In this blog post, we will examine what wave collapse means, focusing on the Copenhagen interpretation and the many-worlds interpretation among the various interpretations of quantum mechanics, and consider the characteristics and limitations of each interpretation.
From the late 19th century through the early 20th century, phenomena began to emerge that could not be explained by classical physics alone. Maxwell and Einstein discovered that light possesses both wave-like and particle-like properties. Max Born predicted that particles, too, possess wave-like properties. The Davisson-Germer double-slit experiment is said to have experimentally demonstrated that electrons possess wave-like behavior. A closer look at the double-slit experiment reveals the following: A device that emits electrons, a plate with two slits, and a screen are arranged in sequence. Electrons emitted from the electron source pass through the two slits and reach the screen; when the electrons’ arrival at the screen is observed, an interference pattern appears. Such a pattern does not appear when there is only one slit. Therefore, the position of an electron must be explained as a wave passing through both slits simultaneously. Quantum mechanics emerged to explain these phenomena. In quantum mechanics, probability waves are described as the fundamental building blocks of nature. Probability waves are used to describe the state of matter. The state of matter includes properties such as position and spin. A probability wave indicates that a value is not fixed at any single point but rather that the probability of occurrence varies at each point. Quantum mechanics was established in the early 20th century, and numerous experimental results from that period and thereafter support the validity of this theory. At the core of this theory lies Schrödinger’s wave equation. As the fundamental equation of quantum mechanics, Schrödinger’s wave equation describes how a probability wave changes over time. However, it remains unclear exactly how such probability waves relate to everyday life. In everyday life, the outcomes we observe are not multiple states but a single, definite state—how can this be explained? What is a probability wave, and is there a way to understand it? To resolve these questions, various interpretations of quantum mechanics have emerged. In a past survey conducted at a quantum physics conference, participants were asked about their preferences regarding each interpretation. Preference for the Copenhagen interpretation stood at 42%, the quantum-informational perspective at 24%, and the many-worlds interpretation at 18%. As seen in the survey, the Copenhagen interpretation is the mainstream interpretation within the physics community. The Copenhagen interpretation is the one developed from the very early days of quantum mechanics by scholars led by Bohr. Brian Greene introduced the core tenet of the Copenhagen interpretation as follows: “Whenever we attempt to observe a probability wave directly, the act of observation itself disrupts it.” The Copenhagen interpretation explains that at the moment of observation, the probability wave can no longer remain in that state and collapses into a single point. It is explained that the result of this collapse into a single point is the reality we are familiar with. This process is called wave collapse. The quantum information perspective explains that the universe itself is composed of quantum information, which constitutes the very essence of the universe. It posits that everything is the result of quantum computations involving this quantum information. From this viewpoint, the entire universe is sometimes viewed as a machine performing quantum computations. Seth Lloyd has written a book that persuasively argues for this perspective. In that book, he explained the role of information and how it relates to actual physical laws. For example, he explained how quantum computation tends to spread unknown information and elaborated on the physical laws related to entropy. The Many-Worlds Interpretation was proposed by Hugh Everett. This interpretation does not accept wave function collapse, which is the cornerstone of the Copenhagen interpretation. Instead, it posits that the universe branches into multiple worlds, and all possibilities are realized. Thus, it explains that in each world, an observer perceives the reality we are familiar with. I find the concept of wave function collapse—which can be seen as the core of the Copenhagen interpretation—unconvincing. As Brian Greene pointed out, the boundary defining what constitutes an “observation” is unclear. The explanation goes something like this: wave function collapse does not occur when microscopic objects interact with one another, but it does occur when an observer makes a measurement; however, this explanation is difficult to accept.
It is natural to assume that the laws of physics apply universally and identically throughout the universe. Since the observer is also part of the universe, I believe it is natural that the laws of quantum mechanics apply equally to all actions, including observation. However, the Copenhagen interpretation explains that wave collapse occurs as a result of the observer’s act of observation. Mathematically, wave collapse is also an operation distinct from ordinary quantum mechanical operations. Although I cannot explain the process by which a probability wave function changes in detail here, it can be described as an operation involving multiplication by a reversible matrix with certain special properties. “Reversible” means that there is a one-to-one correspondence between the result and the state that caused it. However, when wave function collapse occurs, this correspondence is broken. The system becomes fixed in a single state, making it impossible to restore the original state. In cases where the nature of the observation is crucial—such as in the Copenhagen interpretation—the concept of the Heisenberg cut is sometimes introduced. This concept posits that the laws of quantum mechanics apply up to a certain boundary, and beyond that boundary, the wave function collapses. However, this boundary is not clearly defined. It could be set at the level of objects such as electrons or protons, or it could be set at macroscopic objects like humans. This is unsatisfactory because it does not specify where exactly this boundary should be drawn. A well-known example that illustrates this situation is Schrödinger’s cat thought experiment. In this thought experiment, a particle smaller than an atom and a cat appear. The small particle can decay with a certain probability, a process that can be explained by quantum mechanics. A detection device is placed next to it. It is said that the moment such a decay is detected, a mechanism that kills the cat is triggered. This raises the question of whether the cat is dead or alive at that moment. The Copenhagen interpretation explains that the cat’s state—whether alive or dead—is determined the moment it is observed. This explanation is based on the premise that even macroscopic objects do not experience wave collapse. It suggests that even large objects must be considered within the framework of quantum mechanics. Consequently, there are thought experiments that take this situation to an even greater extreme. In this thought experiment, we assume that a friend conducted Schrödinger’s cat thought experiment and observed the cat’s state. In such a case, it does not provide a definitive explanation of at which boundary the wave function should be considered to have collapsed. Regarding this boundary, some view the extent of the observer’s knowledge as crucial, and this is said to be related to probability. Nevertheless, the Copenhagen interpretation has the advantage of easily and clearly explaining the results observed by the observer. In fact, it explains the results of various experiments very well. It suffices to apply wave collapse at the moment of observing the experimental results or when interacting with macroscopic objects. It is a convenient interpretation that does not require considering the quantum state of the observation equipment. One reason for its great success, despite the intuitively difficult-to-accept result of wave collapse, is likely its ability to explain experimental results well. Precisely because wave collapse is such an unnatural explanation, I believe the Many-Worlds Interpretation could be a viable alternative to the Copenhagen interpretation. The Many-Worlds Interpretation does not acknowledge wave collapse. It is said to be an interpretation derived by focusing solely on Schrödinger’s wave equation. Since it does not view the act of observation as subject to any special laws, it interprets the process as simply a change in the wave state as seen from the wave equation. In other words, it is understood that when an observation is made, the wave does not collapse; rather, the observer and the object enter a quantum-mechanically entangled state. To understand this entangled state, let’s examine an example from the perspective of the Many-Worlds Interpretation, which does not acknowledge wave collapse. An electron’s spin can be either up (↑) or down (↓). The observation equipment is a device that measures the electron’s spin. Let’s assume the state display window of the observation equipment has three possible states: up (⟰), down (⟱), and blank (). Let’s look at the situation before the measurement. The electron’s spin and the state display window of the observation equipment can be described as mutually independent probability waves. The electron is not fixed as either up (↑) or down (↓) but is represented by a probability wave. The measuring apparatus would have been set to the empty state () for the experiment, and there would be a probability wavefunction representing this situation. Let’s look at the situation after the measurement. At this point, it can no longer be described as independent probability wavefunctions. The overall state is instead described by a single probability wavefunction that encompasses both the electron and the measuring apparatus.
Specifically, it is represented by a single probability wave function that describes only two possible situations: one where the electron’s spin is up and the observation apparatus’s state window indicates “up” (↑⟰), and another where the electron’s spin is down and the observation apparatus’s state window indicates “down” (↓⟱). This phenomenon, in which multiple states are no longer independent, is described as “entanglement.” The Many-Worlds Interpretation takes this a step further. Looking at the example above, there are two possible situations (↑⟰, ↓⟱). The Many-Worlds Interpretation views the world as split into these two states. That is, in one world, the ↑⟰ situation occurs, and in another world, the ↓⟱ situation occurs. It is said that, upon examining Schrödinger’s equation, there is no major mathematical problem with viewing it this way. If we separate the possible states based on the results of observations and interpret each result as a distinct world, that is precisely the Many-Worlds Interpretation. Thus, every event that can be considered an observation is viewed as an event in which worlds split. Consequently, every possibility that is quantum mechanically feasible is realized in each world. The aspect of the Many-Worlds Interpretation that I find most appealing is that it does not regard the act of observation as something special. Since even the observer is viewed as part of a world subject to the same laws of quantum mechanics, I consider this interpretation to be a more universally applicable one. However, the Many-Worlds Interpretation faces many criticisms. There is no convincing explanation of what it means for the world to split into multiple worlds. Furthermore, the claim that multiple worlds exist is bizarre in and of itself. If worlds are continuously created ad infinitum, there is no way to explain how we can possibly keep track of so many of them. Furthermore, if different worlds are completely separate and cannot influence one another, one might argue that, from the observer’s perspective, the existence of other worlds is entirely meaningless. From that viewpoint, the interpretation itself becomes meaningless. Additionally, there are still quite a few challenges that need to be addressed in the Many-Worlds Interpretation. First, providing an adequate explanation of which world an actual observer will perceive is one of the tasks that must be addressed. There must also be a way to describe phenomena from the observer’s perspective—rather than from the perspective of the whole—in order to explain the phenomena we observe in everyday life. This is because we do not directly observe probability waves, but only their outcomes. The Copenhagen interpretation clearly explains this aspect. The Copenhagen interpretation holds that the world we observe is realized through the collapse of the wave function, and it yields results that align with reality. Furthermore, the Many-Worlds Interpretation should be able to explain the Copenhagen interpretation. If the Many-Worlds Interpretation is the correct one, it should be able to explain—from its own perspective—how all experimental results to date have matched the predictions of the Copenhagen interpretation. Furthermore, we must determine under what circumstances differences might arise between the two interpretations. Therefore, establishing a connection with the Copenhagen interpretation is also a major challenge. I do not support the Copenhagen interpretation’s concept of wave collapse because it is unclear when exactly it should be applied, and I view the practice of isolating measurement as a separate process as problematic in terms of universality. Instead, I believe we should maintain the perspective that the entire universe can be described as a probabilistic wave in quantum mechanics, and that the observer is also part of it. Therefore, I think the Many-Worlds Interpretation and similar theories could serve as alternatives. However, as mentioned earlier, several problems remain with these interpretations as well. As evidenced by survey results involving physicists, no definitive conclusion has yet been reached regarding the interpretation of quantum mechanics. Some of the existing interpretations have a history of being disproved by experiments. However, no such experiments have yet been conducted for the Copenhagen interpretation or the Many-Worlds interpretation. It is possible that experimental designs capable of actually demonstrating the differences between these interpretations may be developed someday. Alternatively, we may eventually conclude that all these interpretations are equally valid. Therefore, I believe that as our understanding of the laws of physics deepens, new avenues for interpreting quantum mechanics will open up. It will be fascinating to witness that process unfold.
