Essay for CLIT/GER 185 taught by Professor Christina Vagt in Spring 2023 at UCSB.
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Galileo Galilei is a well-known philosopher and early scientist for his understanding of natural philosophy and the innovation in the scientific method in the 1600s. In the past four centuries, his ideas of physics development still guide us to explore the unknowing truth of the universe, especially in the confusing modern physics subjects like quantum mechanics. In physics education, quantum mechanics is often hard for students to learn from the beginning, as it involves a deep understanding of metaphysics about observation, evolution, and indeterminism. This essay argues that the underlying principles of quantum mechanics are heavily correlated to Galileo’s scientific philosophy, especially his argument on A priori knowledge constructed by human intuition. Our modern understanding of quantum mechanics extends Galileo’s claim that the universe is only interpreted by ideal mathematics and observed through self-referential mediums.
According to Alexandre Koyré’s interpretation of Galileo’s work Siderius Nuncius, Galileo realized that the telescope constructed by human cultural techniques can bring us further information about our universe beyond our perception, and therefore lead to a better understanding of nature. In other words, scientific knowledge is always A priori based on human intuition, and then verified by experiments, like a telescope, designed by human intuition and implemented by cultural techniques. The experiment is not coming from our experiences but from a hypothesis or a theoretical proposal, as it is the only way to approximately explain and predict the imperfect nature with the ideal knowledge. This idea was the root of the scientific method and guided the exploration of physics for hundreds of years, even today.
The principle of quantum mechanics is an example of constructive A priori theories based on intuition, and it goes so far away from experiences that it often causes confusion among students. Quantum mechanics is developed to explain several unexpected experimental outcomes including the photoelectric effect. However, unlike Newtonian mechanics in which the state of a physical system is represented by mathematical functions of positions and velocities, quantum mechanics abandons these concepts from experiences completely and represents the state as an abstract math object in a Hilbert space (a collection of math objects obeying several axioms). Quantum mechanics argues that the evolution of a physical system can be predicted by a mathematical operation on this math object, namely the Schrödinger Equation. It can provide another abstract math object that exactly represents the ideal physical system after some time. In contrast to classical mechanics, quantum theory is not about how the experimental measurements change, but it is a purely A priori constructive transform between math objects that represent states of a physical system in logic. Finally, to make quantum mechanics effective to predict reality at least in an approximation, a concrete connection between the abstract mathematical state object and the real physical system must be constructed as well, and it is done by a redefinition of observation.
The observation is redefined as a self-referential medium in quantum mechanics, and it can be seen as an extension of Galileo’s telescope. The mapping between the math object and the real physical system is fixed by the same outcome of the observation. An observation of a physical system is effectively a measurement that outputs a number, while an observation of a math object is a corresponding mathematical operation that outputs a number as well. Nevertheless, the outcome of both observations is not deterministic. The math operation has to provide a probability distribution of all the possible outcomes that can be verified statistically by experimental measurements. Thus, quantum mechanics can be considered an impossible machine as statistics can never verify probability with a finite number of measurements. This indeterminism further emphasizes that quantum mechanics is A priori and it is only “loosely” connected to real experiences in comparison to classical mechanics. Most importantly, this indeterminism is itself deterministic and predicted by the quantum theory, which makes the theory a “second-order determinism” as analog to the second-order vision in Vogl’s reflection on Galileo’s telescope that displays both visible things and invisibility. Moreover, we cannot ignore the fact that the observer is an existing physical system that is also governed by quantum mechanics, making the observation indeed a self-referential medium. The modern interpretation of quantum measurement is an interaction between the observer and the object, known as entanglement. Whatever experimental instruments we use, the observation is always a simultaneous and mutual change in the states of both the subject and the object. In the famous thought experiment Schrödinger’s Cat, the argument is that the observation actually affects the system and results in a definite outcome, while the observer is also affected by entangling with the system to obtain information. Possibly the very ideas of observation and quantum mechanics are themselves an observational interaction between our neural activities and, for example, this essay. In Joseph Vogl’s reflection of Galileo, the telescope is not only a tool but a medium that causes the understanding of ourselves. From this Li 4 perspective, quantum observation is a far extension of Galileo’s telescope that not only see nature but also see ourselves.
The discussion above draws a brief connection between Galileo’s scientific philosophy and the principles of quantum mechanics and illustrates that quantum mechanics is A priori knowledge constructed by human intuitions. Inspired by the telescope, Galileo said that the universe is interpreted by geometry. Today we extend it to all sorts of math such as linear algebra and group theory. But math cannot prove the theory of quantum mechanics, and the Schrödinger equation was discovered even by a guess of Erwin Schrödinger. It is treated as true only for the reason that current experiments have not provided a significant counter-example. It is amazing that this “unproven” theory actually brings us splendid innovations like semiconductor chips that changed our world. What is unchanged is Galileo’s scientific method, in which we are constantly rejecting our A priori knowledge by mediums and constructing new ones from human intelligence, and we are marching on the infinitely long way of Physics, searching for the impossible machine of knowledge that explains everything.
