So, why do we need an interpretation of Quantum Theory?
The mathematics of a theory, whether it is classical Newtonian physics or quantum theory is a way of expressing relationships and definitions. The physics consists of the real-world phenomena that the theory is meant to describe. The interpretation is the glue that joins the mathematical structure to the real-world content.
Putting things this way makes it obvious that quantum theory must have an interpretation since all mathematical theories need to include some interpretation of the mathematics.
Perhaps you already understand this point, but assume that the math already comes equipped with a "standard" interpretation. "So really," you ask, "why not just stick to the standard approach to quantum theory, as laid out in most undergraduate texts?"
This attitude is not a ridiculous one, especially in light of how we typically learn Newtonian physics. In the Newtonian situation, the math still needs an interpretation, but there is a rather straightforward one available and it doesn't have any deep problems. For instance, when you were first introduced to the concept of a force as a push or a pull, that was a way of taking the symbol "F" and relating it to something in the real world---better yet, something very tangible. Things like position, velocity, and acceleration are geometrical concepts that relate very directly to the geometry of real-world things moving in space.
While the standard interpretation of Newtonian physics can be tidied up and made very precise, it is pretty robust and the bonus is that it tends to connect to various aspects of our own human experience of the world in a relatively direct way.
The situation is not really analogous in quantum theory. There is indeed a standard, textbook approach to thinking about the theory. It's an approach that works insofar as it gives us a way to extract predictions and confront the theory with observations and experiments. But it lacks a coherent, underlying notion of a real world. Thus, if you want to inject realism into how you think about quantum theory, you will be dissatisfied with the textbook approach. In addition to this issue, it's also the case that all of the interpretations of quantum theory---textbook or otherwise---do not have the direct appeal to experience that the standard interpretation of classical physics has. In fact, all consistent interpretations force you to give up on key aspects of how you think about the real world. For these reasons, the debate about quantum interpretations has raged since the very inception of quantum theory itself, and continues to be a fascinating topic explore today.
More to come soon.
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