Saturday, November 3, 2012

Fractal Time: Absolute or Relative?

This is a discussion entry: based on my fractal discoveries.

  1. The fractal with no observation demonstrates no-time. 
  2. The fractal with observation demonstrates the passing of time, but not absolute time, but relative time.
1. No time: - A fractal in isolated superposition demonstrates no time.

It is not until a reference point is provided, an observation made - that time is time.
When we have a reference point on the fractal, we 'know' position.  The modern clock itself may be a reference point - without it, we could be anywhere, or at any time. Without it, we are lost, we are in the chaos. The importance of a reference in time is just as important as any other reference – it is to 'know'.
Absolute time:
Recently I in this blog I have been exploring two key areas of science in terms of the fractal: the expanding fractal (universe), and the de Broglie wave-function. In both of these entries I have had to action some kind of motion or classical physics mathematics: both demanded some kind of understanding of time; both showed that the time is subjective, is not fundamental. Time is external or exogenous to the fractal. See appendix for working, or see my early entries.

Relative time
Though there maybe no absolute time, relative time may be demonstrated - as (from one stand point, iteration 0on the koch snowflake fractal) future iteration can be viewed. From this stand point, 6 iterations can be viewed into the future, but not more. By zooming into the fractal, one can look back, and one can look forward, so therefore there is a notion of before and after. But where in time these observations are made, in an absolute sense, is impossible to to determine.
Time is one thing relative to another.

The fractality of time
Interestingly, time itself is also fractal in that it can be broken into ever smaller fractions or scales: the story of the universe may be described, in the same amount of time that it takes to describe any other story. All descriptions of time share basic principles: there is a beginning, and there is an end, and details in between. 

From the Expanding Universe entry:
While producing my expanding fractal entry and the wave equations of the fractal, I assumed time was the iteration number - the iteration rate. But is it really? As pointed out earlier, there is not reference to time on a fractal, and that using this iteration rate as the nearest thing is problematic because it is arbitrary or subjective

Wave velocity is equal to: frequency(f) multiplied by the wavelength (λ) 
v = fλ
f: is equal to 1 divided by the Period(T)  
T: is equal to is the time taken for wave to produce one cycle.
λ: is equal to the distance* between the crest to crest or trough to trough
*It is here, with the fractal, that two issues of position (time and distance) present themselves, or as it would be, don't present themselves. Without time, mass, and distance, the calculation (in a classical sense) is impossible. In terms of the fractal their values are not apparent, not obvious, and any attempt to assign values to them are subjective or arbitrary. It maybe concluded that a fractal in isolation has no concept of time, nor distance - something I shall address in a separate entry due to this interesting characteristic, and to the occurrence of this problem.

The one (real) reference to time that the fractal may offer may be found in the iteration: the change from one iteration to another. Again, these are concepts I aim to develop, but for now:
It shall be assumed that T = to the iteration number (i).
T = (i)
So, T (the period from crest to crest in the Koch snowflake wavelength) is equal to 6 iterations: 
T = 6
f = 1/6
To calculate the velocity, we need λ, the wavelength, and to calculate this, we need a distance.
Distance: As with time, I shall address the fractal issues of distance in a separate entry due to this interesting characteristic, and to the occurrence of this problem.

As I have pointed out, the fractal shows no concept of distance: so what to do, leave it?
I am currently working on ways to measure this distance, but until then I'll:
Assume that the wavelength behaves as a sinusoid and that the frequency,  and the wavelength becomes exponentially smaller. 

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