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

a huge thanks to squarespace for sponsoring this video hey everyone parth here and in this video i want to talk about one of the most central and yet most confusing ideas in quantum mechanics known as the collapse of the wave function if you enjoyed this video then please hit the thumbs up button and subscribe for more fun physics content let's get into it let's begin by recalling that any system we study using the theory of quantum mechanics maybe an electron in empty space or maybe an electron and a proton making up a hydrogen atom or anything else for that matter can be described by a wave function this is a mathematical function that tells us all the information we can know about our system most commonly wave functions are discussed in the context of finding particles at different points in space when we make a measurement on our system here's what i mean by this if we take our wave function for this particular particle this electron and we square it technically we take its square modulus then this directly gives us the probabilities of finding our particle in different regions of space so in this case from our wavefunction we can see that the particle is most likely to be found somewhere here and less likely to be found here that's how the wavefunction is most commonly discussed but the wavefunction also contains other kinds of information basically any measurement we can make the wavefunction gives us the probabilities of getting any of the possible measurement results for example we may be familiar with the idea that in an atom electrons can only occupy specific energy levels or shells with the nucleus at the center of the atom the shell nearest to the nucleus called the first shell is lowest in energy the next shell up has slightly more energy and then some more and so on and so forth but in other systems that aren't necessarily simple atoms we can also see energy levels like this a particle can be found in one of many different energy states and the wave function squared gives us the probability of finding the particle in any one of these now interestingly quantum mechanics says that before we make a measurement to find out what state our particle is in the system is not just already in that state and we don't just simply find out what state it's in when we make the measurement quantum mechanics or at least the copenhagen interpretation of quantum mechanics says that the system is in all the possible measurement states at the same time this is known as a superposition of states and the wave function shows us that the system is in all these possible states weighted by what is essentially the probability of finding it in any one of them now this is obviously different to the system already being in a given state and then us just finding out what state it's in when we make a measurement the interesting thing is mathematically these two ideas can be shown to have different consequences which we can test in the real world with experiments we can take each idea put it into our mathematics make a prediction from each one and then test it and we've already done this and all of the experiments we've done so far suggest that this version the superposition of states is at the very least more correct than this version where we just find out what state the system is in for more information on this idea i'll leave some resources in the description below but why do we care about all this well the point is that before we measure our system it's in a blend of all possible states but as soon as we measure it it collapses into just one of these states randomly this idea is known as the collapse of the wave function we have no way of predicting exactly which state our system will collapse into but if we repeat the same experiment over and over then the kind of results we will get tend to match the probabilities given by our wave function this makes sense because if there is 60 probability of getting this state in any one measurement then if we make lots of identical measurements 60 of these should be in this state but the important thing is that we have no way of predicting which state a particular system will fall into before we actually make the measurement and find out now there are a couple of things worth mentioning here firstly physicists are still debating the details of what is meant by measurement some people hear this discussion we've just had about the collapse of the wave function and assume that this means we somehow control the universe because it's only after making a measurement that a system changes however as we said the meaning of measurement is still slightly unclear in quantum mechanics and it could also refer to interactions between different systems without the need for a conscious being doing the measuring secondly although we're looking at the copenhagen interpretation of quantum mechanics in this video it's worth noting that there are other interpretations which follow the same mathematics but assign different physical meanings to each idea they attempt to get around this random wave function collapse as well as the superposition of states but are successful in some things and unsuccessful in other ways our main focus here will continue to be the copenhagen interpretation or the most commonly used interpretation of quantum mechanics and thirdly let's talk about what happens to our system or to our wave function before and after the measurement we've already seen that the process of making a measurement abruptly causes a somewhat random and unpredictable change in the system but what happens before and after this measurement let's start with before remember how i said earlier that a quantum system is in a superposition of all possible measurement states well that was a slight oversimplification what actually happens is that a wave function follows what is known as the schrodinger equation this is one of the most important equations in quantum mechanics it looks complicated but all it tells us is how the wave function changes over time depending on the different energies in the system whether that's kinetic energies or potential energies i've made a whole video discussing the schrodinger equation in a lot more detail check it out up here if you're interested but anyway it is entirely possible that the system is in a superposition of all possible measurement result states as we said at the beginning and that it stays this way over time as it doesn't change or it could be in some other superposition that evolves over time or of course many other scenarios depending on how the system was set up in the first place and as long as it follows the schroinger equation what's important though is that we can look at the wave function as it is at the instant in time just before we make the measurement and we can use that to calculate the probability of getting any particular measurement result when we do make the measurement as we've already seen once the measurement is made there is a somewhat random and unpredictable collapse into one of the possible measurement states and this depends on what the wave function looked like just before we made the measurement this bit is not described by the schrodinger equation and physicists are trying to understand it a bit better they describe it as a discontinuous change because it suddenly collapses into one state rather than continuously flowing from one state to another and then after the measurement once again the wavefunction starts following the schrodinger equation at the instant in time after the measurement based on now this being our initial state so depending on the system and its surroundings the system may just stay in this measurement state or it may start spreading out back into a superposition of multiple states and evolve over time it just depends on the exact scenario but it still follows the schrodinger equation at this point now it's worth mentioning that this is all a basic description of wavefunction collapse based on a system where the possible measurement results are distinct states when dealing with other systems that have a much more continuous set of measurement results like the position of a particle which could potentially be anywhere in a given region of space rather than in specific fixed locations then the collapse occurs into a few close by states reflecting heisenberg's uncertainty principle that's a discussion for another video however now before we finish up i want to take a moment to thank the sponsor of this video squarespace squarespace gives you a beautiful powerful online platform from which to create your website you can build the community on your squarespace website with a fully integrated commenting system that supports threaded comments replies and likes on top of that you can easily display posts from your social profiles on your website you can also connect with your audience and generate revenue through gated members only 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watching and i will see you very soon [Music] [Applause] [Music] you

Channel: Parth G

Views: 47,497

Keywords: wave function collapse, collapse of the wave function, quantum mechanics, physics, parth g, wave function, discontinuous change, schrodinger equation, superposition of states, quantum physics, quirks of quantum mechanics, why is quantum mechanics hard, why is quantum physics tricky, consciousness, quantum consciousness, interpretation of quantum mechanics, copenhagen interpretation of quantum mechanics, copenhagen interpretation

Id: Is_QH3evpXw

Length: 10min 22sec (622 seconds)

Published: Tue Mar 29 2022