The Copenhagen Interpretation
The first ideas assumed things happened the way they appeared to happen. This is not surprising because it follows the historical pattern, our minds being conditioned to think this way. Particles were imagined to behave as waves whilst in transit so that all possible paths could be followed simultaneously. Only when totally obstructed by matter did these waves collapse into a particle and exhibit all the properties for which only a particle explanation seemed reasonable. The particles had to leave an observable record, either as a chemical change on a sensitized screen or as a signal from a detector. Ultimately the result needed to be viewed by an observer so that it could be interpreted. This step also involved the transmission of information by particles. In this case the photons of light caused an image of the result to fall upon the retina of the eye. But again these had to act as waves in transit and so it was decided that everything must exist in some kind of limbo state, as unresolved wave functions, until finally an observer, by the act of viewing, caused the wave function representing an entire piece of apparatus, to collapse into particles.
"The Paradox of Schrodinger's Waves" by John Gribbon (114) illustrates the conceptual difficulties which then arise. Schrodinger conceived a hypothetical cat problem to emphasise the difficulty. He proposed that a cat be imagined shut in a box with a cyanide capsule. Breakage of the capsule could be triggered by a random event which had a 50-50 chance of happening before the box was opened. Now a cat is composed of sub-atomic particles and so has a quantum description as a wave function like anything else. Therefore it could not collapse into reality until observed when the box was opened. Hence the cat had to exist in a state of limbo, as a complex ghost-like unresolved wave function. It would have to exist in two states at once, both alive and dead at the same time. This is the paradox. The conclusion is obvious nonsense.
In "God and the New Physics" Paul Davies (105) describes a further problem to illustrate conceptual difficulties.
An electron is aimed at a target, such as another particle, so that it can be deflected to right or left with equal probability. Hence the unresolved wave functions exist equally on either side. The electron keeps its options open until it is observed. When the observer sees the electron on one side, the wave function instantly collapses on both sides. On the other side it collapses into nothing, because there is now no possibility of its being seen on that side.
He says that mystery surrounds the roll of the observer in promoting such extraordinary changes in the electron's character. Is this mind-over-matter, he asks.
But if the unused half of the wave function collapses into nothing, what could it have been made from in the first place? Or is the entire wave function collected together instantly by some unknown means of transport and caused by some other unknown means to collapse into a particle?
Such an explanation would imply that the wave function was constructed from the same kind of energy as the particle.
The Bohr and Schrodinger Models of the Atom
There is another problem which does not seem to have been recognised. It will be shown later that it is related to that of wave-particle duality it is therefore appropriate to consider the new aspect at this point.
Schrodinger (202) is famous for his wave model of the atom. A previous model due to Bohr had electrons orbiting the nucleus like planets going round the Sun. it will be remembered that the electrons are contained in orbitals which are regions of space surrounding the nucleus. In the Bohr model of the hydrogen atom these orbitals were defined by electrons actually moving in circles like planets going round the Sun. In this case, however, the electric force of attraction between the negatively charged electron and the positively charged nucleus was assumed to create the radially directed acceleration required, (the centripetal acceleration). Electrons were arranged in discrete "energy shells". These are not to be thought of as physical objects. They are simply a way of describing the imaginary surfaces to which electrons would be confined as they moved. The higher the energy state of the orbiting electron, the greater the radius of the shell. To comply with quantum theory a step change in energy existed between these shells. A quantum of light would need to be absorbed of exactly the correct amount to raise an electron from one shell to the next. Conversely, such a quantum, or photon, would be emitted when the electron fell back.
When light is passed through a triangular prism of glass, rays of different colours are deflected or "refracted" by different amounts. So-called "white light" is a mixture of all the colours of the rainbow. Consequently, when the light from a star or the Sun is passed through a glass prism it spreads out to leave a pattern of discrete colours called a "spectrum". Indeed a rainbow is such a spectrum.
When the light from a star is split into its spectrum, then a system of discrete lines is observed among the bands of colour. These lines relate to the quantum energy jumps between energy shells. The electrons exist at high levels due to repeated collisions at high speeds. In fact the temperature of a gas is a measure of the average speed of its constituent particles. At the same time electrons pumped by collision interactions to high energies are always falling back to low levels. The losses involved in falling are carried away by the emission of photons of light. This explains how light arises in the first place. As the electron falls from one shell to the next lower one, a photon having a discrete energy and therefore wavelength is produced. The combined effect of billions of such transitions all yielding exactly the same wavelength of light can be detected. It produces
a discrete bright line when the light is spread out into a spectrum with the long wavelengths at one end and the short ones at the other. Conversely the lines can appear dark. In this case photons are being absorbed by the atoms of a cooler gas through which the light has to pass.
Bohr used these spectral lines to determine the energy differences between shells. All atoms produce such spectral lines as signatures unique to each individual element. By measuring them the composition of stars can be determined. Hence Bohr's model was quite successful in predicting many of the properties of atoms but it fell short of a completely satisfactory model because it had to rely upon observation for the energy steps between shells. Also an atom of hydrogen has only one electron, being the simplest of all elements. Moving in a circle or ellipse, a single electron would define the size of the atom in only one plane. The atom would appear as a very thin disc instead of a sphere.
Schrodinger's model fitted waves around the atom and the energy steps were predicted by the numbers of waves needed. These numbers were integral values, i.e. 1, 2, 3 and so on with no decimals or fractions. Hence in the refined model the required energy quanta were accurately predicted. This is a very crude explanation. The mathematical derivation is immensely complex. It takes account of the attractive force between electrons and the protons of the nucleus, which, like Newtonian gravitation, obey an inverse square law. It is this attractive force which causes the wave functions to curl up to define a ball shape called the orbital.
The positions of the electrons are no longer precisely defined, however. The equations only give the probability of finding an electron at a given distance from the nucleus. This means that the electrons are distributed in a random manner similar to that which would result from throwing a loaded dice many thousands of times. If a dice of cubic form has a number on each face but a small lead pellet is fixed just under the face carrying the six, then after many throws it will be found that more sixes will have appeared than any other number. The number of ones, which are on the opposite face from the six, will appear the least number of times and the remaining numbers, written on the other four sides, will be seen equally often with a frequency intermediate that of the sixes and the ones. A definite pattern is only established when the total number of throws runs into thousands. This is the principle upon which all probability distributions are based.
For the electron in the orbital of an atom this probability is defined by the superposition of wave functions. The wave functions are added up in the manner of numbers. The final number is then multiplied by itself, in other words it is squared. This final pattern then acts as the weighting of a hypothetical many-faceted dice, so that most electrons will be found where the numbers are highest and none will be found where the numbers sum to zero. The pattern of distribution of photons in Young's two-slit experiment obeyed exactly the same rule. For the hydrogen atom, however, a diffuse cloud of electric charge is represented which is of greatest density close to the nucleus. The maximum amount of charge at a given radius measured from the nucleus, taking account of the fact that the area varies as the square of the radius, is then found to correspond with the Bohr orbit. So the simpler Bohr model can still be used to define the size of the atom.
The Schrodinger model of hydrogen, however, defined the orbital as an almost spherical region of space, a shape which accords with observation. Hence the orbital is now represented as a diffuse region of charge, as if the single electron is smeared out in the manner represented by superimposed waves. In more complex atoms, each holding a multiplicity of electrons, the orbitals can have more complex lobe shapes. Here again, however, the electrons appear as if smeared out into a diffuse cloud of a fixed shape.
In FIG.2 the representation of atoms in the crystal follows the Schrodinger model. If the Bohr model had been represented, a circle, representing the orbit of each electron, would have been described.
Although no attention ever seems to be drawn to the matter in any texts on the subject, another paradox is clearly present. If the electrons are real in the sense of being sub-atomic particles having a permanent existence, then they will be committed to Bohr-type orbits, in which case hydrogen atoms would appear as thin discs. Hence there is no way permanently existing electrons could act to provide the distributed cloud of charge matching the Schrodinger model. And the latter is known to give predictions matching observation.
aim, therefore, is not only to find an explanation for wave-particle duality. It must simultaneously resolve this new paradox, explaining how real electrons can fit in with Schrodinger's model of the atom.
Before other ideas offering solutions can be described the historical development of the theory of gravitation needs to be touched upon because this influenced people's thinking.
The Link with Gravitation
Few problems in physics can be treated in isolation because everything interacts with everything else. Difficulties were also being met in trying to find a quantum theory of gravitation. There are four main forces of nature and three of these could be explained very successfully by the newly-emerging quantum theory. These were the electromagnetic force responsible for structuring atoms and connected with light, the strong nuclear force of very short range but of immense strength, which holds the parts of the atomic nucleus together and the weak force responsible for radioactivity. In radioactive decay a heavy unstable nucleus suddenly splits into two parts. There is an immense release of energy which initially manifests itself as kinetic energy by the parts exploding away from each other at high speed.
The strong force enables the immense power of the atomic nucleus to be harnessed by nuclear power stations and atomic bombs. It holds the nucleus together against the electric force of repulsion caused by the positively charged protons, which account for about half its components. When a foreign particle, a neutron caused by fission of another atom, is absorbed by a nucleus the stability is upset. Then the nucleus splits and the parts accelerate away at very high speeds, propelled by the long-range force of electric repulsion.
As well as postulating that energy could only exist in small indivisible "packages", the basis of the quantum theory holds that what seems empty space to us is a total illusion. Instead it consists of a seething mass of so-called "virtual particles". These are being continuously created from nothingness, only to expire a minute fraction of a second later, vanishing back to nothingness. But during their brief lives some of them can transfer momentum between the so-called "real" particles. The latter seem permanent and can be observed directly. The intense bombardment causes real particles to be pushed about by the resulting forces. Some very short-lived and very heavy virtual particles can hit unstable nuclei, so triggering radioactive decay.
The virtual particles responsible for producing forces in this way are known as "mediators". For the electric force these mediators are "virtual photons". They can be imagined as being like the sparks flying off in all directions at random from the "sparklers" displayed on Bonfire Night. The virtual photons selectively "couple" with electrically-charged particles, such as protons or other electrons, to produce the observed forces. Indeed the effects we attribute to electric charge are caused by the selective absorption of virtual photons according to established quantum theory.
All mediators need to arise at the "surfaces" of real particles with special tags so that they are able to recognise only a certain kind of real particle, interacting with only that kind and ignoring all others. Only by such selective coupling could the forces act in the way they do to structure atoms. It is usual in this context to put inverted commas round the word "surfaces" because if the Copenhagen interpretation of
wave-particle duality is adopted, there is doubt whether sub-atomic particles can have surfaces ascribed to them. Whilst travelling ghost-like as waves no surfaces could exist. However, we will later home in on a model which allows particles with at least fuzzy surfaces to be present at all times.
Newton's theory of gravitation could be given a quantum explanation. Mediators of gravitation, the so-called "gravitons", could be ejected in all directions from any type of particle. The rate of ejection needs to be proportional to the mass of the particle. As mediators spread out from a point source to greater radii, their numbers crossing unit area per unit of time, known as "flux", would decrease as the square of the radius. If the force on another object were proportional to the number of mediators intercepted, then Newton's inverse square law of force could be explained. Newton had already shown, centuries earlier, that a planet acted on by an exact inverse square law of force would trace out an orbit represented by a perfect ellipse. This is an oval shape with two so-called "foci" located on the long axis. The sun is situated at one focus so that the orbit comes closest to it at one point, the "perigee" and is farthest away at a diametrically opposite point called the "apogee".
Unfortunately this model would not give predictions matching accurate new observations. For example, orbits were found to be almost elliptical but the axes rotated slightly as well. This effect is known as "precession of the perihelion". The perihelion is the line joining the point of closest approach with the Sun. A halforbit, illustrating precession, is given in FIG.12 of the technical supplement. Then Einstein produced his theory called "general relativity" based on the remarkable concept of "curved space-time". This astonished everybody by accurately predicting the outcome of all tests made. And the accurate prediction of 43 arcseconds per century for the so-called "relativistic" precession of planet mercury was a major triumph which helped his theory gain acceptance.
Einstein's concept was unimaginable, however, except by recourse to analogy and so a new kind of thinking became established. This relied entirely on mathematics and it was no longer considered necessary to be able to imagine physical models based on such abstract assumptions. Indeed any such imagining came to be regarded as unsophisticated.
Then in 1919 Theodor Kalusa added an extra dimension to space so that instead of there being three plus time or, according to Einstein, four dimensions of space-time, there were now five space-time dimensions. He showed that Maxwell's equations for electromagnetism then appeared together with Einstein's equations for gravitation. After some initial scepticism Einstein finally came out in support of this concept by promoting it at a conference in 1921.
If one extra dimension could be accepted, then the way was open to an increase in the number without limit. In addition a new way of thinking gradually became fashionable. Commonsense was no longer regarded as a necessary restriction for acceptance of explanations for natural phenomena. Thinking became more and more abstract in nature because the developing mathematical sophistication was virtually impossible to interpret by ordinary conceptualisation. A new physics developed. Increasingly, explanations for the forces of nature came to rely upon developments of Einstein's concepts of curved space-time with greatly increased curvatures allowed in higher dimensions. Wheeler attempted to explain all the forces in terms of curved geometries. These developments in freer thinking made it possible for new explanations of wave-particle duality to become accepted as reasonable.
The Many Universes Interpretation
The "Many Universes" solution to the dilemma was devised by Hugh Everett in 1957. It would, when applied to Schrodinger's hypothetical cat problem, demand the splitting of one universe into two, like the branching of a tree. One would contain a live cat the other a dead one. The new universe would be almost an exact copy of ours, existing in the same dimensions but interpenetrating our own. Every person in the universe would be copied and each member of such a pair would then exist independently. In variants of the idea the universes exist in the different dimensions or are combined with theories having higher dimensions.
The problem of interpreting wave-particle duality is still regarded as so puzzling that even today Everett's solution is taken seriously. The way Everett seems to have imagined the electron is probably comparable with descriptions shown in Open University broadcasts. Instead of being a tiny particle it is represented as a striped sphere of large size. The stripes are shown perpendicular to the direction of motion and represent the wave functions being carried along. Everett's idea was designed to explain the two-slit phenomenon. A particle like an electron had to pass through both slits simultaneously so that the wave character it was assumed to carry could interfere with itself. This could be imagined by having two spheres centred about separated points, each of which travelled on a separate path so that both slits would be passed through simultaneously. Then the two sets of waves could produce an interference pattern and so control the final point of collapse into a particle on the screen.
This meant that two electrons had to travel, but we could only see one of these. Therefore the other electron must be undetectable and so would have to be a component of another universe. Therefore every time a particle was faced with a choice of two paths, a whole new universe would be instantly created in which the new particle could travel. Then since every universe contains countless millions of particles faced with choices of path, this meant universes were multiplying at an alarming rate. It meant their number must be infinite. This number might be reduced somewhat, it was conjectured, by having universes merge together again. It has even been reported that experimenters have actually observed such merging! Everett's idea is expressed dramatically by DeWitt, one of his supporters. According to Paul Davies (105) he said:
"Every quantum transition taking place on every star, in every galaxy, in every remote corner of the universe is splitting our local world on Earth into myriads of copies of itself .... Here is schizophrenia with a vengeance."
It is not suggested that any of this be regarded as a reasonable proposition. Nobody has suggested any means whereby a whole universe could be copied instantly just to satisfy the difficulties of one tiny particle. Nor has anyone proposed a way in which the huge energy problem involved could be satisfied. Indeed the aim is to propose that an entirely different idea should be considered. It will then be suggested that the reader make a choice based on the ability of the various solutions to predict observed phenomena.
There is one more set of ideas aimed at explaining wave-particle duality which needs to be mentioned before the new theme can be developed. This is the
The Anthropic Principle
The "Weak Anthropic Principle" appears to rest on the idea that there is nothing extraordinary about the highly-ordered universe we perceive. This is because we could not perceive it otherwise, since we could not exist! This is not very satisfying as it completely fails to explain
The "Strong Anthropic Principle" is also related to the dilemma. This idea was developed by the astrophysicist Brandon Carter. He says "The universe must be such as to admit conscious beings at some stage." It rests on the idea that, "The universe exists because we are here." The observer is a necessary part of the whole and is needed to collapse the wave function to yield reality. Therefore the universe came into being to produce forms of life. Indeed life-forms were necessary so that the universe could exist.
The principle is also associated with the idea of an infinite number of universes. In one proposal universes exist one after another, each starting with a big bang, flying out and collapsing in a big crunch. Then before the next excursion the laws of physics are slightly altered by random changes only one having just the right laws for life to develop could be observed.
In another version these universes come into being at random all inter-penetrating one another and each with slightly different laws of physics or physical constants, so that by pure chance one arises having just the right properties to support life forms.
This version is compatible with Everett's ideas, since the universes all exist in parallel. Presumably those which cannot support life-forms are never truly real owing to lack of observers to collapse wave functions.
Unfortunately such ideas lead to bizarre inversions of cause and effect. For example, according to Paul Davies (105) Professor Wheeler writes that there is a sense in which objects (like remote quasars) are created billions of years in the past by observing them in the present! He goes further and says that the observer needs to be regarded as a "participater" because the world outside the observer's brain is created by the thought-processes of intelligent life-forms and so is an illusion created by the mind. There are an infinite number of possible realities all co-existing either as interpenetrating universes or in higher dimensions. The combined thought-processes of all living beings then select one of these realities from their state of limbo. The brains of all living things are bio-computers which act as "reality-structurers" for selection of reality at any given time. The one selected is by a consensus of all brains acting together to form a universal mind.
Not only the present exists as one reality chosen from an infinite number of possibilities existing in limbo, the past can also be so chosen. Hence the history we perceive is also only the one we select. In reality, the hypothesis holds, there are an infinite number of ways the present could have arisen as a result of history.
But he offers no ideas regarding the means by which such creation of matter could be worked. Nor is any means proposed by which participating brains can be connected. Connection would be essential if the universe is to be structured as a result of a consensus of all living brains.
The assumption that an infinite number of systems of matter can co-exist simultaneously in the same place is surely not justifiable by any known form of logical reasoning. There must be some upper limit which specifies a certain number. The question which needs to be addressed here is the justification for such total abstraction of thought.
In addition no attempt is made by any of these theories to show how real electrons can move in a way which is compatible with Schrodinger's description of the atom. Existing as purely intangible waves, no plausible mechanism can be devised for the mediator coupling required to produce the electric force which binds the electron to the nucleus. If the electron is considered as a real particle having a permanent existence, then such mechanisms can be devised. In this case, however, the hydrogen atom appears as a thin disc instead of a ball because the electron is constrained to Bohr-type orbits.
The problems all arise from the need to collapse the wave function to create real particles. Many books have been written to describe and further extend the anthropic principles in both its weak and strong forms. It is for the reader to judge their plausibility.
Surely there must be a more satisfactory answer to the dilemma than any which have been proposed to date? As shown in the foregoing critique, despite the complexity the reader is asked to take on board several aspects stubbornly remain unresolved.
Before we attempt to find a simpler resolution capable of satisfying all known data, it is worthwhile studying further the way light behaves.
The late Richard Feynman (113) in his very readable book
QED graphically describes the difficulties. He says, "It's crazy but that's the way the Universe works!" He was describing the way wave functions control the places where the photons of light appear. They do not travel in the straight lines which casual observation leads one to expect.
For example the reflection of an object in a mirror can be readily described by drawing straight lines whose angles of incidence and reflection are equal as shown in FIG.3. But Feynman gives an alternative explanation in terms of adding up wave functions. These spread out in all directions from a source but the interference pattern strangely cancels out over most of the mirror it falls upon, leaving the observed paths just described. Only along these paths are photons seen to move. Then he really clinches the argument. He scrapes away bits of the mirror in areas far removed from the straight lines needed for simple reflection. He scrapes them in a very special way in narrow bands, leaving intervening bands all uniformly spaced, so that the bits he removes are those which would reflect parts of the wave function.
These would have cancelled waves reflected from the bands he leaves alone. So now wave functions remained uncancelled when viewed from a direction which previously showed perfect cancellation. Then if photons appear where wave functions add up to non-zero values, angles of reflection would no longer equal those of incidence and light would seem to reflect from the wrong part of the mirror. Experiment showed that precisely this effect occurred. Indeed a "diffraction grating" had been generated and the description explained how these worked. This also illustrated in FIG.3. Since the observed spacing is different for different angles of viewing, light of different wavelengths would reflect from different places. This is exactly what happens, so that white incident light is seen split into a complete spectrum of colours. This explains the rainbow effects caused when video discs are placed at odd angles. The iridescent colours of some insects arise in the same way. Their surfaces have a very fine-grooved structure which acts as a diffraction grating.
Light can therefore be spread out into its spectrum by reflecting it from a diffraction grating. A similar result can be effected by passing it through a transparent prism. Richard Feynman also shows how the wave-nature of the quantum theory can explain such effects of refraction through glass prisms and lenses. Clearly the phenomenon of wave-particle duality is deeply involved in all these cases, since photons are carriers of light and their associated radiant energy.
The description of the diffraction grating can therefore be used to further assist our understanding of the phenomenon of wave-particle duality. The quanta of light might be imagined travelling as large diffuse balls of wave functions until they hit the mirror. Most cancel by interference effects, leaving a narrow band which constrains reflection to the observed angles. This angle can be modified by removal of a selected set of wave functions. This proves that photons are controlled by waves in some way. The photon, considered as a particle from collision interaction effects with electrons, can only be minute in size. It cannot possibly be as large as the spacing of the grooves of a diffraction grating. If particle size were the controlling factor, then the photon would either hit a reflecting region and bounce back with "i - r" or hit a groove and vanish by being absorbed.