Quantum Theory and the Idea that Particles Can Be in Two Places at Once

The quantum world is a strange place. If you look at an object, it changes. If you know how fast it’s moving, you can’t know where it is. Measurements that happened in the past can seemingly be erased later. Particles are sometimes waves and can be in two places at once. Cats may be both dead and alive. These are things we say when talking about the quantum world, but is this really what is going on?

Quantum mechanics is an incredibly well-established theory. It has passed every test it’s ever been subjected to. It underlies much of the technological progress we have seen in the past century, for what would electronics be without discrete energy levels, which came to us courtesy of quantum mechanics? We have the mathematics and we know how to work it, yet even after a century of debate, we don’t know what the mathematics of quantum mechanics means.

Let’s take an example: the idea that particles can be in two places at once. We are familiar with particles that are in one place at a time – an electron, say, that hits a screen and leaves a dot. These particles make an appearance in quantum mechanics as a possible solution to the equations, as we expect.

But quantum mechanics is a linear theory, which means if particles in particular places exist, then so do sums of those particles. We call those sums “superpositions”. And what is a particle in one place plus the same particle in another place? It’s not two particles – that would be described by a product, not a sum. Could you say that if we have a sum, then that’s a particle which is in both places? Well, it’s been said many times, so arguably one can.

However, I don’t know what a superposition is, other than a piece of mathematics that we need in order to explain what we observe. We need superpositions because they give particles their wave-like properties. When we see waves interfering in watercancelling out where a crest meets a trough – this is a non-quantum effect, a “classical” effect as physicists say. But it turns out that single particles can interfere with themselves. When we send an individual particle of light, or photon, through two thin slits in a plate – a double-slit – we see, as expected, a dot on the screen behind the plate. But if we continue doing this for many photons, we see an interference pattern built up from individual dots.
The only way we can explain this pattern is that each particle is a sum – a superposition – of two paths, one going through the left slit and one through the right. So why not just say that the particle goes both ways?
Source: https://www.newscientist.com/