My question is about The Copenhagen interpretation of QM. I am confused about what entities this interpretation of QM presupposes. Heisenberg says that quantum states represent the knowledge an observer has of a quantum system but he also says (in Physics and Philosophy) that tendencies (read in terms of Aristotelian potentiae) ground the probability function. Well, quantum states deal with probability functions and are subjective but probability functions are grounded by something that seems to be objective, i.e., tendencies. So, what does Heisenberg thinks about probability in QM? Should it be interpreted only in a subjectivist way? Or in an objectivist one? Or, maybe, both?

Furthermore, I have read that the Copenhagen interpretation is seen as a subjectivist interpretation of QM. How this is in line with the fact that it predicts indeterminism? Does it interpret probability in terms of subjective degrees of belief or not? and I have also read that Bohr remains silent about the entities behind QM statements. Is this latter one the attitude shared by other Copenhageners and the contemporary ones?

  • The last part of section 8 of the SEP article says there wasn't really a single agreed-upon "Copenhagen interpretation", and that between the more subjective-sounding version held by Bohr, and the von Neumann/Wigner idea of conscious observation causing an objective collapse, "in the middle we find Heisenberg talking about the collapse as an objective physical process but thinking that this couldn’t be analyzed any further because of its indeterministic nature"
    – Hypnosifl
    Nov 8, 2021 at 20:59
  • "In the Copenhagen approach to quantum mechanics as characterized by Heisenberg, probabilities relate to the statistics of measurement outcomes on ensembles of systems and to individual measurement events via the actualization of quantum potentiality", see Jaeger's review. But that's Heisenberg's personal take. Interpreting the nature of probabilities is irrelevant to predicting QM measurements, and so minimal interpretation, like Copenhagen, does not have to say anything about them. Doing that takes one beyond Copenhagen.
    – Conifold
    Nov 9, 2021 at 0:17
  • @Conifold thanks. Could you please explain more about what do you mean the Copenhagen is a minimal interpretation of QM? Specifically, why it is minimal? and what entities entails the Copenhagen interpretation?
    – PavlovOlga
    Nov 9, 2021 at 10:08
  • @Hypnosifl Thanks. I am sure to have got it right: Heisenberg thinks that ther is an objective element (that are potentialities) that cannot be investigated by us. For this reason the only think we are able to deal with are quantum states that are our representation of a system. Right? But, this would mean that for Heisenberg there is both a subjective and objective element to consider.
    – PavlovOlga
    Nov 9, 2021 at 10:12
  • A minimum an interpretation must do is verbalize the formalism and connect theoretical concepts to experimental measurements, thus enabling predictions. Copenhagen does that and it is this least common denominator that (probably still) a majority of physicists mean they accept when they say they "accept Copenhagen". Some Bohr-inspired phraseology and imagery is added to the mix with invariably controversial readings of its exact meaning, see SEP. What does it say of "entities"? Nothing specific. They are non-classical, some metaphors.
    – Conifold
    Nov 9, 2021 at 11:08

4 Answers 4


The so-called Copenhagen Interpretation is not a single interpretation but a collection with some common ground. The entities it pre-supposes are particles, fields or potentials, time, space and measuring devices. It is not a subjective interpretation, in the sense that the outcomes of experiments do not depend on the views or beliefs of the experimenter. Particles have 'observable' properties such as position, momentum and spin (observable really means measurable), but the values of those properties are the results of measurements, ie of the interaction between the particle and the measuring device. Importantly, certain properties cannot have precisely defined values simultaneously. For example, when a particle has a well-defined position, it does not have a well-defined momentum, and vice versa.

The interpretation assumes that every particle has an associated 'wave function', which is a function of position and time. The magnitude of the wave function at any point in space indicates the probability that a measurement will localise the particle at that point. Note that the interpretation does not assume that the particle actually is at a point before its location is measured, or that the particle is found at that point by the measuring device- instead it assumes that the act of measurement plays a role in causing the particle to be at the measured location.

More generally, the interpretation assumes that when a property of a particle is measured, the wave function of the particle is changed by the measurement to become one of an allowed set of 'eigenfunctions' associated with the property being measured. The details of this are too complicated to describe here, but the way it works is truly striking once you understand it. Each of the allowed eigenfunctions of one measurable property A may be expressed as a sum of the eigenfunctions of another of the particle's measurable properties B. If a particle is in a particular eigenstate of A, and you subject it to a measurement of B, the particle's wave function will jump in an indeterministic way to become one of the eigenfunctions of B. The probability of it jumping to a specific one of the eigenfunctions of B depends on the extent to which that eigenfunction figured in the expansion of the pre-measurement eigenfunction of A.

In short, the probabilistic nature of quantum mechanics has nothing to do with beliefs. The key equations of quantum mechanics give you the probability that a particle in one specific quantum state will change to another specific quantum state as a consequence of a measurement.


The Copenhagen Interpretation boils down to the probability wavefunction is what is real as opposed to there is a real particle, we just dont know where it is.

Unfortunately when you look at stuff (measure experimental results) it dam well seems like something specific happened. so you have this awkward wavefunction collapse problem which can be summed up as "the moon doesnt exist unless you look at it"

I don't believe that the majority of physicists believe in this dualistic statement, its just said to highlight the problem with the interpretation and highlight the lack of a unified theory. ie you cant apply QM to the moon

  • "ie you cant apply QM to the moon" I'm not convinced that this is the case. In the case of the moon, this is such a big object that we cannot tell the difference between different states, so that the moon looks the same to us even though essentially it is not. Thus, the moon that we actually see didn't in fact exist before we looked at it. There is only very nearly always something there so that the moon seems very real to us. The states where the moon wouldn't be there are so massively improbable that nobody ever get to see that there is no moon. Dec 13, 2021 at 12:23
  • For macroscopic objects like the moon, different parts of it are constantly observing itself ie it's above the en.wikipedia.org/wiki/Quantum_decoherence But, quantum behaviour has been observed in objects big enough to see unaided: youtu.be/dvYYYlgVAao What matters is the flow of information, & whether a system us isolated from it's environment, whether state information is spreading out from the object into correlations in the wider universe
    – CriglCragl
    Dec 14, 2021 at 11:27

quantum states deal with probability functions and are subjective

why do you say this probability functions are subjective? The Copenhagen interpretation considers that these functions would collect, in the limit of large numbers, the objective result of many measurements of the same state, if you could prepare thousands of identical copies. Therefore, as probability density functions these functions would be objective for adherents to the Copenhagen interpretation.


My own Helsinki interpretation of the Copenhagen interpretation goes like this:

Particles exist only as probability waveforms when they are not interacting with other particles. They are not simple sine waves, but for the sake of understanding we can picture them as such.

When they do interact, the outcome depends on which "phase" each of the interacting waves is at the time of interaction. In other words, particles have indefinite properties (the Heisenberg uncertainty principle) until they are measured (an interaction with another particle). Only in the interaction particles "detect" each other's "phase" and for a brief moment both particles have definite properties.

This interpretation explains the probabilistic nature of physical reality and the wave-particle dualism without involving any mystical unknown forces or conscious observers. It's all mathematics. The "phases" of probability waves are the hidden variables, they vary constantly over time as described by the wavefunction and become unhidden only in interactions.

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