Mit Professor Walter Lewi's Physics 801 Lecture 34

all physics of the nineteenth century and really it was cold classical physics examples are tony mechanics which we dealt with his full term and electricity magnetism which you will and counter the next yr nearly part of the century when we learned about the compositional adams it became clear that classical physics did not work on the very small-scale off the items the size of a net in noted ten to two minus ten meters if you take two hundred fifty million of them you line them up that's only one is g nineteen eleven the english physicist run reports demonstrated that almost all the mass of anatomy is concentrated in extreme small volume at the center of the adam recall that the nucleus it's positively charged and their electrons which are negatively charged i orbits around the nucleus and a typical distances from the nucleus thirty electrons is about one hundred thousand times larger than the size of the nucleus as early as nineteen twenty brother ford name to the pro coleman cheppali discovered a note from in nineteen didn't do for which he received the nobel prize but i would imagine that this lecture hall is an add-on and the size of anatomy is defined by the orbits the outerwear bits of the electoral if i scaleatron delete now in this ratio hundred-thousand tu wong then the size of the nucleus will be even smaller than a grain of sense and it just so happens that yesterday i went to plum island i worked for three hours on the beach and i ended up with some sent in my pocket and so i will donate to uwm proto we truly hold onto it will give this to protons that student was so keep it there is one profile and there would be an actual mentos anywhere there near the walls going around like mad in orbit and that would then be how does eleven to think about what other news an atom is all vacuum and i'm all vacuum you think of yourself of being something but we have nothing you can ask yourself the question if you all document why is it then that i can move my hands not forty other hands like a ghost can walk through walls that's not so easy to answer and in fact you can or entered his classical physics and i will not return to that debate which rival faction according to maxwell's equations maxwell's lol electricity magnetism electro because of the attractive force of the pro conduits piled into the proto in a minute office seconds and so evans could not exist let me know that's not true we know that and to exist so that created the problem for physics and of course the danish physicist niels bohr who in nineteen thirteen postulated that electrons move around to look listen well-defined orbits which i distinctly separated from each other and that the spiraling it'll be an excellent into the nucleus does not occur for the reason that an electron cannot exist in between allowed orbited can jump form on orbitz to another but it cannot exist aborted gestion water shaking because it would also implied of the planet that goes around the song cannot afford it the song just at any distance the grand movie just a trifle in or trifle farmer out it would also require discrete orbits it would also mean if you have a tennis ball and you would balance the tennis ball up-and-down the dependable could not reach just any level about the ground but it would only be discreet levels and that is very much against our intuition we'd like to think that when you buy was a tennis ball that it can reach any level that you want to give a just a little bit more energy and it will go under behind her that according to plan a mechanic would not be the always seems rather bizarre noted goes against our daily experiences but before we dismissed the idea of quantizer asian he the compensation comes in when you talk about this creed orbits well you have to realize that the differences india loud heights of the tennis ball and the differences between the allowed orbits of the plants around the sun would be selling capacity this poll that we may never be able to measure it letter which quantum mechanics replace no role in our microscopic world one of the very very small compared to tennis balls and quantization effects a much larger in the stock microscopic world over electrons and adams then in our familiar world baseball's faults and pants and plants the before we continue i would like to repeats to you one of the corner stones of quantum mechanics and it says that the electrons in adams can only exists as well the point energy levels think of them as being orbits around the nucleus and they cannot exist inbetween now when i need a substance the electrons in the items conjoined from in orbit store a lot of out of workers and when they do so they can leave a whole opening an empty space indian orbits but later on they can fall back to fill that opening day cant occupying that place again and when i keep eating substance there is some kind of a musical chair game going on electrons will go to out orbits they may spend their sometime and then they may fall lower orbits in orbits you see here please very precious face and when i pick up the space i have to do work i bring a friend away from the center now is that energy lost i could drop the case and it would pick up connecticut ninety i will get that energy back to educational potential energy will be completed to kinetic energy it'll crash two pieces and it will generate some peaked effective breaking itself of this case some energy in a similar way the energy that you poured into electrons when you bring into out of whether it's is retrieved when the electrons fullback there is a parallel dropping this case and getting to work back that i put him i wouldn't be a nice thing to do through this five hundred year old face but as far as i'm concerned perfectly reasonable to do it is already in let that go and the energy will come out in the forum of heat and also in the form of perhaps some norris electrons full problem how to word it back to in orbit it's not kinetic energy that is released but that comes out often in the form of light electromagnetic radiation lights has energy feinstein formulated kept the lights coat on you had a global iphoto is h times the frequency and h is planks constant named after a max plank an h is about six point six i've spent to minors thirty-four jewel sects now we've also seen in uh... ada wong that mountain underway flanks of lights because the speed of light divided by the frequency and so if i eliminates the frequency but also can write that the energy of a large photo people's eighteen divided by atlanta and so you see the more energetic debatable it's more of the way fine unless and until it is available no matter where and so it could jump from our order to win in orbit is very high than the rate flags will be shorter then when the jump relatively small i can make you some kind of an energy diagram of these jobs and his energy levels energy goes into a correction but if you want to you can think of these ashley position how far do you nex ones are away from the nucleus if you like that if that helps you to this will be delightful it would be to closest to democracy so this would be allowed energy levels allow webbots and if this election jump all the rage here but it could fall back adelaide among made a moment in time and energy could be so much that you couldn't even see the light it could be ultraviolet and this job may still be ultraviolet but nowadays job which is a little less energy but maybe in the group parts of our spectrum so we may see this as blue lights and this one which is a little less then there's this energy regenerate please jump make generate green light and the jump from here to here which is even less they generate red light and a jump from here to view which is leave unless made again the invisible but it may be infrared address the electrons fulfill all toward its two in orbits you expect very discreet and refused to come out very discreet way franks andes wavelength if you would see correspondent through these a lot of transitions between these energy levels so if we could look at that light and sorted out white-collar we would in a way cds energy level now you have in your little envelope the piece of plastic which we call the grading and degrading has the ability decompose delights in colors which we call a spectrum and we're going to be shortly used expect that grading to look at like home helium and lights but before we do that i'd like to hand out as a souvenir to a few people randomly picked something that they can also use uh... it's not a good as your grade ego but it's also nice you'll see more sp spectacular result but not ice cream notice clean all right one for you one for you one for you and one for you you won't want i can tell that you want one for europe comeaux arnold at the site doesn't have anything to go to war all the way over now so this is really for children's bodies which i'm handing out of this boat george cost that you want one of course professor possible wants one couldn't compartments you won't want pocket and you won't want so means usual grading but then at the very end you can always use the set spectacles wit's end don't work nearly as well but uh... this kind of thing i'm going to lightyear both this piece this light which has speedy minutes and that's what you're going to see visual grading if you'll hold your grading properly you may have to rotate it ninety degrees you'll see ordered works when you try it you're going to see very very sharp their alliance at various colors i wanted to realize that the reason why you see a very short narrow lines is only because my light source are very sharp narrow line if you use it on something that is not a very sharp never wine but you're not going to see through degrading very sharp narrow lines but don't confuse the lines that are on the grading re-use the line source that i have here when you start when you look in your grading very shortly you'll see on both sites the wonderful wanted to be a rematch and we will discuss it in a little bit more detail but before you look for you graded our first wanted to simply look at it without degrading because then there's even more spectacular when you lose degrading because you have no clue when you don't use the grading what kind of course i get in there and according to going to see i_d_'s electoral levels so i'm going to make it and ultram his home and this wound i believe he's helium i have a great idea so we have to rotate it so did you see vertical lines on vita sites you may have to rotate it ninety degrees no more and if you look closely printed look on the right side of the lights you'll see a distinct blue line up your view lines green very nice bright yellow wong and you see red and if you go further to the right the repeated several fate that we could see a repeat of that that's more important right now i just wanted to see that the flight which i have no idea that it comes out in very discreet wavelengths very discreet frequencies and they correspond who these jobs from below energy levels to other allowed imaginable but there's nothing in between and when you look on the left side you'll see a mirror image of what you see on the right side o'neill picture of the union has only two electrons i'm not going to put in the a new u_n_ both and that's makeshift richer for reasons that neelam has ten electoral so we have many more bits for many more ways that's electrons can play musical chair along the lines in the red i'm not blocking you at all a lot of lines in the red and some beautiful eyes in the yellow i see some in the green i don't see much in the blue add little bit in the blue but the key thing is i wanted to see that these lines art discrete cities knots just any wavelengths that can be generated it's only be allowed orbits musical game windy electrons one would be to another and that gives you this unique discrete spectrum bodies lie inspector would no longer for border came with his daring ideas but before comic annexed these lines were great mystery but they no longer life i suggest you used his grading use it when you outside nights look at some streetlights particularly sodium lamps and mercury lamps and of course the neo *** a quite spectacular but keep in mind he will not see very nice straight lines unless your light source itself has very nice straight narrow light source look what a mechanic took a big lead in the twenties and it would be impossible for me in the available amount of time to do justice to all the basic concepts however i will discuss some consequences that i rather norm intuitive prior to qana mechanics there was a long-standing battle between physicist wilhite consist of particles or wetter their waves knutson believed strongly repair particles and the dutchman avoidance belief that they will wait and it seemed like in eighteen oh one that a conclusive experiment was done by young which demonstrated unambiguously that lights wheels waves organs was right but as time went on this conflict was growing as there were also experiment that showed a lot of conclusively that lights really was particles and it was one of the great victories of quantum mechanics that it shows that life is both appliance it behaves like waves and other times it behaves like particles it all depends on how you do you experiment in nineteen twenty three lurie dubrovnik made to the daring suggestion that's of particle can behave like away and he specified was very specific that the way frank now it is called the broadway planks ph mock swamps constant divided by two men from all of that particle and let them use the massive article the velocity as we have seen in eight oh one is the momentum is higher led to a friend to short the baseball we'll have a very high momentum which ridicule you know short wavelength and one of the startling consequences is that protons and electrons which everyone at that time considered particles and then also be considered as being weights in nineteen twenty six the austrian physicist wrote an article the nearly two coffin which is famous equation trinity crazy it's cold now which is the ground pillar of quantum mechanics it unifies the rave and a particle character off return to my baseball they come out of the baseball all say hopper kilogram and give it a speed of hunger miles per hour calculates the way flank steak you would find poured into quite a mechanic that way trying to sell absurdly small it is twenty orders of magnitude smaller than the radius albany electoral so does completely meaningless for quantum mechanics plays no role in our microscopic world what some friends and baseball's without taking the election you take the mass of the electoral entered a minor thirty kilograms and you get the electron is speed of three thousand meters per second not only a getaway flames which is comparable put away frank of visible life red lights now something that becomes very meaningful something that can measures now you may argue she will differences that make who cares something is away or whether something is a particle it makes a huge difference those waves crests and they have belize and so if you take who sources of waves you know what a waste two sources packing up and down on the war that we can take to sound sources there are certain locations on the surface of the war where the crest of walking away right at the same time as the belly of the other and so did cancel each other out there's nothing there's no motion of the war recall that that's trucked in interference or to other places readiness constructive interference by the support each other particles can do that too that is very hard to imagine how can one particle was a lot of particle interfere and vanish that the two particles no longer exists so if indeed particles are waging should be able to demonstrate that by having interference pattern of to particles like the waterways and they can't certain locations in space those particles disappear which turned out to be possible but that's a very moment to reduce idea so we can go to class completely we say local particle scandal disappear in kuala mechanics you can think and waves if you want to and then you have no problems with the interference cut and andy destructive interference at certain locations but there are other remarkable consequences of for mechanics classical mechanics you and i a clever enough you think that we should be able determined the position of an object to any actual issue that we require and at the same time the total also its momentum but any extra should you require this dramatic of how clever we are simultaneously object is right there better kick my *** and that is its speed however the german physicist heisenberg realized in nineteen twenty seven that a consequence order mechanics is that this is not possible strange as it may sound to you heisenberg stated that the position and the momentum of an object cannot be measured very accurately at the same time and i will read to you heisenberg uncertainty principle the way we know what it says the daily concepts also exact position over object and it's exact moments and together had no meaning in nature is a profound non classical lightyear and it is hard for anyone of us i mean included to comprehend but it is consistent with all experiments that we can do to date i want to repeat it because it's going to be important opal's follows the very concept of exact position open objects and it's exact moment in together have no meaning in nature what does it mean first let me write down heisenberg uncertainty principle bell company which is the uncertainty in the momentum multiplied by delta expedition uncertainty in the position of that article larger or approximately equal complex called stands divided by two point weakened his ex recall that age barack h bar is approximately and to the minute thirty-four jewel sections you see eighty six point six and spent it on my neck thirty-four if you find that divided by two point you get about into the minds thirty-four what does this mean now what it means that if the position is known to an accuracy delta x loop we'll give you some examples that the momentum you know that truman is not the traumas through the amount bill copy large or equal divided by gopac that's what it means and i'll give you an example which i chosen from the book george gaba wrote a book which he calls there's a poem contin wonderland it's about dreams missed the pumpkins wants to understand the quantum world and there is a professor you'll see a picture of the professor pulp fiction in his dreams various remarkable not intuitive effects of quantum mechanics anyone of these dreams the professor suggests that will make eight bawa and a professor takes a triangle in the pool table and puts a triangle over one billion board so the billiard ball he's constrained its position and a delta x is roughly taken thirty seconds open to any needs that means that the momentum is multum determines knopf determined to an approximate value of one divided by four point three is about three carol braun leaders per second if we give the billy aboard mass of one kilogram dealt upbeat is and okati and so it and it won't get around then the speed all that billiard ball is on the trail month according to heisenberg uncertainty principle by at least approximately three meters per second three meters per second that means seven miles for all and so did billiard ball will go around like crazy triangle and that's exactly what happens in the dream and i'll show you picture from that book there's the balkans is always in pajamas just a reminder that it is a dream i need to use a professors are very old man it has a very nice b uh... after the prestige another week you from this book ivory julia very short paragraph that deals with this the professor says look here i'm going to ports definite limits on the position of this poll by putting it incites but will be triangle as soon as the bulldoze placed indian closure off the whole insights of the triangle became fields up is clearly of art you see separate professor i dislike the position of the bull to the extent of the dimensions of the triangle these results in considerable uncertainty in the velocity and the bull is moving rapidly inside the boundary can to stop it as mister pumpkins it is physically impossible everybody even close based possesses specific motion we physicists call it zero point motion such as for example the motion all electrons in any adam so here you see qana mechanics at work when age bar use mom this is a very norm classical idea because you and i would think and we've always dealt with that in ada wong that you can take an object and place at that location eighty and we say at time t zero it is a and it has no speed and we noted last so we know both the momentum and the position food infinite accuracy but according to chronic and if that's not possible let's not returned to the real world rage barnes noble umbrage barged into the mind of thirty-four and that's not good hehe billiard ball inside this triangle now delta x is the same but into a tube are sent to the minute thirty-four delta p is of course ten to thirty four smaller and sort of velocity it's ten to thirty four times smaller on the tremendous degree to which the velocity is now undetermined insult ridiculously small it is three percent of the minus thirty four meters per second that if you allowed at baltimore bwi steps be in one hundred billion years if you believe it would move only one on the sofa diameter of electron toward meaningless again and so we can you see that quantum mechanics plays no role in our daily microscopic world of baseball's and basketballs and billiards templeton pence and therefore it is completely okay for us to say i have a billiard ball which is at point a and classes one kilogram and it has no speed that's completely completely acceptable mccormick amex has no problems with that that's not true they kind of genetic the diameter of a hydrogen atom is about ten to two minus ten meters so real that phone is confined to a delta x of about ten to the minus ten need us that means the momentum all that electro becomes undetermined according to heighten works uncertainty principle reluctant to buy three four divided by computer minus ten it's about time to minus twenty four him around was a massive electro that's about ten to two minus thirty kilograms solis delta p is also engulfing so it means that they'll come clean that means the velocity of the electoral is undetermined according to heisenberg principle by an amount which is at least tend to minus twenty four she's this project is delta p divided by the mass of the electoral if you spent with mine and that is about ten twenty six meters for a second that is philip of a percent of the speed of light sodium actual is moving only because of the fact better these compliant that's looked cuauhtemoc is all about electrons motion is dictated exclusively quantum mechanics i'm going to show you an experiment in which i want to convey to you how known intuitive heisenberg sponsor the principal is i have here laser beam and this laser beam going to be aim throughway narrow slits i'll make a growing or from this lytle and that's let's which is a political sleeps and the mate never were and can be made you it is like being and here is these opening is split it's only going to be confined in this direction on in this direction tota light i'm out here and then on the screen which is going to be debt free a large distance capital l we're going to c dot lights box the like being going towards me the separation capitol hill i start off resisted all the way open so you're going to see this light spots and then i'm going to make this lifts never never and as i'm going to come into the white bean which are going to see is exactly what you expect you expected dislike disappears and when i come in for that you see exactly what you expect the dislike disappears total export bear on that screen will become their work never the comes a point eisenberg says oc helpful now because of your delta x your knowledge accuracy in this direction where the lights go through is now so high but now i'm going to introduce uncertainty in the momentum of that light the momentum of that life is now no longer determined to infinite accuracy and what that means if you start floating around with the momentum of that lights idiot's direction it no longer go through straight but it goes off at an angle and i'll make you a more qualitative calculation for that so let's look at this slips from above you this right and district has an opening delta x and his delta x we going to make smaller and smaller and let us start with delta x of about one tenth of a millimeter which is spent reminders for me i have lied i know to wave length of the lights and i don't know laid-back equals h divided by pete according to the problem i know the way franks i know it's so i can calculate the momentum about life i have done that take my word for it it is about ten to minors twenty seven kilogram meters protect that's the momentum of individual light vocals bingaman of particles if you can do poured into the program so now i have a delta p the degree to which people maintenance undetermined according to heisenberg there's going to be ten two-minus thirty-four divided by delta x which is ten to two minus force when ever spent in a minute very small momentum itself is going to minus twenty seven so it's only one point during a thousand so what will happen if the like come through here and i'll make a classical arguments i think this is the momentum of the lights as it comes to trade in when it has to be squeezed for his narrow opening heisenberg uncertainty principle demands that it's going to be undetermined the momentum in this direction by roughly ten to two minus thirty or more remembers always larger were equal in other words if i can introduce for instance in this direction or in this direction delta p then i would expect but some of that light goes off in this direction it is this change a moment in this on the problem is a moment in that makes it go up in an angle only in the excel at you if i had this look like this don't expect this to happen in this direction because uncertainty why direction that's not the problem delta y is not very small delta x that is very small so does the election they're going to get your trouble it's only been star trek you get to know precisely what it might go through this election is not the issue sodas angle fade out and i'll be calculated very roughly data is obviously delta p divided by p buffet dot very roughly ten to two minus three radius which is the fifteen th of a degree and if you have at a distance al this distance here is al if you have your screen the spot on the screen if i called a tax cut location l exit location l is always a big day dot clientele and if they are sent to my turf three let's assume this is about ten meters away from us so l is about ten meters then you get then to minus two leaders that is one centimeter one setting either in this election and won't only be done in that direction to suddenly this but when i make this lift weights ten times smaller if i make this victories only one hundredth of a millimeter then this becomes obscenity because now i'd know delta x ten times better and so delta p sometimes mortenson so no i expect to see here atleast this we have twenty centimeters and at least this new york twenty centimeters bear sorting obscenities that a teeny weeny little light source virginia beginning you'll see is a very small spot when i think he's smith never a narrower indeed you will see that you will respond quote and you will see standing around there were and then all of a sudden it begins to spread out and begins to spread out and by the time i'm close to tens of a millimeter the lights pulled there will be maybe down only to it if you make the switch smaller and the photos spread out and i want to show that to you know have to make it very dark and i need my flashlight don't behave laser beam there you see it slip is now although they open not at all the way open and i'm going to close this without float slowly and if you look closely you will see that meal to get my rat laser like two point something out we will see that the lights we'll get squeezed in the horizontal direction you can see already at the left side has very sharp vertical cut off in the right side also getting narrower getting narrower getting error but i know in the early tens of a millimeter yet getting clearly an error if he's getting narrower getting narrower overlook here or not yet at the tens of millions i'm getting there going slowly squeezing it and screening those photos those photo's now are forced to go through an extremely narrow opening and heisenberg very shortly going to jump in and says you're going to pay a price for that you know too well read those photos are in the excel rection the price you pay at nature will now make the momentum on the truman's eniac selection and you begin to see you see it now really begin to see at the center portion widening even photos appear here you see some guidelines for travel not further discussed to date but notice at the light was spreading of course when i squeeze this in a panic it's narrower it's obvious that i lose light but the white that hits the side obviously it is not going through for the white intensity will go down that's just inevitable i'll use fewer photons but look at this photons here therefore don't bear if greenspan sent to me that this portion from here to view it at least one foot i squeeze more this is more than half a meter now i squeeze more is it about while nato already that's crazy even more i close this look now i will alternate slowly and opening it barely slowly and at the moment that the orphans what it looked at it if you guys he's wonderful stray cat looks more like a comment from here to view it at least needed at that center portion of the white spread out since the poor rifles forced to goal for this very now i'm opening it and more alternate more with was it extremely intuitive not only have you seen quantum mechanics at work interlude electrons jumping between orbits which we have also see while not a very interesting consequent upon a mechanic which is heightened brooks uncertainty principle notice spreading all this light can very easily be explained without heisenberg uncertainty principle in fact it was known even in the previous century who high degree of accuracy why this happens and the dark lines we're very accurately explains all i wanted to show is that the spreading of the lights is entirely consistent is heisenberg uncertainty principle and had better be because it would not be possible it would be inconceivable that you could do any experiments that would violate heisenberg uncertainty principle and it is right that you would see on the screen there if thats like sports we'll get narain narain narain narain all the time as we would think classical e that would be a violation of heisenberg uncertainty principle is not possible now there is no way in advance to predict which totals and aware or you can do was quite a mechanics doing experiment with lots of phone calls and then you will get a certain distribution and the distribution will be exactly as you sold there quantity ten x can never predict on individual photo where it will end up we saw that rights pop in the center so if you get his experiment with one photo two date month for corporate bigwigs would be sweet and you had a photographic right there they would keep it there for months you develop it you would see this a pattern that you see there this portal rights today you're right along tomorrow your item on the day after tomorrow you on the day after that the day after that the day after that today after that today after that they after that so don't think that this interference that and that you saw all is the result of two photos going for the state simultaneously model you can do it was one total and you would see exactly the same thing no this idea that you cannot in advance predict what a particular potent will do is a very non classic and have ruptures all the wrong way because our classical way of thinking is and you were no difference from my own creating in this respect if you don't experimental packed in a controlled way who should get on the times exactly results not so fest quantum mechanics all the clerk at mitchell tell you is what the probabilities that something will happen no guarantee but it is very good in predicting probabilities behind so i have great problems with his idearc of not knowing precisely what would happen and yet endless discussions ouija board and others in which he try to convince them that because you couldn't predict what happened that something had to be wrong risk one weekend ice plants being his words were dos not throw backs this was the way with his way of saying it is ridiculous at the outcome of a well controlled experiments is uncertain now almost nine that decades have gone by since the beginning of quantum mechanics and we now know that golf if there is one dubs throwback however goal is bound to the rules of comic annex and cannot violate heisenberg uncertainty principle the lights could not go straight through without spreading when i make this late as narrow as i did mccormick mechanics is bizarre worlds that we rarely experience in our daily lives because we used to basketball baseball's tennis balls it is the way the world pics and out of the molecules can only exist because of quantum account that means you and i can only exist because of quantum mechanics but this will give you something to think about but i warn you in advance because if you start thinking about this we'll give you headaches and will give you sleepless nights editors gave me giving me complicitous nights in the past and even today when i think about the consequences the bizarre consequences of quantum mechanics i still cannot comprehend it i still cannot digest it and i still have headaches and sleepless nights but it may be necessary to go through the sleepless nights if you want to be venture evolve as an independent thinking scientists that sunday all of you will thank you