Fractals and Time, Part III: Unfolding, Timeless Time, and Holography
by Christopher Vitale
Unfolding. Building on the work of Laurent Nottale, Susie Vrobel, and Roger Penrose, theorist Keri Welch has recently proposed a fractal model of time which integrates a wide series of sources to produce a unified account of how “time emerges from timelessness.” The hypotheses which follow build upon what has just been presented to describe, explain, and at times elaborate upon Welch’s notion of a fractal model of time, the ramifications of which sync in many senses with the networkological project. Under unusual conditions, such as the curved space present at the imagined start of the universe, or within a black hole, a quantum potential would not necessarily advance, and in this manner, we can imagine a state which is truly static yet distributed in terms of space and time. Many have argued that our universe emerged from a state precisely like this, a crack which opened in the crystal, so to speak. What’s more, there is currently no way to know whether our entire universe exists within a massive black hole, and some researchers have argued that black holes in our universe each lead to other universes ‘inside’ them.
Theorists have largely been loathe to speculate how it might be that time could unfold, so to speak, from the timelessness of such a state. Since quantum potentials seem to exist in a manner in which each part is mediated by the whole, such that the intensity of the quantum potential at a given point depends on the whole of the potential in relation to its contexts, it would seem that the advance of a quantum particle comes about from the integration of new spacetime contexts into the whole of the potential even as this new whole is folded into each of its new parts, if more intensely at some parts than others.
Based on this, some researchers have argued that fractal shapes such as the Mandelbrot set can provide some clues. As one zooms into a given area of a two dimensional plot of a Mandelbrot set, each level of zoom leads to more detail, to an infinite degree as one continues to zoom. The layers of detail that one will encounter are all iterations and enfolding of the fundmental Mandelbrot pattern into itself, such that the whole is contained in an enfolded manner in all its parts, and yet depending on which area of the plot where one begins one’s zoom, the patterns one will see will be fundamentally different. Most Mandelbrot sets are color coded to describe degrees of inclusion/exclusion from the set, and here we see analogues to degrees of intensity, just as the zoom is analogous to the concept of advance, such that the zoom within the Mandelbrot set from any given point can be seen as analogous to the advance of the whole as percieved from one particular location within the whole as that whole advances. Because our eyes lack the resolution to distinguish incredibly small or large distances, it seems that new shapes appear and vanish as we zoom into the Madelbrot set, even though these shapes are always there, and merely unfold as our zoom proceeds.
All of this is generated from an equation, a relation which is itself static and outside of time, but one which iterates differently depending on how it enfolds within itself. If we imagine something like a Mandelbrot set in three dimensions, and imagine the zoom on a particular location as the movement of a location through time, we see the manner in which it may be possible for a static, timeless relation (the equation) to refract itself in a manner which is fractal and holographic in the manner of quantum potential, but in a manner which appears to be progressively unfold differently at each location even as the whole unfolds. This unfolding is nevertheless taking place within timelessness, for there is actually no progression within a Mandelbrot set, only an increase in resolution and zoom as produced by a computer program as we expand our resolution at one particular location. But in a perfect Mandelbrot set, one not iterated by a computer but existing fully formed in spacetime, this unfolding process does not produce anything new, but simply unfolds what is already there.
If a three dimensional Mandelbrot set were to expand in size dramatically, and a particular location were to stay where it is and have the folded Mandelbrot ‘matter’ expand unfold around it as the whole expanded it, it would likely ‘experience’ something like we experience zooming into a Mandelbrot set, if in four-dimensions. And if this location is occupied by a sentient observer with memory yet limited resolution, this observer would likely experience this expansion as something similar to moving in time. This is because the expansion of the Mandelbrot matter around it in all directions would be percieved as a the zooming we have described, but one which occurs from all sides.
A Mandelbrot Zoom Video
It is in this manner that a timeless relation, the Mandelbrot set, can give rise to what can only be described as change in four dimensions, or the experience of three dimensions of space and one unfolding dimension of time, in a manner which iterates differently depending on the location within this expansion, yet in a manner which always reflects the whole. And in fact, all fractals have a germ, which some researchers have called a fractal’s ‘prime.’ It is not unreasonable to say that The differential unfolding of a multi-dimensional prime could, in theory, give rise to spacetime in the manner described above, as both container and contained, giving rise to time in the process.
Refraction. Is there any evidence that our universe is something like this? Researchers have noticed that the visible universe expands relatively uniformly over time. This is both because space is expanding, but also because older light has more time to reach us. Because it takes time for light to reach us, not only are we looking out in space when we peer into space, but also in time. This has lead some to argue that we are surrounded by the past, enfolded in it, from all sides. For in fact, the most ancient light we can observe comes at us from all sides. For when we peer out at great distance in any direction from earth, we see quasars, young galaxies in the process of formation, relics from earlier times in our universe.
In addition to this, however, we also are bathed, as is every part of the universe, from what we can tell, with a semi-randomly dense energetic medium known as the Cosmic Microwave Background Radiation (CMBR). The fact that it is basically uniform implies that all the universe was in fact originally at the center, a fact which would make sense if expansion from a Big Bang came from everywhere, leading to whatever is far away to seem distant in spacetime. The semi-uniformity would imply that small fluctuations in this expansion of the early universe lead to the clumping of matter and energy into galaxies, at least after a period of intense expansion which largely flattened space itself.
There therefore seems to be evidence to support the notion that our universe is expanding and expanded in a manner similar to what we have just described. If the universe is then fractal in the manner of a three dimensional Mandelbrot set, we might experience something like an unfolding of time from the expansion of a previously quantum state. That said, it does not seem that space is expanding around us in a visibly appreciable manner. Many have argued that the ‘arrow of time’ experienced by humans is the result of the flow of energy in the universe, from high concentrations to low concentrations, with all human processes moving along this flow like leaves floating on top of water moving along in a river. But what grounds the very flow of energy in anything like a flow, a movement in something we have called time, may be due to something like the expansion of a fractal quantum state of the sort we have just described. And since, as many researchers have argued, it seems that the most primordial stuff in our universe is in fact a sort of quantum foam, one which exhibits fractal levels of detail the further one zooms into it (which is equivalent to the degree of energy one uses, hence the need for massive excelerators to view smaller and smaller particles in order to see what particles may have existed in the extremely condensed conditions of the early post-Big Bang universe), it does not seem unreasonable to argue that our universe is in fact the result of a differential unfolding of interfolded forms of the same fundamentally fractal and holographic material.
Developments in string theory seem to provide a way to link quantum foam with particles, providing a mediating state, for string theory may explain the ways in which that of which the foam is composed could complexify into vibrating patterns which give rise to the particles encountered in the world. From such a perspective, the universe may in fact be simply a vibrational pattern which folds and unfolds within itself in a manner which is timeless in and of itself, yet gives rise to the experience of time for those within it.
Some Mandelbrot Fun: Another Video of a Mandelbrot Zoom, set to the song ‘Mandelbrot Set,’ by Jonathan Coulton