Karl Popper’s philosophy of disproversialism provided a method for the verification of scientific theories, which he saw as conflicting with the Copenhagen interpretation of quantum mechanics. However, the Copenhagen interpretation can be reevaluated within Popper’s philosophical framework by applying disproversialism and tendency-based probability theory, and can be seen as complementary.
Karl Popper, who is famous for his scientific disproversialism, also revealed his position on probability theory in the process of explaining his philosophical ideology in his book ‘ The Logic of Scientific Discovery. Based on his theories about the interpretation of probability, he comes to reject the Copenhagen interpretation, the most dominant interpretation of quantum mechanics, to a large extent. His position stems from the logic and assumptions he makes in order to establish his philosophy of disprovability. However, Karl Popper’s philosophy of disproversialism is a very important idea in the philosophy of science, and the Copenhagen Interpretation of quantum mechanics is overwhelmingly supported by physicists. Let’s take a look at whether the Copenhagen interpretation of quantum mechanics is really incompatible with Karl Popper’s philosophy.
First, let’s briefly explain Karl Popper’s philosophy of disproversialism and probability. Karl Popper believes that it is inherently impossible to prove scientific facts by induction. Induction is the process of deriving universal statements from singular statements, and no matter how many individual cases are gathered, it is impossible to fully prove a generalized fact. A famous example of this is the proposition U, “All swans are white.” No matter how many swans we observe and verify that they are all white, we can never fully prove U. Even if we observe all the swans on the planet at one point in time and find that they are all white, if there were non-white swans in the past, or if there will be non-white swans in the future, U will not be true. Popper thus rejects the scientific method by induction. This is called “The Problem of Induction”.
Instead of rejecting induction, Popper argues for a scientific method based on deduction. Consider a general proposition U. Then, no matter how many individual propositions s1, s2, ….. that it is true, it is never guaranteed that U is false. But if there is just one individual proposition s1′ that says U is false, then it is proven that U is false. Consider the case in the previous paragraph. Let U be “All swans are white.” Let s1, s2, ….. , s1000 be the observations that 1000 swans are observed and all are white. The observations s1 through s1000 are not perfect guarantees that all swans are white, but if the 1001st swan is black, then U is definitely false. U is thus disproved. The scientific methodology that proceeds in this way is called falsificationism.
Falsificationism is also the basis for Karl Popper’s distinction between science and non-science. One of the great problems in the philosophy of science has been the establishment of criteria for distinguishing between science and non-science, known as the “Problem of Demarcation”. Karl Popper saw disprovability as what distinguishes scientific theories from non-scientific theories: a theory is a scientific theory if it is a set of general propositions, and each of those propositions can be experimentally disproved. By this standard, Freudian psychology would not qualify as a scientific theory.
In this way, the problem of compartmentalization can be solved in terms of disprovability, and we can also define objectivity as it is often used in scientific methodology. Karl Popper argues early on in The Logic of Scientific Discovery that scientific methodology should be strictly separated from the individual mind. One example is that when describing a scientific study, it is not necessary to describe the process by which the researcher came up with the hypothesis. This is also the logical foundation for his philosophy of antiproofism. This is also the logical basis for his philosophy of antiproofism, which views scientific systems of theory as a series of attempts to construct explanations of reality that are independent of the individual mind. In a similar vein, in later chapters, he argues that natural laws can only be stated in such a way that they are independent of their location in space and time and of the individual observing them. All scientific propositions must be objective by being “inter-subjectively testable”. It is in this context that it is understandable that “reproducibility” is so important in today’s research methodologies.
Taking this philosophy of disproversialism further, we can also set criteria for the validation and adoption of scientific theories. Popper chose four points to consider when evaluating a scientific theory. The first is the internal logic of the theory itself. This is the criterion of internal consistency, which is the absence of contradictions among the propositions that make up the theory. The second is the interpretation of the logical form of the theory. It evaluates whether the theory has the characteristics of a scientific theory. As already mentioned in the previous paragraph, disprovability is a criterion for this evaluation. Third is the comparison with other theories that exist. This considers how the theory would help advance the field of science if it withstood multiple tests. The fourth is the experimental validation of the predictions derived from the theory. Even if a theory is found to be correct, it is only temporarily supported, and there is always the possibility that subsequent experiments will disprove it and discard it.
Let’s take a look at the Copenhagen interpretation of quantum mechanics. The Copenhagen Interpretation is the most mainstream interpretation of quantum mechanics today. Surprisingly, there is no definitive definition of the Copenhagen Interpretation in the literature, but if we take a look at the various articles in the literature, we can see that there is a consensus within the field. First, physical systems generally do not have fixed properties prior to measurement. These properties are represented by a wave function, which includes all the variables known about the system, and there are no additional “hidden variables”. Second, because of this, quantum mechanics can only determine the probability of any outcome from a measurement. Third, every measurement affects the system itself, so that the wave function, which is a superposition of all possible states of the system, irreversibly collapses with the measurement, resulting in the observation. Fourth, because the act of measuring itself affects the system, some properties of the system are incompatible with each other, meaning that certain physical quantities cannot be accurately measured simultaneously for a single system. This is known as the Uncertainty Principle. Fifth, the results recorded by a measuring instrument can only be described in terms of classical physics. Sixth, the wave function has properties associated with probability. Seventh, wave functions exhibit wave-particle duality.
The Copenhagen interpretation, including the sixth and seventh principles, has so far survived without being disproven by the results of any real-world experiments. Examples include Schrödinger’s cat thought experiment, the double-slit interference experiment, and experiments on the material wave nature of electrons. The Schrödinger’s cat experiment is a thought experiment that demonstrated that if we accept the uncertainty principle at the microscopic level, this uncertainty will also affect macroscopic objects, and it is a thought experiment that tests the internal contradiction of the Copenhagen interpretation. Imagine a live cat inside a sealed box, and let the cat’s life and death depend on the state of a certain elementary particle inside the box. For simplicity, let’s say there are two states of this particle, each with a probability of 50%. The particle’s wavefunction gives rise to the cat’s wavefunction, and since the wavefunction is a superposition of all possible states, the cat’s state is a 50/50 superposition of alive and dead. The point is made that this doesn’t make sense because it means that the cat is both alive and dead until you open the box and check it out. However, the Copenhagen interpretation is that the wave function only represents the observer’s perception of the state of the box, not the state of the cat itself. This thought experiment does not show that the Copenhagen interpretation has an internal contradiction: there is a 50% chance of opening the box and finding a dead cat, and a 50% chance of finding a live cat.
Next, let’s look at the results of experiments that address the duality of light and matter, including the double slit experiment. These experiments are prime examples of how the Copenhagen interpretation’s predictions about the external world have survived verification by actual experimental results. In the double slit experiment, light passing through a double slit creates a diffraction pattern on a screen. Since diffraction is a property of waves, this experiment demonstrates the wave nature of light. However, the photoelectric effect experiment shows the particle nature of light. When light is squeezed through metal, photoelectrons will bounce off the metal if certain conditions are met. The problem is that these conditions are independent of the intensity of the light or the duration of the irradiation, and are determined solely by the frequency of the light. If the frequency of the light is below a certain limit, no matter how intense or long the light is, the photoelectrons will never pop out, but if the light is above the limit, the photoelectrons will pop out immediately. These experimental results can be explained by analyzing light as a particle called a photon. The particle nature of matter is so self-evident that even classical mechanics makes it clear. The wave nature of matter is confirmed by the existence of matter waves. When a cathode ray fired by accelerating electrons to high speeds is passed through a double slit, a diffraction pattern appears on the screen. This confirms the wave nature of matter. This and numerous other experimental results on the wave-particle duality of light and matter are not inconsistent with the Copenhagen interpretation.
However, the real argument against the Copenhagen interpretation in Karl Popper’s philosophy comes from a different angle. The foundations that Karl Popper laid in the process of establishing his philosophy of disproversialism may conflict with the assumptions he made about the concept of the wave function. As we discussed earlier, Popper argues that natural laws can only be stated in such a way that they hold true regardless of the location in space and time or the individual observing them. Given that in his philosophy, “inter-subjectively testable” is the criterion of objectivity in science, the Copenhagen interpretation, which claims that the act of measuring itself changes the phenomenon, i.e., that the results of an experiment vary every time depending on the observer, may seem incompatible with Karl Popper’s philosophy. In a similar vein, the question of what constitutes a “measuring instrument” can also be raised.
However, the above problems can be solved by presenting a more rigorous statement of the indeterminacy principle in the Copenhagen interpretation, one that is used in real physics. This solution is in line with Karl Popper’s extension of propensity probability theory, which extends from “experiments conducted by observers” to “natural phenomena themselves”. The propensity theory of probability is one of the variants of the frequency theory of probability. In frequency theory, the probability of a phenomenon is considered to be its relative likelihood (or the limit of its relative likelihood) in a sufficiently large (or infinitely large) population. However, Popper criticizes frequentist probability for its inability to help predict single, localized events. Instead, he proposes a tendentist probability theory, which proposes that nature itself repeats ‘experiments’ in the form of recurring natural phenomena, some of which are observed by humans, and whose probabilities are given by the relative degrees, instead of the context of human intervention in setting up experiments and obtaining probabilities.
Now, in the argument in the above paragraph, replace “measuring instrument” with “any object that interacts with a random particle in the universe” and “experiment” with the set of all these interactions. To be more specific, take any microscopic particle (say, an electron), think of an ‘observation’ as a detector observing a photon that collided with the particle, and state the uncertainty principle in terms of both the particle and the photon. The uncertainty principle can then be understood as follows. We bombard a microscopic particle with a photon whose state is unknown, and then detect the bounced photon to trace back the state of the microscopic particle. The collision of a photon with a particle changes the physical quantity of the particle, and the information directly available from the detection does not provide accurate information about the state of the particle before the collision. This is because light is wave-like, which results in a minimum position error equal to the wavelength of the light, and the particle nature of light results in a minimum momentum error equal to the change in momentum that the particle receives from the collision. If the wavelength is shortened to reduce the position error, the momentum of the photon becomes larger, and therefore the momentum of the particle in the collision changes more dramatically. Conversely, if you lower the frequency to reduce the momentum error, the wavelength will be longer, resulting in a larger position error. In this way, the uncertainty principle can be stated in a way that completely excludes the idea of individual observers.
Karl Popper himself was somewhat negative about the Copenhagen Interpretation, but according to the criteria he proposed, it is at least compatible with his antiproofist philosophy and tendentious probability theory, so it is not yet necessary to discard the theory under these two perspectives. This is one of the reasons why the Copenhagen Interpretation is currently the mainstream interpretation with overwhelming support in the academic community.
Let’s revisit the relationship between Popper’s disproversialism and the Copenhagen interpretation. The Copenhagen interpretation of quantum mechanics has a very unique interpretation. It is the concept of “collapse of the wave function”. This collapse is caused by the act of measurement and describes the process by which a physical system is transformed into a deterministic state. This is inherently contrary to the determinism of classical mechanics. Popper proposed antidefinitivism against the backdrop of classical determinism, but the nondeterministic elements of the Copenhagen interpretation conflict with antidefinitivism and are the main reason Popper rejects it.
Let’s see if these nondeterministic elements can be accommodated within the framework of antiproofism. Popperian disprovationalism evaluates scientific theories in terms of experimentally disprovable propositions. In the Copenhagen interpretation, the state of affairs before a measurement is indeterminate, but the result afterward is clearly disprovable. For example, if an experiment to measure the location of a particle fails to find a particle at a particular location, the proposition that there is a particle at that location is disproved. In other words, the act of measurement itself implies disprovability, so the non-deterministic nature of the Copenhagen Interpretation is not entirely incompatible with disprovationalism.
We can also apply Popper’s tendentious probability theory to the Copenhagen interpretation. Tendentist probabilism holds that natural phenomena themselves have a tendency to produce certain outcomes. The probabilistic interpretation of quantum mechanics is a good example of this tendency. By using probabilistic tendencies to predict the position or momentum of a particle, we can calculate the probability of a particular outcome. This suggests that Popper’s probabilistic approach and the Copenhagen Interpretation’s probabilistic prediction can be complementary.
Popper’s philosophy of disprovability also plays an important role in the development of scientific theories. Scientific theories must be able to be verified and disproved by new experiments and observations. The Copenhagen interpretation has also been subjected to this process of scientific verification. Although Popper criticized the Copenhagen interpretation, it’s worth reevaluating it within his philosophical framework. This is because the development of scientific theories is an important part of the process of scientific progress, as it allows for different viewpoints to be accepted and new theories to be validated and disproved.
