When discussing quantum physics, it is common for people to casually state that particles can exist in two places at the same time. Sabine Hossenfelder, a physicist, investigates what is actually going on.

Science Photo Library/Russell Knightley |

The following is an excerpt from our newsletter Lost in Space-Time. We hand over the keyboard to a physicist or two each month to tell you about fascinating ideas from their corner of the universe. You can register for Lost in Space-Time here.

The quantum world is an odd place. When you look at something, it changes. You can't know where it is unless you know how fast it's moving. Measurements taken in the past can appear to be erased later. Particles are sometimes waves and can exist in two places simultaneously. Cats can be both alive and dead. These are phrases we use when discussing the quantum world, but are they accurate?

Quantum mechanics is a firmly established theory. It has passed every test it has ever faced. It underpins much of the technological progress made over the last century; after all, what would electronics be without discrete energy levels, courtesy of quantum mechanics? We have the mathematics and know how to use it, but even after a century of debate, we still don't know what quantum mechanics mathematics means.

Consider the concept of particles being in two places at the same time. We're used to particles that are only in one place at a time, like an electron that hits a screen and leaves a dot. As expected, these particles appear in quantum mechanics as a possible solution to the equations.

However, quantum mechanics is a linear theory, which means that if particles exist in specific locations, so do sums of those particles. These sums are known as "superpositions." What is a particle in one location plus the same particle in another? It's not two particles; that would be a product, not a sum. Could you say that if we have a sum, we have a particle present in both places? Well, it's been said many times, so one could argue that one can.

However, I'm not sure what a superposition is other than a piece of mathematics required to explain what we see. Superpositions are required because they provide particles with wave-like properties. When we see waves interfering in water, canceling out where a crest meets a trough, we are witnessing a non-quantum effect, or "classical" effect, as physicists call it. However, it has been discovered that single particles can interfere with one another.

When we send a single photon, or particle of light, through two thin slots in a plate - a double-slit - we see a dot on the screen behind the plate, as expected. However, if we do this for a large number of photons, we will see an interference pattern formed from individual dots (see image below).

This pattern can only be explained by saying that each particle is a sum - a superposition - of two paths, one through the left slit and one through the right. So why not just say that the particle is bidirectional?

I dislike this phrase for two reasons. One is that a superposition of two paths is not a physical entity. It is part of an abstract mathematical structure known as a Hilbert space. It simply has no physical counterpart. This is why we are at a loss for words to describe it. It doesn't belong in our world; it's something entirely different.

Another issue with these superpositions is that, while they exist in mathematics, they are not observed. When we observe a particle, it is either present or absent. The interference pattern disappears when we measure which slit the photon passed through. And what is the point of claiming that a particle can travel in both directions if we never see it do so?

The rather dull truth is that superpositions are mathematical structures with specific properties. Because we never experience it, all analogies and metaphors fail. We perceive the quantum world as "strange" and "weird" because we try to explain it using words from our everyday experiences. This is why you come across perplexing popular science articles about cats that can allegedly be separated from their grin or experiments that allegedly demonstrate that reality does not exist. These articles make no more sense to me than they do to you, and that's because they don't make any sense at all.

I should admit that I am primarily an instrumentalist. I don't believe the mathematics of our theories is real in and of itself; I'm content to say it's a tool we use to describe nature and leave it at that. I have no problem with superpositions existing in abstract mathematical spaces as long as they are tools that produce accurate predictions, which they do.

But, as a science writer, I understand the issue: dumping mathematical definitions on an unsuspecting reader is not a good way to build an audience. Even if we were willing to lose readers, it would be counterproductive to our goal of explaining what is going on in mathematics. As a result, we abandon accurate descriptions such as superpositions or Hilbert spaces in favor of headline-grabbing grainless cats and other absurdities. There is no easy way out of this mess. I admit that I have used and will continue to use the phrase "in two places at once." Because at the very least, my audience is familiar with it, which is something.

But, every now and then, I believe we should bring up the mathematical expressions so that our readers become accustomed to them in the long run. It has happened before: we have grown accustomed to discussing electric and magnetic fields, as well as electromagnetic radiation. These are also abstract mathematical entities that we have no direct experience with. However, electromagnetism has become such a fundamental part of our education that we can casually discuss it.

Another reason we shouldn't pretend it's a mystery that mathematical structures have no good verbal explanation is that it distracts from quantum mechanics' actual problems. You may have labeled me as a "shut up and calculate" person, as physicist David Mermin put it. And you'd be correct. But this is precisely why I disagree with quantum mechanics. Quantum mechanics describes what happens during measurement, but it does not define what a measurement is. We can't figure it out. Despite this, we know that measurement is what causes quantum effects to vanish.

Erwin Schrödinger's famous cat thought experiment demonstrated that we don't understand how quantum effects disappear. Schrödinger proposed that an atom that is both decayed and not decayed could be used to cause the release of a toxin that both kills and does not kill a cat. This argument demonstrates that superpositions can be amplified to macroscopic size without the act of measurement. But we don't see dead and alive cats, so what's the deal?

The standard response to this quandary is that the cat is constantly measured. Not by us, but by air molecules and even cosmic microwave background radiation. According to the story, these measurements cause quantum effects to vanish very quickly. However, this is merely a story that is not supported by mathematics. It's a real issue for someone who prefers to listen and calculate.

The proliferation of quantum woo in the media, in my opinion, distracts from the real problem at the heart of quantum mechanics: we don't know what a measurement is. Yes, quantum mechanics is strange. But let's not make it any stranger than it is.

Sabine Hossenfelder specializes in probing our understanding of physics fundamentals. She is the host of the popular YouTube channel Science without the Jargon, and her latest book, Existential Physics: A Scientist's Guide to Life's Biggest Questions, will be released in the UK, US, and Canada in August. She Lost in Space-Time letter questions a fundamental tenet of quantum physics: can particles be in two places at the same time?