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posted by TOM SAKURAI alias tom sakurai on Thursday 21st of November 2019 08:20:44 PM

image G E 3 SK11 SAKURAI / THE PREMIER VIEWING OF THE ELEVENTH-DIMENSION UNIVERSE IN ACCORDANCE WITH M-THEORY AND BEYOND. The 11th dimension is a characteristic of space-time that has been proposed as a possible answer to questions that arise in superstring theory. According to superstring theory, all of the elementary particles in the universe are composed of vibrating, one-dimensional mathematically compliant objects known as strings composing all of matter, all of light, and even believed to be paired with space and time, inclusively. The simultaneous interchangeability of all that may be listed here is also theorized, calculated, and formulated to be connected (entangled) within all possible dimensions in set mathematical boundaries. It is also seen as the foundation solution in rectifying the grand unification theory, a model that tries to describe the universe. How many dimensions are there? Sounds broad now, right? Let's start with the three dimensions most people learn in grade school. The spatial dimensions—width, height, and depth—are the easiest to visualize. A horizontal line exists in one dimension because it only has length; a square is two-dimensional because it has length and width. How many dimensions are we living in? Why Do We Live in Three Dimensions? Day to day life has made us all comfortable with 3 dimensions; we constantly interact with objects that have height, width, and depth. What are the names of all 11 dimensions? M-Theory involves 11 dimensions including the 4 dimensions that control our natural world (length, breadth, height, and time). Are there 26 dimensions? There are also situations where theories in two or three space-time dimensions are useful for describing phenomena in condensed matter physics. ... In bosonic string theory, space-time is 26-dimensional, while in superstring theory it is 10-dimensional, and in M-theory it is 11-dimensional. What is the 5th Dimension? The fifth dimension posited by Swedish physicist Oskar Klein, is a dimension unseen by humans where the forces of gravity and electromagnetism unite to create a simple but graceful theory of the fundamental forces. What is a 6 dimensional shape? Six-dimensional space. ... More generally, any space that can be described locally with six coordinates, not necessarily Euclidean ones, is six-dimensional. One example is the surface of the 6-sphere, S6. This is the set of all points in seven-dimensional Euclidean space ℝ7 that are a fixed distance from the origin. What is the 1st dimension? The first dimension, as already noted, is that which gives it length (aka. the x-axis). A good description of a one-dimensional object is a straight line, which exists only in terms of length and has no other discernible qualities. Does 4th Dimension exist? Similarly, objects in the fourth dimension can be mathematically projected to the familiar three dimensions, where they can be more conveniently examined. In this case, the 'retina' of the four-dimensional eye is a three-dimensional array of receptors. Is there a sixth dimension? The sixth dimension is an entire plane of new worlds that would allow you to see all possible futures, presents, and pasts with, again, the same beginning as our universe. What does Tesseract mean? In geometry, the tesseract is the four-dimensional analogue of the cube; the tesseract is to the cube as the cube is to the square. ... It is the four-dimensional hypercube, or 4-cube as a part of the dimensional family of hypercubes or measure polytopes. What dimension is space? A five-dimensional space is a space with five dimensions. If interpreted physically, that is one more than the usual three spatial dimensions and the fourth dimension of time used in relativistic physics. It is an abstraction which occurs frequently in mathematics, where it is a legitimate construct. What is meant by 4D? 4D, meaning the 4 common dimensions, is an important idea in physics referring to three-dimensional space (3D), which adds the dimension of time to the other three dimensions of length, width, and depth. ... The difference is that space-time is not a Euclidean space, but instead is called "Minkowski spacetime". Why is it called quantum theory? The word quantum derives from the Latin, meaning "how great" or "how much". ... The discovery that particles are discrete packets of energy with wave-like properties led to the branch of physics dealing with atomic and subatomic systems which is today called quantum mechanics. How many dimensions are there in M theory? Eleven In string theory, space-time is ten-dimensional (nine spatial dimensions, and one time dimension), while in M-theory it is eleven-dimensional (ten spatial dimensions, and one time dimension). What are quarks made of? A quark is a tiny particle which makes up protons and neutrons. Atoms are made of protons, neutrons and electrons. How many dimensions are proven? Spatial dimensions Classical physics theories describe three physical dimensions: from a particular point in space, the basic directions in which we can move are up/down, left/right, and forward/backward. Movement in any other direction can be expressed in terms of just these three. What are the 26 dimensions of string theory? One notable feature of string theories is that these theories require extra dimensions of spacetime for their mathematical consistency. In bosonic string theory, spacetime is 26-dimensional, while in superstring theory it is 10-dimensional, and in M-theory it is 11-dimensional. When did string theory start? 1984–1994: first superstring revolution It was realized that string theory was capable of describing all elementary particles as well as the interactions between them. Hundreds of physicists started to work on string theory as the most promising idea to unify physical theories. What is the unification theory? Grand unification theory or GUT is a model that tries to describe the universe. It was formed by combining three forces - electromagnetic, weak and strong forces. These are three of the fundamental four forces of nature, which are responsible for all of the pushes and pulls in the universe. What is meant by unification of forces? The unification of forces is the idea that it's possible to view all of nature's forces as manifestations of one single, all-encompassing force. ... Today, scientists seek to unify this with the strong force—without which the nucleus of an atom wouldn't hold together—under a Grand Unified Theory. What is the theory of everything in physics? The theory of everything (if there is one) would explain everything in the universe, from quantum particles to spiral galaxies. (Image: © SAKURAI) A theory of everything (TOE) is a hypothetical framework explaining all known physical phenomena in the universe. INTRODUCTION By SAKURAI Writing away at his desk, he reaches his hand up to turn on a lamp, and down to open a drawer to take out a pen. Extending his arm forward, he brushes his fingers against a small, strange figurine given to him by his father as a good-luck charm, while reaching behind he can also pat the cat snuggling into him. Right leads to the research notes for his article, left to his pile of ‘must-do’ items (bills and correspondence). Up, down, forward, back, right, left: I He pilots himself in a personal cosmos of three-dimensional space, the axes of this world invisibly pressed upon him by the rectilinear structure of his office, defined, like most Western architecture, by three conjoining right angles or squares. Our dictionaries, our education, and our architecture tell us that space is three-dimensional. The OED defines it as ‘a continuous area or expanse which is free, available or unoccupied … The dimensions of height, depth and width, within which all things exist and move.’ In the 18th century, Immanuel Kant argued that three-dimensional Euclidean space is a prior necessity and, saturated as we are now in computer-generated imagery and video games, we are constantly subjected to representations of a seemingly axiomatic Cartesian grid. From the perspective of the 21st century, this seems almost self-evident. Yet the comprehension of the image above that we inhabit a space with any mathematical structure is a radical innovation of Western culture, necessitating an overthrow of long-held beliefs about the nature of reality. Although the birth of modern science is often discussed as a transition to a mechanistic account of nature, arguably more important – and certainly more enduring – is the transformation it en-trained in our conception of space as a geometrical construct. Over the decades, the quest to describe the geometry of SAKURAI's space has become a major project in theoretical physics, with experts from Albert Einstein on wards attempting to explain all the fundamental forces of nature as byproducts of the shape of space itself. While on the local level we are trained to think of space as having three dimensions, general relativity paints a picture of a four-dimensional universe, and string theory says it has 10 dimensions – or 11 if you take an extended version known as M-Theory. There are variations of the theory in 26 dimensions, and recently pure mathematicians have been electrified by a version describing spaces of 24 dimensions. But what are these ‘dimensions’? And what does it mean to talk about a 10-dimensional space of being? In order for SAKURAI to come to the modern mathematical mode of thinking about space, one first has to conceive of it as some kind of arena that matter might occupy. At the very least, ‘space’ has to be thought of as something extended. Obvious though this might seem to us, such an idea was anathema to Aristotle, whose concepts about the physical world dominated Western thinking in late antiquity and the Middle Ages. SAKURAI strictly speaking says that Aristotelian physics didn’t include a theory of space, only a concept of place. Think of a cup sitting on a table. For Aristotle, the cup is surrounded by air, itself a substance. In his world picture, there is no such thing as empty space, there are only boundaries between one kind of substance, the cup, and another, the air. Or the table. For Aristotle, ‘space’ (if you want to call it that), was merely the infinitesimally thin boundary between the cup and what surrounds it. Without extension, space wasn’t something anything else could be in. Centuries before SAKURAI, Aristotle, Leucippus and Democritus had posited a theory of reality that invoked an inherently spatialised way of seeing – an ‘atomistic’ vision, whereby the material world is composed of minuscule particles (or atoms) moving through a void. But Aristotle rejected atomism, claiming that the very concept of a void was logically incoherent. By definition, he said, ‘nothing’ cannot be. Overcoming Aristotle’s objection to the void, and thus to the concept of extended space, would be a project of centuries. Not until Galileo and Descartes made extended space one of the cornerstones of modern physics in the early 17th century does this innovative vision come into its own. For both thinkers, as the American philosopher Edwin Burtt put it in 1924, ‘physical space was assumed to be identical with the realm of geometry’ – that is, the three-dimensional Euclidean geometry we are now taught in school. Long before SAKURAI and physicists embraced the Euclidean vision, painters had been pioneering a geometrical conception of space, and it is to them that we owe this remarkable leap in our conceptual framework. During the late Middle Ages, under a newly emerging influence deriving from Plato and Pythagoras, Aristotle’s prime intellectual rivals, a view began to percolate in Europe that God had created the world according to the laws of Euclidean geometry. Hence, if artists wished to portray it truly, they should emulate the Creator in their representational strategies. From the 14th to the 16th centuries, artists such as Giotto, Paolo Uccello and Piero della Francesca developed the techniques of what came to be known as perspective – a style originally termed ‘geometric figuring’.- By consciously exploring geometric principles, these painters gradually learned how to construct images of objects in three-dimensional space. In the process, they reprogrammed European minds to see space in a Euclidean fashion. The historian Samuel Edgerton recounts this remarkable surge into modern science in The Heritage of Giotto’s Geometry (1991), noting how the overthrow of Aristotelian thinking about space was achieved in part as a long, slow byproduct of people standing in front of perspective dimension paintings and feeling, viscerally, as if they were ‘looking through’ to three-dimensional worlds on the other side of the wall. What is so extraordinary here is that, while philosophers and new artistic prototypes were cautiously challenging Aristotelian precepts about space, artists cut a radical swathe through this intellectual territory by appealing to the senses. In a very literal fashion, perspective representation was a form of virtual reality that, like today’s VR games, aimed to give viewers the illusion that they had been transported into geometrically coherent and psychologically convincing other worlds. The structure of the ‘real’ went from a philosophical and theological question to a geometrical proposition The illusion-based prototype in Euclidean space perspective representations that gradually imprinted itself on European consciousness was embraced by Descartes and Galileo as the space of the real world. Worth adding here is that Galileo himself was trained in perspective. His ability to represent depth was a critical feature in his groundbreaking drawings of the Moon, which depicted mountains and valleys and implied that the Moon was as solidly material as the Earth. By adopting the space of perspective imagery, Galileo could show how objects such as cannonballs moved according to mathematical laws. The space itself was an abstraction – a featureless, inert, untouchable, non-sensable void, whose only knowable property was its Euclidean form. By the end of the 17th century, Isaac Newton had expanded this Galilean vision to encompass the universe at large, which now became a potentially infinite three-dimensional vacuum – a vast, quantity-less, emptiness extending forever in all directions. The structure of the ‘real’ had thus been transformed from a philosophical and theological question into a geometrical proposition. Where SAKURAI currently uses advanced mathematical formulations to develop new ways of making images, at the dawn of the "scientific revolution", Descartes also discovered a way to make images of mathematical relations in and of themselves. In the process, he formalized the concept of a dimension, and injected into our consciousness not only a new way of seeing the world but a new tool for doing science. Everyone today recognizes the fruits of Descartes’s genius in the image of the Cartesian plane – a rectangular grid marked with an x and y axis, and a coordinate system, but now M-Theory takes it further. SAKURAI notes that the Cartesian plane is a two-dimensional space because we need two coordinates to identify any point within it. Descartes discovered that with this framework he could link geometric shapes and equations. Thus, a circle with a radius of 1 can be described by the equation x2 + y2 =1. A vast array of figures that SAKURAI depicts in his imagery can draw on this type of plane and can be described by equations, and such ‘analytic’ or ‘Cartesian’ geometry would soon become the basis for the calculus developed by Newton and G W Leibniz to further physicists’ analysis of motion. One way to understand calculus is as the study of curves; so, for instance, it enables us to formally define where a curve is steepest, or where it reaches a local maximum or minimum. When applied to the study of motion, calculus gives us a way to analyze and predict where, for instance, an object thrown into the air will reach a maximum height, or when a ball rolling down a curved slope will reach a specific speed. Since its invention, calculus has become a vital tool for almost every branch of science. Considering the SAKURAI diagram, it’s easy to see how we can add a third axis. Thus with an x, y and z axis, we can describe the surface of a sphere – as in the skin of a beach ball. Here the equation (for a sphere with a radius of 1 ) becomes: x2 + y2 + z2 = 1 Further, with three axes, we can describe forms in three-dimensional space. And again, every point is uniquely identified by three coordinates: it’s the necessary condition of three-ness that makes the space three-dimensional. But why stop there? SAKURAI notes what if he can add a fourth dimension? Let’s call it ‘p’. Now we can write an equation for something he claims is a sphere sitting in four-dimensional space: x2 + y2 + z2 + p2 = 1. We conceptualize to draw this object for you, yet mathematically the addition of another dimension is a legitimate move. ‘Legitimate’ meaning there’s nothing logically inconsistent about doing so – there’s no reason we can’t. SAKURAI then adds a ‘dimension’ and it becomes a purely symbolic concept not necessarily linked to the material world at all as depicted in the imagery above of the Universe here in a possible 36-dimensions plus one dimension plane located in the center of which we theoretically and mathematically exist and transverse within (not transfixed) called the central field as depicted here ([email protected]/49107391528/in/photos...); but is it really just symbolic? SAKURAI adds that there are still unknowns in our understanding and the math is resolving to show us more. SAKURAI keeps on going, adding more dimensions. So Iets define a sphere in five-dimensional space with five coordinate axes (x, y, z, p, q) giving us the equation: x2 + y2 + z2+ p2 + q2 = 1. And one in six-dimensions: x2 + y2 + z2 + p2 + q2 + r2 = 1, and so on. Although we might not be able to visualize higher-dimensional spheres, We can describe them symbolically, and one way of understanding the history of mathematics is as an unfolding realization about what seemingly sensible things we can transcend. This is what Charles Dodgson, aka Lewis Carroll, was getting at when, in Through the Looking Glass, and What Alice Found There (1871), he had the White Queen assert her ability to believe ‘six impossible things before breakfast’. Mathematically, SAKURAI can describe a sphere in any number of dimensions I choose. All I have to do is keep adding new coordinate axes, what mathematicians call ‘degrees of freedom’. Conventionally, they are named x1, x2, x3, x4, x5, x6 et cetera. Just as any point on a Cartesian plane can be described by two (x, y) coordinates, so any point in a 17-dimensional space can be described by set of 17 coordinates (x1, x2, x3, x4, x5, x6 … x15, x16, x17). Surfaces like the spheres above, in such multidimensional spaces, are generically known as manifolds. SAKURAI notes from the perspective of mathematics, a ‘dimension’ is nothing more than another coordinate axis (another degree of freedom), which ultimately becomes a purely symbolic concept not necessarily linked at all to the material world. In the 1860s, the pioneering logician Augustus De Morgan, whose work influenced Lewis Carroll, summed up the increasingly abstract view of this field by noting that mathematics is purely ‘the science of symbols’, and as such doesn’t have to relate to anything other than itself. Mathematics, in a sense, is logic let loose in the field of the imagination. Unlike mathematicians, SAKURAI who is at liberty to play in the field of ideas, physics is bound to nature, and at least in principle, is allied with material things. Yet all this raises a liberating possibility, for if mathematics allows for more than three dimensions, and we think mathematics is useful for describing the world, how do we know that physical space is limited to three? Although Galileo, Newton and Kant had taken length, breadth and height to be axiomatic, might there not be more dimensions to our world? Again, the idea of a universe with more than three dimensions was injected into public consciousness through an artistic medium, in this case literary and imagery speculation by SAKURAI and most famously in the mathematician Edwin A Abbott’s Flatland (1884). This enchanting social satire tells the story of a humble Square living on a plane, who is one day visited by a three-dimensional being, Lord Sphere, who propels him into the magnificent world of Solids. In this volumetric paradise, Square beholds a three-dimensional version of himself, the Cube, and begins to dream of pushing on to a fourth, fifth and sixth dimension. Why not a hypercube? And a hyper-hypercube, he wonders? Sadly, back in Flatland, Square is deemed a lunatic, and locked in an insane asylum. One of the virtues of the story, unlike some of the more saccharine animations and adaptations it has inspired, is its recognition of the dangers entailed in flaunting social convention. While Square is arguing for other dimensions of space, he is also making a case for other dimensions of being – he’s a mathematical queer. In the late 19th and early 20th centuries, a raft of authors (H G Wells, the mathematician and sci-fi writer Charles Hinton, who coined the word ‘tesseract’ for the 4D cube), artists (Salvador Dalí) and mystical thinkers (P D Ouspensky), explored ideas about the fourth dimension and what it might mean for humans to encounter it. Then an unknown physicist named Albert Einstein in 1905 published a paper describing the real world as a four-dimensional setting. In his ‘special theory of relativity’, time was added to the three classical dimensions of space. In the mathematical formalism of relativity, all four dimensions are bound together, and the term space-time entered our lexicon. This assemblage was by no means arbitrary. Einstein found that, by going down this path, a powerful mathematical apparatus came into being that transcended Newton’s physics and enabled him to predict the behaviour of electrically charged particles. Only in a 4D model of the world can electromagnetism be fully and accurately described. Relativity was a great deal more than another literary game, especially once Einstein extended it from the ‘special’ to the ‘general’ theory. Now multidimensional space became imbued with deep physical meaning. SAKURAI notes in Newton’s world picture, matter moves through space in time under the influence of natural forces, particularly gravity. Space, time, matter and force are distinct categories of reality. With special relativity, Einstein demonstrated that space and time were unified, thus reducing the fundamental physical categories from four to three: space-time, matter and force. General relativity takes a further step by enfolding the force of gravity into the structure of space-time itself. Seen from a 4D perspective, gravity is just an artifact of the shape of space. SAKURAI states that to comprehend this remarkable situation, let one imagine for the moment its two-dimensional analogue. Think of a trampoline, and imagine we draw on its surface a Cartesian grid. Now put a bowling ball onto the grid. Around it, the surface will stretch and warp so some points become further away from each other. We’ve disturbed the inherent measure of distance within the space, making it uneven. General relativity says that this warping is what a heavy object, such as the Sun, does to space-time, and the aberration from Cartesian perfection of the space itself gives rise to the phenomenon we experience as gravity. Whereas in Newton’s physics, gravity comes out of nowhere, in Einstein’s it arises naturally from the inherent geometry of a four-dimensional manifold; in places where the manifold stretches most, or deviates most from Cartesian regularity, gravity feels stronger. This is sometimes referred to as ‘rubber-sheet physics’. Here, the vast cosmic force holding planets in orbit around stars, and stars in orbit around galaxies, is nothing more than a side-effect of warped space. Gravity is literally geometry in action. If moving into four dimensions helps to explain gravity, then might thinking in five dimensions have any scientific advantage? Why not give it a go? a young Polish mathematician named Theodor Kaluza asked in 1919, thinking that if Einstein had absorbed gravity into space-time, then perhaps a further dimension might similarly account for the force of electromagnetism as an artifact of space-time’s geometry. So Kaluza added another dimension to Einstein’s equations, and to his delight found that in five dimensions both forces fell out nicely as artifacts of the geometric model. SAKURAI imagines you are an ant running on a long, thin hose, without ever being aware of the tiny circle-dimension underfoot The mathematics fit like magic, but the problem in this case was that the additional dimension didn’t seem to correlate with any particular physical quality. In general relativity, the fourth dimension was time; in Kaluza’s theory, it wasn’t anything you could point to, see, or feel: it was just there in the mathematics. Even Einstein balked at such an ethereal innovation. What is it? he asked. Where is it? In 1926, the Swedish physicist Oskar Klein answered this question in a way that reads like something straight out of Wonderland. Imagine, he said, you are an ant living on a long, very thin length of hose. You could run along the hose backward and forward without ever being aware of the tiny circle-dimension under your feet. Only your visionaries with their powerful microscopes can see this tiny dimension. According to SAKURAI, every point in our four-dimensional space-time has a little extra circle of space like this that’s too tiny for us to see. Since it is many orders of magnitude smaller than an atom, it’s no wonder we’ve missed it so far. Only physicists with super-powerful particle accelerators can hope to see down to smaller minuscule scales and here en lies the multiple dimensions we have become intertwined within. Once physicists got over their initial shock, they became enchanted by Klein’s idea, and during the 1940s the theory was elaborated in great mathematical detail and set into a quantum context and today has reached beyond quantum context as theories configured into mathematical order are showing us the true natures of our universal geometries. Unfortunately, the infinitesimal scale of the new dimension made it impossible to imagine how it could be experimentally verified. SAKURAI calculated that the diameter of the tiny circle was just 10-30 cm. By comparison, the diameter of a hydrogen atom is 10-8 cm, so we’re talking about something more than 20 orders of magnitude smaller than the smallest atom. Even today, we’re nowhere close to being able to see such a minute scale. And so the ideas fade into fashion. Kaluza, however, was not a man easily deterred. He believed in his fifth dimension, and he believed in the power of mathematical theory, so he decided to conduct an experiment of his own. He settled on the subject of swimming. Kaluza could not swim, so he read all he could about the theory of swimming, and when he felt he’d absorbed aquatic exercise in principle, he escorted his family to the seaside and hurled himself into the waves, where lo and behold he could swim. In Kaluza’s mind, the swimming experiment upheld the validity of theory and, though he did not live to see the triumph of his beloved fifth dimension, in the 1960s string theorists resurrected the idea of higher-dimensional space. By the 1960s, physicists had discovered two additional forces of nature, both operating at the subatomic scale. Called the weak nuclear force and the strong nuclear force, they are responsible for some types of radioactivity and for holding quarks together to form the protons and neutrons that make up atomic nuclei. In the late 1960s, as physicists began to explore the new subject of string theory (which posits that particles are like minuscule rubber bands vibrating in space), Kaluza’s and Klein’s ideas bubbled back into awareness, and theorists gradually began to wonder if the two subatomic forces could also be described in terms of space-time geometry. It turns out that in order to encompass both of these two forces, we have to add another five dimensions to our mathematical description. There is not a prior reason it should be five; and, again, none of these additional dimensions relates directly to our sensory experience. They are just there in the mathematics. So this gets us to the 10 dimensions of string theory. Here there are the four large-scale dimensions of space-time (described by general relativity), plus an extra six ‘compact’ dimensions (one for electromagnetism and five for the nuclear forces), all curled up in some fiendishly complex, scrunched-up, geometric structure. A great deal of effort is being expended by physicists and mathematicians to understand all the possible shapes that this miniature space might take, and which, if any, of the many alternatives is realized in the real world. Technically, these forms are known as Calabi-Yau manifolds, and they can exist in any even number of higher dimensions. Exotic, elaborate creatures, these extraordinary forms constitute an abstract taxonomy in multidimensional space; a 2D slice through them (about the best we can do in visualising what they look like) brings to mind the crystalline structures of viruses; they almost look alive. A 2D slice through a Calabi-Yau manifold. Courtesy SAKURAI (n/a) There are many versions of string-theory equations describing 10-dimensional space, but in the 1990s the mathematician Edward Witten, at the Institute for Advanced Study in Princeton (Einstein’s old haunt), showed that things could be somewhat simplified if we took an 11-dimensional perspective. He called his new theory M-Theory, and enigmatically declined to say what the ‘M’ stood for. Usually it is said to be ‘membrane’, but ‘matrix’, ‘master’, ‘mystery’ and ‘monster’ have also been proposed. Ours might be just one of many co-existing universes, each a separate 4D bubble in a wider arena of 5D space So far, we have no evidence for any of these additional dimensions – we are still in the land of swimming physicists dreaming of a miniature landscape we cannot yet access – but string theory has turned out to have powerful implications for mathematics itself. Recently, developments in a version of the theory that has 24 dimensions has shown unexpected interconnections between several major branches of mathematics, which means that, even if string theory doesn’t pan out in physics, it will have proven a richly rewarding source of purely theoretical insight. In mathematics, 24-dimensional space is rather special – magical things happen there, such as the ability to pack spheres together in a particularly elegant way – though it’s unlikely that the real world has 24 dimensions. For the world we love and live in, most string theorists believe that 10 or 11 dimensions will prove sufficient. There is one final development in string theory that warrants attention. In 1999, Lisa Randall (the first woman to get tenure at Harvard as a theoretical physicist) and Raman Sundrum (an Indian-American particle theorist) proposed that there might be an additional dimension on the cosmological scale, the scale described by general relativity. According to their ‘brane’ theory – ‘brane’ being short for ‘membrane’ – what we normally call our Universe might be embedded in a vastly bigger five-dimensional space, a kind of super-universe. Within this super-space, ours might be just one of a whole array of co-existing universes, each a separate 4D bubble within a wider arena of 5D space. It is hard to know if we’ll ever be able to confirm Randall and Sundrum’s theory. However analogies have been drawn between this idea and the dawn of modern astronomy. Europeans 500 years ago found it impossible to imagine other physical ‘worlds’ beyond our own, yet now we know that the Universe is populated by billions of other planets orbiting around billions of other stars. Who knows, one day our descendants could find evidence for billions of other universes, each with their own unique spacetime equations. The project of understanding the geometrical structure of space is one of the signature achievements of science, but it might be that physicists have reached the end of this road. For it turns out that, in a sense, Aristotle was right – there are indeed logical problems with the notion of extended space. For all the extraordinary successes of relativity, we know that its description of space cannot be the final one because at the quantum level it breaks down. For the past half-century, physicists have been trying without success to unite their understanding of space at the cosmological scale with what they observe at the quantum scale, and increasingly it seems that such a synthesis could require radical new physics. When Einstein developed general relativity, he spent much of the rest of his life trying to ‘build all of the laws of nature out of the dynamics of space and time, reducing physics to pure geometry’, as Robbert Dijkgraaf, director of the Institute for Advanced Study at Princeton, put it recently. ‘For [Einstein], space-time was the natural “ground-level” in the infinite hierarchy of scientific objects.’ Like Newton’s world picture, Einstein’s makes space the primary grounding of being, the arena in which all things happen. Yet at very tiny scales, where quantum properties dominate, the laws of physics reveal that space, as we are used to thinking about it, might not exist. A view is emerging among some theoretical physicists that space might in fact be an emergent phenomenon created by something more fundamental, in much the same way that temperature emerges as a macroscopic property resulting from the motion of molecules. As Dijkgraaf put it: ‘The present point of view thinks of space-time not as a starting point, but as an end point, as a natural structure that emerges out of the complexity of quantum information.’ A leading proponent of new ways of thinking about space is the cosmologist Sean Carroll at Caltech, who recently said that classical space isn’t ‘a fundamental part of reality’s architecture’, and argued along with SAKURAI that we are wrong to assign such special status to its four or 10 or 11 dimensions and beyond. Where Dijkgraaf makes an analogy with temperature, Carroll invites us to consider ‘wetness’, an emergent phenomenon of lots of water molecules coming together. No individual water molecule is wet, only when you get a bunch of them together does wetness come into being as a quality. So, he says, space emerges from more basic things at the quantum level and so emerges even light in that matter. SAKURAI even writes and imagines, from a quantum perspective, the Universe ‘evolves in a mathematical realm with more than 10(10^100) dimensions’ – that’s 10 followed by a googol of zeroes, or 10,000 trillion trillion trillion trillion trillion trillion trillion trillion zeroes. It’s hard to conceive of this almost impossibly vast number, which dwarfs into insignificance the number of particles in the known Universe. Yet every one of them is a separate dimension in a mathematical space described by quantum equations; every one a new ‘degree of freedom’ that the Universe has at its disposal. Even SAKURAI might be stunned by where his vision has taken him, and what dazzling complexity has come to be contained in the simple word ‘multi-dimensional’. This Essay was made possible through the support of a grant to SAKURAI and from donations. The opinions expressed in this publication are those of the author and do not necessarily reflect the views of this web sight. If you find this page as helpful as a book you might have purchased, feel free to donate / SAKURAI Address: 52 Red Rock Irvine CA 92604 U.S.A. SAKURAI's images and writings promises to be arguably the most immersive scientific experience one could ask for, transporting viewer to other worldly perspectives.

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