In an earlier post, we talked about the strange double life of light and wave-particle duality (read here). Today we move to another idea that is just as unsettling. But before we enter the quantum world, let us travel back to around 260 BCE.

You probably know the famous story of Archimedes and the golden crown. King Hiero of Syracuse suspected that his new crown was not made of pure gold. He wanted to know the truth but without melting, scratching, or damaging the crown in any way. The challenge was simple and impossible at the same time. Archimedes eventually found a clever method, but the real unsung hero in this story is the king himself for asking an ingenious question: Can we learn something about an object without disturbing it?

It feels trivial when we think about crowns and buckets of water, but the question is more subtle than it seems. In everyday life we treat measurements as harmless. You look at something and you assume nothing about it has changed because you looked. You weigh a book and the book stays a book. You measure the length of a table and the table does not care. The idea that one could observe without affecting is so natural that we rarely question it.

Now let us tighten the question a little more. Classical mechanics tells us that we can predict the future behaviour of a system exactly, but only if we know its initial conditions (read this post). These initial conditions serve as a starting point from which the laws of classical physics can determine what happens later or even what happened earlier. In general, the position and velocity of the system at a single instant form these initial conditions. They do not have to be known at the very beginning. They only need to be known at one moment.

So how do we obtain those initial conditions? We measure them. But there is a quiet assumption beneath all this. We assume that measuring these quantities does not disturb the system in a meaningful way. For a thrown ball or a rolling car this is fine. For something much smaller, the story begins to crack.

To see how, we can return to the double slit experiment, the one shown in the figure from the previous episode. This time we do the experiment not with light but with electrons. We send electrons toward the two slits and let them hit the screen behind.

We would expect two bright piles on the screen, one behind each slit. If you look at the figure on the left, that is exactly the pattern you would predict. Yet what scientists actually saw is the pattern on the right. It is an interference pattern, the kind produced by waves. Even when electrons are sent one at a time, the pattern slowly builds up in exactly that wavelike shape. This was captured wonderfully in an experiment (paper here) and there is even a short one minute video in which you can literally watch the interference pattern build up slowly dot by dot. Watch here.

This is already puzzling, but here comes the twist. Suppose we want to know which slit the electron actually passed through. We try to “watch” it by shining light near the slits as shown below.

Surely the electron must go through one slit or the other. Surely we can catch it in the act. The moment we try to observe which path it takes, the pattern changes. The interference pattern disappears. The two piles appear, just as classical intuition predicts. When we stop observing, the interference pattern returns. When we observe again, the piles return. The figure shows exactly this dramatic shift.

Why does this happen?

This returns us to King Hiero’s question. Can we learn something without disturbing the system? At the scale of electrons the answer is no. There is a fundamental limit to how precisely we can measure certain pairs of quantities. This is in the heart of the Heisenberg’s uncertainty principle. In everyday life the limit is so small that it does not matter when we track cars or use GPS. At the scale of electrons it matters a lot. Shining light on the electron means photons “collide” with it. These collisions disturb the electron enough to destroy the delicate interference pattern. Observing the electron is not a passive act. The moment we try to determine which slit it passes through we inevitably change its behaviour.

Because of this, the basic requirement of classical mechanics, which is the existence of well defined position and momentum at the same time, cannot be satisfied for quantum particles. There is no classical trajectory for an electron. The very foundation of classical mechanics fails. This is why we need a new mechanics altogether: quantum mechanics. It is not a small correction to classical physics. It is a completely different framework built for a completely different scale. If one day someone manages to observe a clear trajectory of a quantum particle beyond the uncertainty limit, quantum mechanics would be disproved. Countless experiments have tried to do this. None have succeeded.

You may wonder whether the electron still follows some definite path even if we cannot measure it. After all, the electron must have come from one of the slits and must have arrived at the screen. But if such a definite path existed, the interference pattern would never appear. The question is no longer whether we can measure the electron's position and momentum.

The deeper question is whether these quantities are even well defined for a quantum particle.

Think about that until next time.