01/19/2004: "Faster than light - the sampling rate of the universe."

The postulate that "Nothing can exceed the speed of light" has always bugged me. I first learned this "law" back in high school, and at the same time as I was learning that in one course, I was also being taught in a different course that the speed of light varies when passing through different media. That always struck me as kind of funky, that this universal constant could easily be changed with a simple glass of water. So, over the many years of heavy thinking I have done, one recurring theme is trying to figure out just what the implications of this "Universal speed limit" are. And, of course, how to break it!


In one of my other many ventures, I work a lot with digital video. DV is a beautiful media for aplying thought experiments, because it is a nice, easily contained 3d model. The dimensions are height, width, and time, and when we are talking Digital video, all three of these are sampled at a very specific rate. I am talking about pure, uncompressed video here, as things like compression and adaptive sampling rates complicate the model greatly.

In any video, the amount of information stored is limited by the sampling rate, and the "frequency of change" of elements in the video. Video is governed by the nyquist frequency just like audio is. That is to say, if you want to completely record all the details for a moving picture, then the frame rate must be at least twice the frequency that the fastest "changing" object in the picture is changing.

Now in playing with this (and of course, with Matrix firmly in my mind), I started to think thusly - what if the universe is infact a digital entity, and has somewhere an underlying frame rate. That would
explain why the speed of light is a limit (of sorts), as nothing could ever happen faster than that basic frame rate.

The first problem with this postulate is units. Frame rate is measured in frames per second, or more generically, sampling rate is measured in Hertz, which is 1/T. T is the period, in seconds, and so in scientific notation, sampling rate = s^-1. Now, things can change pretty fast in the universe - there are radio frequencies that are much higher than the frequency of light, and so that obviously is not a limit. The speed of light is a rate of change of position, or in standard notation m/s (or ms^-1).

Notice anything here? Sampling rate is s^-1, speed is ms^-1. But of course, the video we were talking about only has three dimensions, where as th universe has four (at least for the point of this discussion). So, if we extrapolate sampling rate of the video across the forth dimension, we get ms^-1 - the same units as the speed of light. So, it does start to sound as if the sampling rate of the universe can be expressed in terms of speed, and it now seems much more likely that this underlying "sampling speed" may well be the speed of light.

So, in order to figure out how to break the speed of light, we just have to figure out how to "break" the nyquist frequency limit of a Digital Video, and then extrapolate that across one more dimension. Sounds pretty easy really, but that Nyquist frequency limit is pretty tough. In order to avoid "aliasing" (which is the repetition of high frequencies above the sampling rate as low-frequency aliases), you commonly either increase the sampling rate, or filter your input to ensure that there are no high-frequency components. Neither of these are going to help us break the speed of light.

Let us also consider what happens should we break the speed of light without first taking care to avoid aliasing. If we accelerate an object, and it reaches the speed of light (ignoring mass effects for now), then it would seem that the object would suddenly have an instantaneous, momentumless, infinite decelaration. i.e., its speed would change from 3x10^8 m/s to zero in an infinitesimal time. That, I imagine, would come in pretty handy....

TO BE CONTINUED...