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The concept of "wave function collapse", or "collapse of the wave function", is one of the most intriguing aspects of quantum mechanics. It's also one of the reasons why quantum mechanics doesn't make intuitive sense to us yet.

Every quantum system can be described by a wave function. This is a mathematical function that contains all the information we know about our system. When we square it (square modulus), we can calculate the probability of getting different measurement results if we were to make a measurement on the system. For example we can calculate the likelihood of a particle being found in a particular region of space, or in a particular energy level, or any other measurement outcome.

According to the Copenhagen Interpretation of Quantum Mechanics, a system exists in a superposition (blend) of lots of different measurement states all at once. The "weighting" of these states is directly related to the probability of finding the system in each of these states, as seen from the wave function. In other words, more likely measurement result states are more heavily represented in the superposition. And when we make a measurement, the system randomly and discontinuously collapses into one of the possible measurement states. We have no way of knowing which state a particular system will collapse into. This is known as the collapse of the wave function. It is one of the quirks of quantum mechanics.

This is very different to the system already being in a state and then a measurement just gives the observer information about what state the system is in. Check out this video if you want to find out more about how these two ideas are different, and why quantum mechanics goes with the first idea:    • Pure vs. mixed quantum states  

This idea can lead us to believe that we influence the universe by making measurements. However, the physics idea of measurement is still being debated, and could even involve interactions between systems without a conscious observer. Consciousness is not necessarily the key to causing wave function collapse.

Additionally, this strange idea is very much a part of the Copenhagen Interpretation of Quantum Mechanics. In fact, it forms one of the postulates (assumptions on which the theory is based). Other interpretations of the mathematics try to get around this, but have different strengths and weaknesses compared to the Copenhagen Interpretation.

Before a measurement is made, the wave function follows the Schrodinger Equation, which dictates how wave functions evolve over time. Depending on the system and the initial conditions, the wave function can be constant or changing smoothly (continuously) as a superposition of different states.

At the instant the measurement is made, the wave function discontinuously (randomly, suddenly) collapses into one of the possible measurement states. This part is NOT dictated by the Schrodinger Equation. The probability of getting any particular result can be calculated from the wave function JUST BEFORE the measurement was made.

After the measurement, the wave function once again begins to follow the Schrodinger Equation smoothly, with the measurement result as the new initial state. The system may once again stay in that state, or change over time and "spread out" over multiple states.

We also look at how the Copenhagen Interpretation deals with measurement results for continuous and discrete variables.

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Timestamps:
0:00 - Why Quantum Mechanics makes no sense - wave functions
2:10 - Superposition of states in the Copenhagen Interpretation
3:31 - Collapse of the wave function
4:23 - Measurement? Interpretations of Quantum Mechanics?
5:30 - Before, during, and after: Schrodinger vs Discontinuous
8:04 - Discrete vs Continuous measurement results
8:35 - Big thanks to Squarespace - link in description!
9:30 - Outro

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