The Storyteller

The product of the refractive index and the sine of the angle of incidence of a ray in one medium is equal to the product of the refractive index and the sine of the angle of refraction in a successive medium.

Descartes provided a derivation of Snell's law which we now know to be incorrect, even though it gave the right answer. He envisaged light as the motion of small spherical particles. He could see that it is easy to explain light reflected from a mirror as a stream of particles which bounce off the smooth surface, as balls bounce from a wall. The component of velocity of the particles tangent to the surface does not change while the normal component is reversed. In accordance with his general methods, Descartes wanted a similar mechanical description of refraction. When light passes from air into a denser medium such as glass, it turns towards the normal of the surface. If the tangential component of velocity is to remain unchanged for refraction as it is for reflection, light must go faster in the denser medium.

Newton later perfected Descartes derivation and agreed with his conclusion. He claimed that particles of light are attracted to denser mediums when they enter, and so gain momentum perpendicular to the surface. We can compare the situation with balls which roll across a flat surface until they descend a short downward slope onto another flat surface. They will gain energy and speed up, but only the normal component of velocity changes. The result is that they change direction, and if the initial velocity is fixed then the angles of deflection will mimic Snell's sine law. This is the essence of the Cartesian-Newtonian mechanistic explanation of refraction.

At that time, the French mathematician Marin Mersenne was acting as a clearing house for scientific information in Europe. It is no accident that knowledge began to expand rapidly after Johann Gutenberg introduced the printing press to Europe in 1450. Communication has always been of vital importance in the development of science. Mersenne's role was the 17th century equivalent of today's electronic e-print archives on the internet. When he received Descartes's manuscript on optics in 1637 he circulated copies to other scientists including Fermat.

Pierre de Fermat was by profession a councillor of the French parliament, but his passion was mathematics and his theorems in number theory are legendary. When he read Descartes's derivation of the sine law of refraction he was not impressed. For one thing, he felt that some unjustified assumptions had been made. He also felt that, if anything, light should slow down in a denser medium, not speed up. The ensuing argument between Descartes and Fermat petered out quickly without resolution.

Some twenty years later Fermat decided to try and conclude the matter by finding a better explanation for refraction. His philosophy was very different from that of Descartes. Instead of seeking a mechanical analogy he fell back on the old idea of Aristotle that nature always takes the most economical way. In 125 AD Heron of Alexandria had shown that the law of reflection from a mirror could be explained if rays of light were taking the shortest path from the source to destination via the surface of the mirror. This can be easily seen by looking through the mirror at the path of light before reflection. The ray traces a straight line from the apparent position of the object in the mirror to the destination.

If the angle of incidence were not the same as the angle of reflection it would not be a straight line and would therefore be a longer path.

Fermat was interested in problems of finding maxima and minima before Newton and Leibniz developed the general methods of differential calculus. He considered the hypothesis that the path of the ray of light might give a minimum in the time taken for light to go from A to B. This would work equally well as minimum distance for reflection and could also explain refraction.

Imagine that instead of a light ray passing into a block of glass, it is a life guard at the swimming pool. While standing at position A she sees a swimmer in distress at position B. She needs to get to him as quickly as possible but can run twice as fast as she can swim. To get from A to B in the shortest time she would have to follow the path shown.

It is not the path of shortest distance.

She must first get to a point at the side of the pool nearer to the swimmer. The optimum route is given by the equivalent of Snell's law,

A ray of light going from a point A to a point B in a rectangular block of glass with a refractive index of two would take the same route. Thus, in 1657, Fermat showed that if light was being slowed down in a medium by a factor equal to its refractive index, then he could derive Snell's sine law from a principle of least time. He was astonished that he got the same refraction law as Descartes even though his alternative theory predicted a slowing down of light in dense media instead of a speeding up. It was not until 1850, almost 200 years later, that Jean Foucault was able to measure directly the speed of light in different media. He confirmed that light slowed down in water. Fermat was right and Descartes was wrong.

The beauty of Fermat's principle of least time is its generality. The implication is that a ray of light passing through any complex set-up of mirrors and lenses takes a route which gives at least a local minimum of time to go from start to finish. According to Descartes's notion of causality, Fermat's principle is a bizarre way to formulate a law of physics. What we expect are laws which allow us to begin with a starting point and direction for a ray of light, and then work out the route it takes and where it will end up. Of course, Fermat's principle can be used in this way via a derivation of Snell's law, but it seems to work as if the light was given a starting and end position and then worked out the optimum route between them. This is quite absurd in terms of temporal causality.

By the mid 17th century the nature of light was a subject of hot debate. Important experiments by the Italian Francesco Grimaldi in 1648 were then becoming known. Grimaldi had observed diffraction of light and proposed that light had a wavelike nature.

At this time a wave theory of sound was already well established. Galileo had studied a vibrating string and clarified the relationship between frequency and pitch in 1600. In 1636 Mersenne had made the first measurements of the speed of sound by timing the return of an echo and in 1660 Robert Boyle demonstrated that sound could not travel through a vacuum by placing a bell in a jar and pumping out the air. The conclusion was inescapable. Sound must be due to compression waves travelling through the air. Using this theory, Isaac Newton was able to calculate the speed of sound from first principles and obtain a result in agreement with Mersenne's measurement.

Newton's rival, Robert Hooke, was one of those who wanted an analogous theory of light but he failed to see that light must slow down in dense media rather than speed up. In 1673 Ignace Pardies corrected Hooke's oversight and provided a new explanation for Snell's law. If light propagated in a direction perpendicular to wave fronts and slowed down as it passed through a dense medium, then waves become closer together and would be deflected in accordance with the sine law. Christian Huygens agreed but wanted a deeper understanding. Why should the wave theory be in agreement with Fermat's principle? Huygens was from Amsterdam so it is easy to imagine how he might have seen the effects of water waves on the many canals of the city as he walked home across the bridges. He developed an intuition for the behaviour of waves which enabled him to grasp a deep relation between the wave theory of light and the principle of least time. Newton and Huygens were both followers of Descartes's mechanistic philosophy, but they had very different views of the road ahead. Newton liked Descartes's theory of light and incorporated it into his corpuscular theory. Huygens started from a different observation made by Descartes, that crossed beams of light pass through each other without interacting. He must have noticed that water waves and sound waves pass through each other in a similar way. He could not see how this would be possible for light if it was composed of streams of particles.

Huygens explained instead that light propagated from each point of a luminous source in spherical waves. These are analogous to the circular waves propagating from a disturbance on the surface of water, but with immense speed and short wavelength. The speed of light was deduced by Olaus Roemer in 1676 to account for a discrepancy in the timing of eclipses of Jupiter's moons. The short wavelength could be confirmed by an experiment which Newton performed, now known as Newton's rings. Huygens noticed that if water waves pass through a tiny hole smaller than their wavelength they again spread out from that point in spherical waves. He said that spherical secondary waves propagated from any point but are only seen clearly when a barrier shields the contributions from other points. At that time the mathematics needed to express the propagation of waves in the form of differential equations was not available, but by combining Huygens's principle of secondary waves with the effects of interference, it is possible to explain refraction and diffraction. It is even possible to see why Fermat's principle of least time applies: Constructive interference appears at points where light wave fronts passing by different routes from the source arrive after the same time of travel so that they are in phase. This corresponds to the paths of least time. This conveniently reduced Fermat's principle to a deeper wave principle which, to Huygens, had the greater merit of being explicitly causal and Cartesian.

Newton saw things very differently. In his theory, light was composed of particles or corpuscles. These corpuscles undulated with a frequency depending on their colour. This was his explanation for the experiment in which he was able to measure the wavelengths of light of different colours by observing the rings of light between two glass surfaces.

There the matter rested without further progress during the whole of the eighteenth century. Newton's corpuscular theory and Huygens wave principle were seen as opposing theories. Because of the huge success of Newton's mechanics and theory of gravitation, he was the greater authority and his ideas were favoured. Newton objected to the wave hypothesis because light casts a sharp shadow whereas sound and water waves can bend round an obstruction. In the nineteenth century, opinion swung the other way. Thomas Young and Augustin Fresnel were first to revive the wave theory of light with new theory and experiments to study interference and diffraction. With the superior mathematical methods of Fourier and Laplace and the experimental basis of Ampere, Faraday, Henry, Oersted and others, rapid progress was made. James Clerk Maxwell presented the unified theory of electromagnetism in 1864. Nine years later he had derived the speed of light by supposing it to be a form of electromagnetic wave. With this, all aspects of light known at the time including colour and polarisation could be explained. Newton's corpuscular theory was no longer needed, it seemed.

It was not easy for physicists to accept the new idea. At first it was thought that the quantisation may apply only to emission and perhaps absorption of light, and not as a property of light propagation. For the first two decades of the twentieth century, Albert Einstein alone believed that light quanta were real. He applied the same idea to explain the photoelectric effect and successfully predicted the correct law, E = hf - P, of photoelectric emission. In 1915 after 10 years of experiment a sceptical Robert Millikan conceded that the formula was correct. It was Einstein who in 1909 saw the need for a theory of particle-wave duality. It was he too, who in 1917 saw the first signs that determinism was threatened. He understood that in the phenomenon of stimulated light emission, the exact moment at which each light quantum would be emitted, could not be determined from the initial state. To Einstein this was an unacceptable breakdown of causality which he hoped to fix later in a deeper theory. To other physicists who followed it became an experimentally verified fact of life. The breakdown of causality was, however, postponed by a semantic adjustment. We now say that quantum mechanics is indeterministic rather than acausal. We mean that although we cannot determine the outcome of an experiment, the result is still influenced only by the past state and not the future. Cartesian temporal causality could live to see another century.

In 1913 Niels Bohr used the theory of light quanta to explain the Balmer series of emission lines in the spectrum of hydrogen, but what did it mean? In 1923, Arthur Compton derived the relativistic expression for hard scattering of a quantum of light from an electron. The term "light quanta" was replaced by the word "photon" as if to celebrate its wider recognition as a particle. No longer would the reality of photons be questioned. It was impossible to deny the particular side to their nature when the Compton effect was photographed in cloud chambers and energy and momentum conservation was verified.

The almost fantastic story of those discoveries and the years that followed have filled many volumes on the history of science. In that golden age of physics many great scientists rose to the challenge. Heisenberg, Pauli, Fermi, Schrödinger, Dirac, ... the roll-call is endless. Now is a good moment to turn the clock back to the time of Newton and his theory of undulatory corpuscles. One can only marvel at the profound insight implied by this theory. To be sure, Newton was wrong to think that light is faster in dense media. Huygens and Fermat were correct that it slows down. It must also be admitted that everything Newton had observed was later consistent with the wave theory when it found its final form in Maxwell's equations. Yet Newton's anticipation of the quantum theory was no fluke. It grew out of a belief that the laws of physics were unified. Following the chemist and philosopher Robert Boyle, he guessed that everything was built from elementary units. It was Boyle who had christened them corpuscles. History recounts that this was inspired by alchemist sympathies. They wanted to believe that any form of matter could be transformed into another because they dreamt of becoming rich by transforming lead into gold. But their guess that such transformations might come about by rearrangements of the constituent corpuscles was founded on many observations of other physical processes. It was natural for Newton to suppose that light was produced by another transformation of this sort. We know now that he was right, and we should not scoff just because the theory was not based purely on empirical induction from solid observations.

With hindsight we can see the modern theory of light as a synthesis of the principles of Newton, Fermat and Huygens. Explaining how, will lead up to my thesis of the storyteller's paradigm, but first we must go back and trace the development of another principle.

It would descend to a maximum depth of 82.4km where it would reach a speed of 4580 km per hour and it would complete its journey in only 6 minutes 47 seconds.

The brachistrochrone puzzle influenced other mathematicians to look for general methods of solving other similar optimisation problems which involved curves, and so the calculus of variations was invented. Since it grew out of a physical problem, physicists wondered how the new maths might be applied to Newton's laws of mechanics more widely. Remember that according to Fermat's principle, a ray of light follows the line of shortest time through any system of mirrors and prisms. Could there be a more general principle to be found? Gottfried Leibniz was especially keen on the idea. He did not like the Cartesian exclusion of final cause and saw Fermat's principle as an example that demonstrated his point.

But applying Fermat's principle directly to mechanics does not work. Particles do not seem to be trying to get from A to B in the least time possible, otherwise they would accelerate towards their destinations. A free particle goes in a straight line so its path has the minimum length, but it would be better to have a principle which explains why it goes at constant speed too. Leibniz proposed that mechanics optimises the use of another quantity which he called action. Later, in 1744, Pierre de Maupertuis discovered how to make this idea work. For the single particle subjected to no forces the action is energy multiplied by time which is also half momentum times distance integrated along the path. When a particle travels from A to B in a fixed time interval, it does so with the least possible action. Maupertuis attached great philosophical significance to this principle and was ridiculed by Voltaire for doing so. Yet it is hard for a student learning mechanics not to be struck by the beauty and generality of the principle of least action when he first encounters it. Richard Feynman was one such student who heard about it from his high school physics teacher. The consequences for Feynman and for physics were profound, as we shall see.

The calculus of variations and the principle of least action were further developed in the eighteenth century by mathematicians such as Leonhard Euler and Joseph Lagrange. For any mechanical system moving in an energy potential, the action is defined as the kinetic energy minus the potential energy integrated with respect to time.

When the system evolves from an initial state to a final state at given times, it does so in a way which minimises the action. Euler and Lagrange showed how to derive the equations of motion of any system of particles from this principle. This energy difference in the integral is now called the Lagrangian and finding its form for more general situations is the key to any problem of theoretical physics. The principle of least action is a curious discovery from the point of view of causality in the same fashion as for Fermat's optical principle of least time. Recall that in classical mechanics (meaning deterministic motion without the quantum theory), given the initial positions and velocities of particles and the equations of force acting on them, you can in principle predict their subsequent motion. This is the principle of temporal causality. However, the principle of least action tells us how a system evolves given the initial and final positions of the particles and the equation for the action. It is as if the evolution of the system is determined equally by the past and future. Causality is only found indirectly through the derivation of the equations of motion and, apparently, our own psychological bias for prior cause.

The next in line to work on the action principle were William Hamilton and Carl Jacobi. They developed techniques now known as the Hamilton-Jacobi formalism which took them to the brink of discovering quantum mechanics in 1834, eighty years before its time. Recall that Huygens had used his theory of secondary waves to provide an explanation for Fermat's principle which reconciled it with causality. If Hamilton or Jacobi had considered a similar explanation of the principle of least action they could easily have found quantum wave mechanics. As it turned out, we only see this with the hindsight which came from eighty more years of experimentation. It is amusing to consider that we could write a fictional but almost plausible sounding history in which mathematicians discovered all the fundamental principles of physics without ever doing an experiment! In practice, Descartes has to concede that we need those empirical signposts to keep us from straying onto false paths. Does it have to be that way or is it just a human weakness?

In the real story it was 1923 that became the breakthrough year for quantum mechanics. Einstein had already suggested particle-wave duality for light quanta in 1909, but only when Louis de Broglie suggested that the same must apply to electrons did all become clear. He was only a student at the time but he realised immediately that the Hamilton-Jacobi theory pointed in that direction. Duality was, and still is, a hard lesson to learn. It had to be accepted because it made sense, at last, of Bohr's model of the atom. Many who would otherwise have doubted were swayed by convincing experiments. Electron diffraction from metals was seen as the perfect confirmation of deBroglie's matter wave theory. It was the time of the greatest revelations in physics. Within three short years the full theory of quantum mechanics was established and ten Nobel Laureates had earned their physics prizes in the process.

Feynman was born in New York City, 16 years younger than Dirac. He was a popular genius, an outspoken character, over-typically American. His approach to physics was practical and down to Earth. He was brilliant at finding new ways to look at things more clearly and solving physical problems. He found the modern approach to quantum field theory and renormalisation. He explained superfluids and tackled quantum gravity directly. He wrote a series of lecture notes on theoretical physics which will remain standard texts for decades to come. His masterpiece was an alternative formulation of the process of quantisation using path integrals.

Despite these different styles, Feynman was a great admirer of Dirac's work. In 1946 they met for the first time at a series of lectures which had been organised to celebrate the bicentennial of Princeton University. After giving a talk, Feynman found Dirac resting on the lawn outside by himself, and went out to talk to him. He wanted to ask about an expression which Dirac had written in a paper in 1933, about the relation between quantum mechanics and the principle of least action. Dirac had found what he thought was an approximate relationship but Feynman saw that it was exact. This was his opportunity to ask Dirac if he actually knew that. In fact Dirac had not known but said it was a very interesting observation. As a result, Feynman thought some more about it and had a marvellous flash of insight. Suddenly he could see a very direct and intuitive relation between the classical action and quantum theory.

The wave evolves according to a wave equation which Schrödinger gave us and which was later generalised by many others. Now Feynman, inspired by Dirac, realised that the evolution of the wave could also be described in terms of what he called "path integrals". The relationship between Feynman's path integral and Maupertuis's principle of least action is the same as that between Huygen's principle of secondary waves and Fermat's principle of least time. The square was completed.

According to Feynman, in order to find the evolution of the wave function for a single particle between given starting and end times, we must consider all possible starting points A, all possible finishing points B and all paths P which the particle could take in going from A to B. The value of the wave function at the start time is a complex number which can be pictured as the position of the hand of a clock. Suppose that initially the particle has a definite position at A so the wave function takes the value 1 there and zero everywhere else. We now want to know what the wave function will look like at some later finishing time. As a path P from A to B is traced out, the action can be calculated using the classical equations of Lagrange. Imagine that the hand of the clock turns as if clocking up action along the path until it gets to B so that it ends up at some other position on the clock face. For each path from A to B there is a different position value. To get the final amplitude of the wave function at B you have to sum up, or integrate, the values for all the paths. This path integral has a built in normalisation so that the final answer has a sensible value.

The evolution is wavelike since the turning hands of the clock are like the phase of a wave. When the dials read the same values they add together like constructive interference. When they point in opposite directions they cancel like destructive interference. Constructive interference is most pronounced when paths near to the minimum of the action are added together. This explains why the principle of least action describes the motion of the particle in the classical limit.

The path integral makes sense, at last, of the theories of light of both Huygens and Newton. Previously seen as rivals, they are now seen as complementary. The path integral incorporates Huygen's secondary waves and generalises his explanation of Fermat's principle, but it also describes light as particles with an undulatory nature as Newton wanted.

But quantum mechanics deals with much more than just light. Any system which has a classical principle of least action can be quantised using the methods of Dirac or Feynman. A system of many particles interacting through forces which conserve energy can be dealt with in this way. An example is an atom consisting of a nucleus with its entourage of electrons. Classically we would describe such a multi-particle system by giving the positions of each particle in space. The quantum wave function of one particle is a complex valued function on the 3 co-ordinates of space, so it might have been expected that the quantum wave function of n particles would involve n such functions. In fact it is more complicated than that. The wave function is a much bigger complex valued function of the 3n co-ordinates of the positions of all the particles.

It is non-local in the sense that it does not just give independent wave functions for each particle. It also describes correlations between them. If a group of n friends goes out to town for the evening you could give a probability for each bar, club and cinema, that each friend will be there at 11 o'clock. If there are h such haunts that they like to go to, there would be nh such probabilities. However, these probabilities alone would be a very poor description of the total behaviour because some friends like to stick together and are more likely to be found together. There are actually hⁿ possible situations at 11 o'clock and to account for all possible circumstances you must give the probability for each one. The situation for particles is similar except for a few important details. Firstly, as already said, the wave function gives a complex number rather than a real number for each possibility. Also, there are an infinite number of places the particle can be at any given instant, but it may be useful to suppose that space is discrete and finite with only a fixed number h of points. Another crucial distinction between particles and our group of friends is that particles do not have names. There is no way to tell photons apart. They are absolutely identical. This means that we cannot distinguish the difference in circumstance if any two photons are swapped over. We only need to give a probability for the number of photons which can be found at each place. This is less than hⁿ but it is still a large number.

Electrons are a little different again. They are also indistinguishable like photons, but they never appear together in the same place. Electrons are like a group of anti-social friends who detest each other so much that each one avoids being found in the same haunt as any other. Particles actually have just these two kinds of social behaviour. Either they are like photons and do not mind being together, or they are like electrons which stay apart. Particles which are like electrons are called bosons and those like electrons are called fermions.

In the path integral of the system we cannot deal with the path of each point separately because they interact through electromagnetic forces. We must consider all ways in which the system of many particles can evolve from a given classical starting state to a final one. The action for each such possible history contributes to the evolution of the wave function. I hope that the reason for calling it a sum over stories is now emerging. We are looking at stories of particles, like a story of a group of friends who go out on the town. The story has a given beginning and a given ending and we must consider all possible stories which fit; where they could be at each moment of time. In the macroscopic world where physics appears classical, we see only one story but we know that in the microscopic world there are many stories. We are just seeing the one which dominates through constructive interference.

It is worth taking a moment to contemplate the complexity of the system being described. If you were an engineer charged with the task of programming a computer to simulate a galaxy at a level of detail where each particle is described individually you would balk at the task. Even doing it classically, you would require a high precision variable for each co-ordinate of some n = 10⁷⁰ particles, plus a field strength for the electromagnetic forces at each point of a closely spaced lattice over the entire galaxy. That might need h = 10⁸⁰ points. If you are required to solve the problem with quantum mechanics you need to cover the full wave function. If each particle was behaving independently you could get away with about hn = 10¹⁵⁰ variables, but the full wave function requires more like (h/n)n = 10^10⁷¹. Even with today's powerful computers some further approximations will be necessary.

Sometimes people talk about the "many worlds" interpretation of quantum mechanics and the multiverse of possible universes. Sceptics cannot accept it because it is hard to believe that so many things are going on in parallel. Yet quantum mechanics is a theory of many things happening at once and the huge size of the wavefunction for all the particles of the universe is what makes quantum mechanics work. Today physicists are looking at ways to harness the power which lies hidden in these functions. It may be possible to tame them in quantum computers which will do many simultaneous computations as if they are each happening as a separate story.

The Feynman sum over stories is a realisation of the storyteller's paradigm. It is the most fundamental principle known in physics. The quantum theory is more general and more fundamental than any other theory because it must apply to all physics if it applies to any. If we wish to understand why we exist we should not look to the big bang where we think the universe began because the temporal causality of Descartes is not what this paradigm is about. Our real origins lie in the quantum principles which are held in the physics of all times and all places.

The quantum field theories always describe the quantum interactions of many particle systems. Feynman was able to use his path integrals to understand the process better. He found that the equations of quantum field theory could be written out as a sum over diagrams, now known as Feynman diagrams, which show the paths and interactions of particles

The diagrams look just like the paths of particles which described the first quantisation of many particles except now there are nodes where particles can interact. There is a subtle duality between the fields and particles. Quantising particles gives fields, and quantising fields gives particles. Like the cliché of a novel about a writer, second quantisation is confusing and perhaps there is more to be understood about what the double process means.

Pure mathematicians do not usually use ideas from physics to decide what is worth studying. Yet often mathematicians working independently discover the same theorems. Perhaps one day computers will be so powerful that we will be able to simulate creative thought in a computer. Then we will verify that the same mathematical concepts can develop without any influence from physics.

According to Plato's theory of forms, the world of mathematics exists in its own right and knowledge is attainable through the study of logic. There is a hierarchy which puts maths at the foundation, physics above, natural history over that and cultural knowledge at the top. This is the scene of reductionism through Descartes' ontological causality. All knowledge is dependent on what is below, but in our lives we have more direct experience of our culture and natural history. Ultimately we want to explain our own perceptions. There is a positivist philosophy which takes the opposite extreme to Platonism saying that only the things we perceive directly are real. Perhaps the truth is a mixture of both. Is there a larger realm beyond mathematics where different rules of logic can be tried out? Perhaps there is, but it seems like it must contain itself.

The role which mathematics plays in physics is certainly a curious one. It is true that mathematics is the language of the universe. No physicist can work without it. A theory which is expressed in words may have some meaning but it is impossible to verify its correctness unless it is backed up with a mathematical model which makes testable predictions. It is hard to resist believing in an even greater significance of mathematics because we find that the most abstract concepts are applicable to the real world. It is this that Plato recognised so long ago.

If our experiences are like stories then the laws of physics are the grammar of the language in which it is written. But the same story can be told in many languages so how important is the language of physics? We still could not tell a story without words or something similar. The laws of physics can also be written in many different equivalent ways and it is not clear that any one way is more fundamental. This is a special characteristic of the laws of physics. Feynman remarked that if you modify the laws much you find that you can only write them in fewer ways.

In one language of physics, the Feynman diagrams are the words and sentences. We could collect together many diagrams and connect them together in different ways just as we can put together sentences to make paragraphs and chapters. The stories of our experience are told in that way. There are symmetries and dualities which translate from one language to another. In the Platonic sense those diagrams are the forms which exist in the world of mathematics. They join together in every possible way which the rules of logic, the grammar, permit. There is no need for temporal causality in this language. We do not need to look to some creation event where the universe was set in motion. The illusion of temporal causality itself may emerge from such an event but it does not have to be fundamental. It is a part of our story but stories with less linear structure are also possible.

What about the storyteller? Remember that in his mind he did not invent the story. He discovered it. He himself is part of another story. Perhaps this is reflected in the rule of second quantisation. Why do the Feynman diagrams obey the particular rules they do? Those rules determine which particles exist and how they interact. Do they represent some especially rich language? If the storyteller's paradigm were taken to its logical conclusion there would be no fixed Feynman rules. Feynman's sum over stories should be just part of a much larger sum over all possibilities. All of these things remain mysterious and we do not yet know the full grammar and vocabulary of physics.