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"...and was just saying to herself, 'if one only knew the right way to change them-' when she was a little startled by seeing the Cheshire Cat sitting on a bough of a tree a few yards off.

The Cat only grinned when it saw Alice. It looked good-natured, she thought: still it had very long claws and a great many teeth, so she felt that it ought to be treated with respect.

'Cheshire Puss,' she began, rather timidly, as she did not at all know whether it would like the name: however, it only grinned a little wider. 'Come, it's pleased so far,' thought Alice, and she went on. 'Would you tell me, please, which way I ought to go from here?'

'That depends a good deal on whsre you want to get to,'said the Cat.

'I don't much care where-' said Alice.

'Then it doesn't matter which way you go,' said the Cat. '-so long as I get somewhere,' Alice added as an explanation.

'Oh, you're sure to do that;' said the Cat, 'if you only walk long enough.'

Alice felt that this could not be denied, so she tried another question. 'What sort of people live about here?'

'In that direction,' the Cat said, waving its right paw round, 'lives a Hatter: and in that direction,' waving the other paw, 'lives a March Hare. Visit either you like: they're both mad.'

'But I don't want to go among mad people,' Alice remarked. 'Oh, you ca'n't help that,' said the Cat: 'we're all mad here.I'm mad, You're mad.'

'How do you know I'm mad?' said Alice.

'You must be,' said the Cat; 'or you wouldn't have come here,'

-  

 

 

IN SEARCH OF SCHRODINGER'S CAT

John Gribbin 1984

QUANTUM PHYSICS AND REALITY

NOTHING IS REAL

"The cat of our title is a mythical beast, but Schrodinger was a real person. Erwin Schrodinger was an Austrian scientist instrumental in the development, in the mid-1920s, of the equations of a branch of science now known as quantum mechanics. Branch of science is hardly the correct expres-sion, however, because quantum mechanics provides the fundamental underpinning of all of modem science. The equations describe the behavior of very small objects-gen-erally speaking, the size of atoms or smaller-and they provide the only understanding of the world of the very small. Without these equations, physicists would be unable to design working nuclear power stations (or bombs), build lasers, or explain how the sun stays hot. Without quantum mechanics, chemistry would still be in the Dark Ages, and there would be no science of molecular biology-no under-standing of DNA, no genetic engineering-at all "

" Quantum theory represents the greatest achievement of science, far more significant and of far more direct, prac-tical use than relativity theory. And yet, it makes some very strange predictions. The world of quantum mechanics is so strange, indeed, that even Albert Einstein found it in-comprehensible, and refused to accept all of the implica-tions of the theory developed by Schrodinger and his colleagues. Einstein, and many other scientists, found it more comfortable to believe that the equations of quantum mechanics simply represent some sort of mathematical trick, which just happens to giye a reasonable working guide to the behavior of atomic and subatomic particles but that conceals some deeper truth that corresponds more closely to our everyday sense of reality. For what quantum mechanics says is that nothing is real and that we cannot say anything about what things are doing when we are not looking at them. Schrodinger's mythical cat was invoked to make the differences between the quantum world and the everyday world clear.

In the world of quantum mechanics, the laws of phys-ics that are familiar from the everyday world no longer work. Instead, events are governed by probabilities. A radio-active atom, for example, might decay, emitting an electron, say; or it might not. It is possible to set up an experiment in such a way that there is a precise fifty-fifty chance that one of the atoms in a lump of radioactive material will decay in a certain time and that a detector will register the decay if it does happen. Schrodinger, as upset as Einstein about the implications of quantum theory, tried to show the absurdity of those implications by imagining such an experiment set up in a closed room, or box, which also contains a live cat and a phial of poison, so arranged that if the radioactive decay does occur then the poison container is broken and the cat dies. In the everyday world, there is a fifty-fifty chance that the cat will be killed, and without looking in-side the box we can say, quite happily, that the cat inside is either dead or alive. But now we encounter the strangeness of the quantum world. According to the theory, neither of the two possibilities open to the radioactive material, and therefore to the cat, has any reality unless it is observed. The atomic decay has neither happened nor not happened, the cat has neither been killed nor not killed, / Page 3 / until we look inside the box to see what has happened. Theorists who accept the pure version of quantum mechanics say that the cat exists in some indeterminate state, neither dead nor alive, until an observer looks into the box to see how things are getting on. Nothing is real unless it is observed.

The idea was anathema to Einstein, among others. "God does not play dice," he said, referring to the theory that the world is governed by the accumulation of outcomes of essentially random "choices" of possibilities at the quan-tum level. As for the unreality of the state of Schrodinger's cat, he dismissed it, assuming that there must be some un-derlying "clockwork" that makes for a genuine fundamen-tal reality of things. He spent many years attempting to devise tests that might reveal this underlying reality at work but died before it became possible actually to carry out such a test. Perhaps it is as well that he did not live to see the outcome of one line of reasoning that he initiated.

In the summer of 1982, at the University of Paris-South, in France, a team headed by Alain Aspect completed a series of experiments designed to detect the underlying reality below the unreal world of the quantum. The under-lying reality-the fundamental clockwork-had been given the name " hidden variables," and the experiment con-cerned the behavior of two photons or particles of light fly-ing off in opposite directions from a source. It is described fully in Chapter Ten, but in essence it can be thought of as a test of reality. The two photons from the same source can be observed by two detectors, which measure a property called polarization. According to quantum theory, this prop-erty does not exist until it is measured. According to the hidden-variable idea, each photon has a "real" polarization from the moment it is created. Because the two photons are emitted together, their polarizations are correlated with one another. But the nature of the correlation that is actually measured is different according to the two views of reality.

The results of this crucial experiment are unam-biguous. The kind of correlation predicted by hidden- variable theory is not found; the kind of correlation pre- dicted by quantum mechanics is found, and what is more, again as predicted by quantum theory, the measurement / Page 4 / that is made on one photon has an instantaneous effect on the nature of the other photon. Some interaction links the two inextricably, even though they are flying apart at the speed of light, and relativity theory tells us that no signal can travel faster than light. The experiments prove that there is no underlying reality to the world. "Reality," in the everyday sense, is not a good way to think about the be-havior of the fundamental particles that make up the uni-verse; yet at the same time those particles seem to be inseparably connected into some indivisible whole, each aware of what happens to the other

The search for Schrodinger's cat was the search for quantum reality.. From this brief outline, it may seem that the search has proved fruitless, since there is no reality in the everyday sense of the word. But this is not quite the end of the story, and the search for Schrodinger's cat may lead us to a new understanding of reality that transcends, and yet includes, the conventional interpretation of quantum mechanics. The trail is a long one, however, and it begins with a scientist who would probably have been even more horrified than Einstein if he could have seen the answers we now have to the questions he puzzled over. Isaac New-ton, studying the nature of light three centuries ago, could have had no conception that he was already on the trail leading to Schrodinger's cat."

Page 70 

" The cloud of electrons provides the outward face of the atom and the means by which it interacts with other atoms. It is largely immaterial what lies buried that far into the heart of the electron cloud-what another atom "sees" and / page 71 / "feels" are the electrons themselves, and it is the interac-tions between the electron clouds that are responsible for chemistry. By explaining the broad features of the electron cloud, Bohr's model of the atom put chemistry onto a scien-tific footing. Chemists already knew that some elements were very alike in their chemical properties, even though they had different atomic weights. When the elements are arranged in a table according to their atomic weight (and especially when allowance is made for different isotopes) these similar elements show up at regular intervals, one pattern recurring for elements eight atomic numbers apart, for example. This gives the table, when arranged so that elements with similar properties are grouped together, its name "periodic."

In June 1922 Bohr visited the University of Gottingen in Germany, to give a series of lectures on quantum theory and atomic structure. Gottingen was about to become one of the three key centers in the development of the complete version of quantum mechanics, under the direction of Max Born, who became Professor of Theoretical Physics there in 1921. He had been born in 1882, son of the Professor of Anatomy at the University of Breslau, and was a student in the early 1900s, at the tinie Planck's ideas first appeared. At first he studied mathematics, only turning to physics (and working for a time at the Cavendish) after completing his doctorate in 1906. This, as we shall see, turned out to have been an ideal training in the years ahead. An expert on rela-tivity, Born's work was always characterized by full mathe-matical rigor, in striking contrast to Bohr's patchwork theoretical edifices, built with the aid of brilliant insights and physical intuition, but often leaving others to catch up with the mathematical details. Both kinds of genius were essential to the new understanding of atoms.

Bohr's lectures in June 1922 were a major event in the renewal of German physics after the war, and also in the history of quantum theory. They were attended by scientists from all over Germany, and became known (with a not-too- subtle pun on certain other famous German celebrations) as the "Bohr Festival." And in those lectures, after carefully preparing his ground, Bohr presented the first successful /

Page 72   Figure 4.2 (omitted) / Atoms of some of the simplest elements can be represented for many purposes as a nucleus surrounded by electrons in shells corresponding to the steps on the energy-level staircase. The quantum rules allow only two electrons on the lowest step, so lithium, with three electrons, has to put one of them onto the next step up the energy ladder. This second shell has "room" for eight electrons, so thatcarbon has a shell exactly half full, which is the reason for .its interesting chemical properties as the basis of life.

 Page 73 / theory of the periodic table of the elements, a theory that survives in essentially the same form to this day. Bohr's idea stemmed from a picture of the electrons being added to the nucleus of an atom. Whatever the atomic number of that nucleus, the first electron would go into an energy state corresponding to the ground state of hydrogen. The next electron would go into a similar energy state, giving an out-ward appearance rather like the helium atom, whcch has two electrons. But, said Bohr, there was no room for any more electrons at that level in the atom, and the next one to be added would have to go into a different kind of energy level. So an atom with three protons in its nucleus and three electrons outside the nucleus should have two of those electrons more tightly tied to the nucleus and one left over; it ought to behave rather like a one-electron atom (hy-drogen) as far as chemistry is concerned. The Z=3 ele-ment is lithium, and it does indeed show some chemical similarities to hydrogen. The next element in the periodic table with similar properties to lithium is sodium, with Z = 11, eight places beyond lithium. So Bohr argued that there must be eight places available in the set of energy levels outside the inner two electrons, and that when these were filled the next electron, the eleventh in all, had to go into another energy state still less tightly tied to the nu-cleus, again mimicking the appearance of an atom with only one electron.

These energy states are called "shells," and Bohr's ex-planation of the periodic table involved successively filling up the shells with electrons as Z increased. You can think of the shells as onion skins wrapped around one another; what matters for chemistry is the number of electron's in the outermost shell of the atom. What goes on deeper inside plays only a secondary role in determining how the atom will interact with other atoms.

Working outward through the electron shells, and in-corporating all the evidence from spectroscopy, Bohr ex-plained the relationships between the elements in the periodic table in terms of atomic structure. He had no idea why a shell containing eight electrons should be full ("closed"), but he left .none of his audience in any doubt /

Page 74 Figure 4.3 (omitted) / When one carbon atom links with four atoms of hydrogen, electrons are shared in such a way that each hydrogen atom has the illusion of a full innermost shell (two electrons) and each carbon atom "sees" eight electrons in its second shell. This is a very stable configuration.

/ that he had discovered the essential truth. As Heisenberg said later, Bohr "had not proved anything mathe-matically . . . he just knew that this was more or less the connection."* And Einstein commented in his Auto- biographical Notes in 1949, describing the success of Bohr's work based on quantum theory, "that this insecure and contradictory foundation was sufficient to enable a /

*Quoted In Meara and Rechenberg, volume 1 page 357.

Page 75 / man of Bohr's unique instinct and tact to discover the major laws of spectral lines and of the electron-shells of the atoms together with their significance for chemistry appeared to me like a miracle-and appears to me as a miracle even today. *

Chemistry is concerned with the way atoms react and combine to make molecules. Why does carbon react with hydrogen in such a way that four atoms of hydrogen attach to one of carbon to make one molecule of methane? Why does hydrogen come in the form of molecules, each made of two atoms, while helium atoms do not form molecules? And so on. The answers came with stunning simplicity from the shell model. Each hydrogen atom has one electron, whereas helium has two. The "innermost" shell would be full if it had two electrons in it, and (for some unknown reason) filled shells are more stable-atoms "like" to have filled shells. When two hydrogen atoms get together to form a molecule, they share their two electrons in such a way that each feels the benefit of a closed shell. Helium, having a full shell already, is not interested in any such proposition and disdains to react chemically with anything.

Carbon has six protons in its nucleus and six electrons outside. Two of these are in the inner closed shell, leaving four associated with the next shell, which is half empty. Four hydrogen atoms can each claim a part share in one of the four outer carbon electrons and contribute their own electron to the deal. Each hydrogen atom ends up with a pseudoclosed shell of two inner electrons, while each car- bon atom has a pseudoclosed second shell of eight elec-trons.

Atoms combine, said Bohr, in such a way that they get as close as they can to making a closed outer shell. Some-times, as with the hydrogen molecule, it is best to think of a pair of electrons being shared by two nuclei; in other cases, an appropriate picture is to imagine an atom that has an odd electron in its outer shell (sodium, perhaps) giving theelectron away to an atom that has an outer shell containing seven electrons and one vacancy (in this case, it might be chlorine). Each atom is happy-the sodium, by losing an electron, leaves a deeper, but filled, shell "visible"; the chlo-rine, by gaining an electron, fills its outermost shell. The net result, however, is that the sodium atom has become a positively charged ion by losing one unit of negative charge, while the chlorine atom has become a negative ion. Since opposite charges attract, the two stick together to form an electrically neutral molecule of sodium chloride, common salt.

All chemical reactions can be explained in this way, as a sharing or swapping of electrons between atoms in a bid to achieve the stability of filled electron shells. Energy transi- tions involving outer electrons produce the characteristic spectral fingerprint of an element, but energy transitions involving deeper shells (and therefore much more energy, in the X-ray part of the spectrum) should be the same for all elements, as indeed they prove to be. Like all the best theo- ries, Bohr's model was confirmed by a successful predic- /

 Figure 4.4 (omitted) / By giving up its lone outer electron, a sodium atom achieves a desirable quantum mechanical configuration and is left with a positive charge. By accepting an extra electron, chlorine fills its outer shell with eight electrons and gains a negative charge. The charged ions are then held together to make molecules and crystals of common salt (NaI) by electrostatic forces.

Page 77 / tion. With the elements arranged in a periodic table, even in 1922 there were a few gaps, corresponding to un- discovered elements with atomic numbers 43, 61, 72, 75, 85 and 87. Bohr's model predicted the detailed properties of these "missing" elements and suggested that element 72, in particular, should have properties similar to zirconium, a forecast that contradicted predictions made on the basis of alternative models of the atom. The prediction was con-firmed within a year with the discovery of hafnium, ele-ment 72, which turned out to have spectral properties exactly in line with those predicted by Bohr.

 Page 75

 " Carbon has six protons in its nucleus and six electrons outside. Two of these are in the inner closed shell, leaving four associated with the next shell, which is half empty. Four hydrogen atoms can each claim a part share in one of the four outer carbon electrons and contribute their own electron to the deal. Each hydrogen atom ends up with a pseudoclosed shell of two inner electrons, while each car- bon atom has a pseudoclosed second shell of eight elec-trons."

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 I

i (square root of minus one)

Page 75 Chapter 10

The City at the Gate of the Sun

"The early Spanish travellers who visited the ruined Bolivian city of Tiahuanaco at around the time of the conquest were impressed by the sheer size of its buildings and by the atmosphere of mystery that clung to them. 'I asked the natives whether these edifices were built in the time of the Inca,' wrote the chronicler Pedro Cieza de Leon, 'They laughed at the question, affirming that they were made long before the Incas reign and . . . that they had heard from their forbears that everything to be seen there appeared suddenly in the course of a single night . . . '1 Meanwhile another Spanish visitor of the same period recorded a tradition which said that the stones had been lifted miraculously off the ground, 'They were carried through the air to the the sound of a trumpet.'2  

We must now say something about the large and almost incredible buildings of Tiahuanaco. There is an artificial hill, of great height, built on stone foundations so that the earth will not slide. There are gigantic figures carved in stone . . . these are much worn which shows there great antiquity. There are walls, the stones of which are so enormous it is difficult to imagine what human force could have put / Page 76 them in place. And there are the remains of strange buildings, the most remarkable being stone portals, hewn out of solid rock; these stand on bases anything up to 30 feet long, 15 feet wide and 6 feet thick, base and portal being all of one piece . . . How, and with the use of what tools or implements, massive works of such size could be achieved are questions which we are unable to answer . . . Nor can it be imagined how such enormous stones could have been brought here . . .3

That was in the sixteenth century. more than 400 years later, at the end of the twentieth century, I shared Garcilaso's puzzlement Scattered around Tiahuanaco, in defiance of the looters who had robbed the site of so much in recent years were monoliths so big and cumbersome yet so well cut that they almost seemed to be the work of super-beings.  

Page 20 " 'The Britons . . . made choice of Uther Pendragon the king's brother, with fifteen thousand men, to attend to this business.' The armada put to sea 'with a prosperous gale.' The irish heard of the proposed seizure of their monument, and king Gilloman raised a 'huge army,' vowing that the Britons should not 'carry off from us the very Page 21 / smallest stone of the Dance.' But the invaders 'fell upon them straightway at the double-quick . . . prevailed . . . pressed forward to mount Killaraus . . . '

Then the would-be monument-movers were faced with the problem of how to transport those great stones. ' They tried huge hawsers . . . ropes . . . scaling ladders [memories of the lists of weapons in Caesar's Gallic Wars!] . . .never a whit the forwarder . . .' Merlin had to take over. He burst out laughing and put together his own engines . . . laid the stones down so lightly as none would believe . . .bade carry them to the ships,' and they all 'returned unto Britain with joy' and there 'set them up about the compass of the burial-ground in such wise as they had stood . . . and proved yet once again how skill surpasseth strength.'