Paul Dirac (1976) - Basic Beliefs and Prejudices in Physics

I am very happy to be here once again in Lindau. I have attended every one of the physics meetings and I have given a set of lectures at these meetings discussing basic questions in physics. I would like to continue in that way to discuss basic questions in physics, but today I would like shorten my talk a little because I want to tell you also about an important discovery that has been made in the place where I work, that is in the Physics Department of Florida State University at Tallahassee. This is the discovery of some new elements and I am very happy to be able to tell you about it. The question of basic beliefs for physicists is very important for those who are doing research. They must each have some beliefs which they hold onto and discuss and maybe criticize and sometimes they find that one of these basic beliefs is wrong; it then becomes a prejudice and they say one has to discard this belief and set up a new physics without it. That is the way an important discovery comes about; it might even be a revolutionary discovery. Now, Einstein's important discoveries were of this kind. Einstein criticized the notion of absolute time and simultaneity. Previously, people had taken it for granted that there had to be an absolute time. In fact, it was very essential for some of the laws of physics as they were then understood, in particular, Newton’s law of gravitation which was based on action at a distance and that could be only understood with reference to an absolute time. Newton’s action at a distance was criticized by philosophers on the grounds that a body cannot act in a different place from where it is. However, it was found pretty soon that the action at a distance was not really an essential feature of Newton's theory. One could reformulate Newton's theory in terms of a field using Poisson’s Equation, a field which spreads out and which requires action only from one point to a neighbouring point. There was thus an alternative way of describing Newton's Law of Gravitation, on the one hand the action at a distance, on the other hand action through a field. Now you might think that with these two alternative forms, both of which are mathematically equivalent and which both give the same results applied to any example, you might think that these two forms are equally good. But that is not necessarily the case. When one has two forms of a theory which give equivalent results because one of those forms may suggest improvements and developments, Which the other form does not suggest. In the case of Newton, there was the action at a distance form for his law, which did not suggest any possibilities of improvement or development. On the other hand, the action through a field did allow developments and ultimately led to Einstein's reformulation of the law of gravitation. Einstein was led from his deep thinking to suppose that, action, to suppose that the idea of simultaneity has to be abandoned. He was able to figure out that there is really no experimental way of telling when two events are simultaneous. The best one can do is to send signals with the velocity of light. Now light travels extremely fast and the time taken for light to travel from one place to another is quite unimportant, so long as one keeps to phenomena on the earth. But astronomically, the time taken for light to travel from one place to another may be quite large and owing to the delay produced by the finite time intervals, one cannot give a meaning to events being simultaneous when they take place a long way apart. Einstein was led to a new idea of geometry in which the notion of simultaneity was abandoned and instead he had as his absolute, instead of absolute time, the velocity of light. That led to Einstein's Special Theory of Relativity, which is best understood as supposing that space and time form a four-dimensional world, which has a geometry slightly different from Euclid's geometry. The difference, which is expressed very simply in this way in Newton's geometry we have the theorem of Pythagoras, the square of the length of the hypotenuse is equal to this distance squared plus this distance squared. You replace that by having a geometry in which this distance squared is equal to this one squared minus this one squared. You bring in a minus sign that leads to a geometry which is in many ways analogous to Euclid's geometry, but is essentially different in some ways and it is called geometry of Minkowski Space. On the basis of this new geometry, Einstein set up a theory where there is no absolute time, no absolute simultaneity, but he still had the problem of bringing in gravitation. In order to do that, he had to make another drastic change in our basic ideas, namely he had to suppose that space and time are curved instead of being flat, a flatness which one had assumed automatically right from the beginning when people first studied space at all. That flatness is just a prejudice, which has to be given up. One has to think of space and time as forming a curved manifold and this provides the basis for gravitation. The reason why a body falls is because it keeps as closely as it can to a straight line, but the space is curved, and that leads to the body taking a path something like that. This was a revolutionary idea. I don't think people altogether grasped the importance of it because it has the immediate effect that antigravity is impossible. Many people have imagined there could be antigravity, in which bodies fall upwards instead of downwards, but that is quite impossible in terms of Einstein's ideas, because there is no question of a force pulling a body up or down. Every body moves as closely as it can to, it keeps as closely as it can to a path which is a straight line in the curved space, and that involves the particle, the body moving like this. Well, that shows the important ways in which Einstein influenced our thoughts. Now perhaps I should tell you about my own basic ideas. I started physics at a time when people were working with Bohr orbits, and I was very excited about Bohr orbits and thought, and thought that they were fundamental in nature and that they would explain everything in the atomic world. One just had to understand how the Bohr orbits interact with each other. I was working on this for two or three years and my ideas led nowhere, because I had the wrong basic ideas. The advance was made by Heisenberg, who had different basic ideas. Heisenberg had the very good basic ideas that one should base one's theory on quantities which are closely connected to observation. Now we cannot observe Bohr orbits at all, and for that reason, the variables that describe Bohr orbits could not be important with Heisenberg. Instead one has to work with physical quantities, which are each associated with two Bohr orbits. Heisenberg set up a new theory in terms of these quantities related to two Bohr orbits. These quantities are understood mathematically as the elements of a matrix and that led him to a new matrix mechanics. It was a mechanics in which we have to depart from the usual equations of mathematics, which assume that all the dynamical variables commute with each other. It required the setting up of a new dynamics in which a product U times V, the product of two variables need not be the same as V time U. Well it was quite a revelation to me when this discovery of Heisenberg was set up and it showed how wrong I was previously and I felt that one had to adopt different basic ideas and it seems to me now that this basic idea one can have in physics is to suppose that physical laws must be based on beautiful equations. That is the only really important requirement. The underlying equations should have great mathematical beauty. One should look for relations in physics having great mathematical beauty. Now de Broglie had previously already shown the success of this basic idea; simply from considerations of mathematical beauty, he was led to assume a relationship between particles and waves. This relationship is very hard to explain without mathematical terms but it means physically that each article has its motion guided by waves, and the connection between the particle and the waves is provided by de Broglie’s equations, which he discovered just from considerations of mathematical beauty. It was a development of de Broglie’s ideas which led Schrödinger to his wave mechanics and that was a form of quantum mechanics which was found to be equivalent to Heisenberg's form. We then had quite a satisfactory quantum mechanics coming from this work of Heisenberg and Schrödinger, a quite satisfactory mechanics in many ways, very powerful, very beautiful, but it had the limitation that it was not a relativistic theory. It did not apply to particles moving with large velocities. In order to set up a theory, which combined the ideas of quantum mechanics and relativity, one was faced with a serious difficulty. The general quantum mechanics of Heisenberg and Schrödinger involved working with equations which are linear in the operator d/dt, the operator of time differentiation. When one tries to set up the relativistic theory, one is led to equations involving d2/dt2. Now, if one works with these equations involving d2/dt2, one is led to a quantum mechanics in which one can calculate the probabilities of events taking place, but those probabilities are not necessarily positive. A probability, which is not positive, of course, is just nonsense. In order to have a theory which gives you only positive probabilities, you have to use equations containing d/dt, not d2/dt2. Now, at the time when I was working on this in 1927, most physicists were quite happy to use the equations with d2/dt2, but I was very unhappy about it because it meant abandoning some of the basic assumptions of quantum mechanics, which really required one to use d/dt. I remember that I was pretty much alone among physicists at that time in being so dissatisfied with the current state of the theory, and it was this discontent of mine which led me to try to find an equation involving d/dt which should still be relativistic and suitable for particles with high velocity. And I did find such an equation and the use of this equation was very satisfactory in that it led to a mechanics in which all the probabilities are positive. It also incidentally led to equations for the electron which provide the spin and the magnetic moment of the electron. That was an unexpected bonus. I was not at that time looking for a way of describing the spin. I thought that it would be necessary first of all to describe the simplest kind of particle, a particle with no spin, and only after one had a satisfactory theory of the particle with no spin would one be able to introduce later on the spin. This again shows how one's ideas may lead one astray. It turned out that the discussion of the particle with a spin of a half a quantum was really simpler than the discussion of the particle with no spin. Well, there was a theory which worked very well for the electron in that it gave you results in which all the probabilities are positive, but there were still difficulties left with it because this theory allowed negative values for the energy as well as positive values for the energy. One had to have an interpretation for the negative energies because the mathematics did not allow one to eliminate them from the theory. And I was able to think of a way of accounting for these negative energy states by changing one's ideas of the vacuum. One had previously always thought of the vacuum as a region of empty space. It now seemed that one had to replace that idea. One could take as the definition of a vacuum a region of space where the energy is a minimum. That would require one to have all the negative energy states occupied by electrons. There cannot be more than one electron in any state, according to the Exclusion Principle of Pauli, so one could just put one electron into each negative energy state and that is all that one could do with the negative energy states. We then had a new picture of the vacuum where all the negative energy states are occupied, all the positive energy states are unoccupied. Then one had to consider the possibility of an unoccupied negative energy state, a hole in the distribution of negative energies. This, it seemed, would be a particle. The hole would appear as a particle with a positive energy and with a positive charge. How is such a hole to be interpreted? Well, at that time, people believed there were only two basic particles in nature. That was really a prejudice. There was a need for two particles because there are two kinds of electricity, positive electricity and negative electricity, and there had to be one particle for each of those two kinds of electricity. There were the protons for the positive electricity, the electrons for the negative electricity. So it seemed to me that one would have to interpret a hole as a proton. Now right from the beginning I felt that the hole ought to have the same mass as the electron, but there was a big difference in the mass of the proton and the mass of the electron, and that provided a difficulty which I could not understand at the time. Of course the explanation came a year or two later. One just realized that it was a prejudice, that there are only two particles. One should really have more, and the hole should be interpreted as a new particle having the same mass as the electron, but having a positive charge. And these particles are now known as positrons. The climate of opinion about new particles has changed very much since those days. One was prejudiced against new particles at that time. Nowadays people are only too willing to postulate new particles as soon as there is any evidence for them experimentally, or as soon as there is any theoretical reason why it would help to bring in new particles. There are rather too many basic new particles nowadays. Well, a piece of work independent of that, which I did at that time, was to set up a theory of magnetic monopoles. According to the standard electrodynamics of Maxwell, one has magnetic charge appearing always in the form of doublets. Any piece of matter which has magnetic properties would have positive magnetic charge in one place and an equal negative magnetic charge in another place. But simply from a study of the mathematical beauty of equations, I was led to suppose that there might be monopoles, particles with a magnetic charge of one kind only, and the strength of the monopole was fixed by the theory somewhere around sixty-seven and a half times the strength of the electric charge on the electron. This theory of magnetic monopoles has been lying dormant for a long time. People looked for them experimentally and could not find them. But the situation was changed about a year ago, when a set of, a team of four workers, Price and others, claimed to have discovered a magnetic monopole. They claimed to have discovered the magnetic monopole coming in from outer space among the cosmic rays. And the way they did their experiment was to send up a whole stack of sheets of Lexan. Lexan is a kind of plastic, and energetic particles passing through the Lexan do some damage which is shown up if one etches the Lexan plates. They had sent up these Lexan plates with balloons to a high altitude so as to get the cosmic rays before they had been disturbed much by passage through the atmosphere, and they found one example of a particle which they interpreted as due to a magnetic monopole. The reason for this interpretation is that a magnetic monopole produces ionization, which is pretty well independent of the velocity of the particle, while an ordinary charged particle produces ionization which increases as the particle is slowed up. They had evidence of a particle which produced about the same ionization at the top of the stack of plates as at the bottom, just in the way that a magnetic monopole should do. And the charge of this monopole was about two units of what my theory gave as the unit for a magnetic monopole. They published this work. They were rather rushed into publication by circumstances which couldn’t altogether control, and they published it pretty quickly without considering all the implications of it. And this work was very strongly criticized by other physicists. Chief among them was Alvarez. Alvarez proposed an alternative explanation for this particle. He thought that it had started out as a platinum nucleus and that, in passing through the sheets of Lexan, it had lost, it had undergone changes, losing some of its charge, and as a result of those changes, its ionization had not increased in the way that an ordinary charged particle would have its ionization increasing. And they thought that they could account for Price’s results in that way. Most physicists tended to assume that Price was wrong and the reason for that is that many other searches had been made for magnetic monopoles. Very extensive searches had been made in many places. People have studied all places which they could think of on the Earth's surface, going close to the magnetic poles, and they had also studied the sea, and the sediment at the bottom of the sea. They had also studied the moon rocks and all these studies showed no magnetic monopole. Now here comes Price and his co-workers who have one example which they claim is a monopole going against all the other evidence, and for that reason, most physicists were led to believe that Price was wrong and that magnetic monopoles do not exist. There is, in any case, a difficulty with the explanation of Alvarez. Price’s original paper did not give the complete results from the analysis of all his Lexan plates. There were two plates which were kept in reserve and the analysis of the etching of these two plates gave further results which do not fit in with Alvarez's explanation. It becomes very difficult to understand this track of Price by any explanation at all. It seems that one should perhaps assume that the original particle was something heavier than a platinum nucleus and even then, there are some difficulties because Price had set up an apparatus to detect Cherenkov radiation, which should be produced by any rapidly moving particle such as would be required by an explanation of the type that Alvarez was proposing, and this Cherenkov radiation was not detected. Well, that is the situation about the magnetic monopole at the present time. If you just take Price’s work by itself, it seems to provide fairly strong evidence that he does have a magnetic monopole there, and it is difficult to fit in this evidence with any other explanation. But there is the problem of how one can understand the failure to find magnetic monopoles anywhere else, in spite of the intensive searches that have been made. It seems that the only way out of this difficulty is for Price and his co-workers to try and find some more particles of this nature. And that, I believe, is what he is doing. He sees now that there's no need to send up his Lexan plates in balloons to a high altitude. One can just spread the Lexan plates on the ground because these particles have enough energy to come through the atmosphere without being very much disturbed. I believe that these experiments are underway at the present time and we should have to wait for them to get further results before we can understand this situation about the magnetic monopoles. I have to leave this subject undecided. I would like now to pass on to this new work, which has been done in Tallahassee, concerned with the discovery of new elements. Every element has an atomic number, which is the number of protons in the nucleus. There is a number one for hydrogen, two for helium and so on, and among the natural elements, that series continues up to number ninety-two, which is uranium. Now, some elements beyond uranium have been manufactured by man using neutrons produced by reactors. Man has produced element number ninety-four plutonium and a good many other elements around there, elements even going up beyond a hundred, elements hundred-and-one, hundred-and-two, hundred-and-three have been produced. But these very big ones have a very short lifetime, they are very unstable. Now, theoretical people have been studying atomic nuclei for a long time and they have set up a theory according to which the neutrons and the protons in the nucleus form shells, something like the shells formed by the electrons moving around outside the nucleus. And when you have a closed shell, you have especially stable nucleus, nuclei, for which the shells are nearly closed, will also be more stable than those for which they depart from very much from closed shells. Now, there might be some nuclei present, still heavier than the ones which have been made by man, going up to a hundred-and-three. There might be such nuclei, which could be stable or long-lived, if we had them in the neighbourhood of a closed shell. If you take nucleus 126, that would have a closed shell of protons, and you might expect such a nucleus to be especially stable, or more long-lived, than nuclei with smaller numbers. Physicists have been wondering whether such nuclei, super-heavy nuclei as they are called, do exist or not. The theories about the shells of protons and neutrons are not good enough for one to be able to decide whether these exist or not. People have been trying for many years to make these super-heavy nuclei with the help of the heavy machines, trying to get ions of elements to stick together by making them run into each other, but they have failed. Now, if you cannot make them with your machines, there is still a possibility that these super-heavy elements might exist in nature in very small amounts. And there is now evidence that super-heavy nuclei do exist in a mineral called monazite. Cerium is one of the rare-earth elements, and this monazite also contains mixed with it phosphates of other rare earths. It is a crystalline rock, and some monazite also contains uranium and thorium. Now, there exist some old mica deposits. Mica is a transparent material. Now there exists this old mica containing inclusions of small quantities, microscopic quantities, of monazite. Now, if you have a piece of mica with an inclusion of monazite, you would have something like this. This is your sheet of mica, and here is a speck of monazite in it. If this monazite contains uranium or thorium, the uranium or thorium will emit alpha rays, and the alpha rays will damage the mica around and make halos. So you get a halo around the inclusion like this. The uranium and the thorium emit alpha rays with an energy of seven or eight million volts and that energy is shown by the length of the track that one has to proceed along to get to this ring here. So one has a halo around the inclusion with a radius corresponding to the energy of the alpha rays. Now many of these halos have been found, but also a few halos have been found which are much bigger than the normal ones, halos, where the alpha rays extend out to a much greater distance. These are called giant halos. What is the explanation for them? They have been studied by a man called Gentry, who works in Oak Ridge. You will probably not have heard of him, but you will hear very much of him in the future. He has considered whether there is any other explanation for these giant halos and he has come to the conclusion that no other explanation is possible. They have been formed by some element unknown to us, which emits more energetic alpha rays than any alpha rays emitted by the known elements. And as a result of this emission of the alpha rays at some distant time in the past, these giant halos are formed. This mica in which the giant halos are found, is about a thousand million years old and maybe the giant halos were formed at that time in the past. Gentry has been studying these halos for seven years. Now there is a man called Cahill, whom also you will not have heard of probably, but whom you will hear about very much in the future, who had the idea that in these giant halos, there may be some super-heavy elements still surviving in the inclusion here. Perhaps not the elements which produced the halo in the first place, but some products of that element. There might be small quantities of super-heavy elements surviving in the halo. And he set about trying to find them. How can one find new elements? A good way would be to bombard this region with protons and examine the X-rays which come off. X-rays are very characteristic for each element. One can calculate just what the X-rays should be if one knows the atomic number of the element and that this would be a good way of searching for new elements. Cahill works in California at Davis and his laboratory did not have the necessary equipment and facilities for doing this experimental work and for that reason, Cahill came to Tallahassee, where we do have a van de Graaff machine, a tandem van de Graaff capable of producing high-energy protons and we have other equipment which would be needed for this kind of work. Cahill has been working for six months in Tallahassee. This is a picture of one of the giant halos. In the middle there’s a small particle of monazite and this is all damage, which has been done in the mica by the emission of alpha rays of greater energy than any alpha rays which are produced by known elements. This is a picture of the X-rays which were obtained by Cahill and other workers at Tallahassee from an inclusion producing a normal halo, a halo coming from the alpha rays of uranium and thorium. You notice that there are essentially two peaks in this picture, with a valley in between. This peak corresponds to the “L” X-rays from uranium and thorium. This peak here comes from the “K” X-rays produced by various other elements - rare earths and so on. In between these two peaks there is a valley, and this valley is where one would expect to find the “L” radiation of super-heavy elements, if they exist. This valley is the important region. Now Cahill and his co-workers proceeded to examine some giant halos which were sent to Tallahassee by Gentry from Oak Ridge. I heard that one of the specimens got lost in the post and one specimen, I heard, got dropped on the floor and they could never find it again, although they searched all day. However, there were six specimens of giant halos, which they had to work with. This is very similar to the previous, the valley between the two peaks, but now there is some structure in the valley shown by these irregularities here. And this structure would indicate small amounts of some new elements. One must take a closer look at this structure. This part and this part don't interest us at all. The dotted line is a sort of smoothed-out background and you notice very prominently a peak here which corresponds to element number 126. And there is the evidence for the existence of element 126. Now, this evidence was obtained perhaps two months ago. They did not immediately rush into publication, claiming to have discovered a new element. They thought it was best first to study these results and see whether there could be any other explanation for that peak. What they did was to consider all the known elements and see whether any of them could provide X-rays, which would just produce such a peak. Well there are such elements, two of them - tellurium and indium. It might be that there was some tellurium or some indium in the specimen, giving an X-ray line just there. But the spectra of tellurium and indium are both well known and if they have a spectral line here, they should also have spectral lines in certain other places, and looking in these other places, one finds that there is no tellurium present at all, and indium, there might be a small amount of indium, but in any case it would be very small, and it could not provide more than five percent of this peak here. It seems that there is no other explanation for that peak, except for some of the element 126 existing in the inclusion which makes the giant halo. This is some more evidence of the same nature. You see here very well indicated the difference between a giant halo, given by this curve here, and an ordinary halo produced by uranium and thorium here – a very pronounced difference. And this difference is shown with all the specimens of the giant halo. Here, underneath, are the spectral lines of all the known elements which could lie in this region. And one has to examine these peaks and see whether any other element could be producing the peak. In addition to the peak corresponding to element 126, occurring here, there is also a peak corresponding to element 124 here, and a peak corresponding to element 116. And in each of these cases, it seems that there is no other element, which could provide those X-rays. There is reason to exclude the possibility of other elements by examining whether these other elements are present from the X-rays Which these other elements would produce. So there is quite strong evidence for the existence of these three super-heavy atoms. There is also some weaker evidence for the existence of other super-heavy atoms - three more in fact. This shows the same results illustrated in a different way. The background radiation has now been subtracted and that gives a zero line, the middle line here, and the middle line here, and the middle line here. Now there is an upper and a lower line, which show the statistical variations which one would expect in the background. Anything going outside those statistical variations would have a probability of being some definite physical event. The top curve there refers to an ordinary halo and there is nothing there to indicate the presence of new elements. There happens to be this dip here, which is presumably a statistical fluctuation which has gone outside the normal range of statistical fluctuations. Here and here are the corresponding pictures for two of the giant halos. And you see very definitely how there are these peaks going well beyond the region of statistical fluctuations, and it is these peaks which provide the evidence for the new elements. Well, that is the evidence which has been obtained in Tallahassee and the people who have been doing this work are sufficiently confident that they have a proof for the existence of new elements and that there is no alternative explanation. They are now sufficiently confident so that they have sent in this work for publication. It's going to be published in the Physical Review Letters. That is a journal which gives prompt publication to important new work and this will appear in the July 5 number. Theoretical people have also been busy in Tallahassee revising the theories of atomic shells. They have further evidence now with the existence of these stable super-heavy elements. They have to be pretty stable because they have survived in this old mica. The mica is about 1,000 million years old and these super-heavy elements probably have a lifetime also somewhere of the order of a 1,000 million years. There is a man – Philpott – a theoretical worker in Tallahassee and a few others who have been studying these atomic shells in the light of the new data. They find that these super-heavy elements cannot themselves be the cause of the giant halos. If they emit alpha rays, the alpha rays would only have an energy of five or six million volts and that would not be nearly enough to produce the 12 or 14 million volts, which would be needed for heavy elements which are now observed, are the results of disintegration or this 160. With regard to the atomic weights, there is no experimental evidence for the atomic weights of these new elements, but Philpott and the other theoretical workers think that number 126 would have an atomic weight of around 350, much heavier of course than any atomic weight of the known elements. And I would like to say in conclusion that I have not been engaged in this work myself. I have just had the good fortune to be working in the same institute where this work was going on, and I have been able to follow all the developments and am able to see the caution with which the people are observing with their new results, and I see that they will not publish anything without having a strong conviction that it is right. Also, I am very much indebted to this group of workers for providing me with a pre-print of their paper, which is going to appear on July 5, and also for giving me these slides, which I have been able to show to you. I might mention that you are the first people to see these pictures, apart from those who are actively engaged in it. Here is the evidence for the new elements. Thank you.

Paul Dirac (1976)

Basic Beliefs and Prejudices in Physics

Paul Dirac (1976)

Basic Beliefs and Prejudices in Physics

Comment

The title of Paul Dirac’s lecture is a very general one, but in Lindau he immediately announced that he would use some of the time to describe a still unpublished discovery of so-called super-heavy elements, elements heavier than uranium. These should recently have been found at his home university in Florida in certain minerals. This announcement fits very well into Dirac’s general theme of beliefs and prejudices, since we know today that the announcement turned out to be false and that the first known super-heavy elements eventually were produced in large accelerators. Dirac’s main point, though, is that a scientist may have certain beliefs, but that these easily might become prejudices to be discarded as soon as the beliefs are shown to be wrong. He tells of his own belief in the 1920’s that the Bohr orbits of the electrons in atoms would explain everything in atomic physics. This belief (turned into a prejudice) he discarded when Heisenberg showed that it made no sense to think about one Bohr orbit, but that everything actually was based on so called matrix elements connecting two Bohr orbits. Another of his examples concerns the existence of so-called magnetic monopoles. From ordinary experience we know that a magnet always has a north pole and a south pole. But the equations describing electromagnetism seem to allow also magnets that have only one pole. These hypothetical particles were studied by Dirac already in the 1930’s. In his lecture he describes the (then) recent experimental search for monopoles in the cosmic radiation at high altitudes. A balloon experiment had detected a particle track in a plastic detector and the experimenters interpreted the track as resulting from a magnetic monopole. The result was published, but met strong criticism. At the time of the lecture, Dirac still kept an open mind, but we know today that (again) the discovery was false. Even today there has been no trace of magnetic monopoles.

Anders Bárány

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