We have to describe the Quantum world in classical language

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How do we even talk about a quantum system?

Whenever we learn something about nature, we eventually have to put that knowledge into words. We say:

The photon went through this path.
It was detected here.
It had this energy.
and so on..

These are all propositions. They are statements about the world that can, at least in principle, be judged to be true or false. I know this might seem obvious, but we rarely think about it. And quantum mechanics makes this simple fact surprisingly complicated.

Imagine that I perform an experiment: I send a photon into an apparatus and observe where it ends up. Later, I tell you what I did. I cannot simply hand you the quantum state and say, “Here. You figure it out.” I have to tell you something. I have to say:

I prepared the photon in this way.
I placed this detector here.
I measured this quantity.
The detector clicked.

In other words, I have to describe the experiment in a language that you and I already understand. This was one of the central points made by Niels Bohr:

“How far the [quantum] phenomena transcend the scope of classical physical explanation, the account of all evidence must be expressed in classical terms.”

Quantum mechanics may take us far beyond the concepts of classical physics, but the evidence for quantum mechanics still has to be communicated in ordinary, classical terms.

There is an important reason for this. When I say that I performed an experiment, I mean that there was some physical procedure that I carried out and that produced some observable result. I must be able to tell another person what I did and what happened. So even if the underlying quantum world is strange, the description of the experiment cannot be completely detached from the ordinary concepts we use to communicate about experiments.

This creates an interesting situation:

We need classical language to tell each other about quantum phenomena, even though quantum phenomena do not necessarily behave according to classical concepts.

This is philosophically deeper than it might seem at first glance.

There is another subtle point here. Suppose a physicist invents a completely new theory. The theory might contain mathematics that nobody has seen before. It might introduce new objects, new equations, and new physical principles. But when the physicist tries to explain the theory to another human being, what language can they use?

They have to use a language that existed before the theory. This was emphasized by the philosopher and physicist Carl Friedrich von Weizsäcker:

“This verbalized language must be the language spoken by those physicists who do not know yet the theory we are telling them.”

Think about what this means. A new theory is supposed to tell us something new about nature. But the words we use to explain that new theory already carry meanings inherited from our previous understanding of nature. For example, we use words like particle, wave, position, velocity, measurement, etc. But these words were not invented by quantum mechanics. They come from a much older picture of the world. Sometimes a new theory forces us to reconsider what those old words actually mean. This happens in many areas of science. Before Einstein, “time” seemed like an obvious concept. Then relativity forced physicists to rethink what time means. Quantum mechanics does something similar with concepts such as position, momentum, state, and measurement.

So the mathematics may be new. But the language through which we understand the mathematics is inherited from the old world.

Suppose I want to describe an ordinary classical object—a ball, for example. I can make statements about it:

The ball is at position (x) at time(t).
It posses velocity (v), momentum (p) and energy (E), at this particular instant in space and time.

If I know enough about the ball, I can imagine putting together a complete list of such statements. In a classical picture, there is no fundamental problem with imagining that all these properties have definite values simultaneously. Whether or not I happen to know these values, the classical picture allows me to imagine that they are there.

But quantum mechanics?

The uncertainty principle is one expression of this fact.

But quantum foundations go deeper than simply saying that our measurements disturb the particle. Theorems such as those of Bell and Kochen–Specker show that quantum theory does not allow us to assign ordinary, definite, context-independent truth values to all conceivable physical propositions simultaneously. They imply:

There is no single classical catalogue of definite properties that can consistently be assigned to a quantum system.

We can simultaneously ask “Does the particle have position (x)?” and “Does it have momentum (p)?” In classical physics, we expect both questions to have definite answers, whether or not we know them.

Quantum mechanics refuses to give everything a definite answer. If the quantum state is prepared so that position is perfectly definite, then momentum becomes completely indefinite. If momentum is perfectly definite, position becomes completely indefinite.

The problem is not merely that our instruments are imperfect. The structure of quantum theory itself prevents all such classical propositions from being simultaneously definite. This is what lies behind the idea of quantum complementarity.

We seem to have two conflicting requirements:

1. We have to talk about quantum systems using classical propositions, but

2. Quantum systems cannot always be described as possessing definite classical properties simultaneously.

What do we do?

In their 2002 paper, “Information and fundamental elements of the structure of quantum theory”, Caslav Brukner and Anton Zeilinger propose a simple answer.

Instead of asking only:

“Is this proposition true or false?”

we can ask:

“How much do we know about whether this proposition is true or false?”

This is a subtle but powerful change. I know I cannot consistently say that a quantum particle has a definite position and a definite momentum simultaneously. That does not mean I have no information about either quantity. I can still have a quantum state that tells me how likely different position (or momentum) measurements are to produce different outcomes. I can quantify this information about position and momentum.

But I should not confuse: having information about a quantity
with: the quantity possessing a definite classical value independent of context.

This distinction is at the heart of the information-theoretic viewpoint.

This gives us a different way of thinking about a quantum state. Instead of imagining it as simply being a hidden catalogue containing all the properties a particle “really has,” we can think of a quantum state as encoding the information available about the possible outcomes of different measurements. The quantum state does not have to answer every classical question with a definite yes or no. It tells us what can be predicted, with what probabilities, given the physical situation.

I won’t call it a weaker version of physics. It is a different kind of physical description. And it may actually be the natural one for a quantum world.

This is where the word ‘information’ becomes important.

The idea is not necessarily that a quantum state is merely a person’s subjective opinion. Rather, the proposal is that the mathematical structure of quantum theory can be understood in terms of measures of information about possible propositions and their outcomes.

This gives us a way to reconcile the two apparently contradictory facts we encountered earlier. We still use propositions because we have no alternative way of communicating experimental knowledge. But we do not have to demand that every proposition simultaneously possess a definite truth value. Instead, we can assign information about its possible truth value.

A much more quantum-compatible way of talking.

What I find particularly interesting about this idea is that it does not throw away everything that came before quantum mechanics. We do not have to invent an entirely new language or abandon propositions. Instead, we make a relatively small change.

Classical physics tends to encourage us to think:

A physical system has a collection of definite properties.
Our job is to discover what those properties are.

The quantum-information viewpoint suggests something closer to:

A physical system is described through propositions about possible observations, together with the information available about those propositions.

This view changes what we think a physical theory is actually telling us about the world.

There is a temptation, when learning quantum mechanics, to think that the strange part is simply that particles behave weirdly—such as exhibiting interference, superposition, and entanglement—phenomena that have no classical explanation. All of this is certainly strange. But there is an even deeper strangeness.

Quantum mechanics may be telling us that our classical idea of what it means for a physical property to “exist” is itself too strong.

We are accustomed to thinking that every question about an object has an answer in terms of ‘Yes’ or ‘No’. Quantum theory forces us to be more careful. Some questions cannot be assigned simultaneous, context-independent answers in the way classical physics would lead us to expect. And yet we still have to ask questions. We still have to perform experiments and communicate the results. We therefore end up in a peculiar position:

The world described by quantum mechanics may not fit naturally into the classical language we use to describe it. But that language is the very tool through which we discover the quantum world in the first place.

Perhaps the solution is not to abandon our language. Perhaps it is to understand what our language is actually telling us. And that may be why information sits so naturally at the foundations of quantum theory.

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