TITLE: What is the Meaning of the Superposition Principle
QUESTION [0 upvotes]: I am a bit confused as to what the superposition principle actually means. Does it merely mean that you can express any given state as the linear combination of two vectors? If so, isn't that kind of obvious. I mean, mathematically, you could express any given vector in nature as a combination of two other vectors. Or does it additionally mean that a quantum state before measurement, for all intents and purposes, exist in every possible state? For example, does it mean that before detection, a photon has all possible polarizations?

REPLY [0 votes]: It is of course a trivial observation that the sum of vectors is a vector and that every vector can be expressed (in a great many different ways) as a sum of other vectors.  
But in QM, you're often interested not just in the state of a system, but the way that state evolves over time.  So you're looking at a function from the real numbers (representing time) to your vector space (or more precisely to the projectivization of that vector space).  Only certain such functions are allowed, namely those that satisfy the Schrodinger equation.  It is somewhat less obvious that the sum of two allowable functions is an allowable function.  In many contexts, that somewhat less obvious statment is what's meant by the "superposition principle".
{"set_name": "stack_exchange", "score": 0, "question_id": 268961}