Fractals and Time- Not as Fluffy as You Think . . ., PART 1

Fractals have a bad rap for a good reason –  a lot of really cheezy, new-agey stuff has been written about fractals. But fractals are mathematical objects with rigorous applications that need to be separated from the fluffy stuff done in their name.

So it was with a great degree of trepidation that I approached Keri Welch’s dissertation, A Fractal Topology of Time, just completed at the California Institute for Integral Studies, which I hadn’t heard of before, but which sounded quite new-agey. But someone with strong cred in my book recommended it, and mentioned some of the concepts, and they sounded promising.

Well, let me just say that the work done in here is top notch, and really worth reading. Welch largely combines the work of three theorists – French theoretical cosmologist Laurent Nottale, German fractal researcher Susie Vrobel, and the inimitable Roger Penrose – to develop the most rigorous account of the potential relation between time and fractality that I’ve seen to date. This work is really a full on mixture of physics and philosophy, and seems to me to succeed in its endeavor.

While Welch does provide some context in regard to the philosophical tradition, and describes in detail at points certain concepts by Bergson, Husserl, and Whitehead, this is largely a work of philosophy of physics. The implications of her work in relation to continental theory and speculative realisms these days is not developed. But it hits me that there’s a LOT of potential here.

What follows is a summary and sketch of what that might look like. First, though, I need to explain what is meant by ‘timelessness’ in contemporary quantum physics discourse, because her task, as she articulates it, is to use fractals to show how “time can be generated from timelessness.” The rest of this post will do this set-up work, the next post will explain Welch’s work itself.

But first, here’s a bibliography that gives a sense of where I’m getting the claims I make in the next section:

The End of Time: The Next Revolution in Physics, by Julian Barbour

Before the Big Bang: The Prehistory of Our Universe, by Brian Clegg

In Search of the Multiverse: Parallel Worlds, Hidden Dimensions, and the Ultimate Quest for the Frontiers of Reality, by John Gribben

Timeless Reality: Symmetry, Simplicity, and Multiple Universes, by Victor J. Stenger

About Time: Einstein’s Unfinished Revolution, by Paul Davies

A Timeless Universe?

What might it mean for time to be fractal? Firstly, we need to specify whether the time described is subjective or objective, and for Welch, the theories of Nottale, Vrobel, and Penrose allow us to think both, as well as potential relations between the two.

Welch distinguishes three levels of time familiar to all physicists, if not explicitly differentiated as such – linear time, reversible time, and timelessness. Linear time is the time that flows, in which A precedes B, and causes create effects who follow them in time, but there is no reverse causality.

However, many physicists have argued that many quantum phenomenon become comprehensible once we imagine the possibility of bi-directional or reverse causality. That is, unless causes and effects line up both forwards and backwards in time, an event won’t occur. Such an approach solves the apparent physical contradictions brought to light by famous quantum experiments such as the EPR experiment, or quantum erasers (and for more on these, see my post here).

Now if quantum phenomenon experience a ‘smearing’ of spacetime, and if our universe likely started with a Big-Bang-like event of some sort, then it seems likely that the entirety of our universe was squished into an incredibly small, dense packet of condensed spacetime in which quantum rules, such as superposition, time-reversal, spatial spreading, and self-interference apply.

From such a perspective, it might not be absurd to wonder if perhaps all possible universes that could emerge from the Big-Bang were all present, superimposed, condensed in time and space, and that our universe is simply the unfolding of one of these within the ‘extended’ (to use a Whiteheadian term) existence of spacetime which we know as existence in our universe.  Of course, there’s no way to know if the universe is not in fact pursuing all of these simutaneously (a multi-verse interpretation of the cosmos), and if quantum ‘decisions’ create paths that leap between these or split and recombine these (‘multiple-worlds’ interpretation of quantum mechanics).

Some have even argued that our universe is a large hologram. Holograms don’t encode a 3D image in a 2D plane (ie: a photograph), but rather, the difference between a reference rays directed straight at a plane of glass and a rays directed from a multitude of angles at that glass after hitting an object. From this differential encoding, a hologram can reconstruct the virtual image of a 3D object from a 2D imprint.

From this we may begin to question – might not our whole universe not actually have left that original quantum state of the Big-Bang? Perhaps all we see is a 4D simulation of what is encoded in a smaller number of dimensions within a quantum superposition of the ‘Big-Bang’, without the expansion actually having to occur?

It is in the senses listed above that has had many theorists entertaining the possibility that timelessness could exist in our universe beyond the smearing of spacetime seen in quantum phenomenon. Julian Barbour has in fact worked to show what a ‘timeless’, fully spatialized model of the time of the universe might look like. Barbour imagines a quantum superposed state in which every possible universe that could emerge from such superposed state exists as a branch in that state, and that some of these states would include false ‘memories’ or embeddings of some states within others. Our consciousness of the world actually moving through time could simply be a flashing between these states in a way that gives the illusion of movement. Since memories are built into our sense of the world, each snapshot would feel like it had history, even if it didn’t, and even if these slices didn’t come in order. We wouldn’t in fact know the different between a random fluctuation between possible universes and linear progression, for the illusion would be there. While a reeeeeaaal stretch (and in some ways similar to Descartes’ ‘evil god’ argument), at least it seems to me, there is no way in fact to disprove such an approach.

But perhaps we don’t need to look quite this far to find examples of timelessness in our world. The simple photon can take care of that for us. Photons move at the speed of light. Since moving at the speed of light compresses spacetime, what would it be like to be a photon?

We know that as one approaches the speed of light, the world around one seems to stop moving, time slows down and screetches to a halt, and space spreads out really long in the direction of one’s movement. In fact, in one’s direction of movement, one’s sides would become so long and spread out that anything in front or behind you would start to shrink in size, until your sides become lines and eventually a blur and then sheet stretching from one’s front to one’s back. As one approaches the speed of light, one’s environment congeals, for in fact, you have, in a sense, left spacetime for timelessness.

Why then do we see photons? Because we keep smacking into them! Matter and light interact on a regular basis. As a photon smacks into matter, it adds energy to the atom it hits, and is often then kicked back out, but at a modified frequency. The angle and frequency/color of the light as it keeps being smacked around in this sense is precisely what our eyes are sensitized to read.

But what would it be like if you were timeless, like a photon, yet also sentient? Of course, we cannot know, but we can speculate. What would a photon ‘see’ of all this? Since all space is opaque to something moving at the speed of light, and since this entity moving at the speed of light exists outside of time, and since a photon is a quantum particle in which superposition of states is possible, it doesn’t seem unlikely that every interaction that the photon has with matter, and those periods outside of time, are layered one on top of the other, at the same ‘out of time’. In a sense, this spatializes time.

Of course, photons often have short lives, for a photon which hits an atom is not necessarily the same photon emitted by that atom shortly thereafter. But there is also no way to be sure that all the photons in the universe are not in fact multiple appearances of the same photon! For in fact, if any photon is outside of time, how would it appear to us, creatures within time?

We can find an analogue by imagining how a 2D line creature would sense the presence of an entity which could navigate a third dimension (something explored in many of the versions of Edwin Abbott’s Flatland). A 2D creature would see a 2D friend of theirs vanish and appear somewhere else, as if they’d jumped in and out of existence, and went missing for the time in between. But for us in the third dimension, there was no vanishing, just our 3D figure had ceased being sliced by the 2D world of the ‘flatlanders.’

So it is with a photon. If photons are truly outside of time, and have a markedly different relation to space, might it be that there is simply one photon, that jumps in and out of our spacetime, just as a 3D figure seems to jump in and out of 2D space? Some scientists think this could very well be the case. We already know that the phenomenon of ‘gravitational lensing’ allows for multiple copies to appear when gravity warps spacetime so that light rays bend around it, giving the impression to our eye that there are many copies of what is ultimately one. What if gravitational lensing has a more radical analogue at work in regard to photons, seemingly multiplying copies of one photon throughout spacetime? If gravity can make copies of images, might extreme gravity make copies of entities, particularly those which are themselves light?

This further explains why some have argued that it is possible that our whole universe is simply the illusion of movement within a superpositioned quantum state. We are simply ‘reading’ the hologram, which results in the sensation of ‘moving’ through time, in the manner described by Barbour, within quantum fluctuations in this superposed state.

Welch begins her argument by attempting to describe how it might be that time could emerge from timelessness. And she uses fractals to do this.

To be continued . . .

~ by chris on October 12, 2010.

10 Responses to “Fractals and Time- Not as Fluffy as You Think . . ., PART 1”

  1. […] Fractals and Time: Not as Fluffy As You Think . . ., Part 1 […]

  2. […] What follows is Part II of series of posts on the relation between fractals and time. For the first post in this series, see here. […]

  3. […] follows is Part III of a series on Fractals and Time. Part I is here, and Part II is […]

  4. […] series of posts on the relation between fractals and time. For the first post in this series, see here. [Note: Parts II, III, and IV were written separately from Part I, so there may be some […]

  5. […] follows is Part III of a series on Fractals and Time. Part I is here, and Part II […]

  6. […] this is the fourth and final installment of a series on Fractals and Time. For Part I, see here, Part II is here, and Part III […]

  7. I’ve just come across her dissertation. It was “recommended” to me by a friend as a joke. As a Mathematician I can tell you, half of her “maths” is just plain wrong. Her “Interpretation” of some of the equations are random at best. The fact that she dedicated whole pages and Powerpoint sheets to trivial math (absolute value function…pythagoras… seriously?) just shows that she obviously hasn’t even tried looking at the real math behind relativity.

    Yes I know, it’s meant as a philosophical analysis of the subject. But she should have kept it strictly philosophical and not tried to interpret equations.

    While I did find some philosophical aspects rather interesting, everytime anything math related turned up, I wept.

    • it’s been a while since I’ve looked at it myself. I don’t remember it being particularly mathematical, or being particularly problematic in that regard. Can you be more specific? I will eventually revisit it myself when my research returns to these areas (which it will shortly after I’m done editing my current book project), but if its fresh in your mind, that would be helpful. Thanks,

  8. I’ve been dreaming in fractal shapes for years now, and can render them in my head as a process of meditation. It was a few years ago that I found a self-similarity principal in structures of matter. Given that everything we see is space-time, it can be concluded that time is also self-similar and fractal. Now I see fractals everywhere I look. Riverbeds, paint specs, clouds. All you need is two colliding interfaces with an infinite surface area to create a fractal interface, which by definition has infinite surface area depending on your scale. The individual photon is something that I have explored as well; although it is not just the photon, since time is fractal, there is simultaneously one and one infinite photons. Most people’s minds are blown to think that something can be both one and infinity simultaneously. The real key is examples of self-similarity at specific scales, and renouncing that the speed of light is constant anywhere. All atoms exhibit basically the same characteristics, all stars, galaxies etc. There are definite orders of magnitude, in which the self-replication and self-similar nature of our nature becomes apparent.
    The next step is using fractal-reiteration to visualize time/space transcription, in which every current timespace is transcribing itself onto a smaller subset. The smaller you go, the faster things “orbit”, and so a projection of your current timespace can be saved subatomically on a scale where the rotation of a subatomic (much smaller than anything we can imagine) creates a virtual holographic surface fast enough to capture the transmitted energies of the larger timespace. The end result is you looking into a microscope, to see yourself looking into a microscope, seeing yourself looking into a microscope. Time travel is possible, not within a corresponding dimension on the same level as ours, but to transcribe yourself differently on a much smaller dimensional plane, which is where the conservation of energy prevents us from gaining the mas to go up a few levels in the fractal, only down like a waterfall…
    As I said, I’ve been dreaming in fractal shapes continuously for years now, and have had many many nights to comprehend the nature of infinity. If you find this interesting, go ahead and shoot me an email, I love developing this concept with like-minded people.

  9. I am just wondering how far off I am?

    We as a collection of atoms,know we are a collection of atoms.We as a complex organism,know we are an infinitesimal part of what makes our universe a whole. After 5-7 years, every atom in our body is replaced. There are 10X more bacteria than cells in our body.We are an organism of symbiotic organisms that convert photosynthesis into endo/exothermic reactions fueling a life cycle that reproduces another generation of symbiotic organisms.
    Space is 3D SXSYSZ Time is 3D TATB&AOT
    The Arrow of Time(AOT)iterates fractals of TATB into a sinusoidal lattice of spacetime for quanta/particles to track into the future. Each wave/frequency are iterated by the AOT & is quantized specifically for each element of matter. The TATB axes are bound to & iterated into the future by the AOT. Relative to the AOT, TATB’s frequency & amplitude can compress & go negative but is forced into the future via the iteration of spacetime by the AOT, leaving a systems spatial & temporal past behind forever. The AOT’s fractal iteration of space increases as a systems mass decreases. As mass increases, spacetime iteration, or an organisms metabolism decreases. Each bit of matter spirals into the future while tracking the AOT allowing for entropy to cycle through seasons of equilibriums & singularities at varying spatial & temporal scales. The universe & DNA are fractal records of entropic cycles presently & previously iterated by the AOT. The accumulation of data over Time (God) has led to an incremental evolution of our consciousness, logic, our sense of life/death, & ironically, a complex organisms perception of God.
    Time is the cause & effect of ALL infinities. We & the universe are bits of matter & Time compressed within a circle of infinity, being decompressed sinusoidally by the AOT spiraling from NOW to the event horizon of the future .We are entropic temporal loops existing spatially in a continuum of spiraling fractals. We are the epitome of Time in its physical form.

    have i gone totally nuts?

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