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Schrödinger's Cat

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This is a general comment to the long list of Lindau lectures on quantum mechanics given by Willis Lamb. He was one of the many Nobel Laureates who really fell in love with the concept of the Lindau meetings and participated in no less than 19 meetings. Beginning his long series of lectures in 1959, he continued lecturing almost until the very end. I remember acting as chairman for his last lecture, which was given in 2001 and it was quite clear that he regarded himself as at home on the stage in the Lindau lecture hall. If I had not had a meeting program to follow and therefore had to stop him, he would easily have spent another hour giving his lecture ”Quantum Mechanics Revisited”. Because he was really interested in quantum mechanics and wanted to explain it in detail to the young audience, just as a teacher wants to explain something to his students. Of his many lectures, no less than 8 are about quantum mechanics, including lectures on Schrödinger’s cat, quantum mechanics for philosophers, and super-classical quantum mechanics. But his range of interests and topics was even wider, including experimental atomic and molecular physics and several other areas of physics. The text he read for his 1982 lecture, e.g., was first entitled “On the Use and Misuse of Quantum Mechanics”, but was changed to “Quantum Mechanics: Interpretation on Micro Level and Application on Macro Level”. This is a topic, which has 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 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 waves 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 the 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 non-demolition measurement. Lamb argued that this technique would not work and that the detector would not reach the quantum limit, as proposed. As of today (2014), no gravitational waves have been detected. In 1985 Lamb lectured on “Schrödinger’s Cat”, another topic of historical interest. As is well known, Schrödinger invented his cat paradox to show that the probabilistic interpretation of quantum mechanics led to very strange results that he didn’t believe in. Lamb was critical of this particular aspect of Schrödinger’s work, but since he admired other aspects, he also gave a long list of positive things that Schrödinger had done. One can maybe understand Lamb’s interest in quantum mechanics and appreciation of the probabilistic interpretation better by noting that he described himself as grandson to the inventor himself, Max Born. The reasoning goes as follows: Robert Oppenheimer was a student of Born and a teacher of Lamb. Apparently Lamb had approached Born at the Lindau Meeting in 1959, introducing himself as being Born’s grandson. One can maybe understand that Born, then around 75 years old, was not so amused by suddenly finding a new grandson around 45 years old! Anders Bárány
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Transcript: English(auto-generated)
I find it very hard to believe, but I believe the record shows that this is the ninth time that I have been to Lindau, starting in 1959.
I was lucky in my career in that I did something useful when I was fairly young and therefore got a Nobel Prize while I was a lot younger. In fact, it was 30 years ago.
I wasn't eligible to attend the first Lindau conference as a physicist in 1953, and so I wasn't asked. I might have been eligible to attend it in 1956, but I was on my way from California to England at that time
and either didn't get invited or was overlooked. In 1959, I did get to go. I have only missed one conference of the physicists in the intervening years,
and that was something that came up that kept me from coming. I'm sorry to have to read it to you, but my eyesight is not as good right now. In a month I will have had an operation that makes it much better. 1985 is the 60th anniversary of the birth of quantum mechanics.
60 years is a long time. Quantum mechanics was founded in 1925 by Werner Heisenberg, Erwin Schrodinger, Paul Dirac, and a year later Max Born added the essential probability interpretation for the wave function.
With Dirac's death a few months ago, all four of the founders are gone, but their work will be remembered as long as science is a part of our culture.
Heisenberg attended eight of the physics conferences, and I met him at several of those. Heisenberg also went to some of the other conferences in between, so he was here at times that I could not have been here.
Max Born attended five. He also was here more to talk to chemists and medical people. Dirac attended every single physics conference starting in 1953, a total of eleven altogether.
I wish that he were here today. Now, when I have told you about the founders of quantum mechanics, I feel I should mention something about the other people who made enormous contributions to the subject.
First of all, let me say a little bit about Schrodinger. As far as I can find the record, he did not come to any of the conferences in Lindell. However, some years ago his wife was here, and I had always assumed that Schrodinger had been here,
but I can't find it in the record, so perhaps he wasn't. Now, in the course of my lecture about Schrodinger's cat, you may get the impression that I am critical of Schrodinger, and so I would like to put the record straight by saying something about what kinds of things he did do,
for which I have no criticism whatsoever. First of all, he found the Schrodinger wave equation. He got that from the variational principle. He didn't use the variational principle very much except to get the wave equation, but, of course, starting from variational principles is a good thing to be doing.
We heard that as recently as yesterday. Among the things that Schrodinger did was to find a relativistic form of quantum mechanics, and he made great contributions to it. It wasn't as good as that which was made by Dirac,
but it was still a very important thing to be doing. Schrodinger found solutions of the wave equation that were very instructive. He found the wave packet for a free particle.
He didn't like the result of the calculation because the wave packet spread, and he would have preferred that a wave packet should represent something more classically visualizable as a moving particle, and it didn't come out that way. Consequently, he didn't like the probabilistic interpretation of quantum mechanics very much.
But he was not alone in that. Schrodinger wrote, I believe it was in 1955, a book of essays called What is Life? And he made very insightful comments in that book.
I'm sure I would criticize some of it if I had the time, but it's a remarkable book. Schrodinger gave the first quantum mechanical derivation of Heisenberg's uncertainty principle. It may come as a shock to some of you that in Heisenberg's paper in 1927
on the uncertainty principle, he did not use one single feature of quantum mechanics. It was done entirely with non-quantum mechanical physics. Good physics, but not quantum mechanical. And it was Schrodinger who gave the derivation using quantum mechanics.
Now, here is a remarkable thing in my view about Schrodinger that hardly anybody would know about. In about 1915, he wrote a paper on the vibrations of a chain of particles, a non-linear chain.
In other words, a problem in non-linear mechanics, which is a popular subject nowadays. Had he pursued the solution a little further, he would have discovered solitons. Solitons are solutions of non-linear wave equations that have disturbances that move along and stay together.
In the wave mechanics that he worked on later, the wave packet that he had came apart. It came apart because of what we would call dispersive effects. If you combine the dispersive effects with non-linear effects, then you can make a wave packet stay together.
And it always seemed to me a very fortunate thing that Schrodinger did not come to that realization, because if he had, it would have set the course of physics back by perhaps 10 or 20 years. But fortunately, he did not see what he could have done to make a particle stay together in quantum mechanics.
Now, besides the work of the four founders of the theory, who after all have to be chosen a little arbitrarily,
there were a number of other people who contributed mightily to the theory. The theory's contributions involved the density matrix. It turns out that not all of quantum mechanics is to be described by wave functions. But in some cases you need statistical aggregates of wave functions that can be described by some mathematics,
given the name density matrix. These were introduced into physics, I think first by Lev Landau in 1927, the same year by Johann von Neumann, as he would have been called then, in 1927.
And then Dirac in 1930 independently discovered these same kinds of things. And the density matrix plays a very great role in quantum mechanics, but unfortunately it didn't play a great role in the thinking that people did about the subject until much later.
In 1927, Dirac gave a quantum theory of radiation and developed a relativistic Dirac wave equation. And the quantum theory of fields was perhaps spelled out in fullest glory by Heisenberg and Pauli around 29 or 30.
When you consider such a problem, you have an infinite number of degrees of freedom. And that leads to difficulties which have to be superimposed on the difficulties that quantum mechanics provides free of charge.
Now, perhaps I could jump all the way up into the late 40s. Richard Feynman introduced the formulation of quantum mechanics which involved things called path integrals. And the path integrals, as we heard yesterday, are currently a very much in thing.
Perhaps I can give you a little pre-history there that will amuse you. There was a Hungarian physicist in 1925 named Cornelius Lunksos. And he invented, by what methods I don't know, a formulation of quantum mechanics involving integral equations.
There were the Heisenberg-born Yerdon matrix mechanics and the Schrodinger Wave mechanics. And Dirac saw how to put that all together and make quantum mechanics.
But Lunksos made use of integral equations. And he wrote an account of this and sent it to Pauli, and Pauli discouraged him from publishing it. Therefore, this is a hardly known part of the history. But that isn't the end of it.
In 1927, an American physicist named Kennard, who taught for many years at Cornell University, wrote a paper in the Annulander Physique in which he solved all of the soluble, all the problems in quantum mechanics by using Green's functions.
And Green's functions are very, very closely related to Feynman path integrals. And, essentially, except for one little detail, Kennard discovered the Feynman path integral. The one little detail was that he divided the motion up from time t1 to time t2 into three parts, two parts.
Whereas Feynman took little slices. And if you just redo the Kennard theory using infinitesimal time slices instead of big leaps,
you get, with some rather trivial mathematics, the Feynman path integral. And, incidentally, Dirac had come to very similar things in the later editions of his book. Well, now I think I have done enough about explaining his historical remarks.
I have to work in the direction of Schrodinger's cap. In 1925, I was twelve years old and in the eighth grade of school, about ready to begin the study of algebra. I delivered newspapers in those days and I always read the headlines very carefully,
but somehow I missed the announcement of the discovery of quantum mechanics. This was in California. By 1935, I had learned enough quantum mechanics to start doing research on that subject. My thesis advisor was Robert Oppenheimer, who took his doctor's degree with Max Born in Göringen in 1927.
Well, in a very real sense, my father was Robert Oppenheimer. And his father was Max Born. So, during one of the Lindau conferences, I went up to Born
and tried to explain this to him that I was his grandson. And he didn't take it too well because I don't think he liked Oppenheimer very much. So, why should he like one of the lesser offspring?
Well, anyway, I learned a lot about quantum mechanics in Oppenheimer and a great deal of quantum mechanics from other theoretical physicists, too numerous to name here, who worked on quantum mechanics after 1925.
And with all of their help, I did not learn as much as I wanted to about the physical significance of quantum mechanics. I have had to try to fill in some gaps for myself and hope that some of the younger and older students in today's audience
may find my remarks helpful, and if they don't, I hope they will tell me why not. My title today, Schrodinger's Cat, is a timely reference to a book published last year.
Unfortunately, I'm not the artist. Now, I don't know whether you can read the fine print, but I'm going to read this to you, so you don't need to read that.
I have to have the lights on so I can see. Now, this book of John Gribbon's was called Inferts of Schrodinger's Cat. Gribbon took a Ph.D. in astrophysics from Cambridge University. I don't know whether he ever heard any of the lectures on quantum mechanics
that Professor Dirac from time to time gave. Unfortunately, I haven't any easy way to find out, except to ask Gribbon. Gribbon is now a consultant editor for the New Scientist magazine, published in England,
and a writer of semi-popular books on science. The subtitle of his book is, and now I'm reading some of the fine print, Quantum Physics and Reality, and the cover claims that it is a fascinating and delightful introduction to the strange world of the quantum,
absolutely essential for understanding today's world. I can agree with some of that rather immodest claiming. Gribbon's book is well written, and it is quite entertaining.
However, it has a number of non-trivial errors. My opinion that there are flaws in his physics seems to be supported by two reviews of the book that I have read. One by Sir Rudolf Peierls in the New Scientist magazine, and another review by Russell McCormick, who has written a remarkable book
about the history of an imaginary German classical physicist, who grew up in a time between Maxwell and Heisenberg. Well, in 1957, a student of John Wheeler's, Hugh Everett,
introduced the many universes interpretation of quantum mechanics. I have no time to deal with such an inconvenient fantasy, which, as far as I know, is not shared by many physicists. But I have to warn you that Gribbon rather favors this approach to quantum mechanics.
It may be more appropriate for the astrophysics of the Big Bang, than for problems dealing with a smaller part of the universe. But it is quite possible to read Gribbon's book and simply skip over any references that he makes to the many universes,
so it is still an interesting book to look at. To me, it is a strange fact that many famous physicists did not like the dominant role of probability theory in quantum mechanics. Among them were Albert Einstein, Louis de Broglie and Schrodinger,
and, in later times, David Bohm. It is well known that Niels Bohr and Einstein had many arguments on the subject of quantum mechanics, and they considered many Godanken, or thought experiments, including the two-slit diffraction experiment, which has many forms.
Fifty years ago, in other words, ten years after quantum mechanics got started, Einstein, together with Boris Podolsky and Nathan Rosen, published the famous EPR paper, which is named after the initials of the authors.
This paper deals with a system of two particles, which are somehow joined together initially and then, for some reason, come apart and are separated. That leads to a paradox that appeals to some people.
My feeling is that it is easily dealt with and one does not need to lose any faith in quantum mechanics at all. In fact, one should have his faith strengthened, if anything. But I cannot talk about that today. However, in that same year, 1935, Schrodinger published his famous CAP paper in Nacht der Wissenschaftung.
Grubin's book claims that Schrodinger was a German, perhaps he was, but I think he lived in Austria and was there at that time. Later he became Irish. I have a firm belief that none of these problems, none of the paradoxes, were properly treated according to conventional quantum mechanics
in the discussions of these distinguished people. And to save time, I am only going to deal with the CAP problem, but the arguments perhaps will give an indication of the approach that I would take to any of those experimental situations,
imaginary experimental situations. Let me first remind you of some features of quantum mechanics. Quantum mechanics is a generalization of classical, non-relativistic mechanics. The first thing to do in this subject is to define the system of interest.
That means to introduce the coordinates and velocities, or momenta if you are being more sophisticated, of the various parts of the system. There is usually a certain degree of choice here. If the system is taken too large, the mathematics will be too difficult. If the system is taken too small,
some important features of the problem will be neglected. In quantum mechanics, a physical system can, I underline the can, have states which are described by wave functions. These things may be complex quantities. In other words, they contain the square root of minus one,
the imaginary quantity. Wave functions can be used to calculate probability distributions for various functions of the dynamical variables of the system. Wave functions are functions of the coordinates which describe the configuration of the system, and they depend on time in a way described
by the Schrodinger time-dependent wave equation for the system. For a reasonably isolated system, there are some so-called stationary states, but a much larger number of non-stationary states are possible. If the system is not isolated,
or pretended to be isolated, some extra terms will have to be included in the Schrodinger wave equation to allow for external disturbances, or the notion of the system will have to be enlarged to take more of the universe, but hopefully not all of it, into account.
Any observation or measurement made on the system represents a disturbance which should be taken into account in the analysis of the problem. The four founders of quantum mechanics did not tell us much about how measurements are to be made, and what influence, if any, the result of a measurement
might have on the subsequent history of a system. In his 1930 book, Principles of Quantum Mechanics, Dirac postulated that a measurement of an observable would lead to a result equal to one of the eigenvalues,
or characteristic values, of that observable, and would leave the system, miraculously, in a new state whose wave function was the eigenfunction of the observable corresponding to the measured eigenvalue. Von Neumann, in his 1932 book,
which was based on some article he wrote in 1927 in the Goethe and Nachricht, a mathematical philosophical class, in that book he expanded on Dirac's idea, or perhaps preceded Dirac,
I've never been able to tell who came first. He distinguished between two ways in which wave functions could change with time. A, causally, in accordance with a time-dependent Schrodinger equation, and B, a-causally, as a result of a measurement.
Both of these great men left many answers, many questions unanswered. I lectured in Lindau in 1968. I lectured every year I came, but this was one particular lecture. I lectured on the preparation of states and measurement in quantum mechanics.
I had both Born and Heisenberg in the audience. I won't tell you what they said. And I lectured again in 1982 about my unhappiness with Von Neumann's wave function reduction hypothesis. If I return today to the measurement problem,
it is because I learn a lot from thinking about the problem and from talking to a perceptive and critical audience. A very important principle of quantum mechanics was recognized by Wolfgang Pauli in his 1933 Hunt, Rupfel, Zeke article.
This is the superposition principle. For reasons which will be apparent shortly, we denote by L and D. I hope we'll show up a little bit on that. Yes, it's probably going to show up a little bit.
We denote by L and D two possible, suitably normalized wave functions for the system. And L and D will be taken to be orthogonal to each other, which means in a non-technical sense that they are very different functions.
The superposition principle states that an unlimited number of other possible states of the system will exist, which are of the form called the superposition states. And the wave function there is taken to be a linear combination of L and D.
In other words, you multiply the L wave function by a constant factor, or factor A, and the D part of the wave function by a factor B, an amplitude B. The A and B can be any two complex constants
whose sum of squared absolute values adds up to unity. If the wave functions L and D happen to be wave functions for stationary states, then F will in general represent a non-stationary state, which is neither L nor D, but something in between,
with lots of quotation marks around the in between. Consider a system which is in state S. According to the conventional discussion in quantum mechanics, if an experiment can be devised which asks a question, is the system in state S,
that experiment is supposed to give the answer yes. For a system in that same state S, if you ask a different question, you get a different answer. And the answer that you will get is that if the experiment that you use is devised to ask the question
whether the system is in state L, then the results for any one measurement on the system whose wave function is really S may be either yes or no. In a series of repeated measurements for an ensemble of systems, each being in the same state S, the probability for getting the answer yes
to the L question is the absolute value of A squared. The absolute value of B squared would be obtained for the experiments that we're trying to find out if the system was in state D. At this point, we should not worry
about how a system is to be put into a given state S. Furthermore, we should not worry about how experiments are to be designed to get information about the state of the system. I gave some examples of these things in my 1968 lecture, which incidentally got published in Physics Today a year later.
And I will later discuss some simple examples of such measurements which are relevant to the CAP problem. Now we finally come to the CAP problem. Do I have any time left? A little. Imagine a box that contains a radioactive source, a detector that records the presence
of radioactive particles, a Geiger counter perhaps, a glass bottle that contains a poisonous gas such as hydrogen cyanide, a hinged hammer, maybe that's not shown well enough in the picture, held above the bottle by a thread which will be cut by a knife if and only if the counter clicks.
A living cat in good health is placed in the box. The apparatus in the box is arranged so that the detector is switched on just long enough for there to be a 50-50 chance of a click of the Geiger counter.
There's a radioactive nucleus that decays and the lifetime of that radioactive nucleus is such that for the time of the experiment there's a 50% chance that there'll be a radioactive decay. If the detector records the decay, the thread is cut,
the hammer falls, the bottle breaks, and the hydrogen cyanide gas kills the cat. Otherwise, the cat lives. We have no way of knowing the outcome of this experiment until we open the box and look inside. We somehow couldn't hear the click of the counter. What is the problem?
We're told that Pandora opened a box. Did her curiosity kill a cat? We are not told. There's no problem for a classical physicist. He might say that what happens is the will of God. Or, perhaps, in the language of an American comedian,
he might say, it is just the way the cookie crumbles. If the classical physicist is a gambler, he has experienced excitement without calling on quantum mechanics when a card is turned over or a ball settles down
after the spin of a roulette wheel. The problem exists only for a person who knows a little quantum mechanics. A little. Not too much. Just a little. And who believes that quantum mechanics is universally applicable and applies it to the cat experiment.
It's not unlike the situation of somebody who believed that classical mechanics was universally applicable in the years after Newton. A lot of people did believe that and it changed their whole philosophical and theological outlook in various ways which were not fully justified, as it turned out.
Well, such a person who believes those things that I mentioned believes that when the box is opened, the box-cat system is described by a way function, like S, which is a sum of two other wave functions like L and D.
One of these, namely L, represents a living cat. Also an undecayed nucleus, an unclicked Geiger counter, an uncut string, and so on. A hammer still.
And the other, the D part, represents a dead cat with a decayed nucleus. And a broken bottle, etc. The constants A and B of the superposition are each taken to have absolute values of one over the square root of two, so that the probability of finding a live cat is 50%. Until the observer looks to see
whether the cat is alive or dead, the wave function is a superposition, a linear combination, of the two wave functions. The cat may be alive or the cat may be dead. He may be happy to accept von Neumann's sudden change of the wave function,
so that the wave function becomes L, corresponding to a living cat. Well, I've told you what the paradox is. If you think it's a paradox, then maybe I can help you. I now return to the application of quantum mechanics to the cat problem. First of all, I have to tell you some things about quantum mechanics
that dynamical systems can exist in states. However, in general, this means that some process has prepared the system to be in that state. That's a non-trivial matter and you don't find it
happening easily. It is very unlikely that a given and complicated system will have a definite wave function. The best that we can do is to describe the system by a statistical distribution or ensemble of states.
The phrases pure case and statistical mixture are used here. The density matrix ought to be used in discussion. Not one word about density matrices was used in the Schrodinger article and although von Neumann's book is full of discussions about density matrix,
unfortunately he didn't apply it to the measurement problem A pure case is all too easily converted into a mixture by any very small erratic disturbance while a mixture can never be put back into a pure case except by some selection process of a desired member of the ensemble
and that completely wipes out the memory of the past. One is reminded of Lewis Carroll's Sumpty Dumpty, who once broke and could never be put together again. In the case of the cap problem, the system should certainly include the atoms, nuclei,
molecules and macromolecules contained in the box and all of its contents. The model should make provision for the opening of the lid and the disturbance of the system brought about by observations on the opened box and its contents. We will have at least a million, million, million, million
degrees of freedom. No such problem can be solved analytically or numerically except in the most trivial cases. A living cat is not an isolated system. Hence, the cat-box system is not isolated. And even if it were, it could not be assigned
a wave function, but only a mixture of wave functions. Even if it could have disturbed the system enormously. At the very least, it would randomize the complex phase angle of the ratio of B over A that characterizes
the linear combination wave function over there. The combination of D for dead cat and L for living cat. Such a mixed state is an incoherent mixture of the two states of living and dead cat.
If I were to try to talk about a problem of coin tossing using quantum mechanics, I might be tempted to talk about wave functions that were superpositions of wave functions for heads up and tails up. The same kind of information about phase angles would be important there. I will make a few more remarks
about the cat problem. It is a messy, rather pointless problem. There are at least four distinct reasons. First reason, the contemplated treatment of the cat is inhumane. Second, the possible death
of the cat serves no useful scientific purpose. Third, there is no mention at all of the well-known fact that cats have nine lives. But in my view, the overwhelming sin is that,
and it is a different kind of bad taste, if it is bad taste, is that to propose a complicated problem when a simple one would do is that. There is a simple problem that has all of the essential physical features of the Schrodinger paradox and does not involve
any of the complications. Now, let me tell you one way to simplify the problem. Simply take out all of the, pardon the expression, garbage in the box. You don't need this. You don't need the string. You don't need the hammer. You don't need the knife.
You don't need the hydrogen cyanide. You don't need the glass bottle. You do need a cat, perhaps. And there is nothing important about having the 50% probability. A probability of one part in a million would be enough. So, suppose you go to your actuarial life
insurance tables and determine that a night in a box is the time for a typical cat to a probability of one part in a hundred thousand that the cat will die. That is, for instance, how many of you would bet with certainty that I will
appear for the tenth time in Lindell? It's possible, but by no means certain. I'd like to. Well, anyway, all you have to do is put the cat in the box without any cyanide at all. If the cat dies, it's because the cat died.
Well, there's some kind of a random process going on there, and it isn't quite the same as the random process that led to the radioactive decay, but as far as the present state of theory goes, it might as well be the same. However, that's still a very complicated problem because I don't like living cats as a problem to deal with
density matrices and all sorts of techniques that would be very hard to carry out for ten to the twenty-fourth degrees of freedom. We can easily get into a simple situation
which would leave Einstein and Schrodinger unhappy. The above expression, the expression for the wave function S equals A L plus B D has the appearance of the kind of wave function considered in the so-called two-level problem.
In the cat problem, one is foolish enough to think that L and D represent pure case states of the cat. In the simpler case, the wave functions L and D are not wave functions of a complicated system at all, but of a system with one degree of freedom.
The theory of a number of very important problems can be reduced to the theory that one half provides one such example. The one-particle system may in fact have other degrees of freedom such as translational motion, but for some applications only the spin degree of freedom
is important, so therefore the other degrees of freedom don't matter. There is a very great deal of experimental work on two-level systems and it is clear
that nuclear magnetic resonance is an example. That's an application of a two-level problem. The recent development of nuclear magnetic resonance tomography could easily win a Nobel Prize or two. The theory of masers and lasers makes important use of two-level problems.
The Nobel Prizes of Otto Stern, I. I. Rabi, Felix Bloch, Nicholas Johns, Nicholas Bazoff, Alexander Prokoroff, Arthur Shallow, and Nicholas Blumbergen are all related to the two-level problem.
I would not be here today without it. Ms. Bauer told us on Monday how the two-level problem plays a very useful role in elementary particle physics. Let's go back to an early atomic beam experiment
in the 1920s. They heated silver in an oven and they made a beam of silver atoms that they passed into a vacuum chamber. I will add a few experimental facilities that they did not have in the 1920s, but they could have them now. The atomic beam is directed along
the x-axis and increases in magnitude as z goes from negative to positive. The beam of atoms is split by this inhomogeneous magnetic field into two beams,
one moving slightly up in z and the other moving slightly down. Quantum mechanics provides a simple explanation of the experimental findings. The atoms in one beam have a spin orientation quantum number
in the other direction of plus one-half and in the other beam of minus one-half. Individual atoms can be detected and it is certain that whether an atom goes into the plus one-half beam or the minus one-half beam is determined by just the same kind of random process
that Schrodinger invoked for his radioactive decay. No experiment can be devised This, in my view, is the problem that Schrodinger should have been considering. The CAP problem just dirtied the water. It is bad enough as it is.
Furthermore, double or compound Stern-Gerlach experiments can be made. The atoms of the upper beam might be passed into another inhomogeneous magnetic field,
in just the very peculiar way that quantum mechanics will predict. In 1949, shortly before he died, Einstein explained quite clearly why he did not like probability in quantum mechanics. He wanted a theory of the radioactive nuclei which could predict
ahead of time when a given nucleus would decay. Perhaps he had the hope that a hidden variable theory would have at least as hard a problem with the silver atoms of the Stern-Gerlach experiment. Now, through the experimental work of John Bell
and the experiments of Alain Aspect in English, but I could pronounce it in French if I took a little more time, we know that it cannot be done. Quantum mechanics really does work in simple cases and the probability interpretation
is essential. I think it is high time that we recognize that it is inevitable that that should be the case and that we learn to enjoy it. Of course, we have had a genetic code being developed for
who knows how many million years which has made us able, and maybe it's a good thing, to be unaware of the microscopic phenomena that are underlying our existence.
Well, just a few more sentences. All of those paradoxes that I mentioned and more can be discussed in a very good way with quantum mechanics, but it is very important to have a certain degree of good taste. The problem should be made as simple as possible.
Everything that's in the problem should be taken into account. If in midstream you want to change the situation a little bit, you've got a new problem to solve and you'd better be very, very careful about doing that properly according to quantum mechanics. Obviously there are many unsolved problems.
The structure of quantum mechanics has changed in going from 25 until today. One of the problems that interests me most is the problem of how do we deal with continuous measurements
of a quantum mechanical system that is pretty quantum mechanical but on the verge of being classical. Technology isn't quite up to this point yet, but we're getting close. For instance, the gravity wave detectors that are contemplated will, to some degree,
have to be treated with quantum mechanics, and yet they are also highly classical systems. Electrons can be trapped in a kind of macroscopic atom made of electric and magnetic fields, and it's possible to follow the career of one electron for ten months
in a small apparatus like this, and somebody not turned the wrong switch. That's in the work of DeMelt and Gabrielle in Seattle, Washington. The problem of continuous measurements on a macroscopic system
is one that I am working on currently, and I think with enough success to please me, but I haven't anything like the amount of time to tell you about it today. Thank you.