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When you look in the mirror, the image you see looks a lot like you—not exactly the same, because when you raise your right hand, your mirror-self raises its left. What’s more, the mirror image is merely an assemblage of reflected light, without a physical body behind it. Despite these differences, you can see an important connection between you and your reflection.

This type of mirror relation is a familiar and powerful form of symmetry. We can say that a Valentine heart is symmetrical because the left side is a reflection of the right. But the symmetry of your mirror image is different and deeper. A heart is symmetrical because the left and right side happen to have a similar shape. The symmetry between you and your reflection is due to the laws of physics. The nature of light requires your reflection to be symmetrical to you. It is an example of a powerful and subtle type of symmetry known as duality.

Duality is a connection between two things where the properties of one defines the properties of the other. For example, imagine a book lying on a table, with a nail taped to its front cover, pointing up. No matter how you hold the book, the nail will point outward from its cover. If you know what direction the nail is pointing, you also know the orientation of the book. If you know the orientation of the book, you know where the nail is pointing. Thus, there is a duality between the nail and book.

So does the the nail determine the orientation of the book, or does the book determine the direction of the nail? That seems to be a nonsensical question. The duality between nail and book isn’t about one object determining the orientation of the other, but about the connection that exists between two of the nail-and-book’s fundamental properties, neither of which is caused by the other. You could say the same thing about quantum theory when someone asks if light is a particle or a wave.

The duality between particles and waves is a central part of quantum theory. Light is clearly a wave: It has a wavelength that determines its color, and light waves can interact with each other to produce things like lasers. Light is also clearly a particle: It interacts with atoms as discrete photons; a single photon can be deflected like a billiard ball. Particle-wave duality means that quantum objects like light have a symmetry between their particle and wave aspects. They are particles with wave properties and waves with particle properties. They are both, and they are neither. The power of quantum theory is that you don’t need to distinguish between particles and waves. They are simply quantum objects with a duality between their particle and wave natures.

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