Anton Zeilinger, Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences & University of Vienna

I’m very grateful to the Pontifical Academy of Sciences for giving me the opportunity to contribute to Acta. I hope that I’m not exploiting that opportunity too much by presenting some of my personal views on the foundations of quantum mechanics and on the basic messages which quantum mechanics is conveying to us.

I have been interested in quantum mechanics or, synonymously, quantum physics since the very days when I first learned about them as a student. The initial impression was that of an immense mathematical beauty of the formalism of quantum mechanics. The second impression was the fantastic agreement of the theoretical predictions of quantum physics for experiments, and the third and somewhat surprising impression was that there was widespread disagreement about the interpretation of the new theory.

At that point I would like to emphasize that there are two different levels of interpretation of any formal body in physics. The first level of interpretation is what the symbols one uses correspond to in observations in physical reality. On that level, there is no disagreement about the interpretation of quantum mechanics, particularly since it is commonly accepted that the formalism describes the probabilities of obtaining specific experimental results. The second level of interpretation concerns the meaning of a theory, a theoretical description, for our general view of the world (“Weltanschauung”) that is: What does the theory tell us about the world in general, our position in the world and our relation to the world? At that level, there’s a broad spectrum of possible interpretations, which I do not wish to detail here. I want to take the opportunity to present my personal considerations and a few points.

When a physicist observes nature, doing experiments, then one obtains answers, like how fast is a certain body moving, or where is a certain object located, etc. So, from these answers, which we obtain, we construct a reality. In classical physics, this reality concerns all kinds of properties, for example the just mentioned position and momentum, without any inherent limits. The question which I would now like to raise is: What is this relation between information which we obtain by observing nature and the reality which we construct? What is the relation between the two? What is the relation between material existence and knowledge? What is the relation between reality and information?

Here I would suggest that in physics we should only use concepts which can be operationally verified, that is, concepts where we can do observations of the outside world, at least in principle, which give us an answer about the specific property. Also, any statement about the world is a representation of our knowledge. Therefore, I suggest it is of value to consider what it means to have a representation in terms of information. Any information has to be represented in logical statements. Such logical statements have a structure which is determined by the structure of language. I would like to quote Niels Bohr, who requested that any representation of any experimental results has to be expressed in our classical language, in our everyday language, which concerns classical terms, classical notions. Which classical notions? I suggest that these are merely statements about the properties of the apparatus used in specific experiments, such as whether a particular laser with all its features is turned on or off, whether certain crystals are used, or whether a specific telescope is employed. Additionally, they pertain to the results of observations, such as those observed on camera or recorded by some sort of measurement device, maybe simply just a ruler or a clock, etc. So, if all knowledge is represented in language, in logical statements, the question arises of what this implies at first about knowability of the world. In other words, something which cannot be stated in a logical proposition in the sense just described cannot be a feature of the world, at least not a feature of the world which we can observe, which we can talk meaningfully about. Therefore, I suggest it does not make sense for physics to talk about such in principle unobservable features. So, the question is whether it makes sense to even consider such unobservable features.

I suggest that it is impossible to verify any distinction between reality and knowledge, that is, any distinction between reality and information about reality. So, in other words, we cannot even consider reality without considering the information which can be stated about reality. Therefore, my suggestion would be that language determines what reality can be, that is, statements which we can make about the world determine the possible properties of the world. In quantum mechanics, this knowledge is represented in the quantum state, which is generally considered to be the state of the system which we observe or which we interrogate. Yet to be precise, what exactly is the quantum state? The quantum state is just a representation of my knowledge about the world, which by necessity is a probabilistic representation.

It is one of the deepest messages of quantum physics that we have an irreducible randomness of individual measurement results, which cannot be explained by a deeper structure. This feature follows from the property that the quantum state only represents possible answers to future experimental questions. Schrödinger called the quantum state an “expectation catalogue” of possible future measurement results. Which specific feature, which specific prediction of the expectation catalogue is then realized in experimental observation is completely random and beyond the possibility of science to explain. Actually, this new randomness in quantum physics is of a new nature, which has not been seen before in science.

As Heisenberg once pointed out, there are two different kinds of randomness. One may be called subjective and the other may be called objective. Subjective randomness is personal ignorance about the details of a situation, like, for example, when we throw a die and we obtain one of the numbers 1 to 6, the result being random. But, in principle, within classical physics, which is the physics before quantum mechanics, the result is determined by how the die is thrown. It’s determined by the precise way in which the die falls on the table, in which the die interacts with the surface and so on. Randomness here is due to the personal ignorance of the details of the physical process going on.

The opposite of subjective randomness in classical physics is objective randomness in quantum mechanics. Here we have the situation that the assumption of a deeper underlying mechanism, which might explain each specific experimental result, leads to contradictions with possible experiments. That is, in particular, a consequence of quantum entanglement, and the fact that there, the randomness of individual events plays a crucial role. It is also a consequence of the fact that there are theorems for systems in higher dimensions. Visualize the Kochen-Specker Paradox, where even for an individual system the assumption that the observed result is somehow determined prior to performing the experiment is not possible without the complete context of the specific experiments performed.

The quantum state is thus just the interpretation of our knowledge of the experimental setup and all its features, which allows us to make probabilistic predictions about future measurement results, that is, about future classical properties of the observed system. The quantum state itself, as has nicely been presented, for example, in the Nobel Prize speech of John Clauser, does not exist in real space. It exists in an abstract theoretical space, the configuration space.

I suggest that many of the seeming puzzles and paradoxes with measurement and randomness arise from what is called “reification of the quantum state”, that is, the assumption that the quantum state exists out there in real space. Take, as an example, Schrödinger’s cat paradox, where the unfortunate cat is connected to a quantum device whose outcome is random, and depending on the outcome the cat will be alive or dead. Now, very often, this paradox is represented as the cat actually being both dead and alive before the experiment is finally performed. This is clearly not acceptable if the quantum state does not exist in real space. Rather, the correct way to talk about the situation is the fact that our knowledge of the situation does not allow us to make any statements about the state of the quantum system, therefore about the state of the cat, whether it is alive or dead. So as the quantum state is just a representation of our knowledge, it is more than natural to change that representation of our knowledge, that is, the quantum state, by obtaining new information, like, for example, by observing whether the cat is dead or alive. An interesting feature of quantum mechanics now is that it is not allowed to assume that the cat was either dead or alive, that is, in a well-defined state, before the observation.

So, from that point of view, there is no measurement problem. There is no necessity to see the measurement, namely the way in which a specific result is obtained, as a physical process in the physical world. All there is is just a change of knowledge, just a change of mathematical representation.

We might even go further in an admittedly rather speculative way. I would suggest that the only concept which is unavoidable in all our discussions is the notion of information. Reality independent of information is moot and does not make sense in itself. It suggests itself to assume that, therefore, the structure of information defines the structure of physical states. This also determines the nature of reality. Maybe there is an analog to the way in which in Gödel’s Theorem, statements are countable, and maybe this countability reflects itself in the structure of quantum mechanics. Reality is a secondary concept, not a primary concept which is hidden behind the laws of quantum mechanics. Having thus analyzed the relationship between physical reality and information, one might further speculate that maybe randomness is a hint beyond what can ever be found in physical observation. Randomness in a very deep sense hints beyond our method.

I would like to conclude in an admittedly very personal way. The gospel according to John starts with “in the beginning was the word”, or maybe even more fundamentally in the Latin version, “in principio erat verbum”.