Résumé

L’auteur présente son point de vue personnel, selon lequel le problème de l’unification de la relativité générale et des théories quantiques réside dans leur grande différence de caractère. La relativité est une théorie classique offrant une description littérale de la réalité alors que toutes les théories quantiques sont abstraites et n’offrent qu’un moyen de faire des prédictions. L’auteur considère que le temps pourrait être le problème le plus important et examine la proposition de Julian Barbour, selon lequel il n’existe pas. Il se livre à une conjecture spéculative relative à la notion de causalité non standard introduite pour la première fois par John G. Cramer, puis propose une extension de cette idée, en montrant comment elle pourrait conduire à une unification, à une meilleure compréhension du cerveau et du Big Bang.

Abstract

The author presents his personal involvement with cosmology as a scientific artist. He gives an autobiographical summary of his life, starting from his childhood interests in astronomy and constructivism through to his abandoning a possible career in physics to become a kinetic artist. He describes in details his work with kinetic sculpture, in particular, his many sculptures based on waves, the Timeless Universe and Abstract Cosmology Installations. This last work was shown at the Reina Sofia Museum, in Madrid in 2008 as part of the Souls and Machines Exhibition.

The author presents his personal view that the problem of unification of general relativity and quantum theories lies in their very different character. Relativity is a classical theory that provides a literal description of reality, whereas as all quantum theories are abstract and provide only a means of making predictions. The author identifies time as perhaps the single most important problem and discusses Julian Barbour’s proposal that in does not exist. The author presents a speculative conjecture concerning non standard causality first introduced by John G Cramer and then proposes his own extension to this idea, showing how it might lead to unification, a better understanding of the mind and the Big Bang.

Introduction

The Wave Equations

Early on in my research, I made an important discovery that was to be the foundation for many later works. I discovered an interest in waves and vibrations and a particular way that they could be visualized. Waves come in many forms but what perhaps makes them so intriguing is that the many forms share so many properties. When you sense a wave, it contains something universal that it shares with other waves. I started my research in the 80s when new dynamical theories came to prominence known generally under the title Chaos. Now Chaos theory has numerous fields and areas of application. The most famous is perhaps the Mandelbrot Set. This is a beautifully complex mathematical form, but it does not teach us everything we need to know as it is static and Chaos is chiefly a theory about change. Perhaps the Butterfly Effect is the most well known idea that well embodies the idea of Chaos. It says the smallest and most unknowable of inputs can lead to the largest most drastic consequences. In the main the most interesting discoveries of Chaos Theory are to do with the emergence of new forms of pattern and order and are not really chaotic. Lynn Margulis is most famous in this field with her contributions to understanding the origin of life.

What I discovered was a realm of waveforms that could be modulated between the more familiar harmonic forms and these new chaotic forms. I have given them different names at different times but in the first place these waves I explored were waves on a string and so it was natural to think about their connection to string theory. My waves are literally made with string. My original goal had been to build a miniature form of skipping rope powered by two model motors at each end. To my delight when I first switched on my gadget, it exhibited not one simple harmonic form but a host of varied forms. These forms are fascinating to look at and can be enhanced by a variety of methods of lighting them.

In part these forms can be understood using the conventional theory of harmonics but it is their chaotic properties that give them their most distinctive character. In the first place I built small desktop sized sculptures that exhibited these beautiful forms. These were illuminated with chromastrobic light, light that changes colour faster than the eye can see. The colours are still visible when illuminating rapidly moving objects, different parts of the vibrating form will be lit in different colours depending on their phase relationship. Gradually I experimented with building larger and larger pieces until they grew to monumental size as much as 12 metres high.

Today I continue to work with waves and am currently involved with a program to develop more sophisticated chromastrobic light. The lights I am using now are the latest high power LEDs, arranged in groups of red, green and blue; they can produce any colour by varying their relative intensity. I am working toward having complete control of the exact colour at a very high frequency that is synchronized with the wave forms. In this way I can bring out distinctive subsections of the wave related to a particular phase in a different colour. Currently we can divide the phase of the waves into eight regions of variable length and assign an individual colour to each of these, varying the colours freely over time. I have been assisted in this work by Louis Norwood, a young and enthusiastic electronics engineer.

Comparing string theory with the strings in my work, the most radical difference is not the scale or the dimensionality, huge those differences are, it is that string theory deals with vibrations that are very pure harmonics. The physicists’ strings behave like the strings of a musical instrument and do not undergo vibrations with large amplitudes and complex movements. I am sure physicists are for the most part are unaware of my discoveries and it would not sit comfortably within their framework. For string theorists, exploring the higher dimensionality is the primary challenge, the waves in string theory are straight forward. Although a number of mathematically minded people have given consideration to a theoretical analysis of the behaviour of the strings in my sculpture, no one has produced a convincing description.

Timeless Universe

Discovering the chaotic behaviour of string waves was pure serendipity. More recently I have consciously chosen to include a scientific theme in my work. The most complete and perfected installation I have created to date, Timeless Universe, was inspired by the work of Julian Barbour. His book, The End of Time, became the starting point. Inspired by his work but seeking to contextualize it within the wider human search for a cosmology, I chose texts from many other cultures along with signs, mathematical symbols and equations, combining them into a flow of images that were projected onto a collection kinetic light sculptures.

The installation was created at the Sala Parpallo, a gallery in Valencia. I am much indebted to the staff and in particular my curator Angela Molina for making this possible. The gallery is housed in a five hundred years old building and was, as it turned out, particularly well suited. Originally a nunnery, part of the building was sold to the city council some years ago. The main exhibition space was originally the refectory. It is a tunnel shaped room with an arched ceiling around thirty five metres long and six metres tall and wide. At my suggestion they agreed to seal all the windows and repaint the room entirely black and provide a fitted black carpet. It took on a cave like quality of extreme darkness. The space was divided into three sections. Visitors entered from one end and found themselves drawn deeper and deeper in. The first area showed a collection of wave based sculptures, the second a collection of other spinning kinetics, but it was the last area that occupied almost half the total space where I created a new collection of works that together formed the Timeless Universe installation.  They were lit with video projectors but because visitors were not viewing screens but a collection of kinetics, many did not realise how they were lit at all. The impression was of luminous glowing forms suspended in a dark space. Each form possessed a high speed component whirring at a velocity that blurred the details of construction. The material out of which they are made appears to be light, it is transparent and does not look like ordinary solid matter at all. Onto these transparent forms are projected slowly changing images.

The images are generated in real time with code I have written. Early on in my career I dabbled with code writing. I remember the first rush of this most clearly from my days as an art student. Our college at that time did not possess a single computer, but I jumped at a chance to go up to London on a special short course to learn about computer art. In the space of a few days I grasped the elements of a simple language that’s allowed its user to generate designs printed on tractor feed paper using only the standard ASCI symbols. Unlike a standard console, the specialised language allowed the user to define rules for what characters shall be printed at a particular location on the page where the locations are treated as members of a matrix. I rapidly started to write codes that embodied the principle of growth and expressed it as communities of ‘O’ and ‘X’ and other simple signs.  I returned to my regular college carrying a sheaf of tractor feed as thick as a phone directory.

This was to be an isolated taste. I must have been on that course in the mid 70s, just a short while before the advent of personal computers, and when PCs did appear, I was not an early adopter as I judged that what was possible on those models still lacked the visual richness that could be achieved by analogue means. It was not until the 90s that I returned to computing and finally found again my love of writing code. This time, with a colour monitor instead of a tractor feed printer my excitement really took off. I learnt the programming language Delphi. I have tried other languages, but I find this language is very well suited to my needs. It is powerful, creating fast executable code far superior to anything I could achieve with Java or Visual Basic and easier to learn than C++. Over the years I have learnt how to write commands to OpenGL and developed a virtual world of my own that I can populate with virtual kinetic sculptures that subsequently I can project onto my actual kinetics. This has allowed me to bring together my interests in kinetics, a media based on moving parts, with computing in my own distinctive hybrid.

For Timeless Universe, the crucial extra ingredient I knew would be the choice of a suitable collection of « textures ». To a 3D programmer a texture is an image that is used to paint onto a 3D form. The process of painting can be intentionally faithful to the original to image. Construct a box and paint it with suitable photos of a house viewed from each side and it takes on a life like quality. Alternatively we can play tricks with the texture. It can be programmatically distorted so as to make it more or less unrecognizable. At some point around five years ago I created a program I called Cubism, as it possessed a comparable visual feel to the movement in painting and used techniques with modifying textures to explore the boundaries between recognizable and unrecognizable. This I decided would be perfect for Timeless Universe as it well captures our sense of intellectual struggle to comprehend ideas in a visual way. I selected images, many of them from rather dry mathematical sources and transposed them to be part of this kinetic world.

The large installation, Abstract Cosmology, I created for the Reina Sofia in 2008 was entirely new but again explored a realm between recognizable and unrecognizable. I chose as my subject matter a stream of images that relates closely to the earlier piece and continues to explore my interest in non standard causality. I shall have more to say about this at the end of the essay.

The Problem in Physics

I will begin by trying to describe why I think it is so hard to combine relativity and quantum mechanics. Physicists describe relativity, both special and general, as classical theories.  All science that precedes quantum theory is considered to be classical. The big break in thinking that comes with the quantum is largely associated with the introduction of uncertainty but while that is one way to understand the difference between these two realms, there is another perhaps much more important difference. Classical science attempts to build a complete description of reality. In principle a sufficiently thorough knowledge of the world combined with the right theories should allow us to know everything. What is missing from our observations can be inferred from theory. Of course quantum mechanical uncertainty we know now makes this impossible but there is something else different about the classical way of thinking. In classical physics we understand that the scientific concepts actually exist: for example a gravitational or magnetic field is really present and we can measure it. While Einstein replaced the gravitational field with the concept of curvature of spacetime, this curvature is every bit as real and measurable. In quantum mechanics and all later ideas, there is no claim that the ideas under discussion necessarily exist at all. Ideas can become abstract. A quantum state is a purely mathematical entity, it has no physical substance and could not have, as far as we can tell, and yet the state becomes a powerful way to make predictions.

The transformation from a realistic way of thinking to an abstract one is central to how physics changed during the 20th century. While some of the most profound discoveries, for example atoms and their nuclei definitely exist, things become less clear when discussing individual particles or quanta. They exist when we observe them but what is happening between observations remains unknown. By moving to an abstract approach it liberated physicists to think in ways that would have been impossible before: suddenly mathematics was no longer slaved to being a literal description of the world. Any idea, however strange was possible. Relativity when considered in this light seems quite ordinary and old fashioned, and yet at the time Einstein first conceived it, not only was it revolutionary but carried with it deep enigmas that were to trouble Einstein. Much of this tends to be overlooked in the description of the subject because it all seems such a minor point compared with the difficulties that came later.

Einstein worried about spacetime. To see why, consider this. He had shown that how we determine time is dependent on our frame of reference. For observers moving in different frames, not only are their clocks changing at different rates, but their judgement of when events occur simultaneously changes. In a Newtonian world there is only one shared moment that is now, the only time that actually exists. But Einstein found that this is not the case at all. Einstein realised that his theory is saying that this thing we call « now » depends entirely on how you are moving relative to the world around you. And since different observers are each moving in their own frame of reference, then all these « nows » must co-exist. The only consistent way to understand spacetime is to say that it all exists, the past, the present and the future, everything. This troubled him but it is the correct way to think of relativity. It is an entirely static theory of existence where everything resides in a block of spacetime and if we are to accept its literal truth, then not only does the past continue to exist but the future fully exists and is pre – determined. Uncertainty must be an illusion, and its appearance in quantum mechanics the consequence of some still to be discovered limitations in our knowledge. As a piece of classical thinking this cannot be faulted. We must take literally the existence of the physical ideas. But today physicists do not consider spacetime to be a real physical thing. It, like all other ideas in physics, is seen to be a mathematical idea. Einstein lost the battle but did he lose the war? It turns out to be extremely difficult to entirely expunge this classical way of thinking.  To bring about a final peace treaty, and find unification, we need to resolve the underlying conflict in ways of thinking.

Time is one of those deep problems, and if it could be understood better, it might make it easier to achieve unification. I now return to Barbour’s suggestion that it does not exist.  Barbour’s proposal accepts the co-existence notion that Einstein was forced to confront but casts it into a new entity: a configuration space. In trying to understand what that is, I begin as Barbour does with considering the triangle. Imagine a collection of triangles. We are only interested in their geometric properties but we could imagine them as actual physical objects, say like parts of a jig saw collected in a bag. This bag full of triangles is a physical representation of a « configuration space ».

More abstractly we can now imagine using Cartesian coordinates, x, y and z to represent the lengths of the sides of the triangles. Pick a point in space and its coordinates then tell us the particular triangle this point represents.  So our easy to imagine 3 dimensional space can be used as a way of representing all possible triangles. A triangle close to the origin is small. A triangle far from the origin but close to one axis has one small side. An equilateral triangle must lie along a line equidistant from all three axes and satisfy the equations: x = y = z.

Now if we want to construct a configuration space to represent all possible quadrilaterals, we would have to add an extra dimension. One extra dimension will be enough if they are all shapes that can be cut from a flat material but if we further allowed them to be four points in 3D space, then the situation gets more complex again. I will not continue but you will gather that Barbour’s idea requires more and more dimensions. The configuration space becomes impossible to visualise but continues to be simple to express mathematically. The shape however complex in each case is represented as a single point in that configuration space. A configuration space for the shape of the universe then becomes a hypothetical entity that has extra dimensions to indicate the positions of every particle in the entire universe. It has to have at least 3 times as many dimensions as particles in the universe at a minimum. More if we want to assign properties to the particles. While it might seem like a horrific extra complication to replace our familiar idea of reality with this infinitely dimensional entity, to Barbour it offers elegant simplicity because now the entire universe is a single point in this greater whole. To be more accurate I should say the entire universe at any particular moment.

Configuration space can be imagined then as home to a collection of points, all of which are different moments, or « nows », as Barbour prefers call them. The space is huge: large enough to accommodate all the variety of possible configurations as implied by quantum mechanics. We are no longer limited to a single future. Barbour has done a great deal of work on showing that his concept is consistent in principle with physics as we know it, both general relativity and quantum mechanics but what else does it tell us? I asked him whether time travel was possible or precognition. He was dismissive of such ideas and insisted that although his idea encompassed the idea of all possible states of space and time coexisting, it did not imply any extra interconnectedness between those states. This I found unsatisfying.

One of the other great unsolved enigmas is the problem of non locality. Two quanta, once entangled, remain interconnected even when they are moved arbitrarily far apart in space and time. Non locality I have always suspected implies that neither space nor time is fundamental. Distance is as much of an illusion as time. Barbour’s proposal does not address this problem, nor does it allow for any of the more exotic ‘science fictional’ possibilities I asked about. In short despite being mathematically and philosophically strange, it describes a world that still behaves in a normal, perhaps one might say semi classical way.

To other physicists this is potentially a plus. Although they work in the realms of abstract and strange mathematical ideas, for those idea to be useful they have to make predictions that are consistent with the world as we know it in the main. Physics advances almost entirely through very subtle changes in our expectations. Mostly a new theory will predict exactly the same as an old theory but in some very specific circumstance it should make a different prediction and that then becomes the crucial test, as for example when Einstein predicted that the sun would bend light and Eddington confirmed this prediction during a solar eclipse in 1919.

For a physicist today to invent a new idea, the first thing he must do is develop it to the point that he can subject it to some kind of test. Observational tests that would provide proof are the hardest to find and in the age of String Theory have become distant goals. Instead the physicist must look for more abstract and general ideas as a guide. Is his idea self consistent? Is it consistent with the known laws of physics most of the time? This process of critical assessment means that every creative mathematical idea is subsequently subject to a very harsh process of evaluation. There are far more mathematical possibilities that are more or less certainly wrong than any that are likely to succeed.  The situation has become far worse than the proverbial needle in a haystack. The price to pay for going into the realm of abstract thinking is that it has thrown up such a wealth of hypothetical universes.

One of the critical processes that could be applied to test a new theory is to consider how causality operates. It has long been known that physics as it stands now does not contain a clear arrow of time at the fundamental level. This is something of a mystery as although it cannot be deduced from currently known first principles the community of physicists are mostly in agreement that any form of time travel must be impossible. For that reason any new idea that would imply this possibility is likely to be given short order and consigned to the bin. Perhaps physicists are being over hasty in dismissing a class of possible theories as a result of the expectation that this is good test of its probity.

Conjecture

In 2006, John G Cramer, of Washington State University announced that time travel of information might be possible and entirely consistent with standard quantum mechanics. His announcement was met by a chorus of scepticism by other physicists and he failed to receive any official funding to test his idea. He did receive some funds from private donors but did not succeed in his initial attempts with the limited resources he had available to him and the idea rapidly fizzled out, failing even to achieve the notoriety of great failures such as cold fusion. I discussed the idea with a number of physicists and in most detail with Renaud Parentani of the University Paris-Sud. There seems little doubt that Cramer’s specific proposal was almost certainly wrong but the underlying idea was not without merit. It arises from the symmetrical nature of time as expressed in quantum mechanics. The Schrödinger equation evolves over time but with no clear indicator of what direction should be labelled forwards and backwards in time. Schrodinger’s equation specifically contains both a ‘t’ and a ‘-t’ component and Cramer had in 1986 proposed an interpretation of quantum mechanics where information was exchanged in both directions through time but his initial idea did not contain a way to observe this process. While many physicists see no reason to expect causality to ever operate backwards, there is no 100% clear proof of why it should not. Yakir Aharanov of Tel Aviv University and the University of South Carolina is another who continues to explore the time symmetric nature of quantum mechanics.

Sir Roger Penrose of Oxford University has argued that the human mind cannot be explained using the known laws of physics. His conjecture is detailed and technical and rests upon an extension of the ideas developed by Alan Turing with his Universal Turing Machine. He discusses problems that are non computable, specifically certain hard problems in mathematics but by implication I would argue that no computer, however powerful, will be capable of imagination and creativity, since these are also non computable. They are very distinctly human special qualities. The brain maybe thought of as a thinking machine but it cannot be understood by comparison with a computer. Penrose expresses the view that quantum mechanics must be wrong but gives no indication of how changes to physical law could lead to a deeper understanding of mind.

My experience tells me that precognition is real. I wonder: could creative people have some mental pathway giving them flashes of insight through contact with the future? I suspect I am not alone in having this feeling. Perhaps creative people have a greater sensitivity to what does not yet exist? An ability to anticipate that does not work in a rational way? The human mind, even the mind of a mathematician, is not always entirely reasonable. My own speculation leads me to wonder whether precognition could be the missing ingredient that allows us too understand mind. I propose we need to change our understanding of causality. Cramer I believe is right but his scope of focus does not take in this human aspect. Bringing together Cramer’s speculation with Penrose’s conjecture, I propose a deeper understanding of the human mind can emerge from changes in physics specifically relating to the structure of causality. Those same changes would have profound implications for the unification program. There is at least a remote possibility that one single breakthrough might lead to major developments in understanding in these two apparently unconnected fields of study.

I shall briefly explore the implications of precognition and a hypothetical time machine for information. I shall show that, subject to certain constraints, their existence does not lead to logical contradiction. Let us make the assumption that as far as any one observer is concerned there is something that shall be called future.  The future we can be less sure of than the past or present and I will represent the general situation in figure 1 where I conjecture some connection from the future to the present.

I propose that we divide the future into two realms, deterministic and non deterministic as shown in Figure 2. As an example of deterministic, consider the paths of the planets. They are almost perfect examples of the power of classical physics to make precise predictions where quantum mechanical uncertainty plays no part at all. The delta function is used in quantum mechanics to represent a situation where there is no uncertainty. There is only one thing that can happen and that is expressed by saying out of all the hypothetical possible futures, only one fine line contains a non zero and indeed certain probability of happening. In the example I have sited it is the paths of the planets. If we imagine some hypothetical time machine for information, what would this be? Let us say we discover waves that precede an event. Then rather than doing calculations to predict the position of the planets, we could use a new form of telescope to look for the planets future locations. This is just one aspect of the future that is certain.

Citer cet article

Paul Friedlander, « Outside Time », [Plastik] : Être ici et là : La relativité générale et la physique quantique #01 [en ligne], mis en ligne le 8 janvier 2010, consulté le 21 novembre 2024. URL : https://plastik.univ-paris1.fr/2010/01/08/outside-time/ ISSN ISSN 2101-0323