Solving the quantum measurement problem with the fractal

 Addressing ‘The Measurement Problem’ by Fractal Landscapes and Reference Points

In my paper, The Fractal Corresponds with Light and Foundational Quantum Problems, I discuss the measurement problem in quantum physics as being a problem of the fractal also. The issue arises when matter or points of matter are believed to exist in multiple locations simultaneously in the quantum micro world, but this changes when they are observed. This is a significant challenge in quantum physics and one of several topics of the quantum that I address with the fractal.


The isolated iterating scale-invariant fractal is a prime example of the "measurement problem" in quantum mechanics. Without a reference, it is impossible to determine the position and scale of the bit sizes on the superposition fractal. However, once a reference is made, the position and scale become clear. This issue is directly related to the "observation" and "measurement problem" of quantum mechanics and may suggest the decoherence of the quantum state. When the observation is made on the infinite-sized superposition fractal, the fractal "collapses" with no better words to describe the action.

Understanding the fractal reveals this measurement problem is not a problem of the micro quantum world vs. the macro reality as claimed, but is an ever-present problem and property of our reality and a problem prevalent in all sciences. The problem is to do with the fractal nature of reality; instances where there are only repeating patterns and no scale, instances termed ‘fractal-landscapes’. In such places, one only knows position when reference points are given — or when a measurement is made. 

The fractal landscape is a situation where there is only one — same but different — scale-invariant — fractal — pattern. They are demonstrated in this investigation and are prevalent almost everywhere, and when one tunes into them. The obvious examples are the commonly used fractal examples clouds, trees and forests, waves on water, sand dunes, snow and snow drifts.

To further analyse this property of fractals, craters (on the Moon) are analysed. The following figure are real images of ‘same but different at all scales’ craters on the (Earth’s) Moon. Figure 1 is of the Apollo 15 landing from 5000ft above the moon.

Figure 1. The Apollo 15 moon landing from 2000ft looks the same as any height on the flight [1];

Figure 2 Isolated Fractal ‘Crater’ Landscape. An arbitrary image of a scale-invariant — no reference points — crater (actually Earth’s Moon, Lambert crater, see below). 

 While from these images it can be deduced we are looking at craters — they appear as craters — there are many questions that cannot be answered from this image alone. Without any prior knowledge or technology, we are unable to discern — at least — size, position, or time.  Somebody or something with the expertise seeing Figure 4 A may know the geography of the moon and know exactly what it is they are observing, and with this, know what scale the image is; however, most people would not, so this will still serve as a good example of a random fractal landscape. Notwithstanding if we zoom in we see more of the same, it could be the craters are an exact scale of 1:1, or they could be — however unlikely — the scale of the largest structure in the observable universe.  Scale models of the actual largest structures in the universe, galactic clusters are similar in shape and are described in the same way as their ‘smaller’ counterparts or examples.  

To truly understand the significance of the crater images, it's important to consider that they may not depict the actual craters on the moon. There's a possibility that they could be a representation created by tossing objects into a fine powder, essentially a model. To confirm their authenticity, it's necessary to cross-check them with a moon atlas and validate that both the image and the craters depicted are genuine.

Perhaps the fabric of reality is composed of a patchwork of fractal landscapes. If one were to peel away the individual fractals that make up this tapestry, what would remain is a uniform fractal landscape where quantum dilemmas, such as the measurement problem, would reign supreme. Should one find themselves adrift in a complete fractal landscape without any discernible landmarks, they would be unable to pinpoint their location and would effectively be lost.

 Reference Points — ‘Measurement’

When a reference point is added to the fractal landscape image, all these (invariant) problems of scale disappear. From this point on, the scale is known. We are given position, at least more of an idea of it, and it is here that I claim this is what is termed the measurement problem: ‘a measurement’ is made, 'position' is measured, and is done so by the addition of reference points.

Figure 3 Fractal-landscapes. A screenshot from Google Earth of the same crater with altitude, data, and other references.

Figure 4. Scale is only discerned in the Naica crystal caves by the human in the image[2].

Figure 3 is an image of the same Moon crater as shown in Figure 2 only the details — the reference points — are added, and Figure 4 is an Earth fractal landscape, the Naica Crystal Caves [2] with a human added to give scale before which the crystals could be of any size. For the Moon image, the reference points show the following: 

        1.       it is taken from Google Earth of the Moon of the crater, Lambert. This fact alone gives a                         relative time stamp given the technology to provide this of the period of this paper;
        2.       the altitude is not 1:1, it is taken from 200.36km above the surface making the crater in                         question relatively large, some 30,000m in diameter;
        3.       the language system (English) and the number system are a — time — reverence;
        4.       the compass's north direction, is a NASA reference;
        5.        and maybe there are more references, the shadow, the longitude and latitude etc.  

The NASA Apollo crews remarked on this problem of scale, and it was for this reason they needed onboard radar to make a safe landing. Watching the NASA film clip [1] of the Apollo 15 landing from 5000ft up this problem of invariance is clear to see: we — and the astronauts — cannot discern height: the image is similar at 5000ft, 2000ft and only differs when dust is blown from the engines.

The images of Moon craters contain reference points that serve as both observation and measurement tools. By collapsing the non-location issue of the fractal, these reference points reveal scale and position. This process is not a matter of conscious observation, but rather a means of collapsing the fractal landscape. Whether on the Koch snowflake or the Moon craters, reference points serve to collapse the wave evolution of the fractal and provide a fixed position. The Moon crater example illustrates the practical fractal problem that underlies the quantum problem in reality.

Quantum-Classical Transition

The fractal property of a repetitive scale invariant regular pattern can be used to address the quantum-classical transition. While an equation can be created to describe this pattern, the transition itself occurs at the point where a reference point or points reveal the scale and position of the object. In the absence of reference points, classical properties apply throughout the fractal landscape of the quantum state. Thus, the transition is a fractal problem rather than a quantum problem.


1.  Flying Down to Hadley Rille, Apollo 15 Moon Landing, 1971. 2019. Available:

2.  Cave of the Crystals. Wikipedia. 2020. Available:


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