Why Quantum Mechanics Makes No Sense (But Still Works) - Collapse of the Wave Function (Parth G)

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 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

#ad This video was sponsored by Squarespace!

[ParthGChannel]

And as always, let me know what other topics I should cover in future videos :)

[benschmitt]

Just starting my first 400 level quantum course, so you can say this is good timing :) thanks Parth !

[sMeLLwAtER]

I want to grasp these things as you do.

[machawley]

Parth, I love your clear, organized, well laid descriptions. May I suggest that the 'collapse of the wave function' is due to the inevitable loss of energy arising from the transfer of information to the observer.

[hoodaly]

Sorry but this video I did not like. As I understand it, there is a consensus among many physicists that to understand measurement, you have to acknowledge that the act of measuring involves the particle interacting with the measurement apparatus, which itself is a quantum system. It is this continued interaction with the environment that leads to decoherence and subsequently the collapse of the wave function, no magic needed, just a really complicated system to consider.
I find all this talking about the Copenhagen interpretation and what it means, and that we don't know for sure how things work, is counterproductive and cheap. The Copenhagen interpretation is a simplification of a more complex system, a useful tool for calculating, and should be treated as such, and not be taken as the underlying truth that we just don't fully understand.
If I estimate the volume of a cow by simplifying the cow to a sphere, and observing that the volume of water that a cow displaces very accurately matches what I predicted using the sphere ansatz, I would not go on talking about how cows really are spherical and we just don't fully understand how comes that they don't look like a sphere.

[Vball]

Thank you so much. It's hard to put into words how incredibly well said this was compared to every single other video I have ever seen on this subject.

[ParthGChannel]

And as always, please let me know what other topics to cover in future videos :)

[christophergame]

The reason why wave function collapse seems inexplicable to someone is that they have muddled thinking without physical understanding.

[orri]

Hi Parth, have you covered quantum wave packets (with or without dispersion). I have been looking into them and there is not many educational videos on YouTube about them. What I am wondering, is, if particles are quantum wave packets? Anyway I like your stuff and it has helped me in my studies. Thank you for your contribution.

[trancepower]

Ce cauzează colapsul câmpului cuantic, poate fi gravitația?

[boody]

Hypothetically, if there was no maximum speed, but only a maximum perceivable speed would the math work? For example helicopter blades travel much faster than we can visually perceive. If we believed that our maximum perceivable speed was in fact the absolute maximum speed, then the blades seem to be in all possible locations at once. I'm sure a function could be created to determine the probability of the blades position at any given time based on what we believe their maximum speed to be. If we put a detector where we think the blades should be at any given time, would it correlate to our function?

[blinded]

0:59
Shouldn't square-graph be lower?

[MrVsoral]

You mentioned that "...based on the surroundings, the system may either stay in the 'measured' state or start spreading according to the Schrodinger's equation..."
Questions:
1. If (in theory) the system is completely isolated, then would it stay in the measured state, or would it still start to spread into a superposition? If so after how long and what causes this?
2. If the spread after measurement is due to surroundings - then should it not actually lead to 'entanglement' rather than simple evolution as per Schrodinger's equation?

Appreciate if you could comment - thanks.

[MaryK.Sells]

So basically when you let go of one answer and allow the possibility of many. Is the correct way to live. In detachment, even shown in quantum . Wow ❤️

[daltanionwaves]

But remember that waveform collapse doesn't happen in real life. We can slice an instant in time out of real life in an abstract way on paper or in a computer, but a particle is never in 1 state, in 1 place, at say, 10:43am for example. I think perturbation theory and the wave function (and measurement) confuse layfolk because they don't know it's a simplified fictional representation of specified observables like spin or charge. And we use our familiarity with life at human scale to visualize concepts like the wave function, instead of trying to visualize the wave itself!! as it would be observed in nature... Electrons aren't discrete little balls orbiting a nucleus. The stuff that reality is made out of is far more complex and beautiful in reality than it is in a representation in a book. Of course, we need these simplified stick drawings of these things to communicate and teach aspects of them in a bite size digestible way... But don't mistake those simplified representations of pieces of information —with what these things really are in the physical world.

[praneethbvs]

How do we know the system is in superposition of all possible states before we measure it? How do we know that fact before measuring it? Measuring it will collapse so, what made us come to that conclusion before measuring it.

[wulphstein]

A house has many rooms that an occupant can be in. If you find the home owner in one of the rooms, why doesn't the house collapse? Why does the wave function collapse when you detect the electron?

[williamwalker]

Experiments and electrodynamic theory prove nearfield electromagnetic fields are instantaneous. See links below for details. And the reality of instantaneous nearfield electromagnetic fields can be explained by quantum mechanics using the Pilot Wave interpretation of quantum mechanics and the Heisenberg uncertainty principle (HUP), where Δx and Δp are interpreted as averages, and not the uncertainty in the values as in other interpretations of quantum mechanics. So in HUP: Δx Δp = h, where Δp=mΔv, thus HUP becomes: Δx Δv = h/m. In the nearfield where the field is created, Δx=0, therefore Δv=infinity. In the farfield, HUP: Δx Δp = h, where p = h/λ. HUP then becomes: Δx h/λ = h, or Δx=λ. Also in the farfield HUP becomes: λmΔv=h, thus Δv=h/(mλ). Since p=h/λ, then Δv=p/m. Also since p=mc, then Δv=c. So in summary, in the nearfield Δv=infinity, and in the farfield Δv=c, where Δv is the average velocity of the photon according to Pilot Wave theory.

Dr. William Walker - PhD ETH Zurich 1997

*YouTube presentation of above arguments:

*More extensive paper for the above arguments:
William D. Walker and Dag Stranneby, A New Interpretation of Relativity, 2023:

[pappa]

is the electron around the nucleus collapsed because it is interacting with the nucleus? if no, then why?

[macleadg]

I love Parth’s videos. They leave me in a paradoxical state, like quantum mechanics: I feel like I learn something each time, while feeling more ignorant each time…

Seriously, though, these are awesome.