this style. The second is that the non-western musical scales and intervals have always confused me.

A basic note in music typically has two main properties. The first is amplitude, or loudness. The second is frequency/wavelength/pitch.

For the sake of modeling purposes, we will consider sounds produced by a string, typically a piano string,

although any kind will do (guitar, violin, etc.). Amplitude is pretty straightforward. The farther away from straight the string vibrates the more it pushes the air and the louder it sounds to anyone who's listening.

Frequency/wavelength/pitch is generally more interesting. I should first note that, for a given string, frequency and wavelength are related. The frequency is the number of times the string vibrates back and forth per second. So if a string takes one second to vibrate back and forth, we say it has a frequency of 1 Hz. If it vibrates back and forth 440 times per second, then it has a frequency of 440 Hz and is known as middle A. One wavelength is the distance between two peaks of the wave at a given instant of time. The possible wavelengths for a given string are determined by the length of the string. Typically if you double the frequency, you halve the wavelength. That is, a string oscillating twice as fast will have shorter waves, by a factor of two.

These two things, frequency and wavelength, determine the "pitch" that we hear. A higher frequency gives a higher pitch. Also, using the above paragraph, we can see that a a longer wavelength will give a lower pitch (think about the difference in sound between a violin and a bass: two comparably constructed instruments with very different wavelengths).

The main theory surrounding relative pitches was originally based on "what sounds good". Pythagoras noticed that when two pitches were played where the second was 1/2, 2/3, 3/4, ... as long as the first, it made a pleasant sound. From this you can define a few important intervals. First, we get the octave (C-C), which is given by the ratio 2:1. That is, if two notes are an octave apart, one of them is on a string twice as long as the other. A fifth (C-G) is described by the interval 3:2 and a fourth (C-F) is described by the interval 4:3. From this you can map out all twelve tones (C,C♯,D,D♯,E,F,F♯,G,G♯,A,A♯,B). The only problem is that when you go up by fourths and fifths, they meet in the middle, and are off, by just a little bit. So to make a piano, using this kind of tuning, you have to actually select the "key" that it is going to be tuned to. That is, you can choose one of the twelve pitches to be the starting note, and music centered on that pitch will generally hit the correct intervals, but music centered somewhere else might sound noticeably out of tune.

To correct for this, a number of rather sophisticated tunings have been proposed. Each of them relies on adding a fudge factor to one interval to make everything line up. But they all are still based on a given first note. In order to make a piano play any song equally well starting on any note, the modern form of tuning makes notes equally spaced across one octave (the twelve-tone-equal-tempered tuning or 12ET). This means that every interval is going to sound a little bit wrong except for the octave.

That's music.

PFE010: Refrigerators

I will admit that when this came up with my former roommate, I completely dropped the ball.

The question is an age old one:

If you leave the refrigerator door open, will it cool your house?

First up, answer: No. Leaving your refrigerator door open will heat your house, and probably ruin your chicken casserole from last week.

Unlike the airplane on a treadmill situation (which is always unnecessarily confusing) this one is more straightforward, but somehow less obvious.

First, for the sake of completeness and clarity, I should point out that "refrigerator" includes freezer too. Anything that is supposed to keep stuff cold really.

And this brings me to the first caveat or asterisk:

I am assuming that your method of keeping food cold is not more than sixty years ago - it was around the 50s when modern refrigeration became commonplace. I should note right here that an ice box is exactly the opposite of a modern refrigerator in this regard.

Next, I have never seen a refrigerator with a direct exhaust, so I will assume that yours doesn't have one (mine doesn't, unless it goes to the neighboring apartment, I haven't really checked though).

To consider this problem from a physics point of view is a perfect demonstration of both where I previously failed in explaining this and to what Feynman discusses about context. Talking about PV (pressure - volume) graphs and vapor-compression cycles to someone who hasn't studied them, will never be successful even if he/she is involved in science.

While any such explanation is accurate, that doesn't mean it is useful. In this case, the useful explanation relies on a few well known facts. The first thing to keep in mind, is that as the heat gets "pulled out" of your leftover-saver, it has to go somewhere. That heat is energy and doesn't just disappear. Of course, how that heat is "pulled out" has to do with PV graphs and energy cycles, but isn't really relevant to the discussion here because the refrigerator ends up the same as it begins. That is it doesn't consume anything (except for electricity, we'll get to that in a minute) so the net result is that the heat that got in when you opened the door or put your taco leftovers in, has to be kicked out somewhere, typically out the back (and still in your house).

But if this was everything, then leaving the door open basically means that air goes in the front and out the back, or something (while your beer gets warm). So admittedly not cooling the house, but not warming it either, and sending waves of cool freshness over you, standing in front of it, after your long run (or tough walk up the stairs). Unfortunately, we're not this lucky, because  the second thing to remember is that anything that people build is going to be inefficient. There is going to be energy leaked somewhere, and this will turn into heat. Your refrigerator is running and fans are blowing and some crazy freon thing is going on in the back, all of which take energy. Some of this is going to be leaked as heat, somewhere. So, sadly, your house heats up.

Hopefully this explanation sufficed, but if it isn't there is another even simpler one. This has to do with the premise of a closed system. If we first consider the refrigerator as a closed system, all it can do is move heat around from one place to another (best case scenario). In which case no net change to temperature. But a refrigerator is not a closed system, it is plugged in

and uses electricity. Since there is energy being used up by the refrigerator/freezer somewhere in its process of making tasty ice cubes, that energy is going to always eventually end up as heat. Extra heat in your house.

So what about different systems? What if we are allowed to violate our asterisks? An ice box has one external input. Instead of adding electricity to the system, ice boxes merely add ice. While electricity is always going to add heat, if the ambient temperature is warmer than the ice (let's hope so) then the ice box will actually cool the house in addition to the food since heat from the air in the house will eventually result in the melting of the ice.

The other condition was a direct exhaust. If the refrigerator has a ventilation system to toss the hot excess air straight outside then, well, I guess I've just described air conditioning.

That's refrigerators.

PFE009: Airplane on a Treadmill

This was a request (for those wondering about how topics are picked) so if you have another topic you'd like to hear about, please ask and, if I think it's interesting, I will do my best to address it.

Also, I decided to do a post on friction first so things like slipping would make sense.

The "airplane on a treadmill" problem seems to be one of those internet things that just got way out of control when it hit critical mass. To address this, Randal Munroe of xkcd fame put this together which is actually pretty good.

My explanation is going to (hopefully) be a little simpler. But before I address the problem, I'd like to talk about airplanes.

Let's first think about what has to happen for an airplane to fly and remember all of those failed attempts.

If we assume an airplane is already in the air and figure out how to keep it in the air, we can do the same thing, just more so, to get it to take off. So there's an airplane in the air, and mother earth is kind of pissed and keeps trying to make it crash into the ground. So the plane has to provide some sort of lift force. So why not point those big loud engines down, that's a lot of lift right? While this would provide a metric ton (read: way more than enough) lift, it would be nearly impossible to control. Moreover, going forward wouldn't be very easy. I've actually just sort of described how a helicopter works.

Your regular airplane is what we call "fixed wing" (none of those pesky rotors) and flies basically by going forwards really fast.

The wings are shaped in this really neat fashion called an airfoil which, for the purpose of this problem, we can just say that they provide lift when air flows over them. So planes need to be moving fast, relative to the air, in order to take off. As an example, it's easier to take off into the wind than with it.

Onto the airplane on the treadmill problem itself. It should be noted that the main problem here has to do with misconceptions about the problem's formulation. In the most basic sense, the question is:

If you put an airplane on a treadmill, will it take off?

As discussed above, the only way for an airplane to take off, is if lots of air is moving over the wings.

First, we assume that the engines are off, but the treadmill is running. In this (boring case), the plane lumbers forward. You might imagine that the plane would stay still and the wheel would spin, but there is some friction as the wheels turn (imagine pulling a rug out from under a cart - it will largely result in spinny wheels, but depending on the speed of the yank and the stickiness of the wheels, it should go forward some) so the plane would lumber forward and (given a crazy long runway) eventually take off.

Alright, more interesting is the problem of when you turn the jets on. The first thing to note here is that, with the jets on, the plane will move forwards no matter what. You can get all confused about velocities on the bottom of the wheel, and the treadmill, but regardless of what is happening with the wheels and the treadmill, the plane is going to move forward relative to the air (and relative to the ground, we're assuming a calm day here) and will take off.

If that was so easy then what's the confusion all about?

In a typical wording of the problem, the author will try to be clever and explain that the treadmill is matching the speed of the wheels. This tends to lead to pages of confusion talking about reference frames and speeds everywhere on the plane. Planes aren't powered by their wheels. So they can be slipping, spinning extra fast, and the treadmill can be doing whatever it wants, the plane is still going to move forward.

If somebody asks you just admit that you probably don't know what's going on with the wheels in the way they worded it, but point out that the engines will always push the plane forward in the air and it will take off.

That's an airplane on a treadmill.

PFE008: Friction of Tires

The friction force is something that we all experience

(or don't). In spite of the commonplaceness of the friction force, it isn't listed as one of the four fundamental forces: gravity, electromagnetic, strong nuclear, and weak nuclear. Actually none of those even sound like friction. Where's the "makes-the-box-hard-to-push-across-the-floor" force? As it turns out, friction is actually the electromagnetic force (think electrical wires, magnets, shocks, light, microwaves, etc) except on a person sized scale.

The physics of what's actually happened can be reasonably thought of as the actual atoms of the box pushing against the atoms of the floor. More precisely, the electron clouds

of each atom push against each other. Since they both have the same charge (negative) they repel. This is a perfect example of Coulomb repulsion which comes out of the electromagnetic force.

But how does this apply to big boxes full of books? Let's think about what we know. If you fill up the same box on the same floor with more stuff, it's going to be harder to push. So clearly the friction force is proportional to the weight of the object. We also know that it is going to move more easily on hardwood floors than on carpet. So the materials sliding past each other is important too. This actually completely describes the equation. The force of friction is the weight of the object times a constant that describes the materials (typically of values around one half) known as the coefficient of friction. Nothing more complicated than that.

Actually, I lied. But only a little. The constant depends not only on the two materials, but also whether they are sliding past each other (dynamic) or not moving (static). But you knew this already too! When you start pushing on the box, you push harder and harder, until it suddenly starts to move, and then it's moving a whole lot! That is, the static coefficient of friction is (almost always) greater than the dynamic coefficient of friction. In other words, it's easier to keep the box moving once it's started moving, than to get it to move in the first place.

So now you know basically everything there is to know about friction, from a theoretical point of view. Let's apply this to some real life examples.

First: cars. The friction between tires and the road is consistently a source of confusion. For the moment, we will assume that your tires aren't slipping (like when you spin out, or on ice). In this case, your tires experience static friction with the ground.

This may sound misleading because, hey! My car is going fast! There's nothing static about my tires! But remember, static friction is only concerned with the relative motion of the two surfaces. At the point of contact with the ground, your tire is not moving relative to the ground. If it were, your wheels would be spinning and your car not going anywhere (i.e. spinning out). This static friction is what makes your car go forward! Your wheels push against the ground, and the ground pushes back, making your car go forward (and, actually, making the earth spin a very tiny bit in the opposite direction. Don't worry, I did the math (pdf) and we're all good.).

It's interesting to note that the limiting factor in drag racing,

is the amount of friction they can get between the tires and the road.

The next interesting friction example, is ice. Ice is super slippery. I mean, I can't think of another solid that slippery at all. So what makes ice so special? It actually has to do with what makes water so special.

The above discussion of friction only applies when both contact layers are solids. As it turns out, when you're slipping on ice, whether in shoes, on skates, or in your car, you are floating on a very thin layer of water.

This thin layer of water comes out of a bizarre property of water that is true for very few materials. Generally, when something freezes (goes from a liquid to a solid) it gets smaller. The atoms get closer together and they move less. Water does the opposite. When it's in ice form, it forms a structure (which is the same reason why snowflakes are always so pretty) so it actually expands while freezing, or shrinks when it melts. (This is why pipes freezing=bad.) That means that the liquid form of it is actually a bit smaller, so when you step on it, your weight will actually cause a teeny bit of ice on the surface under where you're standing, to turn into water. This is what allows you to slip, slide, or spin out of control.

That's friction.

PFE007: Microwaves

Everybody's got one and they are (essentially) necessary for eating nowadays. I'm talking about a pair of thumbs.

Okay, not really, but microwaves are everywhere. But I can assure you that my microwave is not micro, nor wave like (try big and boxy).

Let's first talk about regular ovens. A regular oven is either gas or electric, but either way there's a heat source at the top/bottom that heats the air next to it. As the air moves around the oven, it begins to heat the food - from the surface inwards. This isn't a particularly efficient way of transferring heat to food (it is good at killing stuff that'll make you puke your dinner) as you have to heat up all the air, then slowly heat your way through your chicken casserole.

Microwave ovens were, of course, discovered by accident (1945). Some guy was doing some crazy physics experiment and noted that the chocolate bar in his pocket melted. Whoa. Something managed to heat up chocolate but not his pants? Let's all take a moment to appreciate this.

He then modified his experiment, made some popcorn, and didn't tell anyone about it.

This machine turns electricity from the wall into microwaves into hot leftovers. Each step is tricky and special. To get from electricity to microwaves, you're going to need some fancy stuff to jack up the voltage, but then mainly just a magnetron (that's what originally liquefied the chocolate). Basically, a magnetron spins the electrons round and round. This creates microwaves of just the right length (you have to build your magnetron just the right size to get just the right length). And tada! Microwaves!

The topic of what is, "just the right length" seems to consistently be a question of confusion. In fact, my graduate professor (who's name I won't mention) said in his quantum lecture today, that microwaves are designed to be the right frequency to resonate water molecules. The wavelengths for absortion of water molecules run at about $1\mu m$ or $10^{-3}$ millimeters. That's really, really small.

As it is, microwaves run on a scale of about 5 inches (it's actually about 12.2 cm or 4.8 inches). Why this value? Well, it turns out, that the government regulates this stuff, and did so before they started putting microwaves in everyone's kitchen. This wavelength had been set aside for sciency stuff (I guess why they were using it back then) and if you run at a different length then you can mess up all the cell phones and wifi's and radios and TVs nearby.

You can actually see this for yourself on your own microwave. I looked at my (rather dirty) microwave and found that it lists 2450MHz as the frequency. This tells you how many times the microwaves go back and forth per second. More than 2 billion times. How can you get a length out of this? Microwave radiation is, essentially, the same thing as light, radio waves, and x-rays. They all move at the same speed, the speed of light. So you can use a simple formula to turn that frequency around into: 4.8 inches. Exactly as expected.

Back to the heating of food (let's be real, that's all we really care about). While microwaves aren't designed to resonant with water, they do heat water better than a lot of other things. Because of how water molecules are shaped, they try to line up with the field produced by the magnetron. But the magnetron will flip it's direction very quickly, causing the water to also flip direction.

All this flipping back and forth heats up the water molecules which in turn heats up the rest of the food. As for how the food actually heats up, it basically depends on where the water is in it. (Some other things will heat up too from this effect, but usually it's less). In theory then, your plate/bowl shouldn't heat up too much. In practice: I keep burning myself.

Are they scary? Can they give me cancer? The short answer is no and no. The only way you can hurt yourself from a microwave (outside of violating any of the safety concerns listed below) would be to actually cook yourself. That is, get the microwave to run with the door open. But even then, all that would happen is you would get hot (and probably burned) - essentially no different from sticking your arm in a regular oven. And plus, getting your microwave to microwave your hand sounds like a lot of work to burn yourself. The point here, is that when the door is closed so little radiation leaks out that the OCD FDA doesn't bother to test regularly (see the third and fourth paragraphs for more information).

Safety concerns (seriously):

1) Stuff in microwaves gets hot. I mean come on, but I still burn myself all the time because I'm an idiot.
2) Liquids can superheat. Because the temperatures in a microwave can increase so fast, if the conditions are right, a liquid may fail to boil until it's been picked up causing it to boil suddenly and explosively. I don't know how to try this and it sounds painful anyways.
3) Similarly, if your plastic container is still tightly sealed, it too can explode (this is much more likely). The pressure from the water inside heating up can blow the top off a container while it is inside the microwave or when you go to open it.
Duh.
4) Metal. Okay, so sometimes it's okay to microwave metal. I mean, the microwave is made out of metal, right? It turns out the shape of the metal is really important. Pointy things are more problematic. Since microwaves can push electrons around inside an object, and metals conduct that electricity, a charge separation can grow (think feet+carpet+winter). But if there is a smooth edge along the entire object, that charge won't be concentrated. In the event of a fork, however, the charge builds up on the point ends (your finger on your body). This can cause a massive spark or even a sustained spark. Either way, you're going to get toxic gas and a possible nasty microwave fire. And you'll look like an idiot.
5) A CD is partly metal, partly plastic, and is pretty smooth, so you should be good right? Well, having done this (I can't find mine, but here's another)

it didn't blow anything up, but there was an awful smell, probably from burning plastic. Likely killed a few brain cells. While pretty, there are a lot of prettier things out there.

So yeah, basically if you remember to open you leftover container and don't put any metal in your microwave you should be good to go. Also bad idea (apparently): firecrackers. Sounds like fun though.

That's microwaves.

PFE006: Levitation

I found out this morning that the Nobel prize in physics was awarded to a pair of Russian physicists, Andre Geim and Konstantin Novoselov for their work on graphene (pdf) in 2004 which also happens to be my area of research. What is interesting about this duo is that Konstantin was only 30 when he did the relevant work.

But more interesting than that is Andre Geim's other notable award: the Ig Nobel Prize. The Ig Nobel prize is awarded for work done in a field that can't and/or probably shouldn't be repeated, but still carries certain merit. Andre's claim here was that in 2000 he levitated a frog

in a magnetic field. "But people have levitated lots of stuff before, including trains!" you cry out, and rightly so. But trains are made of metal, frogs aren't. Geim was demonstrating levitation for all of us to see, essentially doing what I am doing.

How does this work? Well you place a frog in a tub in a strong magnetic field... yep. Magnets again. Crap.

Not to worry. The relevant physics here comes from the fact that the frog is mostly water. It turns out that water is rather diamagnetic (there are metals that are much more so, but I haven't found any bismuth frogs hopping around after a rainy day). Diamagnetic is a big word, but isn't actually all that scary. Remember how one magnet could be brought near a paper clip and the paper clip temporarily acted like a magnet and was attracted to it? The paper clips are what we call paramagnetic (the original magnet that got all this started, like those on your fridge, are called ferromagnetic). Paramagnets are attracted to nearby magnets while diamagnets are repelled. The actual behavior at the atomic level that describes the difference is definitely out of the scope of this post. But suffice it to say that a diamagnet in the shape of a frog, in a strong enough magnetic field can float.

That's levitation.

PFE005: Silicon Art

Science is an art and art is... I don't really know what art is.

Computer chips are god-only-knows what kind of tangled mess.

So many colors, so many lines. How did somebody figure out how to put all the right lines in the right place? There are, of course, millions, maybe even zillions of different ways to design an integrated circuit to get the job done, so designers seem to tend to feel a sense of pride about their creation. And this leads naturally to, art.

The top layer of a chip is going to be insulating, so it doesn't really do anything. So manufacturers typically etch a serial number on it, and perhaps a company logo. But since nearly no one was ever going to look that closely at it except for maybe their competitors, they got creative.

In my research into silicon, I came across a private company called chipworks started photographing these pictures. I have attached a few of my favorites. All of the galleries can be found here.

That's art.

PFE004: Inspiration

My inspiration for this crazy line of reasoning came from a lot of different things.

First, I realized that I was explaining a lot of really cool, but sometimes kind of hard to explain things to people of all different knowledge levels on a regular basis and repeatedly. I needed to organize my explanations.

In school you're supposed to learn physics and things, but I've also learned about myself. I've found that I like learning about how speakers work, what happens if$$q_e\neq q_p$$or efficient means of trapping energy from the sun. These aren't necessarily the sorts of things that will be covered in a typical lecture setting, but I still love finding out about them, and the satisfaction is overwhelming.

The thing that made me start to organize this is an instance of my first regular webcomic (and still is my firefox homepage). It makes you ask, how much explanation is enough? Baking soda+vinegar=bubbles. Is that enough? What should a "lay person" know about the wacky physics phenomena that go around him/her every day?

I often hear that people have a natural drive to understand the world around them. I know I do, as well as anyone else involved in physics. There's no other reason to do physics. But is this true of everyone? From my experiences, categorically no. People do not want to know what's going on around them, in my observations.

Are people just apathetic? Or is something else going on? Certainly there is a large apathy factor. Not just laziness, but a true desire to not know, to not cloud one's mind. But I think if that were the only factor, curiosity would still win out in many more people than it seems to.

The other reason for the lack of intense curiosity on "how the world works" stems from how complicated it all is. Not just complicated but counterintuitive. The sitting in a computer chair holding a spinning bike wheel thing still blows my mind every time (if you don't know, watch this). I can do the equations, and even expect it to happen, but when I sit there and grab the wheel and turn it, and I turn, I just about lose it. My body is totally unprepared for the crazy phenomena. So it seems that our internal "physics awareness module" failed to load when humans were invented. For some this just heightens the mystery. For others, it looks like a mountain too big to climb.

That's inspiration.

PFE003: Magnets

Magnets: How do they fucking work?

I'm pretty sure it's magic. Or it could be this:

I'm pretty sure it's not this though.

Richard Feynman is credited as being many things and of having many skills. One such skill is his ability to explain things to anyone. Unfortunately, when it comes to magnets, he seems to be stuck and talks about the question "Why?" and other such things.

So how do magnets work?

First, what do we know? We know that sometimes two magnets attract each other, and that if you flip one they will repel each other. We also know that the force is really quite strong. One teeny magnet can lift a paper clip off the ground. But to do so, it has to overcome the gravitational force of the entire planet.

So we've seen that magnets are super strong. But more importantly, they seem to have a direction. If you flip a magnet around, it behaves in the opposite fashion next to other magnets. Moreover, a magnet can make certain metallic objects behave like magnets when they are near by, but they then lose this property as soon as you remove the original magnet.

But the nail and the upper paper clips look the same, so something must be changing in the paper clips at a very small level.

This is about as far as practical observations can take us. But first, let's talk about electricity. We all use electricity all the time, but rarely see the results of it first hand. One example when we do, is with balloons. Rub a balloon on your hair and it will stick to the side of your head. This attractive force comes from a difference in charge between the two.

The magnetic force is very closely tied to the electric force (actually, they're the same force). While we think of the electric force as an attraction (or repulsion) from the separation of charge, the magnetic force is an attraction or repulsion from the movement of charge.

Moving charge leads to a push or a pull? Okay, at this point you're going to have to take my word on it or pretend it's magic. I'm happy either way.

Once you've accepted this magnetic force, the reason that some things show it on a large scale and some don't has to do with how their very atoms behave. As the electrons move about the atoms, sometimes, across large portions of a metal, all the electrons are spinning in the same way. This allows the magnetic field to add up, and it adds up a lot, enough to be much more powerful than gravity from the entire earth!

That's magnets.

PFE002: Perpetual Motion

When deciding how to treat a new paper, there are a number of criteria one uses to determine its crackpot level. That is, there are a lot people out there who try to publish junk under the premise of complicated science. It's the job of actual experts in their field to police this.

An extremely popular crackpot theory that comes up time and again is perpetual motion.

Most of the designs that may seem like perpetual motion rely on energy from the sun, or, more generally, a hidden energy source.

When evaluating a mechanism for perpetual motion (and to figure out where the flaw in the argument must be) I look for a way to get energy out of the system. In the example above, I would likely attach a generator to one of the pulleys to generate electricity. But then something must move the rope to make the pulley move. Clearly, there is a gravitational attraction between the blocks and the earth, and the one on the right has a larger mass, so it moves down causing the system to rotate.

Of course this system is silly, but it demonstrates the process for identifying certain classes of crackpots, an essential part of physics or any hard science.

That's (not really) perpetual motion.

PFE001: Moments

First, a photo story on the importance of moments (don't worry if you don't know what they are yet):

Thanks to the good engineers at Virginia Tech for the content.

Moments of inertia is one of those abstract things learned in kinematics. Understanding things going up and down and friction is easy, but this requires a bit of a step

Formally, a moment of inertia is usually represented by the letter I. For inertia? I'm not really sure. Anyways, here's the formula:$$I=\sum_{i=1}^Nm_ir_i^2$$It is interesting (and relevant to this example) to note that this formula depends on the axis of rotation. This axis isn't always obvious, but here it is along the crane, specifically where it flips over.

There are two reasons that the crane would flip. The first is if the center of mass of the object is outside of the base (anyone who has tried to balance something on end understands this, at least qualitatively). In the third picture, however, the car is out of the water and the crane, while leaning, seems to be doing generally alright.

The other potential problem has to do with applying a force out at a distance. The math here is unnecessary for our purposes, but basically the farther away the car is from the axis of rotation, and the heavier the car weighs in addition to how hard the crane is pulling, needs to be effectively "balanced out" by the rest of the crane. The calculation for this involves the moment of inertia of the whole crane. Needless to say, this is something that any good crane operator should be aware of.

That's moments.