This blog post explores the compatibility of Karl Popper’s philosophy of empiricism and the Copenhagen interpretation of quantum mechanics.
Carl Popper, who is famous for his scientific anti-positivism, also expressed his position on probability in the process of explaining his philosophical ideology in his book “The Logic of Scientific Discovery.” And based on his theory of probability interpretation, he largely denied the Copenhagen interpretation, which is the most dominant interpretation of quantum mechanics. His position stems from the logic and assumptions he established to establish the philosophy of anti-positivism. However, Karl Popper’s philosophy of the counter-proof is a very important idea in the philosophy of science, and the Copenhagen interpretation of quantum mechanics is also a theory that is overwhelmingly supported by physicists. I would like to consider whether the Copenhagen interpretation of quantum mechanics is really incompatible with Karl Popper’s philosophy.
First, let’s briefly explain Karl Popper’s theory of refutationalism and probability. Karl Popper says that it is essentially impossible to prove scientific facts through induction. Induction is the process of deriving universal statements from singular statements, and it is impossible to prove universal facts perfectly, no matter how many individual cases are collected. A famous example of this is the proposition “All swans are white.” No matter how many swans you observe and confirm that they are all white, this is by no means a perfect proof of U. Even if you observe all the swans on Earth at one point in time and confirm that they are all white, the statement becomes false if a swan that was not white in the past exists or if a swan that is not white is born in the future. Therefore, Popper denies the scientific methodology of induction. This is called “The Problem of Induction.”
Popper argued for the scientific methodology of deduction instead of denying induction. Consider a general proposition U. Then, no matter how many individual propositions s1, s2, ….. that are true, there is no guarantee that U is never false. However, if there is only one individual proposition s1′ that is false, then it is proven that U is false. Let’s look at the example in the previous paragraph. U is “All swans are white.” Let the results of observing 1,000 swans and finding that all of them are white be denoted as s1, s2, …., s1000. The results of observations from s1 to s1000 do not guarantee that all swans are white. However, if the 1,001st swan observed is black, then U is definitely false. U is thus disproved. This method of scientific methodology is called falsificationism.
Falsificationism is also the criterion that Karl Popper used to distinguish between science and non-science. One of the important problems in the philosophy of science was the establishment of criteria for distinguishing between science and non-science, which is called the “Problem of Demarcation.” Carl Popper viewed the point at which a scientific theory is distinguished from a non-scientific theory as the possibility of disproving it. In other words, if a theory is seen as a collection of general propositions, and each of those propositions is likely to be experimentally disproved, then the theory is considered a scientific theory. According to this standard, Freud’s psychology does not qualify as a scientific theory.
If we solve the problem of compartmentalization based on the possibility of counter-evidence, we can also define objectivity, which is often referred to in scientific methodology. In the opening of his book “The Logic of Scientific Discovery,” Karl Popper argues that scientific methodology should be strictly separated from the individual’s mind. One example is the line drawn when describing scientific research, which states that it is not necessary to describe the process by which the researcher came up with the hypothesis. This is also the logical basis for his counterfactualism philosophy, which sees the counterfactualism philosophy as a series of attempts to build an explanation of reality in which scientific theories are established independently of the individual’s mental world. In a similar vein, in the following chapters, he argues that natural laws can only be described in terms of their establishment regardless of their position in space and time or the individual observing them. All scientific propositions must be “inter-subjectively testable” to ensure objectivity. This is why reproducibility is so important in research methodology today.
If we go further from this philosophy of falsification, we can set standards for the verification and adoption of scientific theories. Popper selected four points to consider when evaluating scientific theories. First is the internal logical consistency of the theory itself. This is a criterion for internal consistency, which determines whether the propositions that make up the theory are not contradictory. Second is the interpretation of the logical form of the theory. This is an assessment of whether the theory has the properties of a scientific theory. As mentioned in the previous paragraph, the criterion for this assessment is the possibility of refutation. Third is a comparison with other existing theories. This is to consider the question of how this theory will help advance the field of science after it has withstood various verifications. Fourth is the experimental verification of the predictions derived from this theory. Even if the verification is judged to be correct, the theory will only be temporarily supported, and there is always the possibility that the theory may be discarded after being disproved in subsequent experiments.
Now, let’s take a look at the Copenhagen interpretation of quantum mechanics. The Copenhagen interpretation is the most mainstream interpretation today. There is surprisingly no definitive definition of the Copenhagen interpretation in the literature, but if you compile various academic papers, you will find that the following is agreed upon within the academic community. First, the physical system generally has no definite properties before measurement. These properties are represented by the wave function, which includes all the variables that can be known about the system, and there are no additional “hidden variables.” Second, this means that quantum mechanics can only determine the probability of a certain outcome from a measurement. Third, the act of measurement itself affects the system, and the wave function, which had superimposed all possible states of the system, irreversibly collapses with the measurement, resulting in the observed result. Fourth, since the act of measurement itself affects the system, some properties of the system are incompatible with each other. In other words, it is not possible to simultaneously and accurately measure certain physical quantities for a single system. This is called the Uncertainty Principle. Fifth, the results recorded by the measuring equipment must be described only in the realm of classical physics. Sixth, the wave function has properties associated with probability. Seventh, the wave function exhibits wave-particle duality.
First, the Copenhagen interpretation, which includes the sixth and seventh principles, has survived verification by actual measurement and experimental results. Examples of this include Schrödinger’s cat thought experiment, the double-slit interference experiment, and experiments on the wave-like nature of electrons. First, Schrödinger’s cat experiment is a thought experiment that shows that if the uncertainty principle is accepted at the microscopic level, this uncertainty will also affect macroscopic objects, and it is a thought experiment that tests the internal contradictions of the Copenhagen interpretation. Let’s put a live cat in a closed box and let the cat’s life or death be determined by the state of some elementary particles in the box. For convenience, let’s say that there are two states of this elementary particle, each with a probability of 50%. At this time, the wave function of the cat is created by the wave function of the particle, and since the wave function is a superposition of all possible states, the state of the cat is a superposition of half alive and half dead. If that is the case, it is not logical because it means that the cat is both alive and dead until you open the box and check. However, the Copenhagen interpretation interpreted that the wave function represents only what the observer perceives about the state inside the box, not the state of the cat itself. It means that there is a 50% chance of finding a dead cat and a 50% chance of finding a live cat when you open the box. Therefore, it cannot be said that the Copenhagen interpretation has internal contradictions based on this thought experiment.
This time, let’s look at the results of experiments that deal with duality in light and matter, including the double-slit experiment. These experiments are representative examples of the Copenhagen interpretation’s predictions about the outside world surviving verification by actual experimental results. The double-slit experiment with light shows that light passing through a double slit creates a diffraction pattern on the screen. Diffraction is a property of waves, so this experiment shows the wave nature of light. However, the photoelectric effect experiment shows the particle nature of light. When light is shone on a metal, photoelectrons are ejected from the metal if certain conditions are met. The problem is that this condition is independent of the intensity or irradiation time of the light and is determined solely by the frequency of the light. If the frequency of the light is below a certain threshold frequency, no matter how long and intense the light is, the photoelectric effect will never occur, but if the light is above the threshold frequency, the photoelectric effect will occur immediately. The results of these experiments can be explained by interpreting light as particles called photons. The particle nature of matter is so self-evident that it can be clearly explained even by classical mechanics. The wave nature of matter can be confirmed by the existence of material waves. When an electron is accelerated to high speed and passed through a double slit, diffraction patterns appear on the screen. This also confirmed the wave-particle duality of matter. In addition to this, numerous experimental results on the wave-particle duality of light and matter do not contradict the Copenhagen interpretation.
However, the real controversy that can be raised about the Copenhagen interpretation in the philosophy of Karl Popper appears from a different angle. The foundations that Karl Popper built in the process of establishing the philosophy of refutationalism may conflict with the assumptions set for the concept of wave functions. As discussed earlier, Popper argued that natural laws can only be described in a way that is independent of the position in space and time or the individual observing them. In his philosophy, the fact that “inter-subjectively testable” is the standard of objectivity in science means that the phenomenon changes depending on the act of measurement itself, that is, the Copenhagen interpretation, which claims that the experimental results vary depending on the observer, cannot be compatible with the philosophy of Karl Popper. In the same context, the question of how to define “measuring instruments” can also be raised.
However, the above problem can be solved by presenting a more rigorous description of the uncertainty principle in Copenhagen interpretation, which is used in actual physics. This solution is also similar to Karl Popper’s extension of the “experiment performed by the observer” to “natural phenomena itself” in the extension of the probabilistic theory of trend. The “propensity theory of probability” is one of the variants of the frequency theory of probability. The frequency theory of probability considers the probability of a phenomenon as the relative frequency (or the limit of the relative frequency) in a sufficiently large (or infinitely large) population. However, Popper criticizes the frequency-based probability theory for not being useful in predicting local single events. Instead, he proposes a tendency-based probability theory, which is a form of “experiment” in the form of repeated natural phenomena in nature itself, in which humans intervene to set up experiments and obtain relative probabilities as probabilities, and then humans observe some of these and obtain probabilities from them.
Now, let’s replace the “measuring device” in the controversial point of the above paragraph with “any object that interacts with any particle in the entire universe,” and replace “experiment” with the collection of all such interactions. To be more specific, we will set a certain microscopic particle (for example, an electron) and consider “observation” to be the detection of photons colliding with the particle by a detector. And the uncertainty principle is described in consideration of both these particles and photons. Then, the uncertainty principle can be understood as follows. After colliding a photon with a microscopic particle whose state is unknown, the state of the microscopic particle is traced back by detecting the photon that is bounced off. The collision of photons and particles changes the physical properties of the particles, and the information that can be directly obtained from the detection cannot accurately capture the state of the particles before the collision. This is because light has wave properties, which cause a minimum positional error equal to the wavelength of the light, and the particle properties of light cause a change in momentum that the particles receive from the collision, which causes a corresponding minimum momentum error. If the wavelength is shortened to reduce the positional error, the momentum of the photon increases accordingly, so the momentum of the particle changes even more in the collision. Conversely, if the frequency is lowered to reduce the momentum error, the wavelength becomes longer, so the positional error becomes larger. This method allows us to describe the uncertainty principle without the concept of individual observers.
Karl Popper himself has taken a somewhat negative stance on the Copenhagen interpretation, but according to the evaluation criteria proposed by Karl Popper, the Copenhagen interpretation is at least compatible with Popper’s philosophy of refutationalism and the theory of probability of trendism, so it is not necessary to discard the theory under these two perspectives. This is one of the reasons why the Copenhagen interpretation is the mainstream interpretation that currently enjoys overwhelming support in academia.
Let’s take another look at the relationship between Popper’s falsificationism and the Copenhagen interpretation. The Copenhagen interpretation in quantum mechanics takes a very unique approach. It is the concept of “the collapse of the wave function.” This collapse is caused by the act of measurement and explains the process by which a physical system is transformed into a definite state. This is essentially contrary to the determinism of classical mechanics. Popper proposed falsificationism against the backdrop of classical determinism, but the non-deterministic elements of the Copenhagen interpretation conflict with falsificationism, which is the main reason Popper denies this interpretation.
Then, let’s see if these non-deterministic elements can be accepted within the framework of refutationalism. Popper’s refutationalism evaluates scientific theories based on propositions that can be experimentally refuted. In the Copenhagen interpretation, the state before measurement is not definitive, but the results after measurement are clearly refutable. For example, in an experiment that measures the position of a particle, if the particle is not found at a certain position, the proposition that the particle is at that position is disproved. In other words, since the act of measurement itself implies the possibility of being disproved, it is difficult to say that the Copenhagen interpretation’s non-deterministic nature is completely incompatible with the theory of disproval.
One can also apply Popper’s trend-oriented probability theory to the Copenhagen interpretation. Trend-oriented probability theory views natural phenomena as having a tendency to produce specific results. The probabilistic interpretation of quantum mechanics is a good example of this tendency. Using probabilistic tendencies to predict the position or momentum of particles allows us to calculate the probability of a particular outcome. This suggests that Popper’s probabilistic approach and the probabilistic predictions of the Copenhagen interpretation may be complementary.
In addition, Popper’s philosophy of falsificationism plays an important role in the development of scientific theories. Scientific theories must be constantly verified and falsified through new experiments and observations. The Copenhagen interpretation has also been developed through this scientific verification process. Although Popper criticized the Copenhagen interpretation, it is necessary to re-evaluate this interpretation within his philosophical framework. This is because it is an important process in the development of scientific theories, in which various perspectives are accepted and science progresses through the verification and refutation of new theories.
