The Quantum Zeno Effect

Posted on August 28, 2012 by danielfeldman

Ok, so based on the fact that “quantum” is in the title, I’m sure your first urge is to stop reading. “Quick, Dan is going to throw some complicated physics at me….RUN!” It’s true that quantum mechanics represents some of the strangest physics we’ve come up with, but I promise, no crazy math. Mainly because I’m not that great with the machinery of quantum mechanics either. But this is something really cool, so I want you to indulge me and continue reading. I’ll do my best to keep it interesting.

So who was Zeno, anyway? He was an ancient Greek philosopher, known for his paradoxes. I want to call your attention to one of them in particular: the arrow paradox. Imagine an arrow flying through the air. Take its flight and break it down into each individual moment. At any given infinitesimal piece of time, the arrow is stationary: it is not moving to where it is because it’s already there, and it is not moving to where it is not, because it is not moving. So if motion is impossible at individual moments, and time is made up of moments, then motion as a whole is impossible.

Compare this to the famous adage that a watched pot never boils. We know that this isn’t true, and that really you staring at the pot makes you bored, and so time seems to slow down. But the pot still boils after a specific amount of time.

Now for some physics. In classical physics, systems are deterministic: what that means is that a system has distinct properties (such as position, speed, etc.) that I can precisely measure and predict based on the laws of physics. Say I put Al Gore in an empty room. I want to let him run wild, and measure his position after three minutes. According to the laws of kidnapped, failed presidential-candidate physics, Al Gore will always run to the window and attempt to open it so he can escape. I know that no matter how many times I measure his position, after 3 minutes, he will be at the window attempting to escape. This is deterministic, because even if I run the experiment 100 times, Al Gore will always be in that same spot.

But what if Al Gore (and the room) were the size of an atom? Then we’d be in the quantum world, where physics is probabilistic. This time, after 3 minutes, there are probabilities associated to each possible position he could be occupying in the room. This is known as Al Gore’s “wave function”, which describes the probabilities I just mentioned. As an example, there could be an 70% chance that he is at the window, 20% chance he’s on the floor, and a 10% chance he’s where he started. Due to this probabilistic nature, I won’t know where he is until I “make a measurement”, in which I can find out where he is. Once I make this measurement, akin to looking in the window, I know with 100% certainty where he is, and the wave function “collapses”, meaning that it is 100% at my measurement and 0% everywhere else. If I then look away from the window, his wave function “evolves” (changes) again, and it goes back to multiple non-zero probabilities (maybe now there’s a 15% chance he’s on the other side of the room, crying).

I hope I haven’t lost you yet. Let’s re-examine the watched pot, but this time, the pot is a “quantum” pot. At the initial start time, the water in the pot is not boiled. As time passes, the water will have a probability that it has boiled and a probability that it has not. It is only when we examine the water that we see if it has boiled or not. If we make multiple measurements spread out long enough (maybe we examine the water every minute), then eventually, we will catch it when it has a non-zero probability of it being boiled, and so it will eventually boil. But what happens as we examine it at smaller time intervals? Maybe we effectively stare at the pot the whole time. Then its wave function stays collapsed, meaning that there will always be a 100% chance it is not boiled, and a 0% chance it is boiled. The main idea is that the more you measure a quantum system, the more it is disturbed—if you make really fast measurements, one after the other, then a system’s wave function doesn’t have time to “evolve”, and so the system is not going to change.

And so my friends, a watched quantum pot never boils! This effect is known as the Quantum Zeno Effect, because it resembles his famous paradox which talks about measuring at infinitesimal time intervals. In general, quantum physics is mostly math and little interpretation: most of quantum mechanics is hard to understand in the physical world (in real life, water in heated pots always boil). But experimentally, quantum physics is an extremely precise, working theory, and has to be right. It’s the interpretation to the real world we have trouble with. That’s what makes it so mind-boggling, so strange, and so exciting. I will leave you with the words of David Griffiths, the man who wrote the textbook I’ve learned the most quantum from:

“[Quantum Mechanics] has stood the test of time, and emerged unscathed from every experimental challenge. But I cannot believe this is the end of the story; at the very least, we have much to learn about the nature of measurement and the mechanism of collapse. And it is entirely possible that future generations will look back, from the vantage point of a more sophisticated theory, and wonder how we could have been so gullible.”

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Leap Seconds and Earth’s Rotation

Posted on August 26, 2012 by danielfeldman

As most of you probably know, the “longest day of the year,” which should really be referred to as the “day of the year with the most sunlight,” is the summer solstice (the first day of summer, typically June 21st for the northern hemisphere of Earth). All days of the year are actually the same length…24 hours. But not in 2012. For those of you paying attention, there was a slightly longer day: June 30th. You probably didn’t feel the difference though—it was 86,401 seconds long, compared to the usual 86,400 seconds. That’s right, we had what’s called a leap second. But why?

Interestingly enough, it has to do with the Moon (shocked, right?). For those of you who learned about tides in school (yes Bill O’Reilly, we can explain them), you should know that the Moon is in the middle of a tug of war with the Earth, and as such, the part of Earth closest to the Moon feels the most tugging, causing the tides. Because the oceans are feeling this tugging against the continental shelves on Earth, a great amount of friction is felt—this is slowing down Earth’s rotation ever so slightly. It also causes the Moon to get farther away from Earth—it’s receding from us about 2 inches every year!

Think back to my last entry, where I talked about angular momentum. A spinning object will want to stay spinning unless something affects it. If the spinning object loses energy, it slows down. The Earth, in this case, is the spinning object. It rotates completely (roughly speaking) in 24 hours. However, the aforementioned friction is causing Earth to lose some of its energy to heat—in the same way your hands heat up when you rub them together and produce friction—which slows the Earth down. If the Earth spins slower, that means the length of the day gets longer. To be a little more precise, the Earth’s day is getting longer at a rate of about 1/500th of a second each century.

It may seem small compared to the lifetime of a human being, but think about how long the Earth has been around. Back when dinosaurs roamed the Earth, there was a time when a day on Earth was 23 hours long. But even in this timeframe, that of a human lifetime, the effects are still real.

For a long time, humans used the Earth as the most precise measurement of time. Sundials used the shadows caused by the Sun to tell the time of day, but wasn’t of much help at night. Early analog clocks and watches were very accurate and useful at all times, but were often a little too slow to keep up with the Earth’s more precise measurements, and so would have to be adjusted every now and then. With the invention of atomic clocks, everything changed. Suddenly, we had clocks more accurate than the Earth…after a while, the Earth slows enough that it gets to be almost a full second behind our atomic clocks.

That’s where leap seconds come in. Ever since the 1970’s, we’ve been adding “leap seconds” to compensate for the Earth’s slowing. Every so often, we add one second to the last day in either June or December to allow for the Earth to catch up to our atomic clocks. Neat, huh? There’s actually an organization known as the International Earth Rotation and Reference System Service that keeps track of the Earth’s rotation, and decides when to add a leap second to the year. So far, we’ve added 25 total leap seconds since the practice was introduced. Certainly an important job…but it seems a little boring to me. I’m glad I’m not watching the Earth rotate…that’s like watching the grass grow.

But this system does have some controversy. There are some problems with adding leap seconds, most of which are computing related. Proposals to end the practice have been submitted, and a decision is set to be made in 2015 at the World Radio Conference. Who knew a few extra seconds could make such a big deal? It goes to show you how much each moment matters.

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Will The Earth Collide With The Sun? (No)

Posted on August 6, 2012 by danielfeldman

Yesterday, a young friend (perhaps a few young friends) posed this question to me: “When will the Earth collide with the Sun?” I will amend the question to “will the Earth collide with the Sun” so that I can provide the answer: no.

To understand why the answer is no, we must first understand a few concepts of physics, mainly that of angular momentum. If you remember, an object in motion (or at rest) will want to stay that way unless it interacts with something that will change its motion. For instance, when you are running really fast, you find it hard to slow down, because your body wants to stay in motion–to slow down to a halt, you create friction between your feet and the ground (as well as with the air), and you eventually come to a stop. This type of momentum is called linear momentum–the tendency for moving (or resting) objects to continue in that direction unless something else interferes. This is why, in baseball, the player running to first base always runs way past it…even though he/she would want to slow down once they step on the base, it takes a while before they can.

The same thing is true for angular movement, like spinning or circular motion. Think about when you spin a bucket around–when the bucket is spinning around, it’s hard to keep it from completing the circle, because it wants to continue moving. This is appropriately called angular momentum, and it’s the reason we don’t fall into the sun.

For anyone who has been to a museum (often ones with scientific backgrounds), you may remember the neat spiral wishing well coin funnels, where you drop a coin in and it spirals in towards the center. These are popular with science museums because they are perfect examples of the principle of angular momentum. What happens when you drop a coin in? It starts out going in a circle at the outer edge. According to angular momentum, unless something interferes with the coin, it should remain moving in a circle around the hole in the middle forever, staying at the same height and speed. But that doesn’t happen, because gravity and friction remove energy from the coin, slowing it down. When the coin slows, it loses angular momentum. Because the coin is slowing down and losing angular momentum, it begins to spiral into the hole in the center, and eventually, drops into the middle and comes to rest.

Now think of the Earth as the coin and the Sun as the hole in the center of the funnel. The Earth is going around the Sun in a circle (well, it travels in an ellipse, but it’s the same idea), and it has a speed in which it is traveling. Therefore, the Earth has angular momentum which keeps it traveling in the circle. Like the coin, if you wanted the Earth to collide with the Sun, it would have to slow down, and therefore lose angular momentum. While the interactions the Earth undergoes on a yearly basis are very complicated, suffice it to say that the net interactions are luckily negligible, and so we are not spiraling towards the sun.

Don’t believe me? If we were losing angular momentum, and were spiraling into the Sun, then our orbit around the sun would be shrinking, and our distance from the Sun would be shorter. While the Earth is getting warmer, this is not why (see: Climate Change for more information). What is noticeable, however, is that the Earth’s rotation is slowing down ever so slightly. Over time, the length of our day is getting slightly longer, and this has caused us to establish leap seconds to help compensate.

And so, thanks to angular momentum, we have much more important things to worry about than the Earth falling into the Sun. Will the Earth collide with the Sun? No.

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Fire, Energy, and the Nature of Science

Posted on June 29, 2012 by danielfeldman

What is energy? This is the simple, three word question that stumped me while I was tutoring physics this year. I was surprised when I realized that nobody had ever asked me this before, and even more so when I (quickly) realized that I did not have a good answer. Sure, I know the definitions of “types of energy” that I’ve memorized over the years–the ones that allow me enough of an understanding to solve some basic problems. But what is energy? Do you know? I’d love to hear your answers!

This is a problem that pervades many areas of science, not just physics. I’ve run the undergraduate gamut of physics, and very rarely have I ever heard this question asked: “OK Professor, but what is it?” And when the question was asked, the most popular response was “it doesn’t matter, as long as you know how to solve the problems.” I feel enlightened already.

Part of the problem is the nature of science itself. In many cases, we don’t know what something is. Like Richard Feynman, I’m perfectly fine living with the fact that I don’t have an explanation for what energy is. I know it’s a concept that physicists use to solve complicated problems, because it’s defined as a conserved quantity of nature. We say that everything in the Universe has some sort of energy, which manifests itself in a variety of forms: kinetic energy, which is the energy of motion; potential energy, which is the energy an object has that can allow it to do some kind of work; and internal energy, which is usually thought of as temperature and can usually be released in reactions in the form of light (remember, heat is just another form of light called infrared radiation). But I haven’t actually answered the question–a physics professor of mine literally admitted in one of our classes that potential energy doesn’t really exist, but rather it’s just a concept that physicists use to help them solve problems more easily.

But we can’t always be let off this easily. Many things in the real world do exist, and we often fail to ask the simple question. Alan Alda recently posed one of these questions in his flame challenge: “What is a flame?” The contest was for people to submit explanations for flames in a way that 11 year olds can understand (and possibly find fun as well). When I heard about this contest, I was similarly taken aback, because I realized just how hard it was to explain what a flame actually is, especially in a way that a 5th grader can understand. Apparently, as an 11 year old, little Alan Alda posed this question to his teacher, who gave a cop out answer akin to what most professors I know would give: “it’s oxidation.” How informative.

There’s two points I am trying to make here. The first is more direct, and it is that we need to spend more time asking one of the most important and simple questions: “What is it?” The reason I got interested in science as a kid was because I loved to ask that question, and to receive useful answers. I became even more excited when I realized that we don’t always know the answer, but we can spend time finding it out. The enlightenment you can get when you receive an answer (whether from a teacher, an experiment, or otherwise) can be really gratifying and exciting. The second point is an indirect spinoff of the first, which is that many teachers (of all levels) need to spend more time embracing this understanding. I find that too many focus on how to solve problems that they breeze through the concept like it doesn’t matter.

But in my opinion, it matters most of all. Before I can face the unknown problems of the Universe, I have to come to some sort of understanding of how it works. We don’t know everything, but that’s what exciting–and the things we do know need to be explained. And without the concepts, science is just plain boring. That’s why people like Bill Nye are so popular–they explain science in a way that we can all understand. And as scientists and educators, I think we all need to spend at least some time asking (and answering) the simple, tough questions. In my opinion, this is the best way to make science (especially physics) much more interesting and fun to both children and adults.

Consider this my challenge to you all. What is energy?

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