 One of the most mysterious, most enigmatic, most interesting, most mind-blowing experiments ever in physics or even the sciences is definitely the double slit interference experiment. This is one of those experiments that questions the way and the manner that we perceive reality. It not only tells us something deeply fundamental about the nature of the subject of quantum mechanics, but it leads us to question some of the fundamental assumptions about the nature of reality and the way we perceive it. It leads to certain deeply philosophical questions about how and what we think and perceive about this physical world. It even leads to some deeply metaphysical questions. And sometimes may also lead to some spiritual discussions. But I am not going to go into all that. What I am going to do today is just present to you the facts of this particular experiment and what it tells us about the nature of reality at the most microscopic quantum level. You know Richard Feynman used to say that if you want to understand the mystery at the heart of quantum mechanics, then you only need to look at the implications of a single experiment which is the double slit interference experiment. On the surface of it, this experiment is a very simple experiment. It was originally performed in the early 1800 by Young in the very famous Young's double slit experiment for light. If you have studied optics, you must have studied this particular experiment. In the Young's double slit experiment, he essentially passed a radiation through two slits and got an interference pattern on the other side, thereby proving that light is a series of wave fronts. It is a wave. It is very simple on the surface. But what if we perform the same experiment for certain other kinds of particles? Here I have four different setups for four different kinds of situations that I am going to demonstrate to you one by one. And at the end of this video, I'm going to tell you five mind-blowing predictions, mind-blowing conclusions about the way quantum mechanics works at the microscopic level that we can infer from this particular experiment. So let's begin. So essentially, the experimental setup consists of, let's suppose, a source. All right. So we have a source. It could be a source of particles. It could be a source of waves. It could be a source of microscopic entities like electrons. And this source emits those particles or waves. And it once passes through a slit S1 and second time it passes through a slit S2. And the third time it passes when both the slits S1 and S2 are open. We are going to take a look at what sort of intensity profile of those particles or waves that we get when they pass through individual slits and when they pass through double slits. Essentially this is simply an experiment where a slit simply means an opening on a wall. So some sort of a particle or a wave is incident on this wall having an opening. It is able to penetrate through and create some sort of an intensity profile on the other side. So a detector or a measuring device can detect those kind of intensity profile. First of all, we are going to look at classical particles. What do I mean by classical particles? By classical particles, I mean particles that we perceive in our day-to-day life. You know like a ball, like a marble, like a grain of sand or wheat seed or a bullet or something like that. Any classical particle, if it is subjected to this kind of an experiment, what happens? So imagine that you have some kind of a gun. By gun I mean something that is shooting particles over and over again. So imagine that you have a gun which is constantly shooting these particles towards this particular wall containing a slit. Now these particles could be bullets. We could have bullets here. We could have some kind of a pellets or we could have some kind of a small paintball. So it could have anything that has this particle grainy nature. If it is subjected to a single opening on the other side, some of them will penetrate through and it will create an intensity profile on the other side, an intensity profile that looks something like this. That means those particles will go and hit the other side of the screen on the other end and it will distribute themselves in some sort of a normal distribution kind of a shape. So it will create somewhat a spot on the other end. If we re-perform the experiment but with the other slit open then again we will have these particles passing through the slit and end up creating some kind of an intensity profile something like this. What if we keep the both the slits open now? So there is a gun, a source of bullets that is shooting bullets or some kind of a particle that has this grainy nature to it that we observe in our day to day life and both the slits are open. So the particles are now capable of passing through both the slits. So they are going to get collected on the other side and they are going to get collected one after one after another and you will get an intensity profile something that looks like this. If I say that the intensity profile when only slit S1 was open is I1 and the intensity profile when the slit S2 is open is I2 and the intensity profile when both the slits S1 and S2 are open is I then quite simply put for classical particles the intensity profile when both the slits as open is equal to I1 plus I2. By intensity I mean let us suppose the number of particles that hit the wall on the other side maybe per unit surface area or something like that. Essentially the number of particles gets added up together in a kind of a lump. Now the lump could be created by anything I have used the example of bullets here you could perform this experiment for let us suppose grains of sand falling through two slits or you could re-perform this experiment for any kind of a grainy salt kind of a material penetrating through two slits what you end up getting on the other side are these two lumps combined together. Now whether you see two separate lumps or whether you see one giant lump basically depends upon the distance between these two slits. If the distance between these two slits is quite large enough you might see two separate lumps of these grainy particles if the distance between these two slits is not large enough they are very close to each other you might get just one huge lump together but essentially the total number of particles on the other side is I1 plus I2 intensity profile of 1 plus intensity profile of 2 that's quite simple it's very easy to understand we have a very common sensical notion that this is what's going to happen. Now what if we deal with the second situation which is I'm going to call as classical waves by classical waves I mean light I could have light or I could have some other waves like maybe ripples on the surface of a water but light is a better example because this gives us the Young's double slit interference experiment results. So essentially if you have a source that is emitting some sort of a monochromatic radiation alright if you have a source that is emitting monochromatic radiation then we can think of the light moving through space as wave fronts. So when it comes near this split slit S1 the secondary wave fronts are created on the other side and they end up creating an intensity profile on the other side that looks something like this you end up getting an intensity profile like this which is basically a huge spot on the other side this is what happens when single slit is open now usually when we perform a single slit experiment we end up getting a single slit diffraction pattern which means that you get a maxima a spot in the middle and there are secondary maximas on the other side but let's just consider the central maxima for our purposes here okay so we are just looking at the central maxima and ignoring the secondary maximas here because we are interested in the interference that is created. So if we do the same experiment but with the other slit that is open which is S2 then now the light passes through the slit S2 and you end up getting the central maxima somewhere here but what's interesting is that what if both the slits are open if both the slits are open again the monochromatic source creates these wave fronts they create secondary wave fronts because of both the slits now these secondary wave fronts they interfere with each other resulting in what is called an interference pattern something that looks something like these these oscillating dark and bright fringes these dark and bright bands these oscillating maximas and minimas which is called the interference pattern is created on the other side and the reason behind that is very simple the reason behind that is because we have essentially light which has wave nature because when we deal with light what happens is that the intensity of a light wave is essentially given by the modulus square of its amplitude so let's suppose I am dealing with the intensity profile here which is the I1 okay and the intensity profile here which is the I2 okay so I1 is equal to the modulus square of the amplitude Y1 let's suppose and the intensity profile I2 is equal to the modulus square of the amplitude Y2 you see what happens with waves is that whenever you have two waves let's suppose you have one wave this is one wave alright that is passing through slit S1 and this is another wave that is passing through slit S2 then the way they combine is that their amplitude gets added up so if the wave passing through slit S1 is I1 and the wave passing through slit S2 has an amplitude Y2 then the resultant has an amplitude of Y is equal to Y1 plus Y2 it is the characteristic of waves that waves interact with each other through interference that means if two waves are in phase they will constructively interfere if two waves are out of phase they will destructively interfere this is because the instantaneous amplitudes of the waves gets added up so that the resultant pattern that we get the resultant intensity profile that we get on the other side is actually equal to I which is equal to Y modulus square where Y is equal to Y1 plus Y2 modulus square you can clearly see from here is that this is not equal to I1 plus I2 this is not equal to I1 plus I2 because this is Y1 plus Y2 modulus square if you simplify this further you should get something like Y1 modulus square plus Y2 modulus square plus some other additional term let me just write down the additional term because you must have done this kind of a derivation if you have studied the Young's double slit interference experiment which comes out to be something like 2 I1 root over I2 cos alpha which is equal to I1 plus I2 plus 2 root over I1 I2 cos alpha the most interesting thing to notice here is that this whole thing is not equal to I1 and plus I2 see for classical particles the intensity profile is a sum of the intensity profile of first and the second experiment but in the case of waves the intensity profile is actually I1 plus I2 plus this oscillating term this del here is a phase difference and this is an oscillating term because of the phase difference which results in this interference pattern and this interference pattern can be observed not just for light but any kind of a classical wave so whenever you have waves maybe you can perform this experiment or with ripples on the surface of a pond then these ripples when they pass through both the slits they end up creating the secondary wave fronts which interfere and because of the changing path lengths at different points you end up getting these oscillating bands of maximas and minimas dark and bright regions which is essentially the interference pattern here everything is okay till this particular point now begins the interesting part what if we do not take classical particles like bullets or classical waves like light but quantum particles first of all I should clarify that even though I have said that light is a classical wave we have seen in our previous lectures that light has dual nature so what I mean by classical wave is that in this particular experiment it is demonstrating wave behavior alright in this experiment it is demonstrating wave behavior and we can replicate the same experiment not just for light but also ripples passing through the surface of a water so essentially what I mean is that this result is true for all kinds of classical waves out of which light is particularly one example so what if we perform this experiment for electrons you see in my previous lecture or in the couple of lectures we have talked about the dual nature of matter particles like electrons we have talked about the De Broglie hypothesis we have talked about the Davison and German experiment which demonstrated that electrons behave like waves that electrons are capable of diffraction through some kind of a crystal material so electrons are very weird particles electrons even though we think of them as particles localized objects that move through space through a fixed trajectory that has a certain kind of graininess associated with it because classical particles have a certain graininess associated with it what happens if we substitute the source with some kind of an electron gun alright let's suppose there is an electron gun that is creating a large beam of electrons which first fall on the open slit S1 and some of those electrons are capable of passing through the slit S1 the intensity profile that we get is kind of expected we end up getting a spot on the other side or a bunch of spots distributed in the form of a circle or something on the other side let's suppose we call this intensity profile I1 similarly if we have these electrons passing through another slit S2 we end up getting a similar kind of a continuous distribution that we saw earlier but this time I am going to call this as I2 now what do you predict what are we going to get if both the slits are open you see electrons are classically speaking particles we think of them as particles point mass particles localized in space having some mass having some charge traveling along a trajectory that is how we think about them right but what this experiment reveals is that if a source of electron is emitting large number of electrons that are being you know bombarded onto two open slits next to each other then the intensity profile that we end up getting is somewhat similar to that of light so we end up getting this kind of a interference pattern we get an interference pattern for electrons the electrons will hit the wall on the other side at different kinds of points they will redistribute themselves so that you end up seeing these kinds of I should not say dark or bright but you see these kind of bands where the electrons are distributed in one band and the another band is empty and then another band and on and on this kind of an oscillating pattern of electrons redistributing themselves on the other side so electrons are demonstrating interference pattern just like light was demonstrating interference pattern quantum particles like electrons are demonstrating interference pattern this is one of the most interesting conclusions in quantum mechanics because it tells us that electrons as we know it has this wave property that is capable of interference why do we get interference pattern it is because waves has in its nature the capacity to interfere amplitude of waves gets added up and we end up creating constructive or destructive interference in certain regions constructive interference here destructive interference here so that the total light energy is distributed into these dark and bright fringes but the same thing is happening for electrons electrons are moving in such a manner that there is some sort of a wave motion associated with that movement and that wave nature of the electron is capable of interference and it is capable of redistributing the electrons in these alternating bands so that means the electrons are passing through both the slits s1 and s2 and are interfering with itself and redistributing themselves into these kinds of alternate bands or these kind of interference pattern so this is the mind-blowing conclusion of quantum particles like electrons by the way not just electrons this kind of an experiment has been performed for electrons particles like neutrons protons even atoms and we have seen interference pattern for all these microscopic particles so now the question is what is the nature of this interference because when we talk about interference we think of waves and their amplitudes getting added up together you know and amplitudes adding up when there is a same phase canceling each other out when they have opposite phase so what is the nature of this interaction the electrons passing through both the slits something that is even more mind-blowing happens when we decrease the brightness of the source when we make the source how do I say it less and less and less so that the electron gun is not shooting large number of electrons at the same time but instead it is shooting one electron at a time what happens then so if we kind of decrease the brightness of the electron gun or I mean if we decrease the number of electrons that the electron gun is shooting on this slit so that only one electron is traveling at a time what ends up happening is that so a one electron is being shot by the source it passes through one of the slits forms some kind of a spot on the other side the next electron goes forms another spot on the other side third electrons forms a spot fourth electron forms a spot fifth electron forms a spot six electron forms a spot and on and on these spots are being created as the electron passes through the double slit and what we see is so mind-blowing that when we keep on repeating this experiment over a large period of time the electrons and their spots redistribute themselves in these alternate patterns or these bands that basically look like an interference pattern so what is essentially happening is that the electron and its wave whatever that is is passing through both the slits at the same time a single electron is passing through both the slits at the same time and the wave associated with that is interfering with itself and creating an interference pattern on the other side when I was a small child and I read about this experiment I was reading the book of brief history of time by Stephen Hawking I still remember to this very day I was traveling in a bus and I was just casually reading the book the brief history of time by Stephen Hawking and there is a particular chapter in which Stephen Hawking was talking about this particular experiment and I was reading it with such intense attention and when he reached this particular point in which he wrote the single electron is passing through both the slits at the same time I kid you not I had my mind blown I was so surprised that I was asking so many questions how is this possible and even today I think I still ask myself those questions how is it possible it is extremely difficult to grasp I understand it is extremely difficult to even accept you see our brains have developed have evolved in the macroscopic world of low velocities and large particles so it is very difficult for our brains to grasp what is happening at the microscopic world how particles are behaving in the microscopic world but in physics in science what the experiment says we have to accept even if we are feeling extreme discomfort in accepting this idea our brain is trying to make sense however way it can or even trying to reject this but this is an experimental result for electrons even if the electron gun is shooting one electron at a time if we repeat this experiment over a large period of time we end up getting this interference pattern which means that a single electron is passing through both the slits at the same time it doesn't stop here the mystery becomes it goes even deeper now you may ask what if we try to set up the experiment so as to check if the electron is passing through both the slits at the same time what if we place some kind of a detector some kind of a light source on the other end we shine light on the other end on both the slits so every time an electron passes through a slit light will get scattered and we will be able to detect that and we will know if the electron is passing through both the slits at the same time or one slit at the same time what happens then well let me tell you my dear friends and students what happens then okay same experiment a source of electrons okay it experiences a penetration through one slit it experiences this kind of a intensity profile fine second case scenario slit s2 is open it experiences this kind of an intensity profile fine so this is i1 this is i2 fine third case scenario what happens is okay the source is emitting electrons fine and the electrons maybe are penetrating through s1 or maybe penetrating to s2 i don't know they essentially there is a light source here in this side okay so let's suppose there is a light source i'm going to call this as light source so you can think that we are shining light on the other end and maybe there is a scientist looking through a microscope and every time an electron passes through either slit s1 the light gets scattered from slit s1 and he detects okay electron has passed through it and maybe the light electron passes through slit s2 and he detects the light gets scattered from s2 and he detects that the electron has passed through it two very bizarre consequences first of all when we perform the same experiment but with some sort of a light source on the other end that is capable of detecting whether the electron is passing through slit s1 or s2 the interference pattern vanishes we do not see the intense interference pattern again instead we see the pattern for classical particles you see in the third case scenario we ended up getting an intensity profile which is similar to that of the intensity profile of classical waves that means i is not equal to i1 plus i2 because we ended up getting these oscillating interference pattern right but in the fourth case scenario when we had quantum particles like electrons but we had some kind of a detector on the other side to detect whether the electron was passing through which whichever slit the intensity profile in that situation this appears disappears and we end up getting a situation where i is actually equal to i1 plus i2 this is bizarre this is bizarre what is happening not only the intensity profile disappears but the detector never detects both the slits at the same time that means whenever the electron gun shines or bombards electrons on the both the slits the detector detects only one slit at a time so if slit s1 goes click that means electron has passed through slit s1 then maybe after sometimes slit s2 will go click that means the electron has passed through s2 and then maybe electron will pass through s1 again click maybe the electron will pass through again s2 click so the detector measures the electron to pass through either slit s1 or slit s2 but never both of them at the same time so not only we do not get the interference pattern when we try to detect through which slit the electron is passing through but we do not see the electron passing through both the slits at the same time either and the interference pattern disappears so when we try to measure through which slit the electron passes through then we do not get the interference pattern and when we do get the interference pattern, we do not know through which lid the interference happens or through which lid the electron passes through. The electron that displays interference, we do not know its exact trajectory and the electron whose trajectory we do know does not display interference. This leads to the characteristic indeterministic nature of quantum mechanics. When we do know the actual trajectory of the electron, we do not see the interference because of its wave nature and when we do see the interference because of its wave nature, we do not know the actual trajectory of the electron because we do not know through which lid it has passed through. This led to one of the foundational assumptions or predictions in quantum mechanics known as the Heisenberg's uncertainty principle which says that we can never really make or create a setup through which we can detect through which lid the electron is passing without destroying the interference pattern itself. The electrons my dear friends, my dear brothers and sisters, my dear fellow teachers is behaving like a wave. The electron that we know as a particle, we think of it as a particle, we visualize even when we are saying the word electron, I am visualizing it as a particle in my mind is actually behaving like a wave that is capable of interference. But what's even more interesting is that when we try to measure or detect the electron, we see it as a particle and its wave nature vanishes. You see what I'm getting at? When we try to detect or measure the position or the trajectory of a particle, its wave nature vanishes and when we let the electron be, we do not measure its wave nature becomes apparent. So when we try to look at the electron, it looks like a particle but when we let it be, it is behaving like a wave. When we look at the particle, when we look at the electron, it behaves like a particle but when we let it be, it behaves like a wave and demonstrates interference. This split personality of the electron is kind of similar to the split personality of the photon that we studied earlier and this is known as wave particle duality. So finally, here are five most interesting predictions or conclusions from this particular experiment about the nature of quantum mechanics. First of all, wave particle duality. Electrons, just like photons, have dual nature. They have wave-like characteristics. They have particle-like characteristics. In certain experiments, they behave like waves. In certain experiments, they behave like particles and when they behave like waves, they do not behave like particle and when they behave like particles, they do not behave like wave. This is the essence of quantum mechanics and the wave particle duality. everything that we know of in the microscopic domain, whether it be a photon, whether it be an electron, whether it be a neutron, whether it be a proton or an atom or a molecule, all of them demonstrate both wave-like aspects in certain experiments and both particle-like aspects in certain experiments. Therefore, wave particle duality is one of the important essence of understanding the microscopic domain. Number two, complementarity principle. The reality of a quantum system is not that it is a particle or it is a wave, it is both. Whatever this is, is neither purely a particle or purely a wave, it is both. The wave aspect and the particle aspects of these quantum entities is complementary to each other and necessary to explain the system completely. We can never explain a system purely based on particle aspects or purely based on wave aspects but we require both the aspects to describe these quantum mechanical entities completely. Number three, superposition and the collapse of the wave function. Here I'm going to tell you something about how quantum mechanics behaves without going too much into the detail. In quantum mechanics, particles or systems can exist in multiple states at the same time before measurement. So before measurement an electron can exist or pass through both the slits S1 and S2. So an S1 and S2 represents two different states of the electron and the electron can exist in both of them before measurement. This is known as the principle of superposition of a wave function in quantum mechanics but the moment you make a measurement we end up coming up with what is known as the collapse of the wave function. That means a wave function collapses onto either one of them. You don't see both the states at the same time when you make the measurement but when you make the measurement the system collapses into one or the other. I will interpret on this maybe in detail in some later video. Fourth, the effect of an observer. You see the moment an observer comes into the picture it disturbs the system so that the interference pattern completely vanishes. This is something very new in this scientific world because in science, in physics we have something called objective reality. We like to believe that the world is objectively behaving on its own without the interference of the observers even though the observers us scientists detectors exist but the reality of the world exists independently of the observer but this is one of those experiments that suggests that the moment you try to make an observation it disturbs the result of the system thereby bringing into question whether reality at the microscopic level is purely objective or not. The presence of measuring devices disturbs the system and its results. This could lead to some deeply philosophical discussions but I'll keep that as a tangent here and lastly finally the Heisenberg's uncertainty relationship. As I just now mentioned it is impossible to create a setup in which we can definitely know the exact slit through which an electron pass through thereby definitely knowing the trajectory without disturbing the interference pattern. This leads to one of the fundamental equations in quantum mechanics known as the Heisenberg's uncertainty principle. If you want I can take two minutes of your time to just derive it for you. So let's suppose that an electron is passing through a single slit and then because it is a wave it goes and creates a spot that has a certain this kind of an intensity profile. So for a single slit diffraction pattern there is a certain kind of a what do you call an angle associated with the first minima right. So let's suppose the angle associated with the first minima is given by theta we know from single slit diffraction pattern formula that lambda is essentially equal to a sin theta where a is the width or the width of the slit. So let's suppose that this is the x axis and this is the y axis. So I am going to say that the width of the slit essentially represents the uncertainty associated with the position along the y axis. So I am going to call that as del y. Hence this becomes del y or rather I should say that this becomes sin theta is equal to lambda upon del y where del y is the uncertainty associated along the y axis of the particle's position because the moment the electron passes through a slit that is the uncertainty associated with its position along the y axis. But now because the electron passes through the y axis and because it sort of has this kind of a maxima that has a certain kind of a spread its momentum along the x axis I can say is what px and its momenta along the y axis is I can say py and its momenta let's suppose along this direction is p then based on a simplistic calculation here I am just trying to convey to you the qualitative information how what we can derive from here what is py or rather what is del py let's suppose the uncertainty associated with the momenta along the y axis that could be comparable to py itself yes what is py however py is essentially equal to p sin theta right theta is this so p sin theta so this is equal to p sin theta but what is sin theta sin theta I have already obtained here is basically equal to p lambda upon del y but we know from De Broglie hypothesis that what do we know we know from De Broglie hypothesis that lambda is equal to h upon p so lambda p is equal to h so therefore this becomes p lambda is equal to h upon del y and if we combine del py is equal to h upon del y together what do we get del y into del py is almost equal to h del y into del py is almost equal to the Planck's constant this is the Heisenberg's uncertainty relation of course it is not the exact relation I have tried to come up with a very qualitative understanding based on diffraction via a slit but this basically says that the uncertainty in the position of the particle along the y axis is associated with the uncertainty of the momentum of the particle along the y axis and they are both inversely correlated and this leads to one of the foundational pillars of quantum mechanics which is the Heisenberg's uncertainty relation and that can also be conveyed from this particular interference experiment so this is all for today I am Divya Jyothidas this is for the love of physics I hope that I was able to convey the information and everything that I know about this particular experiment the double slit interference experiment and what it tells us about the nature of quantum mechanics I hope I was able to do justice to this particular experiment and I hope you found this video interesting and you found this video informative and you found it very intriguing there are many mysteries about this world that are yet unknown there are many questions about this world that puzzles everybody and if I was able to intrigue any one of you into studying about this in a deeper fashion then I think my job in this video is done so that is all for today thank you very much I will see you next time bye bye take care