On the Use and Misuse of Quantum Mechanics

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On the Use and Misuse of Quantum Mechanics
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1982
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Willis Lamb was one of the many Nobel Laureates who really fell in love with the concept of the Lindau meetings. Beginning his long series of lectures and participations in 1959, he continued participating until the very end (he passed away in 2008). I remember acting as chairman for his lecture in 2001 and it was quite clear that he regarded himself as at home on stage in the lecture hall. His range of topics was wide, from experimental atomic and molecular physics to fundamental questions of the interpretation of quantum mechanics. The text he read for his 1982 lecture was entitled “Quantum Mechanics Interpretation on Micro Level and Application on Macro Level”. This is a topic, which had historic relevance, starting with the discussions of Albert Einstein and Niels Bohr at the Solvay conferences around 1930, continuing with Erwin Schrödinger’s cat paradox and continuing further with the renaissance of quantum measurement theory during the 1960’s and 70’s. Actually, it is still a hot topic today, mainly due to the enormous progress in experimental technique. In 1982, the direct detection of gravitational radiation was discussed. According to Einstein’s theory, two heavy stars rotating around each other will give rise to gravitational radiation that will carry away energy from the system and make the rotation slow down. Such an indirect effect was discovered by Russel Hulse and Joseph Taylor in 1974 (Nobel Prize in Physics 1993). In his lecture, Lamb was critical of a theory behind one of the detectors planned to see a direct effect of gravitational waves. Since this effect would be a microscopically small change in length of a macroscopic beam pipe, the plans involved using a technique named quantum nondemolition measurement. Lamb argued that this technique would not work and that the detector would not reach the quantum limit, as proposed. As of today (early 2011), no gravitational waves have been detected. Anders Bárány
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so ladies and gentlemen you this morning you will have heard lectures in all three dialects of english a slight of one with a slight swedish accent one with a slight japanese accent and one with a strong american accent. of. sometimes it helps for people for whom english is in the native language to hear the material. spoken with a slight accent. i hope mind can be understood. and another thing i believe that i was scheduled to stop this lecture properly at the eleven thirty or as some people so you have twelve of. i will try to stop sooner than that because i wish to go on the a trip to my now. the. i. however i also wish to eat lunch today so that to them anyway but i do have a lot of material to cover and therefore i'm going to read the text a reasonably quickly. a quantum mechanics is a very wonderful tool for dealing with problems in atomic and molecular and condensed matter physics as well as with many parts of chemistry and it can be based on a small number of axiomatic statements which are easy to apply but hard. to understand. so this same quantum mechanics can be extended in very plausible ways to apply to electromagnetic radiation in interaction was matter many problems in nuclear physics have been treated with quantum mechanics and the reconciliation of quantum mechanics and special little to be three. has had considerable its success with the general relativity things are rather more difficult still many problems of sub nuclear physics and high energy phenomena have also been treated with quantum mechanics but the theory is pushed rather for from its roots of when dealing with such. problems my main object to this lecture is to deal with the interpretation of quantum mechanics on the atomic level and with the application of that theory to more macroscopic systems which for example among other things might include measuring instruments. it is tempting to think that quantum mechanics might be applicable as well too much larger parts of the universe such as was life and beyond of but i will try to give you some reasons why such a temptation should be resisted. experience and common sense teacher start to learn anything about a sub microscopic system is a difficult task. our intuition is a most on reliable guide in this domain we have ingrained concepts a bell. the meaning of reality which no doubt will be designed by professor they are in the next lecture and about causality the relation between cause and effect and about our schuman role as observers of natural phenomena. all these things are concepts are most inappropriate for dealing with the sub microscopic world of the development of the mathematical structural quantum mechanics probe is your than the formulation of a satisfactory interpretation of the theory and description of the process of measurement. quantum mechanics can do a lot for us if we if we regard it simply as a set of computational rules for dealing with simple dynamical systems for instance we can calculate the energies of stationery states of atoms and to make an immediate connection with hyper surgeon spectroscopic observations of the last century. for this one does not need to worry very much about the interpretation of the way function which describes the state of the system but only to calculate the energies of stationery states when we come to discuss scattering processes or radiative transitions between stationary states. or the theory of measurement of dynamical variables however we have greater need for a better understanding of the meeting of the way function in the last few years arts i have seen a number of papers dealing with interesting applications of quantum mechanics to large scale phenomenon these. range from problems in physics optical communication theory molecular biology all the way up to the story of the whole universe i have been quite suspicious about the validity of most of this research. one example of this is found in the surrey. he expects the expanded by kipp thorn and carlton caves of caltech on quantum demolition measurements of gravity waves gravity waves probably have not been detected yet perhaps they have but not everybody think so but to many people working on much more sense. steve detectors and the probably someday gravity were still be detected. however. of those the it. the exceedingly limitations imposed by quantum mechanics and such measurements of is so the subject of the the to the topic is the subject of the discipline called quantum on demolition measurements this work represents part of a major program at cannes. all tech to build the most sensitive detector possible for gravity waves estimates based on an intuitive application of the uncertainty principle to the experimental configuration set a quantum limit on the smallest signal which could be received a storm. the caves and others have searched for methods to quote beat the quad a limit on called their papers are very impressive and persuasive unfortunately for them or more likely for me if they make use of. a form of assumption about quantum mechanics with which i do not agree. to put her briefly i could say that they postulate the reduction of the ways packet hypothesis of phenomenon. there are very similar ideas expressed in the first chapter of professor directs book on quantum mechanics. i probably disagree with the. the. statements expressed by those. the authors but i disagree more strongly with the use of those so hypotheses by the people involved and gravity waves measurements of gravity waves detector typically consists of a very massive cylinder one of its very high i.q. law. molds is put into vibration by a passing also grab a facial radiation in simple terms the system consists of a forced support harmonic costs later and should be very familiar to all students have textbook quantum mechanics at issue is the cause. question how one can measure coordinate the momentum of such a large system the method is to trace out the time dependent shape of a gravitational wave polls by following a motion of a reference office on the massive oscillator there is general agreement was to grow. occasional fields which are to be studied in this research can be defeated completely classically so there is no need to worry about the quantum theory of gravitation in this study noted the need to talk or brother time the sort of the quad all aspects of gravitation there will be plenty of on quantum. mechanical disturbances of the detector to cope with but thorn in caves wish to go further and the quantum limit since this is required for the detection of some types of expected rover to shovel radiation. my feeling is that they may probably succeed if the phenomena hypothesis is correct and will sail if it is not. perhaps and three or four years so that one of those gentlemen would be sure to tell you what to. they did another thiel for quantum mechanics has been applied to macroscopic phenomena isn't the story of optical communication here we might consider a signal generator such as a laser a transmission medium perhaps between the earth and the moon and a detector which might consistent with. for one hour per device and associated electronic circuits sense the phenomena reduction hypothesis plays an essential role in the story of the foundations of which were elated bell telephone labs but many of the people work on the subject i believe that this theory is fatally flawed. quantum mechanics is now over fifty years old fifty five years old i taught graduate courses in that subject for over thirty five years at columbia stanford oxford yale and build the university of arizona. my lectures always began with an explanation that one must first learn the rules of calculation and quantum mechanics before one can understand the physical meaning of the subject somehow all the time always ran out before i could give a proper discussion of the interpretation of quantum mechanics. have i did give an hour's lecture on the subject here and one dollar and nineteen sixty eight of this was subsequently published in physics today. two months ago i gave a long series of leak age. lee pages lectures at yale university on the third of measurement and quantum mechanics and those that will be eventually published in the that universities press in the little the top in the little time available available to me today i will have to confine my discussion to a very simple form of quantum mechanics. max and i will have to keep hidden many elegant features of the more general theory i will mostly be considering a dynamical system in which one particle is moving along a straight line. the dynamic of variables to be measured will be limited to will coordinate such as x. and energy such as the hamiltonian to move by a simple h for hamiltonian i will mostly use the way of mechanical formulation of quantum mechanics and what's the state of the system was described by the shooting. wave function which is a function of sex and t. side effects and she said. suppose that we have a simple problem in classical mechanics of particle mass animals along a line under the action of some specified conservative potential energy field vivax the system is described by the mass him and the form of the potential function of the objects the state of. the system can be specified by giving the particles coordinate to coordinate x. and velocity v. was the object of the exercise is usually to predict the future future state of the system at a time greater than searle and that's done with the help of the newtonian equations of motion given the initial state that time to your pulse. several it should be obvious that if a certain time we want to change the mass of a particle or source s. of x. which is acting on the particle we will subsequently have a different dynamic or system and a different set of differential equations a record since of most of the soul. it is a good idea to know at all times what problem we're trying to solve. there's a great deal for funding and that last sentence and old it is so inadequately observer would say. with a little more sophistication we can introduce concepts like momentum which is a product of mass times velocity and we can introduce or hamiltonian function of excellent p the newtonian equations of motion or replaced by hamilton see questions which i believe are on the. you graft your the bottom. and though. well i now want to deal with the corresponding problem in quantum mechanics starting simply i look at the shooting requirement for a completely isolated system and will probably that's on the next. you have to. the speaker. that's the soaring we question the. now that equation may not be car carbon marvel but i'm going to take it over literally. but i have seen students who were this equation inscribed on t. shirts. as a bit of fancy i would like to pretend that most astound this equation on a tablet at mount sinai. of coral he understood that all shop else they'll sell not kill all and other commandments he did not know the meaning of the strange equation with its mystery as symbols and did not wish to confuse people by telling them about the extra tablet. as a result we had to wait many thousands of years for another chance of enlightenment. unlike most us we probably know today forked over age for his own planks constant improved by iraq. but effect or whatever to pi of i scored a minus one and t. standing for time the the hamiltonian operator age is derived from the classical hamiltonian function age of six and p. and by replacing the momentum p by a differential operator age four. override the bug eight x. sometimes a partial derivative the hard thing to understand in this equation is the meaning of the way function side effects and t. the notion of away function is borrowed from classical field theories but unlike those there is no direct physical interpretation to be given of this. singer ways auction in cirque instead certain rules or pasta later for using the way function to calculate quantities of physical interest. along those are the probability density w. of the x. and t. which is the absolute square miles away function and the expectation value of a dynamic or quantity as so that simply there could be many dynamic or quantities to be considered that the stands for a general one. and that is calculated by evaluating and and roll consisting of a sandwich made have to weigh functions and the operator if placed between them. the idea that the absolute square away function is to be regarded as a probability density comes from the work of marks born on collision theory and from directs more general formulation of quantum mechanics as a bridge between matrix and wave mechanics. i'm not consider a few simple cases first let the way function be one of the. i can functions of the hamiltonian the operator age of x. and pay the tickets no time for them to explore. you grew up for. that equation the top it represents leo and i can tell your problem and though that is characterizing a stationary state court use of him with an energy stationary state energy is sublime the probability density for that state is given by a. dubbed the us which would be called the use of and and that's the absolute square view of the x. and that is independent of the time and hence the use of the word stationary state of the way function is that is taken to be normalize so that the total probability. but for finding the electron any places unity of. if one measures somehow the operator h for this state if you measure the energy of the state's you find the value isa been with certainty. i'm saying that but the mere fact i say it doesn't explain how all this is to be done but to the certain model that has to be. served in courses in quantum mechanics as you will know for but each time one measures some other dynamic or quantity such as x. one may get our different value of the measurement and only when an ensemble of measurements has been a studied are made it when an ensemble of measurements has been made. those one obtain the probability density w. some and of x. which can be calculated by the euro equation given there are. as a second case let us consider. a wave function sayyaf x. and of what you can't really there is stands for the variable tea and that is of a got hell has a substitute am honored standing for the time of some measurement so that way function as a function of x. and t. for the time of measurement and desist take. to be a linear combination of two was a stationary states of the atom you one and you too are stationary state way functions for do it for two different energy i've been very use the one of the two and grow they can be shown to be orthogonal if you know what that means which you don't need to. and if the if the way it functions or normalized the way function so i will also been normalised it's the complex coal fishnets see one c. to our normalize to unity made a way which are you do not see their but the some of the squares of the seas morrissey to should be you. thirty. if the dynamical variable ages repeatedly measured for a system with this way function one sometimes get see one and sometimes get seek to and there is no way to predict in advance so which result will be obtained the relative probabilities with which the two energy. going values or obtained as the results of measurement will be given by the quantity see one absolute squared and see to observe square well have now given you a little bit of both little bit of measurement there in quantum mechanics if you find it very big so do i. we talk about measurements but we don't know how to make some. talk is cheap. but you never get more than you pay for. of my attitude towards such problems has no doubt been influenced by contact with some research an experimental physics in which single highly isolated atomic states are precisely manipulated by microwave or optical frequency fields in the discussion of the measurement of any dynamic. cool verbal or physical system i want to specify exactly in language of the quantum theory of what apparatus is necessary for the task and how to use it at least in principle i am not satisfied with hand waving or a black box approach or with a. as for more logical scheme my starting point is this reading records and for a completely isolated system which we have already seen on a few previous the grass. the manifest role of the way the equation is to allow us to calculate the future state of the system side of tea from its initial state sides are all for a system with the given how much tony an operator which is usually of the form of the kinetic and the potential energy and together the first problem is to get our system into the. desired starting state sides are all this is called preparation of the initial state we may then let the way function evolved under the guidance of the shorting years equation and tell a time t. some him when a measurement is to be made. i gave a discussion of the problem of state preparation and my nineteen sixty eight lecture and a little hardly anybody here are heard that lecturer world simply take the result for granted. which is that we can start the system off pretty well and he stated that we please not all quantum mechanical systems even if isolated are described by away function we simply may not know the starting with a function in that case the best that we can do is to consider that the way function. might be won or another of several possible way functions and the sign of probability distribution for the various possibilities of the way function would then be used to work out what should happen to each of these separate ways functions and predicted results would be obtained by air. averaging over the ensemble always functions of the story would lose a great deal of its causality if we have to do this but sometimes we would be in a case for the work or a way function description is possible one speaks of a pure case or otherwise have a mixture of the thirty used usually uses density made for us. these instead of ways functions for the necessary kind of book keeping but it is possible to get along without using density major sousaphone works with an ensemble with functions once converted into a mixture a pure a case can never be recovered without the use of some kind of sobering process which is equivalent to the. the proper a shove a completely new state instead of making a measurement on the original system which was new system we should have been concentrating on. the way of equation will apply only if the system has the hamiltonian age the costs to plus the but we do have to permit some disturbance of the system if we are to allow an observation. of the system for instance a measurement of some quality any disturbance whatsoever will represent a change of the dynamic a problem and points and hence we will certainly have to use a different shorting recordation to describe the system during the time it's enjoying the process of measurement quantum mechanics allows. i would say at most three general kinds of disturbances the first. from the application of a classically describe or extra or force with a corresponding additional term added to that hamiltonian we might apply and external electrical magnetic field and treat those fields classically the second way would be from the dynamical coupling of another quantum. medical system to the first system to make a larger combined system which from then on for ever more would be the system we should be studying of the third way would be a from the intervention of an observer putting the observer in quotation marks. who attempts to learn something about the system by looking at it or looking at some associated measuring instrument which has so for time at least been part of the of the look of an enlarged system. in the second case the adult system has to be defined in terms of new variables not little x. and pay but let's say big x. and p. and the discussion of this case the simplest when the upended system is an unknown quantum stayed at the time of union the enlarged but. still isolated system is from then on regarded as the system of interest and its reading recordation can be used to follow its time development the third case will be discussed below but perhaps i should allow you to anticipate that to in my view a living observer is not a suitable are. object for hamiltonian treatment whether in quantum mechanics are in close circle the second and third cases play a central role in the story of quantum mechanical measurements in case reais an observer interacts with the system. phenomena made of pasta at austin cold the reduction of the way of pocket wave packet hypothesis to deal simply with the change of the ways function in such a case this postulate states that when an observer gets a result of the measurement. most props we should say maximal measurement of the the way function of the system collapses into the i can function appropriate for the variables being measured. for reasons given below i do not think that's an enormous possible it is either hell's help fall or necessary of for the understanding of quantum mechanics and for the discussion of gravity way detectors and. instead one can try to give a quantum mechanical description of the combined system of consisting of the measuring apprentice in a known quantity state brought in the interaction with the original system of in first and pursued as in case to as if we have a dynamic a problem as long as the to interacting systems are united in the. one isolated combined system the description is given by a wave function however to use the measuring instrument we must separate off from the original system and look at some property such as a needlepoint or position from which we hope to infer something about the state of the original system. as a result of the separation of the united system into two parts neither of the separate systems world from that time ever more have a definite way function each will be in an incoherent mixture of single system pure case states one can interpret this as a rising from the on. uncontrollable interaction between the two parts of the system during the time that the the. it's that they were united are a this is similar to what would happen in case one it's a random perturbation were applied to a single system if you had a single system in the one on probation the system would remain in a jerk a state but if it is your letter. and the operation and didn't know which would have to make an ensemble and you would have a mixture of a number of writers on this subject of assumed that after the separation the measuring system would have a definite way function with a definite phase relationship between various so complements which were being. rather than the total ways function this would leave them with the unwelcome situation of an essentially classical measuring instrument which might be in a state represented by a definite superposition of several legal point of states. of the transfer of attention alluded to above from the system of interest to the combined system and then to the measuring instrument only postpones the need for understanding the most from a process which surely becomes more difficult as the system becomes larger and larger. ultimately one would be led to consider still larger system such as the electromagnetic field of optical radiation the right to know and optic nerve of the ri the brain the mechanism of consciousness and eventually the whole universe. for the measurement a position of an electron within an atom i adopted for my liking sixty eight lecture any method which is the quantum mechanical transcription of a classical one that might be used to determine the probability distribution for us lawyer in a row. in one would quickly grat book great clasped one's fingers around a small region that point exhibition on and find out by some subsequent but not on quantum mechanical operation whether one had caught of an electron or a flight or not. process would be repeated many times for similarly prepared adams to build up a probability distribution this represents a rather destructive procedure as the electrons way function is disturbed even a theory electron is not found when an electron is found or cut one electron his court one will. have prepared the state of a very well localized particle. and though but that is of no help for solution of the original problem on most of the occasions an electron will not be caught but its way function in the room will nevertheless the severe seriously affected by the effort. a it is here that the reduction hypothesis runs into trouble if the electron is caught its status pretty well known that might be thought to match the reduction hypothesis maybe so but the state is out of a different problem than the one we were supposed to be considering. of the we have engaged in preparation not measurement if the electronics not caught the future development away from action is disturbed and of its gravity waves were trying to detect or something like that tone will be serious problems of wind is similar. considerations are applied to gravity way detection the ensuing complications are highly undesirable. i should mention that in his nineteen thirty three book mathematical foundations of quantum mechanics phenomena give a quite different measurement a quite different method for measuring a position coordinate which had the advantage over the one i've just described you'll have more faithfully modeling a conventional measuring apprentice the system of interest. had canonical variables little xom little p the measurement system had variables capital acts and capital p.. the interaction hamiltonian was taken to be proportional the product little x. capital p. and this would be very hard to realize in practice but no i wouldn't quibble built out but what i would complain about is that except in an absurd limiting case the method does not have void the conversion of the way function interested. just to call mixture. and therefore the a lie processes so of sales but this was not recognised. but let us now consider a system which at the time of measurement a piece of and was described by the two states superposition way function which we have their at later times the way function will evolve according to the shorting require asian. into away function like this the which differs from the form above by the presence of two exponential factors which have an absolute magnitude of one but a phase the depends on the time elapsed after the time of measurement t. minus to subsume would be the time elapsed. and the notice that the probabilities for funding the of electronics state one or state too. the are given by the same expressions as before and they are independent of the time because the exponential factors have you are marginally we will have to repeat this whole operation many times in order to determine the values of the probabilities piece about the different members of the ensemble could easily have different waiting time. times no doubt this would. it's all for the bring this up. the different members of the ensemble could easily have different waiting times no doubt this would happen quite naturally while we were thinking about how we could determine their energy values that would of course convert the pure case way function into a statistical mixture of randomly phase way functions which would be destroyed by a density matrix. instead of a cure case we function well i have to discuss the way that we would do tell whether the east adam was in state one or two when that's done with a stern girl locked up for us which we can think of as being a kind of coupling of the system to a system for measurement and though. that discussion is pretty well known. if so that so i think that i shouldn't to take the opportunity to go on until the appointed time for the termination of the lecture of the but to. the the conclusion with which i would like to leave you is that though when one is starting a year the motion of a massive cylinder of surly microscopic size. it is going to be awfully hard to have no the hamiltonian on the cyst acting on the system and if you do make a measurement you will have to take into account with exquisite persuasion. the the. the introduction of phone any additional term some hamiltonian and no matter what you do or you will lose any knowledge of the way function of the osce later the two that you might have had to begin with so that. as the measurement procedure goes on looking again and again to see how the gravity waves so evolving it will be necessary to take into account the fact that the way function of the system of interest is becoming even less a picture a case where a function of might have been. and the result will be that don't know the the the calculation will have to be don't all over again a cave some form have made a calculation on the basis that after every little motion of the same made late could say that the wave function had collapsed to the. value that it would have failed if they had the system in oregon state but so the prestigious for getting a system in oregon state of energy are sufficiently elaborate to play would not be able to do the out of. furthermore in order to conduct the procedures that quantum mechanics recorders they would have to have an ensemble of gravity waves detectors and they would be well off if they had an ensemble of gravity waves falling on the system and the gravity waves something that you take when you got hurt and the you can't be sure the next will be the same. kind of way of so the final conclusion is that they will not be to quantum limit but let them come and tell you about how they differed. and so on.
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