The Einstein Podolsky Rosen (EPR) Paradox - A simple explanation

hello today I'm going to take up the challenge of a question that was put on one of my videos and tell you about the einstein-podolsky-rosen paradox sometimes shortened as the EPR paradox now I'm going to keep this very simple and very basic consistent with the theme of these videos to explain things in simple terms so if you are an expert in this look away now it's not actually an issue that I'm particularly well schooled in but I should do my best to explain it in simple terms there will be no mathematics the einstein-podolsky-rosen paper was written in about 1935 and 1936 written by Albert Einstein Boris Podolsky and Nathan Rosen and essentially they were challenging where the quantum mechanics had got it right at the time quantum mechanics was about 10 years old I suppose you could say that the originator of quantum mechanics was debroglie who had postulated that particles like electrons could also be regarded as waves and that they would have a wavelength given by lambda equal to Planck's constant H divided by the momentum which for an electron would be its mass multiplied by its velocity and that he postulated in 1924 it was a radical suggestion because it made the notion that particles which had always been thought of as matter could somehow be thought of as waves and it was Davisson and Germer who subsequently showed that you could get diffraction patterns from electrons and you can only get diffraction patterns from waves Schrodinger picked up this idea in 1925 and developed the famous Schrodinger wave equation and you can see lots of information on that in my other videos the Schrodinger wave equation and all the theory that was developed from quantum Kanaks was demonstrated to be a correct analysis simply by looking at the spectral lines of hydrogen where those lines precisely agree with the electron transitions within an atom in 1927 just two or three years later Heisenberg came along with his famous uncertainty principle which is usually written as Delta X Delta P is greater than or equal greater than or equal to H bar over 2 what this essentially means is that within quantum mechanics terms in sub atomic terms there are certain quantities that you can't measure both at the same time in this case its position and momentum you cannot measure the position in them and the momentum of an electron at precisely the same time if you measure one precisely the other is undetermined and that is also the case for example if you take the spin of a subatomic particle let's consider an electron that will have a spin which could be in any direction but the component of that spin in say thee let's call this the Y Direction the component that spin will either be up or it will be down those are the only two options and the component of the spinning let's call this the X direction will either be that way or that way those are the only two options for the components now what Heisenberg's uncertainty principle says you cannot both measure the Y component and the X component at the same time if you measure one precisely the other is completely unknown the concepts of quantum mechanics were developed and in a number of places but in particular in Copenhagen where Niels Bohr and a number of colleagues were working to develop the theories and we get what's often called the Copenhagen interpretation of quantum mechanics which essentially says that in the quantum mechanical world things are uncertain and you're unpredictable until you measure them particles have a wavefunction now it's important to make this clear that we are not saying that lots of electrons become a wave we are saying that every individual electron is itself described by a wave function and it was Max Born who has the honour of also being the grandfather of Olivia newton-john who made the postulation that if you take the wave function and square it or more accurately if you take the wave function multiplied by its complex conjugate that was a representation of the probability of finding the particle at that point so if this is a graph of the wave function against position X then the wave function squared gives the probability of finding the particle at X but you have no way of knowing where that particle is you only know what the probability of it being in a particular place is until you measure it and when you measure it if you find the electron is for example here you actually locate it at that point then what the Copenhagen interpretation says is the wave function collapses what they mean by that is you can no longer have a wave function because the wave function is essentially describing the probability of finding the electron at any of these points but you know where it is you just found it it's here so they can no longer be a wave function it collapses into a single point because that's where the electron is now a further consequence of the Copenhagen interpretation was that if you get two particles that essentially derive from one common source that they are what is called entangled that is quantum entanglement so if for example you have let's say some energy and out of that energy you get pair production let's say you get an electron and a positron produced from energy on the principle of e equals mc-squared you've got energy you can create you can create matter and then what the Copenhagen interpretation says is that that electron and that positron will be entangled this means that the properties of one will influence the properties of another let's give an example we usually say that the electron moves across to the laboratory run by Alice and the positron moves across to a laboratory run by Bob and they are each going to measure the electron or the positron spin on the let's say the y axis remember that was that was here so we're going to measure the coordinate of the electron spin or the positron spin along the y axis and remember that can either be up or down but there's absolutely no way in quantum mechanical terms of knowing in advance what it's going to be you can measure it but you cannot predict it now the point is that if Alice measures the spin of the electron and finds that the spin is up in the Y direction then it must follow because of entanglement that the spin of the positron in the Y direction will be down and that has been experimentally verified the two particles are in some way linked so that if you find that this is up and this one would be down or if that had happened to be down that will be up you've no way of knowing what they will be before you measure them but as soon as you measure that one you know what that one will be and the reason for that from the Copenhagen interpretation is that where you've got one system producing two particles they do not have an individual wavefunction in fact they have a shared wavefunction and what the Copenhagen interpretation says essentially that these this is a superposition of wave functions these two particles contribute to one overall wave function and that's the reason why they are entangled and that's the reason why you can have this certainty that if one of them is found to have an up spin the other will have a down spin now let's consider exactly the same situation I'll draw it again we have something like maybe energy and it gives rise to an electron and a positron and it goes to the labs of Alice and Bob and Alice measures the spin of the electron in the Y direction and finds that it's up it could be down but let's just for the moment assume that it's up she had no way of knowing that before she did the experiment but it turns out that it was up we know that therefore when Bob does the measurement he will find that it is down but let's suppose the Bob doesn't do that experiment instead he measures the spin of the electron in the x axis now it can either be that way or that way but if he were to find out that it were if he did the experiment and he found out for example that it was that he would also know from Alice's experiment that the coordina in the Y direction would have to be down and that would mean that he would know both the Y direction and the X Direction coordinates but according to Heisenberg he can't because that's the uncertainty principle you cannot know both the y coordinate and the x coordinate at the same time what that means therefore is if Alice measures the y coordinate of this electron Bob can measure the y coordinate of this positron but he can't measure the x coordinate of that positron because if he did he would then be able to know both the Y and x coordinates and according to the Copenhagen interpretation that's not allowed so here's the einstein-podolsky-rosen paradox how does that positron know what is happening over here in Alice's poetry if Alice doesn't measure the y-component of this electron Bob is entirely able to measure the X component of this positron but if Alice measures the Y component of this electron Bob won't be able to measure the X component of that positron how do these two particles know what's going on well there are two possible explanations one is that the two particles are somehow communicating one with one another instantaneously and this could be across the whole universe you don't know what's going to happen to these two particles they can fly off and travel enormous distances but the implication of quantum entanglement is that each is keeping in touch with the other to make sure that what is happening to one has a consequential effect to what's happening on the other but that would mean that information would have to be transmitted instantaneously that is faster than the speed of light and that breaks the rules of special relativity the other alternative option is that somehow when these two particles are born when they are created they have a kind of form of I call it DNA they have some information within them it's called the technical term is hidden variables they have information embedded within them that will govern their behavior such that they always act in a way that is as it were complimentary but my word they'd have to have an awful lot of information hidden away inside them to govern every single eventualities that might happen to them they have no way of knowing when they're made what interactions they're going to have with other particles for example a positron probably won't live for more than a fraction of a second before it meets yet another electron and when it meets that electron it will annihilate and form energy again how does that electron here know that it's entangled partner no longer exists and therefore there's no need for any entanglement either through instantaneous communication which seems impossible because it would mean traveling faster than the speed of light or through some kind of hidden variables or DNA embedded in each particle which seems highly unlikely because a it would mean that you would have to have a huge amount of information embedded and B you have no way of knowing of what the future holds in terms of interactions with other particles so that's the paradox how do we know how is one particle know what's going on unless of course each particle knows what is happening to every other particle in the universe at all times now that's not as mad as it sounds because that is in essence what the power exclusion principle says in my video on atomic physics I showed that the power exclusion principle says that no single party you cannot have two electrons that have the same four quantum numbers or we say are in the same quantum state so for example I showed that if you have two hydrogen atoms coming together to form a hydrogen molecule each of them will have a ground state it's called the 1s level each of them will have a ground state but as they come together those states will have to separate so that they are at a slightly different energy level in order to obey Pauli's exclusion principle that says you cannot have two electrons in precisely the same state and I also showed that when it came to copper for example where you will have beings of atoms and therefore billions of electrons in the outer orbital which is the 4s1 orbital but where you've got all those these are all individual electrons sorry individual atoms with these ground states you cannot have an electron in the same ground state so the states have to as it were a just themselves so that they form a band and every one of these states is just slightly different in energy from the other you see what some people assume is that what you really mean is that no two electrons can have the same quantum numbers or can be in the same quantum state in a single atom but that isn't true here you see two atoms of hydrogen the ground states have to adjust here billions of copper atoms the ground states of the outer orbital have to adjust so that no two electrons are in precisely the same state they will be just marginally different in energy terms and the implication of this is that no two electrons in the entire universe can be in precisely the same state which means that since electrons are constantly moving between energy levels in atoms that somehow they have to know what energy level is still available for them to jump back down to because they're not allowed to jump down to any energy level that is occupied by another electron anywhere in the universe now how do they know that and that's the essence of the einstein-podolsky-rosen paradox they either know it because they're all keeping instantaneously in touch with one another which means information is traveling faster than the speed of light or they all have an inherent DNA which governs their actions and the actions of everything else but that would mean that each electron would have to carry a massive amount of information or as some people now say you just have to accept that in the quantum mechanical world things are different and you cannot explain them by the kind of rationality of classical mechanics there has to be a reason why this happens and of course science will continue to try to investigate that reason to understand quantum mechanics is very good at describing what happens we still have to establish why well I hope that's given you a simple introduction to the einstein-podolsky-rosen paradox I didn't want to get any more complicated than that and it is very basic experts will probably be cringing but I hope it gives an easy introduction

Channel: DrPhysicsA

Views: 293,799

Keywords: Einstein, Podolsky, Rosen, EPR, Paradox, Quantum, Mechanics, de, Broglie, Schrodinger, Heisenberg, Simple, Explanation, Pair, production

Id: 0x9AgZASQ4k

Length: 17min 53sec (1073 seconds)

Published: Sat Apr 07 2012