Memorial Day Distractions

Summer is upon us. That means summer research, and online games. In order to help you through this three day weekend and beyond, I thought I'd share some of the more physics inspired games I've been playing lately to pass the time.

I really enjoy physics based games. When done right, I think they can not only be fun and engaging but have the opportunity to teach you something.

Cryopreservation

I'd like to start a short series of posts on what I'm doing this summer. Like most all of the first year physics graduate students, I've found a research group at Cornell for the summer, and if everything goes well, I'll continue working with them after the summer is done. This is good for three reasons. First, I'm getting paid, so I can do things like pay rent. I'm not all about the money, but having a place to live is a big deal to me. Second, I'm getting a chance to explore a new area of research, with limited expectation of commitment on my part. Third, if everything works out, I've found the group I'll be working with the for the next 4-6 years. I'd like to spend a few posts here on The Virtuosi discussing first the physics I'm considering, and then what I actually do. Today I'm going to talk about the most exciting sounding piece of my work, cryopreservation.

I was born on Wednesday

Probability is a tricky thing. There are a lot of nonsensical answers to be had. I just read an article about the recent Gathering for Gardner meeting that took place. Gathering for Gardner is a unique meeting for mathematicians, magicians and puzzle makers where they get together and talk about interesting things. The meetings were inspired by Martin Gardner, one of the awesomest dudes of our time, who unfortunately just passed away.

The question put to the floor was the following:

"I have two children. One is a boy born on a Tuesday. What is the probability I have two boys?"

Think about that for a moment. Not too hard though. The answer turns out to be surprising. Upon reading the question, I thought about it for a long time and managed to confused myself entirely. Thinking I had gone crazy, I wrote a little python script to test the riddle, which only left me more convinced I had gone insane. I've spent most of the night thinking about it, and after making it half way to crazy, I've come around and am momentarily convinced the puzzle makes perfect sense.

I'm going to attempt to convince you it makes perfect sense, but I plan on doing it in steps so as to reduce the bewilderment.

Why is the Grass Green?

I was outside talking with Alemi last week and we were both startled to realize that the frozen white tundras of Ithaca had somehow transformed into fields of green.  Apparently the snow was a temporary fixture that covered real live grass.  Neato, gang!  

The joy at seeing green grass led quickly to surprise, confusion and then anger.  Why the heck is grass green?  Well, things look a color when they reflect back that color.  So grass is green because its pigments (chlorophyll) absorb only a certain range of the visible spectrum, reflecting back the greenish bits.  But if I know anything about approximating the sun as a blackbody, I know that it has a peak output of around 550 nm (i.e. green) light.  So what's going on?  Why are plants blatantly rejecting the most abundant kind of light?

Flying back

Those of us originating on the right side of the atlantic ocean are familiar with a little quirk of international flights: the flights home are shorter. Specifically, going from Tel Aviv to New York takes about one hour longer than going the other way around.

This is an oddity, and the very first explanation that comes to mind the rotation of the Earth. After all, our naive image of a plane going up in the air might be something a little like a rock being thrown up from a moving cart, and we would imagine the plane to pick up some relative speed by not rotating as fast as the Earth. Is this a factor in the plane's movement?

Fishy Calculation Followup & New Contest

So, some you may remember when I attempted to calculate how much the oceans would lower if you took out all of the fish in an earlier post.

Well, the results came in a while ago, but I forgot to mention that I lost the contest. I was about two orders of magnitude off from the winning answer.

In light of my failure, I'm going to try again in the newest contest. This time the question is a bit stranger:

How many buff hamsters would it take to completely power a mansion?

I encourage all of The Virtuosi readers to enter as well, it only takes a minute to come up with some number.

Good luck one and all.

Esoteric Physics I - The Hall Effect

What we usually do here at the The Virtuosi is take an interesting problem, and work out the physical principles behind what we're seeing.  Or pose a question and try to answer it.  Now, I'm a big fan of this kind of thing, which is why I've done so much of it.  But I worry that it might give a slightly skewed view of physics.  Sure, physics explains things.  That's why we do it.  But not everything in physics is laser guns and solar sails.  There are a lot of interesting physics phenomena that the general public will never hear about, because they're just too, well, esoteric.  What I'm going to do is occasionally talk about such effects, and, for some of them, give you applications for these strange effects you might see on a day-to-day basis.  Today I'm going to examine the Hall effect.

Physics of Baseball: Batting

Summer is upon us, and so that means that we here at the Virtuosi have started talking about baseball. In fact, Corky and I did some simple calculations that illuminate just how impressive batting in baseball can be.

We were interested in just how hard it is to hit a pitch with the bat. So we thought we'd model hitting the ball with a rather simple approximation of a robot swinging a cylindrical bat, horizontally with some rotational speed and at a random height. The question then becomes, if the robot chooses a random height and a random time to swing, what are the chances that it gets a hit?

Cell Phone Brain Damage: Part Deux

I thought I'd take another look at cell phone damage, coming at it from a different direction than my colleague. Mostly I just want to consider the energy of the radiation that cell phones produce, and compare that with the other relevant energy scales for molecules.

Cell Phone Energy

So, lets start with cell phones. I looked at my cell phone battery, and it looks like it is rated for 1 A, at 3.5 V. So when it is running at its peak it should put out about 3.5 W of power in electromagnetic waves (assuming it reaches its rating and all of that energy is fully converted into radiation). But what form does this energy take? Well, its electromagnetic radiation, so its in the form of a bunch of photons. In order to determine the energy of each photon, we need to know the frequency of the radiation. Surfing around a bit on wikipedia, I discovered that most cell phones operate in the 33 cm radio band, or somewhere between about 800 - 900 Mhz.

How much energy does each ~ 1 Ghz photon have? We know that the energy of a photon is:
\[ E = h \nu \sim 7 \times 10^{-25} \text{ J} \sim 4 \times 10^{-6} \text{ eV} \]
it will be convenient to know the photon energy in "eV's". 1 eV is the energy of a single electron accelerated through a potential of 1 volt, or
\[ 1 eV = (1 \text{ electron charge} ) * ( 1 \text{ Volt} ) = 1.6 \times 10^{-19} \text{ J} \]

So my cell phone is sending out signals using a bunch of photons, each of which has an energy of about 4 micro eVs.  Lets consider the energy scales involved in most molecular processes and compare those scales with this energy.

Solar Sails III (because two just isn't enough)

One thing that I've wanted to quantify since reading Intelligent Life in the Universe, an outstanding book by Carl Sagan and I.S. Shklovskii, is the idea of exogenesis. Exogenesis is the hypothesis that life formed elsewhere in the universe and was somehow transferred to earth in the form of some small seed or spore. Now since E.T. E. coli presumably do not have little tiny jetpacks or other means of active transport, they would need to traverse the cosmos in some passive way. One such way would be solar sailing.

Way back in Solar Sails I, we derived equations describing the maximum speeds and time-of-travel for various distances for a given solar sail. Each of these equations was a function of the surface mass density of the sail, which is just the amount of mass per unit cross-sectional area. All we need to know is the cross-sectional area and mass of a given object and we can apply these equations to just about anything!

Ask a Physicist: Volume I

We have received our first Ask a Physicist e-query! An entity known only to us as "Hungry" writes:

"We had a dispute at a dinner party about whether blowing on hot food actually makes it cool down faster, or only gives you something to do while you wait for your food to cool."

While it is questionable whether or not I am indeed a physicist (but people do pay me to do physics) and whether I will answer definitively (there'll be some hand-waving), I'll give it my darndest.

Solar Sails II

[NOTE: In my hurry to make up for weeks of non-posts, I managed to almost immediately knock Nic's first post from the top of the page. It's got the LHC, black holes, and about 3 full cups of metric awesome, so make sure you check it out (after reading this one, of course).]

Last time we did some calculations on how fast and far our solar sails can go, but those calculations were just for the sail itself. If you are going to do any science with it, you're going to need a payload. Let's take it a step further and make it an actual spaceship (with people and everything!)

Solar Sails I

Solar sails are in the news again, and this time not just for blowing up. The Japanese space agency is launching what they hope to be the first successful solar sail tomorrow. In honor of that, we will be discussing the physics of solar sails.

First of all, what the heck are solar sails? Solar sails are a means of propulsion based on the simple observation that "Hey, sails work on boats. Therefore, they should work on interplanetary spacecraft (in space)." Boat sails work when air molecules hit into the sail and bounce back. By conservation of momentum, this gives the boat sail an itty bitty boost in momentum. Summing over the large number of air molecules moving as wind, the boat gets pushed along in the water. A similar process works with solar sails, but instead of air molecules doing the hitting, it's photons. Since each photon of a given wavelength has some momentum, by reflecting that photon the solar sail can gain a tiny bit of momentum. Summing over the large number of photons coming from the sun over a long time frame we can get a considerable boost. So let's see how good solar sails are.

Solar Sails Addendum I

As requested, below is an explicit evaluation of the silly looking integral in Solar Sails I.  If you just want some hints to do the integral, see Solar Sails Addendum II.

Solar Sails Addendum II

This is the schematic version, if you just wanted hints.  The full solution is given in Solar Sails Addendum I.

Why Black Holes from the Large Hadron Collider Won't Destroy the World

Hi everyone. As this is my first post, I thought I'd introduce myself. Like the rest of the Virtuosi, I'm a graduate student in physics at Cornell University. I work in experimental particle physics, in particular on the Compact Muon Solenoid, one of the detectors at the Large Hadron Collider. I'll post more on what I actually do at some point in the future, but I thought I'd start with a post in the spirit of some of the other fun calculations that we've done. My goal is to convince you that black holes created by the LHC cannot possibly destroy the world.

To start with, the main reason no one working on the LHC is too concerned about black holes is because of Hawking radiation. While we usually think of black holes as objects that nothing can escape from, Stephen Hawking predicted that black holes actually do emit some light, losing energy (and mass) in the process. In the case of the little bitty black holes that the LHC could produce, they should just evaporate in a shower of Hawking radiation.

That's great you say, but Hawking radiation has never actually been observed. What if Hawking is wrong and the black holes won't evaporate? Well, the usual next argument is that cosmic rays from space bombard the earth all the time, producing collisions many times more energetic than what we'll be able to produce at the LHC. To me, this is a fairly convincing argument. However, let's pretend we don't know about these cosmic rays and that there's no Hawking radiation. We can calculate what effect black holes produced by the LHC would have on the earth if they do stick around.

Freezing in Space II - Turn On The Sun!

Yesterday I considered how long it would take a human to freeze in space.  However, I considered only what would happen if you were not absorbing any radiation from nearby sources.  Today we consider what happens if you do have hot objects nearby.  Namely, the sun.  The sun provides a lot of energy, even as far away from it as we are.  It keeps the earth at a comfortable ~20 C, good for us humans, and provides the energy for life on earth, also good for us humans.  That's a lot of energy.  So maybe the sun can keep you alive when you're adrift in space.  Or at least keep you warm.  I still think you'll asphyxiate.

Freezing in Space I - Blackest Night

In the last post I made, I discussed the fact that humans radiate energy.  In that post I calculated that we actually radiate quite a lot of power.  This immediately raises a few questions, the most obvious one being: How long would it take you to freeze in space?  This question is multifaceted, and I'm going to split it between two parts.  This first part, 'Blackest Night' is how quickly we'd freeze if we were completely lost in space, nothing anywhere near.  The second part, 'Turn On The Sun!' will address what would happen in near earth orbit.

Human Radiation

Things are still busy here at the Virutosi.  Hopefully in a week or so we'll be back to normal, and much more active than we've been recently  Anyways, today I'd like to consider human radiation.  It is well known that any object will radiate energy based on its temperature.  Even more interesting, we radiate at all wavelengths, though at the human body temperature our radiation is sharply peaked in the infrared.  Even so, we still put out some x-ray radiation.  As a professor of mine once said, consider that next time you sleep with someone!  Given all this, the question on my mind today is:  how does the energy we radiate daily compare to the energy we consume?  That is, why don't I lose weight sitting here typing on the computer?

Letting Air Out of Tires II

In a recent post I calculated how cold air coming out of bike tires should feel.  However, at the end of the post, I did note that there are competing explanations for why the air cools.  There's the approach I took, which is adiabatic cooling, but there's also something called the Joule-Thomson effect.  The Joule-Thomson effect has the interesting property that helium being let out of a bike tire would actually be warmer, which suggests an immediate way to test which effect is dominant.  We pressurize a bike tire with helium, and see if the valve gets cold or hot.  This is exactly what I did.

Physics as Magic?

There's a nice post over at Physics Buzz that I thought I might draw your attention to.  The central quote for me is:

"Speaking strictly about technology - which is often the knowledge attained by physicists put into practical use by engineers - physics has created some pretty amazing things. Cars, planes, iphones, medical treatments, lasers, 3-D movies, and the Large Hadron Collider. We are constantly WOWED by science. Unfortunately, the less someone understands how these things work, the more they begin to believe anything is possible. In other words, if you don't understand the parameters that allow for amazing things (like jets!) you also don't understand the parameters that would prevent other things (like energy generating heart replacements). If you don't understand anything about physics and technology, then it appears to be nothing short of magic, and magic has no bounds..."

Letting Air Out of Tires

Have you ever noticed how when you let air out of a bike tire (or, I suppose, a car tire) it feels rather cold?  Today we're going to explore why that is, and just how cold it is.  Many people consider the air escaping from a tire as a classic example of an adiabatic process.  What is an adiabatic process?  It is a process that happens so quickly there is no time for heat flow to occur.  For our air in the bike tire this means we're letting it out of the tire so quickly that no energy can move into it from the surrounding air.