Physics Tutor: Quantum Mechanics in the 5th Century

Posted by Mike Goldman on 10/9/13 8:30 AM

physics tutor

Welcome back to our series on the wonderful strangeness of quantum measurement!

In this final post, let’s see what an ancient Greek philosopher has to tell us about the working of modern quantum mechanics.

The philosopher Zeno lived in a Greek colony off the coast of Italy during the 5th century BCE.  He was born just before Socrates, Plato, and Aristotle, at a time when Rome over on the mainland was a fledgling little city-state.  He is famous today for his paradoxes, which force us to consider the basic facts of time and space in a new and counter-intuitive way.

Let’s look at one of these paradoxes, the paradox of the arrow. 

Imagine you shoot an arrow at a target, and you snap a slow-motion picture of the arrow as it flies.  In this one instant, this infinitesimally thin slice of time, the arrow appears to be frozen.  In your photo, the arrow hangs motionless in the air.

Now imagine that you take a series of pictures as the arrow flies – click, click, click – a hundred pictures of the arrow perfectly frozen in midair.  Now imagine that you are constantly photographing the arrow.  The camera whirs, and there is not a moment of time when you don’t freeze the arrow in place.  Zeno reasoned that if any stretch of time – a second, a day, a decade – is just a series of moments, and if the arrow does not move during any one moment, then the arrow must not move at all.

Obviously, this conclusion is false; the arrow flies to its target over the course of a second or so, just as it moves an infinitesimally short distance during each infinitesimally thin slice of time.  Further, the fact that we were photographing the arrow didn’t affect its flight at all.  If we had covered the camera’s lens and closed our eyes after launching the arrow, it still would have hit the same target in the same amount of time.

What happens if we stop considering an arrow and consider an atom instead?  In the quantum world, can we slow down an atom if we take its picture quickly enough?

Amazingly, it turns out that we can!

First, a small bit of background.  Let’s consider an atom where the outermost electron can be in one of two states: a ground state, which has a low energy, and an excited state, which has a high energy.  To minimize its energy, the atom spends almost all of its time in the ground state.  We can, however, shine a laser pulse on the atom, which gives the atom energy and puts the electron in the excited state.

The atom will stay in the excited state for a while, but eventually, the atom will spontaneously emit a photon to get back to the ground state.  Much like nuclear decay, where the radioactivity has a specific half-life, this process is random but it follows a characteristic timescale.  50% of atoms remain in the excited state after the first 10 nanoseconds, 25% after the first 20, 12.5% after the first 30, etc.  This timescale, the specific choice of 10 nanoseconds, is just an intrinsic value of the atom and its environment.

Can we slow down this timescale, though?  Can we stretch out the decay so that 80% of atoms survive the first 10 nanoseconds without emitting instead of just 50%?  We can, and this phenomenon is called the Quantum Zeno Effect after the arrow paradox.

How does the Quantum Zeno Effect work?  Measurement!

Quantum measurement is the key to this process!  If we continually measure the state of the atom, we are continually forcing it to choose either the excited state or the ground state.  Since the atom starts in the excited state and we never give it time to decay, then we can, in theory, force the atom to stay in the excited state for as long as we want.

This notion is a bit abstract, though, so let’s consider another metaphor.  Say you’re tired and you’re trying to fall asleep.  You lie there, drowsy but fully awake.  The act of falling asleep is instantaneous – lights out! – and there’s some constant probability that you’ll fall asleep in any given minute.  You go to bed at 11 pm, and there’s a 50% chance you’ve fallen asleep by 11:15, 75% chance you’ve fallen asleep by 11:30, 87.5% chance you’ve fallen asleep by 11:45, etc.

That’s all fine – you’ll be asleep in no time – but there’s a problem.  Your little brother is in the bunk below yours and, for some utterly incomprehensible reason, he was able to wolf down a king-size candy bar just before bedtime.  At 11:10, you feel a kick and hear, “hey, are you awake?”  If you are lucky enough to have fallen asleep already, you don’t wake up and you’re free to continue enjoying your dreams.  If you hadn’t fallen asleep, well, then you’re fully awake now.

Since you’re fully awake, you need to reset your probability clock.  There’s now a 50% chance you’ve fallen asleep by 11:25, 75% chance you’ve fallen asleep by KICK!  Ugh, alright, it’s 11:12 and you’re fully awake again.  Your brother, in his impatience, barely even gave you a chance to doze off.

You can see that the more frequently your brother kicks your bunk, the less likely it is that you’ll ever be able to fall asleep.  Sure, there was some probability that you would have fallen asleep between 11:10 and 11:12, but it was very small.  If your brother continues to kick every 2 minutes, then you’ll eventually fall asleep but it will probably take quite a long time.

This is the same mechanism, essentially, that is at work in the quantum world.

If we continually measure the state of the atom, we slow down its decay.  We actually do slow down the flight of the arrow, from archer to target, with the click of our camera’s shutter.

I hope that this series has given you a taste of some of the more counter-intuitive aspects of quantum mechanics.  These phenomena – slowed arrows, quantum coins, entangled poker chips – may seem fantastical, but the underlying concepts have been observed in labs all over the world.

Stay tuned for the next post, when we return to the classical world!

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