On Multi-Dimensional Time, Time Quantization and the Nature of Reality

That's a pretty audacious blog post title...

By way of background: I've been wondering for some time how a photon "experiences" the universe. That has lead me to reading up on quantum physics, relativity, string theory, and the "arrow of time," among other things. I'm not even close to pretending I understand all the evidence and current theories. I got into physics basically by wanting to know how the universe really works. I did study physics in college (as a minor), but I didn't do all that well. I always thought I was seeing equations fit to evidence, especially in undergraduate thermodynamics. That's what scientists do, fit experience to their ability to make predictions. It's fine, but I always wanted to get to the core of things.

Anyway what I'm curious about is something which follows from relativistic treatment of energy vs. mass. It seems to me that photons are basically frozen in time, "to us." Yet if you were a photon what would your experience of the sub-light-speed world look like? It seems obvious to me, though it is just a leap of faith, that photons themselves transit "time." Yet in a different way...

So, questions, suggestions, hypotheses:

Can a particle move in "space" but not in "time?" If so could that knowledge be used to explain wave/particle duality? What about the ability to explain quantum "probabilties?"

Regarding wave/particle duality: let's imagine that a photon is trapped to only explore time dimensions orthogonal to "ours." By doing so it seems apparently frozen in time. To us. But what about its interactions with other photons (apparently travelling non-orthogonal bases re: each other)? Can we explain the apparent ability of photons to the see the "future" as a compression in our time-basis? How can a time-static (in our basis) particle do anything other than experience all of our times at once? That's the idea...

Regarding probabilistic outcomes in quantum physics: "Probabilities" suggests to me too little information to make specific predictions. Can we use the notion of multi-dimensional time to help understand the empirical evidence we see for probabilistic particle-particle interactions? In essence we may never be able to reach the information needed to make non-probabilistic predictions for specific interactions. But knowing that the time-frame interactions involved are the reason for that uncertainty seems to be a potential step forward.

It seems interesting to me to consider the notion of multi-dimensional time. I haven't got a clue as to how to wonder about this more rigorously, though. One extra topic which I believe fits into the notion of how reality "works" is drawn from computational theory: recursion. We know that the world is a giant feed-back system. But is it quantized in terms of information? Is there a finite amount of information and thus computational ability present in the workings of the universe? I have a few thoughts on that but generally speaking it feels to me like the universe cannot be capable of supporting an infinite level of precision. And so everything is quantized...

more universe-as-lava-lamp action

harley 2 pukes carbon dioxide snowballs and gushes ice.  but only when it gets close enough to the sun.  it would be interesting to hear the ice cracking and hissing as it gets thrown off.

Dispersion Test

I've been playing around with LuxRender and Blender... particularly I've been tweaking materials and angles to get rainbow caustics for a scene. I rendered a whole mess of bad attempts and eventually I decided to analyze the situation very closely. So I set up an experiment of sorts.

For the final scene I only want rainbows from this effect... I don't want white light at all. That means I want only parallel light rays going into the ball. To do that I put a light source inside a long tube with the light at one end and the glass ball at the other. The tube is cylindrical. The light source is circular but... also inside the tube is a "choke" of sorts that turns that light source into a thin circular ring. To keep the camera from seeing the icosahedron the light tube incorporates a "back mask".

The target of the light is an icosahedron (d20 for those in the know) subdivided twice. Its material is completely transparent with an index of refraction of around 1.8 and a Cauchy B coefficient (at least what LuxRender calls it) of somewhere around 0.4. I forgot to record the specific numbers for this picture (duh) but these are high relative to normal glass; they were chosen to enhance the dispersion.

On the other side of the light tube is a white matte surface used to record the "splatter pattern". In early tests I noticed that the incident white light that made it straight through to the matte surface with very few bounces (basically coming straight through) washed out the rest of the pattern. So to combat that I placed a circular black hole right in front of the icosahedron to capture and cancel it... Here's a shot of the dispersiontest.blend setup in Blender.

Ok, so here's what came out... The only real suprise here is just how incredibly dense this is. I expected to see a few rainbows but wow. As an image in and of itself it isn't all that artisically interesting. However it's pretty amazing from a technical standpoint.

This picture took approximately 60 hours worth of CPU time to generate. Ugh... I hope LuxRender gets CUDA/OpenCL acceleration soon.

I played with changing the shape of the incident light a bit too. More on that later...

Update: This got a mention on the LuxRender forums :) Thanks guys!

Update 2009/6/16: I created a short animation with the ball rotating...