## Friday, April 30, 2010

### The Beer Diet

I know it's been pretty quiet over here this week.  The semester is winding down (a week of classes left), and that means that things have been kicked up into another gear.  We've got four or five ideas bouncing around at the moment, so hopefully we'll get some up soon.  Today I'd like to talk about the beer diet.  A while back, there was a rumor going around that if you drank ice cold beer your body would burn more calories heating the beer than the beer contained.  It turns out that this false, and I think the claim relied on a lack of knowledge that the American food Calorie is actually one thousand calories (note the difference in capitalization).  Let's prove this to ourselves.

## Tuesday, April 27, 2010

### Cell Phone Brain Damage... or not.

For better or worse, cell phones are a part of our lives. I say this because they can be convenient when needed, but there's nothing more annoying than a dropped call or an inconveniently timed ring tone. Since many people carry their phones with them daily, there has been a number of studies which ask what are the long-term health effects of cell phone usage. While the controversy rages among medical researchers, I decided to find my own answers by doing a calculation based on the power output of a simple hand set.

## Sunday, April 25, 2010

I came across what might be the best advice any student (nay any human being) could possibly ever receive reading a book today...

## Thursday, April 22, 2010

### End of the Earth Physics III- Asteroids!

No day of earth destroying celebration would be complete without that apocalyptic all-time favorite: the asteroid. And to be fair, it deserves to be the favorite. Of all the doomsday predictions out there (nuclear holocaust for the cynics, death by snoo-snoo for the optimists) it is the only one that is just about certain to occur at some point in the geological near future. On top of that, it's one that we could potentially avoid with enough time and some neat ideas .

Let's model an asteroid impact on the earth. We will assume an asteroid starting from rest at infinity and falling to the surface of the earth due to earth's gravity only. Now obviously these assumptions are not exactly correct. We can imagine our asteroid not starting from rest or feeling some force due to the sun. Each of these would certainly change our answer, but should still be within an order of magnitude of our result.

### Earth Day - Earth Units

In honor of Earth day, I thought I would take a look at what it would mean to do physics in 'Earth' units. What do I mean by that? Well lets be anti-Copernican here, in fact lets assume the opposite of the
Copernican principle, and state that the Earth is privileged in the universe and define all of our units around the Earth.

So, I will put a little subscript earth on all of the 'earth' units. They are to be read as 'earth meters' or 'earth amps', etc. We will take as our starting point the mass, radius and day of the earth, normalizing all of our standards to that. This gives us our initial conversion factors
$1 g_{\oplus} = M_{\oplus} = 5.9742 \times 10^{34} \text{ kg}$
$1 m_{\oplus} = R_{\oplus} = 6378.1 \text{ km}$
$1 s_{\oplus} = T_{\oplus} = 86,400 \text{ s}$

From this, we can figure out what all of the other 'earth' units would be.

### Nobody Really Gets Quantum

Nobody Really Gets Quantum / Etgar Keret

On Yom Kippur eve Quantum walked over to Einstein's house to seek forgiveness. "I'm not home," shouted Einstein from behind a closed door. On the way home people taunted him and somebody even hit him with an empty can of coke. Quantum pretended not to care, but deep inside he was really hurt. Nobody really gets Quantum, everybody hates him. "You parasite" people cry out when he's walking down the street, "why are you dodging the draft?" - "I wanted to enlist," Quantum tries to say, "but they wouldn't take me, because I'm so small." Not that anybody listens to Quantum. Nobody listens to Quantum when he tries to speak up for himself, but when he says something that can be misconstrued, oh, then suddenly everybody's paying attention. Quantum can say something innocent like "wow, what a cat!" and right away the news says he's making provocations and run off to talk to Schrodinger. And anyway, the media hates Quantum most, because once when he was interviewed in Scientific American Quantum said that the observer affects the observed event, and all the journalists thought he was talking about the coverage of the Intifada and claimed he was deliberately inciting the masses. And Quantum can keep talking until tomorrow about how he didn't mean it and he has no political affiliation, nobody believes him anyway. Everybody knows he's friends with Yuval Ne'eman.

### End of the Earth II - Blaze of Glory

In honor of earth day today, many bloggers are posting things about how to save the earth, or retrospectives on earth days past. We here at The Virtuosi decided, what better way to celebrate the earth than to figure out how to destroy it? So that is exactly what we intend to do. This post will focus on the destruction of the earth by a laser beam. This is a familiar concept. Whether it is Marvin the Martian or the Death Star, destroying planets with lasers (or threatening to) is a common theme.

We will be considering two questions today.  The first is fairly obvious:  how much power would the death star need to destroy the earth?  The second relates to a topic of continuing interest of mine: how much would the death star recoil upon firing?

## Wednesday, April 21, 2010

### Laser Launching

Lasers seem to be on my mind recently.  Just yesterday, the class I TA for (E&M for engineers) talked about the momentum carried by E&M waves.  This called to mind a discussion I had with a housemate a few weeks back.  He had heard somewhere that 'they' were thinking of launching satellites with lasers.  No way, I thought to myself.  Satellites are too heavy.  However, his question has been hovering around in my mind, so I've decided to try and answer it: can we use a laser to launch a satellite into orbit?

### Laser Gun Recoil: Follow-up

Matt Springer over at Built on Facts has a very nice post following up on my earlier analysis of whether or not a laser gun would recoil.  In my analysis I came to the conclusion that the momentum delivered was much less than that of a conventional gun, but that the impulse, and hence the force delivered, was about the same.  However, that force was delivered over a ~30ns timescale, which left open the question of whether or not the wielder would be able to feel that recoil.

While I had thought to possibly return to this issue at some point, Matt has beat me to it.  This is fortuitous, because I wasn't sure quite where to start with the question, while he approaches it in a very sensible, clear manner.  The gist of his post is that he compares our response to short time scale forces to our ability to sense sound.  I won't go through his calculations, you can check those out for yourself, but he concludes that it is very unlikely that we could feel the recoil of our laser gun.

Case closed.  Though, like any good scientist, we may choose to reopen it later if more evidence comes to light.

### Q Factors

When I walk in my door when I get home, I hook my keys, which I keep on a carabiner, onto a binder clip that I've clipped onto my window sill.  Its a great way to never lose your keys.  But one thing I always notice is that when I hook it on, it swings, and every time it swings it makes a click.  This you might expect.  What always surprises me is how long the keys keep swinging.  They seem to swing for a surprisingly long time, minutes.

It always catches me off guard.  In order to explain why, I get to talk about Q Factors

## Saturday, April 17, 2010

### The End of Earth Physics I

I was reading the Wikipedia page for the Hitchhiker's Guide books the other day and found that it started as a series of radio shows called "The Ends of Earth." At the end of each episode, the Earth would be destroyed. Since I feel like this is the best way to end any TV show/movie/book/news broadcast/Mayan calendar, I will shamelessly steal the idea.

Since this is the first End of the Earth post, we will start small and just consider the boiling off of all the world's oceans. To be precise, we will consider how much energy it would take to turn all the world's water at 0 degrees Celsius to water vapor at 100 degrees Celsius.

## Friday, April 16, 2010

### Entropy and the Arrow of Time

Somebody I talked to yesterday about what should the topic of my post be suggested that I should write something about cosmology, in particular the Big Bang and the ultimate fate of the universe. Being mostly interested in condensed matter, I am by no means an expert in cosmology (I’ll leave that to Corky). However, I will not abandon the request, but instead, spin it in a more condensed matter direction, by talking about Entropy.

### Physics for non-physicists

This is my first (but certainly not the last) post in this blog, so let me introduce myself. My name is Nikolay, and as most of the others contributing to the blog, I am also a first-year graduate student in physics at Cornell.

So, what is my motivation to join the team headed by Mr. Alemi in contributing to the blog? I happen to have many friends that are not in physics. In fact, probably due to the fact that I graduated from a liberal arts college, many of my friends have never taken any physics beyond that one class in high school, which due to both the inherent difficulty of teaching physics at introductory level and the lack of good high school physics teachers was often an unpleasant experience that scared them away from physics for life. Now, imagine what my difficulty is when on a daily basis I have to answer the question: “So what do you study/work on as a graduate student?” I usually try to come up with a sentence or two describing the essence of what I am doing without going into too many details, but even that is a daunting task. There seems to be a disconnect between the world in which a physicist lives and the general public. As Chad Orzel pointed out in the talk that motivated the creation of this blog, this is not the general public’s fault, but our fault as physicists of not really committing enough effort in relating our knowledge to the rest of the world.

In short, my goal is to create a series of posts about physics geared to people with no physics background that would build upon each other and culminate with a post providing an answer to the question of what my research project is beyond the generic words I would often resort to that would rather leave most people confused. I plan to use as little math as possible, which will not be an easy task considering that math is the language of choice for physics. However, mathematics is just a tool, and physics is not about equations and complicated algebra, but about how nature works, which we should be able to formulate in plain English. I know I am embarking on a difficult task, so wish me luck, and please leave your thoughts in the remarks section of the blog, since any feedback would be appreciated.

## Thursday, April 15, 2010

### Onsager's Tour de Force

In 1943 in a tour de force of mathematical physics, Lars Onsager solved the 2D Ising Model.

His solution has proved crucial in furthering statistical mechanics, allowing theorists to check all of there approximation schemes against analytical results.

I call his effort a tour de force because it was a huge mathematical exercise, his solution spanning 33 pages. I also call it a 'tour de force' because I have seen it referenced as such in no less than 5 different sources, as well as numerous times in speech. This got me wondering, just how many times is Onsager's solution called a tour de force...

### Another Reason Why The Core is Stupid

I assume everyone has heard of The Core, the terrible scifi movie from 2003.

If you haven't you're missing out on what appears to be, according to Discover magazine, the worst sci-fi film ever. There are already numerous sites that discuss the bad science in the core (here, or over at Bad Astronomy), but they all seem to ignore another fundamental problem with the plot.

I don't think I'll give too much away if I tell you that the basic premise of the movie is that the earth's core has stopped rotating, and so the earth's magnetic field is collapsing, which they claim will mean that all of the previously deflected microwaves (note: EM radiation is not bent by a magnetic field) will cook us all. Now, a lot of people have focused on the microwaves bit, which while bad science, one could argue that we would still have some bad effects from loosing our magnetic field.

The problem I have is that the Earth's magnetic field cannot change that abruptly.

## Wednesday, April 14, 2010

### Locating the Sun Photo

This photo has been making the rounds on the internet lately:
Originally from here.

Its a time lapse photo of the sun taken from a pinhole camera from June until December. The real question is: Where was this photo taken?

## Tuesday, April 13, 2010

### The malleability of theory

There were some undergrads in my office for office hours the other day, asking questions for the midterm. I'm teaching the engineering course on optics and waves (also known as Things that go Sine) and the students were looking at a problem dealing with quarter-wave plates.

A quarter-wave plate, the question goes, is a kind of optical instrument that turns light with linear polarization into circular polarization. Show, it continues, that it also turns light with circular polarization linear.

After a minute or two of discussing how a quarter-wave plate work ("what, does it act differently on different axes?" giggled one, and everybody gasped when I said yes) we went to the math. I wrote down the equations for light with linear and circular polarization,

$E_0 \hat{x} \cos\left(kz-\omega t\right) \to \frac{E_0}{\sqrt{2}}\hat{x}\cos\left(kz-\omega t\right) + \frac{E_0}{\sqrt{2}}\hat{y}\sin\left(kz-\omega t\right)$

with a little arrow in between them to signify that the quarter-wave plate turns one into the other.

### Bubbles!

Ever wonder why don't you see a standard rainbow when looking at a thin film such as soap stretched across a membrane ready for bubble making? Well, I encountered this problem when I presented my intro physics section with a quiz question today. Properly stated, the question was...

## Sunday, April 11, 2010

### On the Nature of Many Penny Systems

The other day I was on my way through ye olde internets to the Quantum Leap episode index at Wikipedia, but stumbled over a quote by Feynman by accident:

"There are 10^11 stars in the galaxy. That used to be a huge number. But it's only a hundred billion. It's less than the national deficit! We used to call them astronomical numbers. Now we should call them economical numbers"

So this got me thinking. What if we decided to pay the national debt...in pennies? Seems fair enough, we don't really want to pay it and when you don't want to pay something but you have to you pay it in pennies. Hooray!

## Friday, April 9, 2010

### On the Superposition of Hip and Hop

For posterity, completeness and another superfluous Scott Bakula reference I present the following. It is an expression, through the majesty of song (rap), of our love for all things quantum and undead ( or perhaps a superposition of dead/ not dead states...? ).

We all know that the great physicist Paul Dirac, was not a vampire. What this rap presupposes is... maybe he was? If so, he would almost certainly be named Diracula. He would be especially good at physics. But he would especially be totally rad at rapping.

Without further ado, the Diracula Rapula:

### Fishy Calculation

Aaron Santos over at A Diary of Numbers, author of How Many Licks?, has posted a Fermi Contest.

For the uninitiated, a Fermi Problem is a seemingly unanswerable problem, which you can actually estimate reasonable by breaking the problem down into smaller parts. They're really fun, and I intend to post more in the future.

The question at hand is: How far would the oceans sink if we took all the fish out?

I'll answer in two very different ways.

## Thursday, April 8, 2010

### Would a laser gun recoil?

Today I'd like to approach a question near and dear to many a geek heart: do laser guns have recoil?

Let's motivate our question a little bit.  I've wondered about this question since I saw star wars.  Though I'm no firearms expert, the recoil in guns must come from conservation of momentum principles. Momentum is conserved in a system. The gun starts with zero momentum. We fire, give the bullet momentum, and so to keep the system at zero momentum, the gun must gain equal and opposite momentum. That is, the gun will move backwards.

All of that was for conventional guns. Light carries momentum, so if we fire a pulse of light, we expect our laser gun to recoil. So yes, they do have recoil. Satisfied, dear readers? Neither am I. The question we really mean to ask is, does a laser gun have noticeable recoil?

We've added a new feature here at the Virtuosi.  Ask a Physicist.  To the right in the sidebar you will see a link to our shared email account.  Feel free to send us email asking any question you desire.  We will do our best as starting PhD Graduate students to answer.

Wondering about some physics principle?  Want to know what life as a grad student is like?  Want to know our favorite music?  Ask away.

## Wednesday, April 7, 2010

### Lessons in Prohibition: One

"Holy lack of self control, Batman!"

Cornell University Department of Physics-A P6510 Auxiliary Report

Introduction:
I feel terrible. Batman made me feel terrible. Batman also cost me 20 bucks.

### Falling water - hot or cold?

Hello everyone! Since this is my first post as one of the virtuosi, I should probably introduce myself a little. I'm a first year graduate student in physics at Cornell university. I did my undergraduate work at Oberlin college (I know, you've never heard of it), and I'm currently just trying to keep my head above water and take in as much physics as I can. Additionally, I'm trying to find work for the summer, I might post more on that later.

Today, the question that is on my mind is: How much does a water droplet heat up when it goes over niagara falls?
(image from http://grandcanyon.free.fr/)

Let's begin with a little motivation. Why would a water droplet heat up when it falls? Well, the physical mechanism is that as it falls through air, air resistance dissipates energy. This energy is dissipated mostly as heat, so we expect to put some additional heat into our water droplet as it falls.

More quantitatively, assume the water is going to fall from some height h to the ground. The gravitational potential energy of our water droplet is given by
$PE=mgh$
where m is the mass of the droplet and g is acceleration due to gravity. We assume that the particle starts with no initial velocity. It is very easy to place an upper bound on how much the droplet will warm. The maximum heating will happen if all of the potential energy were converted to thermal energy. The temperature change wound be
$mc\Delta T = mgh$
so
$\Delta T = \frac{gh}{c}$
Where c is the specific heat of water.

Niagara falls is 51m tall, g is 9.8m/s*s and c is 4.1kJ/kg*K so this gives a maximum temperature change of .12C=.22F, fractions of a degree.

However, we can do better than this.

## So me and Jesse got to thinking today about Railguns. Every year in Physics 213 a common homework problem is a rather simple model of a railgun. We tried to think about a more realistic model.  We simulated a rail connected to a voltage source with a limiting resistor, moving under its own magnetic field with a back-emf.

Short answer:  Doesn't work very well if you limit the current, but works great if you dump a MA or so down the wire.

See the full solution after the jump.

## Tuesday, April 6, 2010

### LaTeX Test

Hopefully $\LaTeX$ is now enabled thanks to the tip at: WatchMath.

This is a test.

$E = mc^2$

$\frac{1}{\sqrt{2 \pi \sigma^2} } \int_{-\infty}^\infty dx\ \exp \left( -\frac{ (x-\mu)^2 }{ 2 \sigma^2 } \right) = 1$