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Back to basics




Recalibration of distance: cm to pWf)109



Recalibration of time: s to pWf)144



Sensorial & standards calibration: colour, pWf)95



Sensorial & standards calibration: pitch, standard to pWf)130—pWf)137



Sensorial & standards calibration: A-size paper to pWf)110—pWf)117

Due to the digital nature of this page, measurements shown are not in actual scale but for comparative use only. concept 28
by WLFR



We feel as if space and time are continuous, as if we could ever divide them into smaller, and smaller, and smaller units. But this is not the case. The German physicist Max Planck (1848–1947) defined the smallest units of space (length) and time apparent in our universe. They became known as Planck length and Planck time. There is no smaller unit of length, or time, in our universe than 1 Planck length, or 1 Planck time. They are incredibly small. Of course, mathematically, one could say that 0.5 Planck time could exist. But there is nothing in our current state of physics referring to that. In effect, one could say that Planck length and Planck time are the pixels (or the frame rate) of our universe. String theory, at the present our most viable way to the understanding of all of the universe, is dependent on these constants. 1 Planck length, also written as lP, is the length of a string in string theory. 1 Planck time, written as tP, is its period. There is nothing smaller than that.

pWf) (Planck-to-World formalisation) is a project trying to draw conclusions from that, and proposing to expand this knowledge to everyday life. Why? Because of a deeply felt need to be exact. Why? Because of the fact that all standard measuring units are based on arbitrary units, no matter they are part of the standardised SI-system (like the metre, the second, etcetera). To give an example: the second is defined as 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom. This number, 9192631770, has nothing to do with nature. The choice of the caesium-133 atom has neither. It is a choice based on culture, translated to natural reality. First, society thought up the second, and after that, it linked it to nature. Ending up with this irrelevant number. This order of events is of course inevitable, but it is in fact the reverse of what would be logical.

We aim to recalibrate our culturally defined units to equivalents that are in sync with the building blocks that they relate to — the building blocks of our universe. Those of the pixels of time and space. Because it could make some things easier in calculation, but mainly because we think it tickles the imagination, it creates a glimpse of understanding in the bond between the building blocks of everything we know and the real, everyday world we live in. A bridge between two seemingly incomparable points on the scale of the universe.

So — forget your normal units of measurement. Forget the metre, the millimetre, the nanometre. Forget the inch, the foot, the yard, etcetera. Forget the second, the minute, the hour, the week, the month, the year, the century, and so on. Imagine, just for a moment, the universe as an infinite computer screen. As we said, this universe has pixels — as your computer screen has pixels — and these pixels are 1 Planck length wide. Next to that, your computer screen also has a frame rate (the number of times it refreshes the screen to simulate movement — to move your arrow across the screen, for instance, or to play a video). On the scale of the universe, the frame rate of everything is 1 Planck time. Furthermore: time and space, according to Einstein, are essentially the same kind of thing. This means that the pixels of our universe can be expressed in spatial length or in length of time. 1 Planck length is the same as 1 Planck time. Which means there is just one scale — not two separate ones for time and space.

Of course, measuring everything using Planck time and length as a base unit is not directly very practical for most things. Even an atom is already extremely large in terms of Planck length. We have chosen to use the harmonics of Planck time and length to develop a system that shows the most of the relationship between any length or time on any scale, and Planck length or time. This means that we have calculated the doublings of Planck length and time up to very large distances: 1 Planck length, 2 Planck length, 4 Planck length, 8 Planck length, 16 Planck length, and so on. To double something, we raise it to the power of two.

This means that 1 Planck length is 2^0 lP, 2 Planck length is 2^1 lP, 4 Planck length is 2^2 lP, 8 Planck length is 2^3 lP, 16 Planck length is 2^4 lP, etcetera.

This system is comparable to the octaves of music, like on a piano (tuned in just intonation). If you hit the standard A on a piano keyboard, a string will oscillate with a frequency of 440 Hz — it vibrates 440 times per second. If you hit the next A, one octave higher, it will have a frequency which is twice as high, 880 Hz. The next A, again an octave higher, will have a doubled frequency again, 1760 Hz. So if you go up five octaves, the frequency of this A will be 2^5 times the frequency of the first A. If we would extend the piano with higher and higher octaves (inaudible to the human ear), we would need an extension of 130 extra octaves to get close to a frequency of 1 oscillation per Planck time. But not exactly, because the standard musical scale, like our other units, is not tuned to Planck length and time. To retune the piano in harmony with Planck time, in harmony with the universe so to speak, we would have to lower the notes to roughly 96.785% of the original tuning. The standard A, from 440 Hz, would become approximately 425.855 Hz — which is the equivalent of 2^135 tP. We would notate this value as pWf)135. The highest audible A would become pWf)130 and the lowest pWf)139.

Likewise, we can look at visible light that is in full harmony with Planck time/space, since colours are frequencies in the electromagnetic spectrum. However, the range of frequencies that people can see is much smaller than the range of frequencies that we can hear, all colours fall within one octave. But it turns out there is one colour which is Planck-harmonic. It is a bright shade of red with a frequency of approximately 468.23271 THz, or pWf)95. A screen approximation in HTML hex colour value would be #ff1300. There is even a (controversial) scientific theory that our sense of smell is depending on the vibration frequencies of molecules. If this turned out to be true, Planck-harmonic odours would be found from pWf)100 to pWf)107.

Industry standards could also be recalibrated to the pWf) model. Take for instance the A paper series like A3 and A4 paper sizes. In this system, the shorter and the longer side of the paper have a ratio of 1 to √2, or 2^x to 2^(x+0.5). A new paper standard, harmonic with Planck time/space could include pWf)113 x pWf)113.5 (167.841 mm x 237.363 mm), between A5 and A4, or pWf)113.5 x pWf)114, between A4 and A3.

Using this method, we would like to recalibrate all units in our world to a system that reflects the absolute scale of things, and shows clearly when values are more, or less, harmonic with the building blocks that form them on the smallest scale.

The pWf) model also serves as a grid for numerous other WLFR projects, which will be made available here in time.

You will find pWf) in our clinique.