The question of whether a particle goes through both slits in the double-slit experiment is a misleading one, rooted in classical thinking. Quantum objects like electrons don't have definite paths like marbles. Instead, their behavior is described by a wave function, which evolves according to the Schrödinger equation and spreads through both slits. It's the wave function, not the particle itself, that interferes, creating the characteristic interference pattern. When measured, the wave function "collapses," and the particle is found at a specific location, but it's not meaningful to say which slit it "went through" before that measurement. The particle's position becomes definite only upon interaction, and retroactively assigning a classical trajectory is a misinterpretation of quantum mechanics.
In his blog post "Did the Particle Go Through the Two Slits, or Did the Wave Function?", Professor Matt Strassler tackles a common misconception regarding the famous double-slit experiment in quantum mechanics. He meticulously dissects the nuanced interpretations often applied to this fundamental experiment, emphasizing the critical distinction between a quantum particle and its wave function.
Professor Strassler begins by clarifying the nature of a wave function. It's not a physical wave propagating through space like a sound wave or a water wave. Instead, it's a mathematical tool, a complex-valued function that encodes the probabilities of a particle's properties, such as its position, momentum, and spin. This wave function evolves over time according to the Schrödinger equation, much like the amplitude of a classical wave evolves according to its respective wave equation. However, this mathematical similarity doesn't imply a physical equivalence.
The double-slit experiment highlights this distinction. When a single quantum particle, like an electron or photon, is fired at a barrier with two slits, its wave function effectively propagates through both slits simultaneously. This is not to say the particle itself splits and travels through both slits concurrently. Rather, the wave function, which describes the probabilities of the particle's possible locations, evolves in a manner that reflects the presence of both slits. This wave function interferes with itself, creating an interference pattern on a detector screen placed behind the slits. This pattern, characterized by alternating bands of high and low probability, is a hallmark of wave behavior.
Strassler meticulously emphasizes that the particle itself does not travel through both slits. The particle is a single, indivisible entity. It's the wave function, the mathematical descriptor of the particle's potential states, that interacts with both slits. When the particle ultimately interacts with the detector screen, it does so at a single, localized point. The position of this point is probabilistic, governed by the wave function's interference pattern. The act of measurement, the interaction with the detector, forces the wave function to "collapse," meaning the probability distribution instantaneously concentrates at the point of detection.
He argues against the common but misleading visualization of the particle "riding" on the wave function, or the wave function acting as a "pilot wave" guiding the particle. The wave function is not a physical entity that carries the particle. It simply encapsulates the probabilistic information about the particle's state. It's the inherent probabilistic nature of quantum mechanics that dictates the observed behavior.
Furthermore, Professor Strassler clarifies the language used when describing the experiment. Phrases like "the particle goes through both slits" are inaccurate shortcuts. The more precise, albeit less intuitive, statement is that "the particle's wave function evolves through both slits, influencing the probability of the particle's ultimate detected position."
In conclusion, Strassler stresses the importance of clearly differentiating between the quantum particle, which is a discrete entity, and its wave function, which is a mathematical construct describing the probabilities of the particle's properties. The double-slit experiment demonstrates the wave-like behavior not of the particle itself, but of its associated wave function, which ultimately determines the probabilistic distribution of the particle's location upon measurement. This understanding is crucial for accurately interpreting the strange and counterintuitive world of quantum mechanics.
Summary of Comments ( 241 )
https://news.ycombinator.com/item?id=43353947
Hacker News users discussed the nature of wave-particle duality and the interpretation of quantum mechanics in the double-slit experiment. Some commenters emphasized that the wave function is a mathematical tool to describe probabilities, not a physical entity, and that the question of "which slit" is meaningless in the quantum realm. Others pointed to the role of the measurement apparatus in collapsing the wave function and highlighted the difference between the wave function of the particle and the electromagnetic field wave. A few mentioned alternative interpretations like pilot-wave theory and many-worlds interpretation. Some users expressed frustration with the ongoing ambiguity surrounding quantum phenomena, while others found the topic fascinating and appreciated Strassler's explanation. A few considered the article too simplistic or misleading.
The Hacker News post "Did the Particle Go Through the Two Slits, or Did the Wave Function?" generated a moderate discussion with several insightful comments. Many commenters grappled with the philosophical implications of quantum mechanics and the interpretations presented in the linked article by Matt Strassler.
One recurring theme was the interpretation of the wave function. Some commenters echoed Strassler's view, emphasizing that the wave function represents the possibilities of the particle's behavior, not the particle itself. They pointed out that the act of measurement forces the wave function to "collapse," resulting in a definite outcome (the particle being detected at a specific location). This led to discussions about the nature of reality and the role of the observer in quantum mechanics.
Another point of discussion revolved around the concept of "which-way" information. Commenters debated whether it's meaningful to ask which slit the particle went through, especially in situations where no measurement is made to determine the path. Some argued that the question is inherently meaningless in the absence of measurement, while others suggested that the particle might take both paths simultaneously in a superposition.
Several commenters also delved into different interpretations of quantum mechanics, such as the Many-Worlds Interpretation (MWI) and the pilot-wave theory. They compared and contrasted these interpretations with the more conventional Copenhagen interpretation and discussed their implications for the double-slit experiment.
Some commenters also expressed appreciation for Strassler's clear explanation of a complex topic. They praised his ability to communicate difficult concepts in an accessible manner.
A few commenters raised more technical points, discussing the mathematical formalism of quantum mechanics and the role of wave interference in the double-slit experiment. They highlighted the importance of understanding the underlying physics to avoid misconceptions about quantum phenomena.
Finally, some commenters shared links to related resources, such as books and articles on quantum mechanics, further enriching the discussion. Overall, the comment section provided a thoughtful and engaging exploration of the fundamental questions raised by the double-slit experiment and the interpretation of quantum mechanics.