The Quantum Zeno Effect

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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