Quantum Entanglement Explained for Beginners | Physics Concepts Made Easy

hey what's up you luck path here and today we're going to be talking about quantum entanglement now lots of you have asked me to talk about this topic quite frankly because it's a mind-bending discussion to be had but in this video I just wanted to lay the groundwork using some basic mathematics nothing too complicated only high school level stuff so that when we come to understanding the intricacies of entanglement it becomes a lot easier and we can then properly discuss the really weird really mind-bending stuff before we get into it though I quickly want to mention that in my previous video celebrating 10 thousand subscribers on this channel I said that I would give away a book now if you haven't seen that video already then click the link up here check it out and I will be posting a video pretty soon picking the giveaway winner because not only have we crossed 10,000 subscribers we've now crossed 20,000 subscribers that's like amazing and crazy I'm still in shock but basically yes so I'll be uploading a video pretty soon announcing the winner of a giveaway anyway let's get into the video now today we're going to be imagining a system that consists of two electrons it's important to note though that we don't necessarily want these electrons to be close enough to each other to be interacting with each other in fact we don't even care if they're that close to each other or whether they're on the opposite ends of the universe we're not particularly interested in the behavior of these electrons in terms of where they are or how they're moving or we care about is a property that's inherent to these electrons as well as other subatomic particles known as spin now let me just quickly say if you know about spin already then skip to this timestamp here many of you interested in quantum physics will have already heard of spin but one question I get asked a lot is what exactly is being well if you have that question then you're out of luck this video is not about spin I will make one about spin in the future but for now all I can give you is the following spin is a property that these electrons will have just like their mass or their charge but the interesting thing about spin is that it's a property that gives them inherent angular momentum now those of you that have heard of angular momentum already will recall that it comes about due to some sort of curved motion or some sort of rotation some sort of angular velocity whether that's spinning around an axis or moving around a planet or something along those lines however when it comes to spin spin is an inherent angular momentum that these electrons and other subatomic particles have inherently they don't necessarily need to be moving along a curved path or rotating about anything to have this spin they just have it the other thing you should know about spin is that it comes about when we consider special relativity alongside quantum mechanics and that's all the detail that we're going to go into here so like I said when we're considering our system of two electrons or we care about now is the spin of each electron and electrons can take one of two spins we call it spin up or spin down represented like this and by the way the pointed bracket on the right-hand side and the straight line on the left-hand side is just a notation thing it's just a way of representing these quantum states which I'll make a video about at some point I have actually mentioned it in previous videos and I will link those in the description below but for now all we care about is the arrows that point upwards representing spin up and the arrow pointing downwards representing spin down anyway so we now have these two electrons in our system we're going to label them particle a and particle B if we were to go and measure the spins of these two electrons we would find one of four possible combinations either particle a is in the spin up orientation and B is in the spin up orientation or a is in the spin up B is in the spin down or A's and the spend-down B is in the spin up or both of them in the spin down orientation so if we measure the spins of both of these particles we can find one of these four possibilities in fact we will find one of these four possibilities now quantum mechanics being the weird mind-bending set of ideas it is tells us that when no external system is interacting with our original system so for example when I'm not making a measurement or when nothing else from the external world is interacting with our system then our system is in a superposition of all four possible states in other words it's sort of in a quantum soup where it's in all possible combinations all at once kind of like our Schrodinger's cat can be dead and alive at the same time but that brings up too many problems and we're not going to go into that here so when the system is left alone to do its own thing and when nothing else is interacting with it not even us taking measurements of these electron spins we can write the state of the system as it is now left alone as a superposition of those four possible combinations we show that our state is in a mixture of all possible combinations by adding all of those states together and crucially the numbers in of each possible combination of spin up spin down spin up spin up and so on and so forth is directly related to the probability of us finding our system in a particular state when we measure it now another really weird and interesting thing about quantum mechanics is that it tells us that if something external interacts with our system so for example if we go and we measure the spins of these electrons then we cause the system to collapse into one of the four possible combinations we will never measure these electrons to be in a superposition of up and down States we will always measure them to either be spin up or spin down but whilst we're not measuring them they're in a superposition a soft soup of all possible combinations if we had the exact same system lots of times let's say millions of times and we went in and measured the spins of each of the particles in each of those copies of our system then the proportion of systems that we find in a particular state is directly related to the number in front of the state that we mentioned earlier specifically if we square the number in front of each term that gives us the probability of finding our system in that particular state now those of you that know about imaginary numbers will realize that these numbers that I'm talking about in front of each state can actually take complex values and in that case the probability of finding our system in that particular state is actually proportional to the square modulus not just the square of those numbers but if you don't know about complex numbers don't worry about it and we're only going to be using real numbers just to keep things simple now everything I've mentioned up until now you may or may not have seen in other videos talking about quantum entanglement but what I'm hoping is that the next bit that I talk about is going to be relatively new something that not many people have discussed before and if you're not a physics student at university or you know studying physics in that level then you're probably unlikely to have seen it I'm hoping let's go back to our initial system which consists of two electrons a and B here's how we can tell if the two electrons form an entangled state we said earlier that the mathematical expression representing our entire state when it's not being measured was the quantum superposition of all possible states this is what it looks like it's just a long mathematical expression but if we can separate this mathematical expression into one chunk just talking about particle a and one chunk and just talking about particle B then this is a separable state and therefore this is not in Tangled however if we cannot separate this mathematical expression into just one chunk talking about particle a multiplied by one chunk talking about particle B then it is an entangled system now this sounds really complicated so let's go through it step by step let's start by talking about what we mean when we say entangled system well for the purposes of this video we will say the following let's imagine that's something interacts with just one of the electrons in our system not both because we're imagining that actually quite far apart from each other so let's imagine I measure the spin of one of these electrons let's say I measure the spin of particle a if we have an entangled system then the probability distribution of spins you know the likelihood of me finding a particular spin whether that's up or down for particle B will change after I measure the spin of particle a compared to the probability distribution that we had before and this is what we mean by an entangled system if something interacts with just one part of our system for example particle a then the whole system is affected specifically the probability distribution of finding an up or down spin for the other particle in this particular case and we can say there's quite generally the interaction of something external with one part of our entangled system causes the entire system to be affected in fact when discussing quantum entanglement people often use very special cases to illustrate what they're talking about they use states known as Bell States this Bell State for example is a very special case of the general quantum state that we talked about earlier when dealing with two electrons each of which has a spin and with this particular vowel state we can see that the probability of both electrons being in the spin up state was 0 and the probability of both electrons being in the spin down state was 0 before we made our measurements and this state they're really brilliantly illustrates what quantum entanglement is all about because let's say I was now to go and measure the spin of particle a let's say I found it to be spin up in that case I now know that the system has collapsed into this particular state which means that the spin of particle B must be spin down and vice-versa let's say I measure the spin of particle a and I found it to be spin down then I know that the system is collapsed into this state and the spin now must be spin up for particle B in other words before we did any measuring to our system there was an equal probability of our particle B being spin-up or spin-down states but after the measurement we caused the system to collapse into a particular state and the probability of the other particle the one that we haven't measured of being in a particular spin state was now 100 percent we knew with certainty without measuring what the spin state of that particle was now we've just talked about an entangled state but we said earlier that if we couldn't mathematically separate them into one bit that just talks about particle a multiplied by one bill that just talks about particle B then this was a separable state and this was the opposite of entangled well what do we mean by mathematically separating this state well to understand this we're gonna have to go back to a lobe of high school mathematics specifically being able to multiply out brackets our state will be mathematically separable if we can write it like this the first bracket just contains information about particle a and the second bracket just contains information about particle B this looks scary but it isn't at all in fact if you remember how to multiply a practice then we can use the foil method to expand out these two brackets and when we do it looks something like this kind of familiar right we've we've seen this state before some number multiplied by a and up being up plus a super that means a superposition of some number multiplied by 8 and up being down plus so on and so forth this is the state that we had earlier the general state for our quantum system consider our consisting of two particles particles a and B each of which could be in the spin up or spin down state but here's the kid we may or may not be able to go backwards and factorize this state into one bracket just talking about particle a and one bracket just talking about particle B and this very specifically depends on the numbers a B C and D because depending on the values of a b c and d we may or may not be able to factorize and as we've mentioned already it's not necessary for us to be able to factorize our state and write it as one bracket about particle a one bracket about particle B this only happens for separable States in fact the Bell State that we mentioned earlier is not possible to write like this we can't write it as some information about particle a solar Li multiplied by some information about a particle beep so Li try it yourself before now let's just discuss one possible entangled state and one possible separable state and let's imagine what would happen if we were to measure the spins off just one of these electrons in each one of these states with a separable state we can firstly write it out as the full quantum state and then we can factorize it and write it as the bracket just talking about particle a and the bracket just talking about particle B multiply together now for the state we can imagine calculating what the probability would be a finding particle B now in a particular spin state let's say we want to find the probability of finding B in a spin up position before we do anything to the state while we're not interacting with it in other words before we've done something to particle a that could potentially affect particle B and the way that we would go about finding that probability is looking at all the possible states that result in the particle B being in the spin up state and then squaring their probabilities the numbers in front of their states and adding those two together when we do that for this particular state this is the probability of finding particle B in the spin up state before we've done anything to our system now let's say we go in and make a measurement on particle a let's say we find particle a to be in the spin up state which means now that we've caused a system to collapse into one of these two possible states it can no longer be in a state where particle a is been down because we've just made it to be we've just measured it to be spin up well in this situation after we measure the spin of particle a to be in the spin up position we can calculate with the remaining States without accounting for now the probability of finding particle a in the spin up state that's not relevant to us anymore because we've already measured to be in the in the spin up state we can calculate the probability of finding particle B in the spin up state that probability is this surprising right doesn't it doesn't it kind of look similar to what we had before and equally if we had measured particle a to be in the spin down state the probability of finding particle B in the spin up state would still be this problem of C here I'm only saying that I'm not saying the numbers out loud because I haven't actually done the examples yet but you'll see them in the final video anyway basically here's what this means we've taken our separable state and we've calculated the probability of finding particle B in the spin up state before we did any measurements on any of the system then we made a measurement on particle a and we calculated the probability of finding particle B in the spin up state once again but this time after having measure the spin-off particle 8 and regardless of what the result of the spin of particle a was we still found the probability of finding particle B in the spin up state the same as before so crucially the probability of finding particle B in the spin up state before any measurements were made to the system is the same as after we made measurements to particle a and it doesn't matter what the result of particle a's measurement was the probability of finding particle B in the spin up state is still the same this is true for a separable state however this is not the case for an entangled State let's take this state as our entangled State you can try and prove to yourself that we can't write it as a separable States but here's the point let's say before we make any measurements on this state we can calculate the probability of our system being in an orientation such that particle B is in the spin up position that likelihood is this however let's now go and measure the spin of particle a and here's what's going to happen let's say we measure particle a to be in the spin up system now the wavefunction has collapsed so that particle a can only be in the spin up orientation which means that the only states that we need to consider are these states here and notice the probability of finding particle B in the spin up state after making a measurement on particle a is different to before McInnis measurement of particle a and what's even more annoying is that if we had instead measured particle a to be in the spin down state just by chance then the probability of particle B in the spin up state is different to before as well so here's what we can take away from that for an entangled system the probability of finding let's say particle B in a particular state is whatever it may be however if we make a measurement on particle a the other part of the entangled system this affects the probability of finding particle B in a particular spin state regardless of us touching particle B or making a measurement on particle B and what's even more annoying is that the result of the particle a measurement will affect the probability distribution of particle B how weird is that in other words if we were to find particle a to be spin up this would change the probability of us now finding particle B later on in the spin up state compared to if we'd found particle a in the spin down state very quickly let's talk about the Bell state because one's the most easy to talk about in other words for this particular state we've prepared it such that the probability of both being spin up is zero and the probability of both being spin down a zero there either only going to be in the spin up spin down orientation or spin down spin up orientation before we make any measurements so the state is in this condition right now the probability of measuring particle B in the spin up state is 50% because we've only got two possibilities and each one is equally likely however after we measure particle a this is what's gonna happen let's say we measure particle a to be in the spin up state now the probability of particle B being in the spin up state is 0 because we said earlier that that was never gonna happen that wasn't even a possibility equally if we measured particle a to be in the spin down state the probability of particle B being in the spin up state is 100% so not only does measuring particle a affect the probability distribution of particle B the actual result of what we measure in particle a is going to affect the probability distribution of particle B how weird is that now guys I don't know if I've explained this thoroughly enough and I don't know if I've been clear enough so if you have any questions leave them down in the comments below I'm gonna save a conceptual discussion for another video because I feel like this is already too much to try and digest in a in one short 20 minute video I'm hoping it's gonna be less than 20 minutes but yeah I'm gonna save the discussion for later let me know what you think about this video and if I haven't been clear about something that let me know in the comments down below as well because this one is probably one of my more ambitious projects I don't usually go into this much mathematical detail so again let me know if you've got any questions and also if you did enjoy the video then leave it a thumbs up and subscribe to my channel if you haven't already let me know what other physics topics you want me to talk about and with that all being said I am going to stop this video here because I feel like I've talked too much thank you so much for watching and I'll see you next time right however if we cannot mathematically separate this expression into one chunk just talking about part or a multiplied by one chunk just talking about particle B then it is an in-tank that's really annoying

Channel: Parth G

Views: 111,376

Rating: 4.9002209 out of 5

Keywords: Quantum Entanglement, Entanglement, Physics, Quantum Physics, Quantum Mechanics, Quantum Entanglement Explained, Parth G, Physicist Explains, Quantum State, Bra Ket Notation, Bell State, EPR Paradox, Quantum Entanglement for Beginners, Superposition

Id: -WSWz1H3mJg

Length: 17min 46sec (1066 seconds)

Published: Tue Oct 22 2019