Category Archives: Featured

Sending Your Secrets Safely with Chaos

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The theory of chaos is an extraordinarily broad mathematical topic, and we all have some intuition for what it means when a system is chaotic. The ideas of unpredictability, spontaneity, intractability, turbulence, and perhaps randomness, all come to mind. But deterministic chaos is somewhat different than our intuitions would have us believe. If you watch the shape of a flickering flame, the whitewater in a rocky river, or the price of crude oil in North America, you’re definitely seeing behavior which can’t be described without chaos. But you’re also most likely seeing the effects of any number of random influences on the system, whether a faltering breeze or some oil speculator’s whimsy. Chaos theory deals with the behavior of deterministic systems—that is, systems with no random inputs. All the intricacy and intrigue of chaotic behavior can arise in systems which might seem deceptively uncomplicated, like a pendulum hanging from another pendulum, or three stars orbiting each other.

But if you’ve ever heard of the “butterfly effect” (a term coined by a pioneer of chaos theory, Edward Lorenz), it’s likely your intuition is right about the central feature of deterministic chaos: chaotic systems have high sensitivity to initial conditions.

If chaotic systems are so unpredictable and temperamental, how can we possibly make chaos work for us? One answer is encryption. Continue reading Sending Your Secrets Safely with Chaos


Seeing Without Looking: The Quantum Bomb

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Some of the most dramatic and unintuitive experimental results in quantum mechanics have come from dedicated physicists’ insistence on pushing the bounds of what should be physically possible (but not all, as Henry Becquerel’s serendipitous discovery of radioactivity reminds us). Dedication to probing the strangeness of quantum physics has been paying off for over a hundred years.
One of the more recent and striking successes of quantum theory, first posited in 1993 by Avshalom Elitzur and Lev Vaidman of Tel Aviv University, is the idea that we can actually detect an object without using photons or any other particles to look at it. What in the world does that mean? Well,

Imagine you’re tasked with determining whether a new (highly classified) special “quantum bomb” is operational or is a dud. This quantum bomb has two characteristics that make it extremely volatile:

  1. If the bomb is operational, it will explode when a single photon of light strikes it;
  2. If the bomb is a dud, it will not interact with photons in any way.

This may be an extremely strange and dangerous bomb, but you’ve found yourself before a problem which seems impossible: any light you shine on the bomb, perhaps to test it, will just cause an explosion. How can you possibly test that the bomb works without causing it to explode?

You need to perform an interaction-free measurement.

Continue reading Seeing Without Looking: The Quantum Bomb