Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal

Blair D. Macdonald ã 2020

Abstract

Making sense of the nearly 100-hundred-year-old quantum nature of light and matter, with its — to name a few — wave-particle duality, measurement problem, and entanglement ‘spooky action at the distance’ — remains the greatest questions to physics. Since the 1980s, fractal geometry, a new and exciting field of mathematics — that the fathers of quantum mechanics did not have and has not been tested for quantum properties — has developed. Can the isolated fractal explain the quantum? An experiment was conducted on a simple — but isolated — fractal testing whether the geometry of fractals corresponds to quantum enigmas. It was found the isolated fractal emerges by a duality of propagation — of an oscillating sinusoidal wave — of ‘bits’ — of information — iterating in a superposition of time, scale, and symmetry, with a possible constant speed, demonstrating all the hypothesised. The quantum ‘measurement problem’ was addressed as being a problem of isolated scale-invariant fractals — or fractal landscapes — where position is only ‘known’ when additional (fractal) information is added — which ‘equally’ gives rise to a (quantum-like) ‘uncertainty’ problem. Also, quantum entanglement and other quantum features were explained by the fractal model. Consequences of the model were discussed, notably to its relevance to the nature of light (the speed of it etc.), the behaviour of the atom, time, knowledge and our reality, and the model’s direct inextricable connection with cosmological observations and conjectures. Finally, it was concluded that the model is preliminary but fundamental.

Keywords: Foundational Quantum Mechanics, Fractal, Light, EMS, Measurement Problem, Entanglement

Quantum Fractal 200831.docx

Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald

Preface

The idea of running an experiment on a fractal and testing it for quantum relevance has its roots long before I knew anything much about cosmology or the quantum: both were very daunting to me at the time I was first thinking about fractals. I had for a long time been interested in the natural sciences and also deeply interested in fractal geometry. It started with my day job where I teach economics at the secondary school level; I was teaching the common ‘supply-demand’ model I noticed that it seemed to behave as a fractal where it is produced and consumed and grows and develops, and it seems to have a shared equilibrium; and so, I questioned this, is this a coincidence? The more I thought about the fractal the stranger – even weirder – it became to me, especially an isolated one — it was very strange. It occurred to me that in an ‘infinite’ fractal there is no location and it appears to be no scale; and so, the question was begging, where are you on it exactly? I would go out looking for fractal landscapes and would think about the implications of this ‘non-location’ to our reality. Once, when I talked about my problem to my (interested) class, one of my student’s said: ‘that sounds like quantum mechanics’, I said: ‘Yes, I think so too.’ But at the time I was afraid to investigate – ‘no one understands quantum mechanics’ – right?! When my mind turned to thinking about what ‘an observer’ — there is no better word or term for it — would experience if they were within a fractal and looking back in time I immediately released my thinking had relevance to cosmology; especially when I found the observer would experience acceleration. I am no mathematician, or even scientist, and I have trouble with writing (that is not an appeal for empathy); but, with the encourage of other colleagues and friends and family I have come this far. One of them— a PhD in physics — said: ‘Blair! No one is thinking like this!’ ‘What do you have here!’ he said to me. ‘Write it down!’ In 2013 I made a start and wrote up this fractal cosmology experiment and then went onto write up my economics (supply- demand) fractal experiment. I am now satisfied and confident the geometry of the fractal offers a solution the great physics problem of our time: to make sense of the ‘small scale quantum world’ and unify it with the large. Having finished this work, I think I offer a new and sufficiently different contribution to quantum foundations — a new insight. My aim now is to gain some support and funding so as to publish my work in a reputable journal.

ii Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald

Table of Contents

1 INTRODUCTION 1

2 METHODS 4

2.1 Testing for Light Properties 4 2.1.1 Iteration Beat-Speed 4 2.1.2 Testing for the EMS 5 2.1.3 Frequency and Wavelength 5 2.1.4 Speed 5

2.2 Testing for ‘Quantum’ Properties 5 2.2.1 Fractal Configurations for Analysis 5 2.2.2 Superposition 6 2.2.3 Supersymmetry 6 2.2.4 Wave and Particle Duality and Spin 6 2.2.5 Observation, Measurement, and Position 7

3 RESULTS 7

3.1 Light Properties 8 3.1.1 Spiral Propagation 8 3.1.2 The Koch Snowflake Spiral 8 3.1.3 Bit Rotation through 360 Degrees 9 3.1.4 Sinusoidal Wave 9 3.1.5 Logarithmic Sinusoidal 9 3.1.6 The Wave Period 9 3.1.7 Changing Frequency (f) 9 3.1.8 Changing Wavelength (λ) 10 3.1.9 Wave Speed 10 3.1.10 Constant Speed 10 3.1.10.1 Constant Speed via fractal production 10 3.1.10.2 Constant Speed via iteration beat 10 3.1.10.3 Moving at the Speed of the iteration bit 10

iii Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald

3.2 Quantum Properties 10 3.2.1 Superposition 11 3.2.1.1 Supersymmetry and Super-topography 11 3.2.2 Wave Propagation. 11 3.2.3 Demonstrating ‘Discrete Particle’ 11 3.2.4 Demonstrating Wave and Particle Duality 12 3.2.5 Observation — measurement 12

4 DISCUSSIONS 12

4.1 Fractal Demonstrating Light Properties 13 4.1.1 Changing Frequency (f) 13 4.1.2 Changing Wavelength (λ) 13 4.1.3 Constant Speed 13 4.1.3.1 Constant Speed via fractal production 14 4.1.3.2 Constant Speed via iteration beat 14 4.1.3.3 Constant, Unrelenting Propagation to an Observer at the Frontier 14 4.1.4 Moving at the Speed of the Iteration 14

4.2 Fractal Demonstrating Quantum Properties 15 4.2.1 Superposition 15 4.2.2 Super-symmetry and Quantum Spin 15 4.2.3 Quantum Wave Propagation and Behaviour. 16 4.2.4 Demonstrating the de Broglie wavefunction and the Fast Fourier Transform 16 4.2.4.1 Fast Fourier Transform 16 4.2.5 Observation, Measurement, Decoherence 16 4.2.6 Demonstrating Discrete ‘Particle’ 17 Demonstrating Wave and Particle Duality 17 4.2.7 Uncertainty Principle 17 4.2.7.1 The law of complementarity. 18 4.2.8 Quantum Entanglement 18 4.2.8.1 The Non-local Fractal 19 4.2.8.2 ‘Classical’ — Local — Change 19 4.2.9 Kochen-Specter theoem 20 4.2.10 Contrary ‘Spin up’ and ‘spin down’ 20 4.2.10.1 Contrary and Reality 20 4.2.10.2 Antimatter 21 4.2.11 Addressing ‘the Measurement Problem’: Fractal Landscapes and Reference Points 21 4.2.11.1 Fractal Landscapes 22 4.2.11.2 Super-scale Superposition 24

iv Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald

4.2.11.3 Reference Points — ‘Measurement’ 24 4.2.11.4 Relative and Absolute Reference Points 26 4.2.11.5 Quantum-Classical Transition 26 4.2.11.6 Measurement and Consciousness 26 4.2.12 Solving the ‘Unification of the Quantum Mechanics with Cosmology’ 27 4.2.12.1 Fractal Field, Gravity and Spacetime 28 4.2.12.2 Research Proposal to Test Inflation Epoch for Fractal Properties 28 4.2.12.3 The Vacuum Catastrophe 28

4.3 Raised Questions and Limitations 29 4.3.1 What is the Fractal? 29 4.3.1.1 My Thoughts on the Fractal 29 4.3.2 If this science, where is your Prediction? 30 4.3.3 Where is the Particle? Where is the Wave? – in Reality? 30 4.3.4 Pi (p) 31 4.3.4.1 Unifying Exponentials with Cycles 31 4.3.4.2 Experiment to Test of Pi in the Fractal 32 4.3.4.3 The Economics Demand Function the Wave Function of Our Reality. 32 4.3.4.4 The Fractal Derived Demand Curve the de Broglie Wave Function? 32 4.3.5 Duality — Complementarity 33 4.3.6 Insights into Time 33 4.3.6.1 Time and Measurement of Reference Points 33 4.3.6.2 Iteration Beats 34 4.3.6.3 Absolute vs Relative Time: 34 4.3.6.4 Iteration-Time and the Genetic Clock 34 4.3.6.5 Time and Uniformity 34 4.3.6.6 The Fractality of Time 35 4.3.6.7 The Paradox of Our Perception of Time 35 4.3.7 Addressing the Emptiness and Symmetry of the Atom 35 4.3.7.1 Atomic Symmetry 36 4.3.8 Fractal Decay and a Wave Package 36 4.3.8.1 Atomic Half-life 37 4.3.9 Demonstrating Evolution 37 4.3.10 Insights into Knowledge 37 4.3.11 Determinism and Freewill 37 4.3.12 On Quantum Interpretations 38 4.3.12.1 Many worlds 38

5 CONCLUSIONS 39

v Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald

6 ACKNOWLEDGMENTS 40

REFERENCES 41

vi Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald

1 INTRODUCTION Quantum physics — after nearly one hundred years from its conception — remains one of the greatest enigmas known to science. In its own strange ‘duality’ — a term synonymous to only ‘the quantum’ — it is characterised on one hand by immense practical application and supported by the greatest of experiments, in all defending it as one of the strongest principles known to science. It is said to be one of humans’ greatest accomplishments. On the other hand, at its foundations it remains a complete mystery as to what it is and what it means. It baffled its founding scientists, and it continues to baffle the modern thinker. Is light — and all matter for that matter — a wave, or a particle, or is it ‘duality’ of both? And, if so — if yes — what does this mean for our understanding of reality? What is it to observe or measure something? How do we explain its ‘non-locality’ ‘spooky action at a distance’ —entanglement? No one has solved these and its other related problems; not to mention offer a gate way to unify it with its parallel paradox, general relativity, and our observations and conjectures surrounding the expanding universe.

During much the same period as quantum mechanics was developing another area of an equally ‘strange’ and ubiquitous paradigm of mathematics was developing in parallel — since the 1980s actually: it is chaos theory and fractal geometry. They are — the quantum and the fractal — very similar; but, are they the same? To date, no one has directly tested the fractal (attractor) as a contender to break this quantum deadlock. Ian Stewart in his popular book: Does God play dice? A New Mathematics of Chaos [1] made the important remark: “chaos (and thus fractals) was unknown in Einstein’s day...”; but today — notwithstanding fractal geometry concurs with near-scale cosmological observations and that fractal geometry is expressed enthusiastically by modern mathematicians that ‘we are surrounded by them’ and that they hold as an important and real description of reality — the fractal has been dismissed and even trivialised when discussing such topics. Fractals are treated as a novelty, interesting images; the stuff for mystics. Well, they have that — the mystics — in common, that is a truth. Even if this is not so — that fractals are important — and too harsh, no one has tested the simple fractal by simple experiment or even treated them as a candidate to

1 Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald solve the quantum problem like the geometries of the past were tested to make sense of the cosmological problems of the time: Copernicus’s concentric-circles, Kepler’s ellipses, and even Einstein’s curved spacetime. Is ‘our time’s geometry — fractal geometry — the solution to these foundational questions, and are the clues this geometry is presenting to us in our reality being ignored? Is it the geometry that can unlock the door to unification?

For some time I have worked with the fractal, thinking understanding it may lead to an understanding of the universe — I am not the only one to think such things — and I finally produced my (recent) work ‘Making Sense of Cosmological Observations and Conjectures by a Fractal Geometry Experiment’ [2] in 2019 where I revealed that the fractal — also — has a duality of perspectives and that this property is present in all fractals, for instance, a duality between how it is (objectively) produced and how it is (subjectively) viewed or consumed. One other dual perspective revealed exponential acceleration which I claimed corresponds to cosmic observations and conjectures, and the other — important to this study — points to cycles or oscillations and also that when isolated, the iterating/emergent fractal is a very ‘strange’ thing in that there seems to be no location or position until one is determined by, well— there are no other terms better for it — observation or measurement. It also seemed very reminiscent to the way light, the electromagnetic spectrum (EMS) — and importantly to how what is termed quantum mechanics — is described: the fractal behaves as a wave and is made of — emergent from — bits, and it can treat ‘superposition’. It was from this time on, that I began to listen to experts on quantum mechanics and I wondered and wanted to test: are the two — the quantum and the fractal — the same?

In my said fractal-cosmology paper I showed — by experiment — that the emergent (retrospective) fractal corresponds to many — if not all — the problems associated with cosmology; including, Hubble-Lemaitre[3],[4] and accelerated[5],[6] (‘dark energy’) expansion arising from a ‘singularity beginning. My findings correspond to observations of galaxy distribution and demographics and conjectures such ‘cosmic inflation’. Importantly, it opened the door to a second paper to address the ‘progressive perspective’ of the fractal: one I suspect is the quantum.

2 Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald

To understand more of the fractal duality, Figure 1 below shows these two simultaneous perspectives or frames of reference of the fractal, in this case, the classic fractal Koch Snowflake: ‘A’ is the forward-looking — cyclical/oscillating — perspective, what I term the progressive view; and ‘B’ the retrospective — exponential — view, looking backwards from within the set.

Figure 1. Development and Expansion of the Koch Snowflake Fractal. The schematics above demonstrate fractal development by (A) the (classical) forward or progressive Snowflake perspective, where the standard sized thatched (iteration ‘0’) is the focus, and the following triangles diminish in size from colour red iteration 0 to colour purple iteration 3; and (B) the inverted retrospective perspective where the new (thatched) triangle is the focus and held at standard size while the original red iteration 0 triangle expands in area — as the fractal iterates.

The former — progressive view — is the focus of this investigation: here, we see a fractal ‘snowflake’ emerges in shape by iteration with the addition of new but diminishing sized triangle ‘bits’. The convergent structure is set in as a snowflake-like shape at — and around — 7 ± 2 iterations. In this, the initial triangle bit remains constant in size; diminishing sized triangle ‘bits’ (blue 1, black 2, and purple 3) are added to the original bit size (red 0) producing a — in the case of triangles — a snowflake shape. The iteration production speed is of a constant ‘beat’ of new bits, and potentially infinite. Here, only iterations 0 to 3 are shown, but the pattern is developed so much as we can expect it to continue — in an isolated environment. Figure 1-B shows the alternative ‘dual’ retrospective perspective of ‘looking back from within’ is shown. Here, the newly produced bit-size are held constant in size (the double thatched bit size ‘0’) and the previous bit sizes — by the same order of events as described for Figure 1-A — grow in size. This dual frame of reference will be key to my discussions.

3 Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald

In this investigation I hypothesis the answer to the quantum — and cosmological — enigma lies with fractal geometry: specifically, in the progressive forward-looking perspective of the fractal. By analysing the isolated fractal from a progressive perspective (Figure 1-A), the fractal geometry can explain the enigmas associated with light and the quantum problems: Young’s wave interpretation of light [7]; Maxwell electromagnetic spectrum (EMS) exponential sinusoidal wave, constant speed (c) and increasing frequency (f) with decreasing wavelength(y)[8],[9]; Planck and Einstein’s quantum origins [10],[11] wave and ‘quantum’ particle in a simultaneous duality[12],[13],[14] and particles sharing information by quantum entanglement’s faster than light ‘spooky action at a distance’[15], demonstrating spin and anti- particles[16]; and the measurement problem. The model will give insight into the nature of time and the odd properties of the atom[17]. I will show: the progressive and retrospective perspectives of the fractal are dual aspects of the same geometry, together, they unify quantum observation problems with cosmological observations.

This model should not take away from what has a has already been achieved — namely Albert Einstein’s General Relativity[18] but, should complement it. It will reveal that a simple ubiquitous geometry can explain our reality or at least give further insight into it. Even if this study is seen to be incomplete naive or trivial, this study should at least open the minds and the door — a new door — of enquiry to a quantum unification and our understanding of reality.

2 Methods Using the simplest of fractals, the Koch Snowflake fractal, fractal geometry was tested for quantum properties. The following is a description of how light and quantum properties were conducted on the fractal. The description for producing Koch snowflake is for this investigation implied knowledge.

2.1 Testing for Light Properties To test for the iterating fractal sharing possible ‘light’ wave-like properties the following specific methods were followed.

2.1.1 Iteration Beat-Speed

4 Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald

The emergence of the fractal is a result of the iteration of a ‘simple’ rule. This iteration — or repetition — is ‘set’ to an arbitrary and discrete ‘beat’ measured in undefined units. For purposes of this investigation, this arbitrary ‘beat-speed’ is assumed constant and termed iteration-time. This problem of undefined units of time measurement will be a topic of its own in discussions.

2.1.2 Testing for the EMS The pattern of propagation with emergence was traced. At each iteration-time, an arbitrary position marker was added to the pristine triangle bit in the form of a ‘red dot’ mark placed arbitrarily on the apex of the new triangle bit. This red-dot was graphed with respect to iteration time as the fractal shape emerged.

2.1.3 Frequency and Wavelength The sinusoidal behaviour with exponentially increasing frequency coupled inversely decreasing wavelength was tested for.

2.1.4 Speed A universal constant ‘speed of light’ was tested for. The speed is assumed to be the same wherever it is measured in the universe — at no matter the speed of the observer (Einstein reference). Does the fractal demonstrate this constant speed? Does it behave as v = fλ where v is speed? To do this the red dot position was traced throughout the fractal set were tested for a universal constant beat speed — a constant speed from any measurement ‘position’ within the set — and whether this speed is determined by and set by the production of new bits.

2.2 Testing for ‘Quantum’ Properties The iterating fractal was tested for quantum behaviour, including wave-particle, measurement and decoherence, superposition and entanglement.

2.2.1 Fractal Configurations for Analysis To test the fractal for quantum properties different questions were asked about the fractal. These questions were framed as 3 possible states or ‘configurations’ (‘1.’, ‘2.’, and ‘3.’ below). These configurations are:

1. A pristine (coherent) set: where all bits are identical or coherent at all places and at all iteration-times in the set.

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2. An arbitrary change is made to the pristine triangle bit (as described in configuration 1. above). In this case, a ‘red-dot’ was added arbitrarily to the apex of the pristine bit. This change would be found to be coherent (the same instantaneously) throughout the set — at all places and at all iteration-times. This was to demonstrate coherence after an arbitrary change in the set. This change was made instantaneously, with no propagation or iteration, and is distinguished from the following (3.) configuration by this spontaneity. This change also assumes there were no (taken from quantum mechanics) human ‘measurement’ or ‘observation’ of the set; it was just done. 3. Converse or contrary to ‘configuration 2.’ An arbitrary change was made to the (triangle) bit by the arbitrary addition of the red dot to the apex of the triangle only this time it was not instantaneous — it propagated. The ‘change’ was not throughout the set at all places at all times — as if not measured or not observed — but was instead propagated by iteration at the ‘production (or iteration) speed’ of the fractal. The changing of the set is assumed to be from — or inferred by — a ‘measurement’ or ‘observation’ of the set from a position within the set.

2.2.2 Superposition To test for superposition the fractal set was set to configuration 2.2.1 - 1 where the set was assumed to be infinite iteration-time age and so showing positions of triangle bits in an infinity of positions. Any change to a bit, as assumed with configuration 2.2.1 - 2 is assumed to be instantaneously made to all bits within the set.

2.2.3 Supersymmetry When I use the word supersymmetry it is not in an attempt to take it from how it is used in ‘particle physics’ theory and show that it is demonstrated with the fractal, but rather, it is thought to be the best description, the best word, for what the fractal demonstrates. In the true sense of the prefix ‘super’ to show all symmetries at the same time; the fractal demonstrates this superposition as all positions possible at the same time when in isolation.

2.2.4 Wave and Particle Duality and Spin The fractal was tested for whether it demonstrated wave propagation and simultaneously ‘particle’ behaviour — central to quantum theory. It was also tested if the fractal demonstrates both wave and particle at the same time. Following from the

6 Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald coherent 2.2.2 superposition an analysis was made of ‘snowflake’ as it was 'produced’ to get to this position. When the set was iterating, the propagation of bits (configuration 2.2.1 - 2 or 2.2.1 - 3 above) was traced — assuming a specific rule of non- supersymmetry (see 2.2.3), where the rotation of bits was in one ‘clockwise’ direction. It was tested for sinusoidal wave propagation of bits with iteration time. It was then tested for the effect of an observation; do the bits become ‘isolated’ and ‘clear’ — revealing position?

2.2.5 Observation, Measurement, and Position Demonstration of quantum ‘observation’ problem was tested for with the fractal. More precisely, a ‘position’ within an infinite fractal system was given. From an initial condition setting of a superposition fractal — configuration 2.2.1 - 1 — an arbitrary change or location was made within the set — configuration 2.2.1 - 2 or 2.2.1- 3.

3 RESULTS As the fractal iterated the following were found, as per the introduction and methods.

The results of the iterating fractal are presented in Figure 2 below.

Figure 2 Fractal Logarithmic Sinusoidal Spiral. ‘A’ shows the transverse wave propagation of a ‘red dot’ on a fractal Koch Snowflake to iteration (i) 6, and to superposition infinity (¥). ‘B’ shows the rotational aspect of the

7 Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald

triangle bits and the respective bit size; rotating clockwise through 360o. ‘C’ shows the Sin wave produced at each iteration-time — assuming bit size remains constant: the real is a logarithmic sinusoidal.

3.1 Light Properties The following pertains — from the evolution of the emergent fractal — to properties the EMS and light.

3.1.1 Spiral Propagation Figure 2 A shows the propagation of a ‘red dot’ on new triangles from iteration time (i) 0 to i6 is shown. In this ‘classical perspective of the snowflake fractal, a logarithmic sinusoidal spiral pattern is produced. The dots propagate in an arbitrary clockwise direction as the set iterates. The infinite position of propagation is also shown (¥).

The spiral is produced by the rotation of the triangle bits (3.1.3). Had the bits not diminished in size the spiral curve would not have formed, at least in the same way.

3.1.2 The Koch Snowflake Spiral Tracing a curve through the propagating ‘red dots’ produces a spiral curve: shown in red in Figure 2 A and in more detail Figure 3. The Koch Snowflake Spiral curve in Figure 3 is an approximated curve as it is produced by a method of scribing cycles from the centre points of respective triangles.

Figure 3 The Koch Snowflake Spiral A spiral curve (in red) is produced by a method of scribing circular arc from respective triangle centre points.

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Note, the red curve appears to be a continuous curve; however, as it runs through discrete points, these discrete points are the only points possible; no triangle apexes where the ‘red dot marker’ is located are to be found between the successive ‘dot’ points on the red curve of the Figure 3 spiral.

3.1.3 Bit Rotation through 360 Degrees Figure 2 B shows the rotation of the triangle bits, and also shows the position of the ‘red dot’ with respect to the bits original bit size and diminished bit size. The triangle bits rotated 360 degrees in 6 iterations: 60 degrees per iteration. The last, the 6th iteration bit is very difficult to discern. Any bit size beyond this iteration, from a fixed observation position and no ‘zooming’ into the set, will not be discerned.

3.1.4 Sinusoidal Wave Figure 2 C shows a plan view of the position of ‘dots’ as they propagate through time. It attempts to graph the change in amplitude through time without adjusting for the change in bit size.

3.1.5 Logarithmic Sinusoidal As the fractal bits propagate with iteration (as described above in 3.1.1) the bits logarithmically increase in frequency — the beat per time unit passes a defined mark — while simultaneously the amplitude and wavelength will decrease, again logarithmically, as fractal iterates. As a result, the red dot can be said to propagate as a sinusoidal logarithmic wave. As can be seen that the perimeter of the forming emergent fractal is made-up of an infinity of triangles/'particles' and these together act as or form a wave. When a change is made to one of the triangles (the red dot on iteration 0) and this change iterated, as demonstrated, the wave is revealed.

3.1.6 The Wave Period So, T, the period in iterations, from crest to crest in the Koch snowflake wavelength is equal to 6 iterations. T = to the iteration number (i).

T = (i)

T = 6

3.1.7 Changing Frequency (f)

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The frequency of cycles passing a fixed point in a given ‘time’ of the fractal increases exponentially with iteration-time.

f= 1/6

3.1.8 Changing Wavelength (λ) Inverse to the frequency of the fractal propagation the frequency of cycles increases the wavelength of the cycle decrease exponentially in size.

3.1.9 Wave Speed The speed of propagation of the information complies with v = fλ: as f exponentially increases, λ exponentially decreases.

3.1.10 Constant Speed The following are different perspectives on the issue of constant speed.

3.1.10.1 Constant Speed via fractal production It may be interpreted that there is a constant speed of production of bits at the frontier of the fractal curve. The bits are produced as a function of the beat time of the fractal.

3.1.10.2 Constant Speed via iteration beat It may be interpreted that there is a constant speed with respect to the bit size, something akin to the way light is currently understood and described, as to be constant to the observer, no matter the speed of the observer.

3.1.10.3 Moving at the Speed of the iteration bit It is possible to assume one could ‘travel’ at the speed of the iteration production speed (3.1.10.1).

3.2 Quantum Properties The isolated fractal demonstrates quantum properties in more than one way. Firstly, I will explore insights from the iterating fractal as described in the experiment above that pertain directly to quantum mechanics, and then I will discuss what I term fractal landscapes and show how this ‘quantum’ problem of ‘observation’ of ‘measurement’ pertains to all knowledge and is indeed a feature of the what is termed the ‘classical’ world. With fractals — in terms of the quantum problem — there is no small scale/large scale divide.

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There are so many aspects to the fractal with relation to the quantum problem. As a result of this, it is difficult to find an appropriate order to present my findings; the findings are — after all — all aspects of the same geometry. I shall begin with superposition, and follow on with particle and then duality and others.

3.2.1 Superposition The iterating fractal — composed of identical bits — in perfect isolation (separate from all other fractals, more on this in 4.2.5) directly demonstrates the concept of ‘superposition’. There is perfect coherence of bits throughout the infinite set. This is shown in Figure 2 (A ¥).

3.2.1.1 Supersymmetry and Super-topography Under the same state as the superposition as described above, the (fractal) set is also in a state of supersymmetry where the isolated identical triangle bits are in a ‘coherent’ state of all (rotational) symmetries at one time; the rotations are in both directions at one time. In this case, supersymmetry relates to super rotational symmetry, before observation, of the triangle bits. Without observation they propagate in all directions, clockwise and anticlockwise; with observation, their propagation direction is set — either clockwise or anticlockwise. Supersymmetry may also include all the possibilities of the fractal shape. In this study, I have chosen triangles, producing snowflakes; however, any shape will produce the same property, whether emergent — produced by iteration — or not. This — shape or topography — is in a sense a kind of super- topography.

3.2.2 Wave Propagation. The experiment showed — in Figure 2 and Figure 3 — that the isolated iterating fractal, with its identical bits, rotates as a propagating sinusoidal spiral action. This motion is by a translational wave and the fractal forms — or evolves — by bits of information rotating perpendicular to this motion.

3.2.3 Demonstrating ‘Discrete Particle’ The ‘triangle bits that make up the fractal shape are discrete: there are no positions between the iteration positions. There are no ‘half’ iterations and no half bits. The red line denoting the curve (Figure 2) joining the discrete bits is not real; there are no positions on this line other than the said or shown apexes of the triangle bits. Positions

11 Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald on the line can be calculated using imaginary (i) numbers – just as they are used with current quantum and light calculations.

3.2.4 Demonstrating Wave and Particle Duality While the fractal is in superposition, bits are all places at all times — as shown in Figure 2 (A ¥). The fractal is made of bits, these bits can be viewed independently; equally, these bits — in the process of forming the fractal — are part of a way of wave propagation. They are simultaneously independent identities and a wave.

3.2.5 Observation — measurement To overcome the scale and or position invariance problem associated with the superposition snowflake fractal, position and scale are only revealed when another object — arguably another fractal object — is positioned in the frame of view. This new object gives reference, and locks in the scale; without it, the object is all sizes and all positions. When an ‘observation’ or a ‘measurement’ made, position and scale are (better) known.

When an observation or measurement is made there is a ‘collapse’ — there is no better word to describe this process — in the chain or wave structure that came before the observation to produce the fractal structure. From the observation position of the observer, without any technology to magnify, can view 7 ± 2 iterations ahead — this is the progressive view of the fractal, Figure 1-A —; and >7 ± 2 iterations can be behind — the retrospective view of the fractal, Figure 1-B).

4 DISCUSSIONS The spiral propagation of information — the red dots and triangle bits in Figure 2 and Figure 3 — of the fractal demonstrates and directly corresponds to how light photons and the electromagnetic spectrum is described by physicists. Equally, the — its particle components — of the fractal in isolation also independently corresponds with how quantum entities are described: they behave — as if in parallel — as physicists describe quantum mechanics. The geometry of the fractal may offer a direct solution to the problem of ‘the quantum’ and reduce it to a behaviour, a result and structure, of as known modern geometry. The following discussions aim to expose, explore and explain

12 Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald how the fractal corresponds to the quantum problem and also to cosmological problems conjectures and observations.

4.1 Fractal Demonstrating Light Properties The process of fractal development by iteration corresponds to light is described. It is not a linear propagation but is a spiral wave that oscillates, changes in frequency and size (wavelength) logarithmically, and propagates, so as a wave — a wave composed of bits. From this observation, it may be that the structural geometry of light and the mathematics surrounding light is the mathematics and geometry of the fractal; that light is a fractal by nature. To understand light is to understand the fractal. When we do this, the problems associated with lights behaviour and properties are addressed. This includes Thomas Young’s wave interpretation[7], Maxwell’s electromagnetism equations [8],[9] corresponding to its constant speed, and Einstein’s special theory of relativity[11], where the speed of light in vacuum c featured as a fundamental constant; and finally its particle — photon[10],[19] — nature.

4.1.1 Changing Frequency (f) Just as lightwave theory is described; the frequency of cycles passing a fixed point in a given ‘time’ of the fractal will increase. Time is an arbitrary or undefined concept in terms of this analysis and will be addressed in section 4.3.6.

4.1.2 Changing Wavelength (λ) Inverse to the frequency of the fractal propagation — and consistent to light theory — the as the frequency of cycles increases the wavelength of the cycle decrease logarithmically in size.

4.1.3 Constant Speed The speed of light is assumed to be a universal constant; the same wherever it is measured in the universe — no matter the speed of the observer [11]. The following discussion is to whether the fractal can demonstrate this constant speed and whether this ‘light speed’ a property shared by fractals. This property remains a great question for me and interpreting the fractal with respect to this problem is still open. The following are different perspectives of this problem.

13 Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald

4.1.3.1 Constant Speed via fractal production I questioned whether the constant speed of light — with respect to the oscillating sinusoidal wave structure that I assume to be the same as light propagation — pertains to the emergent production of the fractal; the coming into existence of the triangle bit at the production end of the fractal (demonstrated in all the figures above). With some thought and investigation, it was found this is not the best solution; the speed cannot be constant along the range of the fractal propagation — as claimed by light theory. The bits grow exponentially larger proportional to the wavelength; so, the distance between know points (the dots in the model) also grows and so the speed slows as the wavelength increases — the converse being true.

4.1.3.2 Constant Speed via iteration beat There is one property of the fractal that is constant; it is its iteration beat and with this the propagation of information with this beat. No matter the position of an observer in the fractal the iteration beat is the same, it is constant. This would say the fractal may transfer information at a constant speed along the propagation range. The problem with this claim is similar to the above 4.1.3.1 only with opposite consequences. The speed cannot be reasoned to be constant along the fractal propagation range as, again, the frequency and wavelength and thus the distance changes, so the speed will increase proportionally to the wavelength.

4.1.3.3 Constant, Unrelenting Propagation to an Observer at the Frontier At any position inside the iterating fractal set, the fractal will continue to emerge in front to the observer — in the form of Figure 1A — corresponding to the iteration beat. This is to say an observer moving at the speed of iteration — and thus propagation speed — or is following the new bit, where there will always be a new bit ahead forming a fractal geometry in front. This observer’s perspective may be the best contender on how light behaves with respect to the observer. From whatever position in the fractal set the information will propagate ahead, and maybe at a perceived constant speed. This perspective also gives direct insight into the ‘arrow of time’.

4.1.4 Moving at the Speed of the Iteration If an observer is assumed to be moving at the frontier of the fractal set — where the first bit comes into existence — this observer would observe no emergent fractal shape ahead of them, and a concept or perception of time will be absent. If this is so, then

14 Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald insight and claims for Einstein’s special relativity should hold: the fractal is consistent with our understanding of light and time. More on this when I discuss ‘time ‘and the fractal.

4.2 Fractal Demonstrating Quantum Properties Before I start, the reader must know that my thinking around what is termed quantum problems first began or came out of problems I was having with the isolated fractal. At that time, I was not aware of quantum; I was drawn to it when I slowly learnt that others were having the same problems I was having. I am now convinced they are one, and the same. The isolated fractal demonstrates quantum properties in more than one way: it appears they — the quantum and the fractal — are the same as they have equivalent descriptions, to describe one is to describe the other.

Firstly, I will explore insights from the iterating fractal as described in the experiment above that pertain directly to quantum mechanics, and then I will discuss what I term fractal landscapes and show how this ‘quantum’ problem of ‘observation’ of ‘measurement’ pertains to all knowledge and is indeed a feature of the what is termed the ‘classical’ world. With fractals — in terms of the quantum problem — there is no small scale/large scale divide.

4.2.1 Superposition The isolated fractal iterated to ‘infinity’ directly demonstrates the concept of superposition as described in the field of quantum mechanics. The identical bits can ‘be in all places at one time’ within the set. The bits are coherent; just as with quantum particle coherence.

4.2.2 Super-symmetry and Quantum Spin The supersymmetry state of the fractal points to the quantum spin of a particle. The isolated, identical triangle bit is all symmetries at one time, and if we call the rotational symmetries spin, then their ‘spin’ will be described just as quantum theorists describe them. They can spin in the same direction of rotation (clockwise or anti-clockwise) or

15 Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald an alternate or opposite direction of rotation; this is akin to spin up and spin down. Also, the fractal may demonstrate no rotation at all if the bits are assumed to be identical as under configuration 2.2.1 — 1. and 2.

4.2.3 Quantum Wave Propagation and Behaviour. The superposition fractal (Figure 2) develops and evolutions is a ‘wave package’ and this development corresponds to how quantum wave functions are described. The fractal develops by the propagation of constituent particles: so, the wavefunction is a function of the fractal. These bits or particles are in all place at all iteration-times when not — as described by quantum mechanics — observed. It should be possible to describe this wave by the Schrödinger equation[12], and positions within the set by the Borne probably function.

4.2.4 Demonstrating the de Broglie wavefunction and the Fast Fourier Transform The scale-invariant wave may pertain to all objects: this corresponds directly to the predictions of the de Broglie[13] and Bohn quantum ‘pilot wave’ and how it is described. If it is assumed quantum particles and fractal bits are synonymous, fractal bits are any object in our reality. Through the fractal, these independent objects can be seen to be as part of a greater wave fractal structure.

4.2.4.1 Fast Fourier Transform In Figure 2 we can see the wave action of the fractal development and the associated increasing wavelength with iteration-time. If the quantity of bits per iteration time is understood to be the frequency of bits ‘per unit time’, and the area of bits the amplitude of a wave function, the fractal set may be described by the Fast Fourier Transform as quantum wave functions are. The Koch snowflake is a compressed summary of all the wave activity in the (fractal) system. If so, this discovery may offer insights to the Fast Fourier Transform and all its applications — including with atomic physics (see below). It also implies every fractal attractor, from trees to waves and clouds, may be described as a Fourier Transform, and also every market, at any scale: the complete fractal attractor is, therefore, a perfect example of a Fourier Transform — a range of bit frequencies per iteration time, all in one ‘superposition’.

4.2.5 Observation, Measurement, Decoherence

16 Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald

Position and Scale of the bit sizes cannot be determined on the superposition fractal, without a reference. When a reference is made, position and scale are known. This directly corresponds to the ‘observation and measurement problem of quantum mechanics and points to the decoherence of the quantum state. When this observation is made — in the fractal set — the infinite (sized) superposition fractal 'collapses'. There are no better words available to describe this action. Again, the fractal and the quantum appear to be synonymous.

4.2.6 Demonstrating Discrete ‘Particle’ The discrete bits that make up the fractal shape act as or are akin to as how discrete photons or electron or any other quantum entities, are described by quantum theorists. They are discrete: there are no positions between the iteration positions just as Planck’s first conjectures is described. This demonstration shows no ‘half’ iterations and no half-sized bits; this is consistent and corresponds with quantum mechanics. Predictions of positions between the discrete bits may be calculated using complex numbers just as with quantum mathematics.

It may well be possible to interpret the particle as being the complete emergent fractal — the snowflake — and that many snowflakes make up a larger superstructure. Again, this is akin to how are particles are often described; that they also are waves.

Demonstrating Wave and Particle Duality Just as the ‘point’ positions — electrons — on an atom are (weirdly) described as being — both at the same time — a particle and ‘a smeared out’ wave; here we see a corresponding model. The fractal — in total and in part — can be described in such a way also. For the fractal, in isolation, this demonstration has shown it is not so ‘weird’ and possible. Strip away the reference points from reality (more on this in section 4.2.11) and we find ourselves in a — as it is described by quantum mechanics — in a quantum state. This state, as I will attempt to explain, is possible in reality.

4.2.7 Uncertainty Principle Here I run the risk of total conjecture; the uncertainty principle is not a feature of the fractal that stands out, but equally I think it can be addressed. So far, I have attempted to explain how — independent of any knowledge of quantum theory — the fractal shares many, if not all, the problems outlined by so-called quantum mechanics; so can it

17 Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald also shed light on the uncertainty problem. So far, position, scale and direction of growth (the ‘spin’) of anyone triangle on a (Koch Snowflake) fractal (Figure 2) is only ever known when a reference point — another measurement or observation — is made. One (observer) can never know where they are on the fractal without having a reference.

So, it may follow, given the uncertainty principle is associated with quantum mechanics that the fractal too may demonstrate this. When the fractal is in superposition, or even supersymmetry (reference section) position, scale, and the direction of the wave propagation is not known — without observation. With this observation, position scale and direction are fixed and so speed — or momentum — of the fractal propagation is simultaneously given up. When a reference or a measurement is made, position and scale are known; but even then, this reference an insecure measure — as all things are of a fractal 'fuzzy' nature, the measurer too.

4.2.7.1 The law of complementarity. When researching the uncertainty principle, I came across Bohr’s complementarity principle; this is particularly caught my attention as I have found the fractal demonstrates something akin to this but maybe even more poignant, that everything seems to come in duality. More on this later.

4.2.8 Quantum Entanglement The following pertains to the EPR paradox[15] and quantum entanglement where it was argued that it is impossible for ‘entangled particles’ to instantaneously correlate or match properties between any arbitrary distance without some kind of ‘hidden’ or ‘spooky’ variables at play. It must be said that this is not an obvious feature of the fractal and any solution that I offer here would not have come about unless it had already been claimed as a problem to the quantum. Nonetheless, this demonstration with the isolated fractal shows it is feasible to explain entanglement by the fractal. Better minds than this author may be able to make more of this fractal being similar to entanglement problem in the future.

To show the isolated fractal can demonstrate and explain the enigma of quantum entanglement the following assumptions or properties of fractal are:

18 Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald

1. the fractal is in perfect isolation with no interference (or observation) from other ‘fractals’; 2. it is in a state of fractal superposition and supersymmetry (section 2.2.1 — 1 and Figure 2); and 3. all ‘bits’ of the fractal is identical in all times and places.

This superposition/ supersymmetry implies there is no observation and no (iteration-) time to propagate the information throughout the set (by ‘classical means’); the set is ‘full’ to infinity and any change is instantaneous throughout the set. By example; if the (infinite) fractal set is assumed to be — say — yellow in colour (configuration 2.2.1 - 1), then it is this yellow in colour throughout the set. This pre-observation position of the fractal can be changed — to another colour for example (configuration 2.2.1 - 2) — however, once again, these changes are assumed to be instantaneous and throughout the superposition fractal set at the instance of the change — no classical propagation. This initial property setting allies with the quantum entanglement postulate that photons are first ‘loaded’ or ‘entangled’ before observation.

4.2.8.1 The Non-local Fractal Given the above assumptions, if an observation were to be made by a second observer situated at an arbitrary distance from the first observer somewhere in the set, this observer would observe what the first observer observes — yellow in the example — and this will be the same — yellow — throughout the fractal system. This is consistent with how quantum entanglement is described. The change would be instantaneous, and thus non-local.

4.2.8.2 ‘Classical’ — Local — Change If the first observer were to arbitrarily but physically change the colour for example of the set (configuration 2.2.1 -3), this change or information would by necessity have to propagate at the speed of the fractal propagation, the speed of information, and this speed will always be slower than the instantaneous non- observation from superposition. This ‘slow speed’ is akin to the slow ‘classical’ speed of light that Einstein highlighted and his ‘spooky action at a distance’ argument. In this circumstance, in terms of the second observer position in the set, they experience the change made as the fractal is no longer in superposition.

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4.2.9 Kochen-Specter theoem Anton Zeilinger emphasises in his discussions on entanglement that by the Kochen- Specker theorem ‘the feature of the system does not exist prior to the measurement’[20]; this holds for the fractal also. It may be claimed as a rebuttal to this fractal entanglement demonstration that the ‘scenario’ was set up prior — that the dot or the colour was selected and was not random — and that this is unlikely in reality. Yes, they are set up; but, this ‘scenario’ is really and only here to demonstrate that it is plausible to show that identical shapes or other changes to the set — to infinity — can ‘weirdly’ demonstrate what quantum mechanics ‘weirdly’ does in reality. The process can equally be random as claimed by (if understood correctly) the Kochen-Specker theorem; it can be any shape and any form.

4.2.10 Contrary ‘Spin up’ and ‘spin down’ While the isolated fractal may be able to demonstrate non-local behaviour — the instantaneous change of a state of all positions — by changing the whole fractal set; it may also be able to show the concept of contrary ‘spin up’ and spin down’— as explained by Lee Smolin in his recent book Einstein's Unfinished Revolution [21]. In this investigation, here too the fractal may demonstrate contrary spins. In this case, spin or rotation left, and spin or rotation right. If a rule is set to show the contrary rotation when an observation is made, then it will, when one side is observed, the other will be the contrary. It is possible to model this; although it does feel like conjecture — at the limit of what I believe this model can demonstrate.

The properties of quantum spin that pertains to elementary particles — photons and electrons and other — may be addressed by how the isolated ‘fractal bit’ demonstrates a ‘supersymmetry’ of positions as described in 4.2.2. These symmetries, rotations or oscillations can be rotating in all directions at the same time — supersymmetry — and if chosen, just as with how entanglement is explained, alternate or opposite rotations — ‘spin up’ and ‘spin down’ as it is defined in quantum mechanics — may be observed, though — again — this is not an obvious configuration.

4.2.10.1 Contrary and Reality This contrary view is something I have addressed in earlier papers concerning how the fractal demonstrates foundational principles of economics. Is the fractal produced; or equally, is it — to the ‘contrary’ — consumed or viewed. There is also an opportunity

20 Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald to write more on this concerning knowledge. I argue, that through the fractal, the great debate of philosophy —relativism versus realism — can directly be addressed; and here too — related directly to my economic conjecture — the question is prevalent, is the fractal produced or is it consumed? To me, there is only one answer, and the contrary view is an illusion.

4.2.10.2 Antimatter Following from the above, the contra spin demonstrated by the fractal points directly to dual particles — an antiparticle. It appears akin to Dirac’s antimatter particle [16]. Again, similar to the economy application, this concept of ‘anti’ pertains more to whether the set is produced of consumed. To know it is produced has an anti that it is consumed and these — by the fractal — are mutually exclusive understandings.

4.2.11 Addressing ‘the Measurement Problem’: Fractal Landscapes and Reference Points ‘The measurement problem’ is claimed to be one of the central issues of quantum mechanics; I believe this can be directly addressed by the fractal. Measurement has two features to be addressed: 1) that the superposition ‘wavefunction’ ‘collapses’ upon ‘observation’ to an undefined — probabilistic — ‘point’; and, 2) this ‘process’ is claimed to be only the evident in the domain of the micro — atomic and subatomic — level, and that for the ‘large’ — classical — macro level, while it is claimed and thought to apply here also, there is no evidence for this bazar feature taking place. Notwithstanding that in this study I have already demonstrated wave-particle duality with the fractal and that an observation on the fractal has a similar effect parallel to how quantum mechanics is described — where position is given and the ‘infinity’ collapses — I can show that by understanding fractals in reality — what I term ‘fractal landscapes’ — the problem may be solved. The measurement problem may not indeed be an issue of large and small but rather an issue of information or reference points on a fractal landscape. Reality on the so-called macro may be non-quantum because it is interlaced in a multitude of complex fractal landscapes; but strip back these landscapes to where we are left with a mono-scape of a single but complex shape or pattern and this situation, which I shall explain is real as, presents problems — problems of orientation position and knowing — at all scales.

21 Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald

4.2.11.1 Fractal Landscapes A fractal landscape is simply a landscape that consists of one fractal pattern or system. The easiest examples are the commonly used as fractal examples: clouds, trees and forests, waves on water, sand-dunes, and so on. One of my favourites is snow and snowdrifts; but for this investigation, I shall use the craters (on the Moon) as my example. Figure 4 and Figure 6 show just that: images of craters on the (Earth’s) Moon.

Recall that fractals are described or defined as being repeating patterns that repeat the ‘same but different’ at all scales: in a fractal landscape we see shapes — fractal shapes — that look all ‘the same’ but are — often, but not necessarily, — ‘different’ from one another. Of course the triangles in the Koch Snowflake are not different from one another and apparently nor are elementary particles as they are described. If one finds themselves in a total fractal landscape, with no reference points, they will be what we term ‘lost’; they will have no idea where you are — and that they could be anywhere.

Figure 4 Isolated Fractal ‘Crater’ Landscape. An arbitrary image of a crater. No scene of scale can be deduced: it could be large, it could be small.

While we know they are craters that we see in the image, even if they are really not from the moon, they look like craters; the question I wish to focus on is what size or scale are these craters? And how do we know? This problem of scale invariance reveals itself an important property of the fractal: the craters pictured could be of any size. They — the craters — could be of an exact scale of 1:1, or they could be — however

22 Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald unlikely — the scale of the largest structure in the observable universe; if you think this is unlikely — that they could be the largest structures of the universe — the actual largest structures in the universe, galactic clusters — something I have addressed directly in my fractal cosmology paper — are similar in shape and are described in the same way as their ‘smaller’ counterparts or examples. Without any prior knowledge or technology, we are unable to discern its scale. 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 [22] 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 the dust is blown from the engines. ‘Similarly’ this scale invariance problem associated with pure fractal landscapes is revealed in the images of the Naica Crystal Caves [23] contrast the scale of the crystals to the scale of the human. The crystals could be of any size.

A B

Figure 5 Fractal-landscapes. A: the Apollo 15 moon landing from 2000ft looks the same as any height on the flight [22]; B: scale is only discerned in the Naica crystal caves by the human in the image[23].

It must be made clear that somebody or something with the expertise seeing that Figure 4 crater may know the geography of the moon and know exactly what it is that is observing and with this, know what scale the image is of; however, most people would not, so this will still serve as a good example of a random fractal landscape.

There is something more about the imaged creators and relevant to knowing; the image may not even be of the real craters on the moon as it is meant to portray: it could be produced from throwing objects into fine powder — it could be a model. In this case, verification from an atlas of the moon will show the image and the craters are real. It is

23 Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald also important to note that this example this fractal crater landscape has not come about by iteration — the assumption of this investigation — and thus is not a typical emergent landscape: this being the case, it does show the range of possibilities and properties fractals share; in this case, all fractals are distributed by a — Pareto distribution — power law, whether they are produced by iteration or not. Notwithstanding the above, what we do see here are craters, and because of the scale indifference we see a fractal landscape, and it is this property of the fractal that I am attempting to demonstrate and they will serve to help me demonstrate the problem of measurement and observation in our reality.

4.2.11.2 Super-scale Superposition Scale-invariant (fractal) landscapes without any reference points present a similar non- position problem as experienced with quantum mechanics: there is no exact position because scale is not revealed. I argue the two — the quantum and the fractal — have the same problem and that the problem is all about fractal landscapes. Fractals are in a sense — from the term superposition — a super-scale of landscapes: it could be a pattern of anything, trees, craters, duns, and so on. I claim that reality presents us with this super-scale problem also: if we were to strip away the details of reality, down to where there is just one layer, one pattern, one fractal landscape — just as with the craters on the moon in my example — then we would be in a state of not at all knowing our position. We would be lost! In this state, there is no direction, my position, no history; there is the only pattern.

4.2.11.3 Reference Points — ‘Measurement’ However, 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, or 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 or the position is measured by the addition of reference points.

Figure 6 is an image of the same crater field as shown in Figure 4 only the details — reference points — are added. These reference points give (more) position and add to our knowledge of the system. From this image, the many reference points to help us know by revealing:

24 Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald

1. it is taken as a screenshot from the program Google Earth — Moon, of the Moon crater Lambert. This fact alone gives us a basic timestamp — a reference — by the technology to provide this image and information.

Figure 6 Observed Fractal ‘Crater’ Landscape. A screenshot from Google Earth of the Moon with altitude, data and other references.

2. the language system (English) and the number system also give a — time — reverence; 3. the altitude, it is not 1:1 by taken from 200.36km above the surface making the crater in question very large, some km in diameter; 4. the compass north direction, a NASA reference; 5. and maybe more references, the shadow, the longitude and latitude etc.

What is important to my argument is that it is the above reference points that are ‘the observers’: that it is ‘they’ that gives position, they make the measurement, they that collapse of the super-scale problem of this crater scape fractal landscape. Using the quantum mechanics language; the addition of reference points collapses the fractal

25 Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald landscape. Reference-points throughout my demonstrations, be it on the Koch snowflake or the craters or other, ‘collapse the wave evolution’ of the fractal and give position. If this is so, then this example of craters on the moon stands as an example of the quantum problem existing in our reality. The quantum problem is a practical fractal problem.

Note: If you find I opportunistically use the word ‘wave’ and ‘collapse’ here; please review my claims and findings in section 4.2.3 — where I have shown the fractal demonstrates ‘wave’ and the ‘collapse’ of it.

4.2.11.4 Relative and Absolute Reference Points The reference points I have used in the examples above are absolute reference points — they don’t change. In reality, we are faced with relative reference points; not only are they changing as they too are fractals and have a complexity all of their own. This has insight has huge ramifications for knowledge and understanding; something I would like to further develop but it is outside the scope of this investigation. In essence, what I am saying is if a once thought to be reliable reference point were to become isolated and fuzzy we would — again — find ourselves in a state of superposition. The reference points would be meaningless and would leave us lost.

4.2.11.5 Quantum-Classical Transition Can the fractal address the quantum-classical transition: the point where something becomes classical from being quantum — or visa-versa? I think it can.

Notwithstanding what I have already claimed in this section, the fractal addresses the classical by its property of a repetitive scale-invariant regular pattern — keeping with my example, craters. We can study this pattern, ‘draw a line through data’, and create an equation that describes it. The problem of transition between the ‘quantum and the classical’ is simply the point where — as I have attempted to explain in this section — a reference point (or points) disclose the scale and position of the object in question. The transition is a fractal problem and not a quantum problem.

4.2.11.6 Measurement and Consciousness It should be emphasised that this fractal landscape with reference points does not at all demonstrate that it is a conscious being ‘making an observation’; if we — the human observer — observe without any reference points, we only observe a fractal landscape,

26 Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald nothing whatsoever to do with the position is verified, and we are essentially lost. Our observation — in this context — is insignificant to the problem. We consensus beings only gain position from the provided reference points, as demonstrated above, looking for them. With reference points we can — as the observer — get closer ‘to knowing’ where are we are — in the scale of things.

One point should be made here, and this is not to come across as a contradiction to the above; and it is that our conscious observation does in one sense give a position, a reference point. With our conscious observation we know we are in a fractal landscape, and this fractal landscape view is limited to the fractal distance — 7 ±2 iteration sizes. More than that, without anything else we are lost.

4.2.12 Solving the ‘Unification of the Quantum Mechanics with Cosmology’ In this paper, I have laid out that and the quantum atom is all properties of the progressive — forward-looking — fractal. In a previous paper[24] I laid out that the same fractal shares a dual and simultaneous perspective — a retrospective, backwards- looking perspective from an observer in the set — that pertains almost all of the cosmological problems we observe and conjecture. The results showed — quoting from its abstract —

“area(s) expanded exponentially from an arbitrary starting position; and as a consequence, the distances between points — from any location within the set — receded away from the ‘observer’ at increasing velocities and accelerations. It was concluded that the fractal is a geometrical match to the cosmological problems. It explains Hubble - Lemaitre and accelerated (Dark Energy) expansion; inhomogeneous (and said fractal) galaxy distribution on small-scale and large-scales[25]; and other problems — including the cosmological catastrophe and the early inflationary expansion epoch of the universe[26].”

Putting all these properties of the fractal together, fractal geometry offers a direct solution — or at least gateway — to a unified theory of the quantum and the cosmos. The solution is a question of geometry: the retrospect it the cosmos and the progressive the quantum. Or put another way, the retrospect is from an observed position with an iterating emergent; the progressive is a view of an unobserved quantum system.

27 Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald

4.2.12.1 Fractal Field, Gravity and Spacetime Notwithstanding the retrospective fractal offers insight into ‘dark matter’ structure throughout the cosmos; the unification of the dual perspectives of the fractal set out in this paper does not directly invoke gravity and thus Einstein’s General Relativity[18]; however, it is thought that it complements it. It is thought that gravity operates as by General Relativity within a fractal framework and not spacetime. Spacetime is not at all consistent with a fractal perspective and not necessary. Progress in this area may be drawn from the work of Laurent Nottale and his work: Scale Relativity and Fractal Space-Time: A New Approach to Unifying Relativity and Quantum Mechanics [27].

From my work, I posit the iterating fractal behaves as a ‘field’ consistence to quantum and gravitational fields. In my earlier works, I have described how the growth of the fractal enacts a force upon objects within this field. I have used the words ‘fractal distance and fractal paradigm; these all pertain to a fractal field.

4.2.12.2 Research Proposal to Test Inflation Epoch for Fractal Properties In my fractal cosmology paper (page 19) I deduced an expansion equation concerning (iteration) time. If the iteration speed of a fractal is set to the real-life photon rate or speed it may solve the inflation epoch problem. The following comes from the paper:

“From the above equations: if the iteration (production) speed of triangle bits of the (inverted Koch) fractal is set to correspond to the frequency or ‘clock’ of photons of ‘light’ propagation and this 72.59 iterations — to expand from the Planck area size to a size of 1 — is found to be consistent with conjectured inflationary epoch speeds, this will verify the said fractal claims. It is expected it will correspond: 73 iterations (per unit time) is very fast, as was the inflation epoch. Such a finding will improve our understanding of both light and the geometry of space.”

4.2.12.3 The Vacuum Catastrophe Also in my fractal cosmology paper[2] I addressed the Vacuum Catastrophe and claimed — through the conducted experiments there in — that this dilemma is as a pure consequence of the duality properties of the fractal: Lambda is accelerated expansion is the retrospect perspective of the fractal and the quantum a progressive osculating perspective. The two ‘problems’ are different aspects of the same geometry.

28 Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald

4.3 Raised Questions and Limitations Many questions and issues are arising from this finding — all of which, at this point, is beyond the scope of this investigation, but not beyond the scope of reason. I have set a partition here so as not to distract from my key findings and discussions; so that I can claim and speculate on separate — but related — terms.

4.3.1 What is the Fractal? Following is derived from a rebuttal I received that the fractal is trivial and does not conform to Hilbert space. I argue that it is a geometry like all others, and is well described and should — though it is beyond the ability of the author — be able to be shown to correspond to the said. All I’m arguing is that by an experiment this geometry fits patterns in our reality and is akin to ellipses and parabolas in planetary studies.

4.3.1.1 My Thoughts on the Fractal ‘Fractals are everywhere’ as Mandelbrot revealed, and are described as emergent objects that develop and grow with iteration — through time. In reality, examples are found in the shape of clouds and trees. I argue everything is fractal and we should not give examples: it is more interesting finding what is not. Fractals possess — if viewed from a fixed position or observation — a property of scale-invariance and regular irregularity (same but different); they are the same but different — at all scales. , and are classically demonstrated by the original Mandelbrot Set, and more simply by the Koch Snowflake (Figure 7, A and B — respectively).

29 Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald

Figure 7 (Classical) Fractals. (A) The boundary of the Mandelbrot set; (B) The Koch Snowflake fractal from iteration 0 to 3. Reference: (A) [28]; (B) [29].

The classical fractal shape — as demonstrated in the Koch Snowflake above — emerges as a result of the iteration of a simple rule: the repeating the process of adding triangles in the case of the Koch Snowflake.

4.3.2 If this science, where is your Prediction? I have been directly asked this question, and it has been expressed as an essential by the likes of Anton Zerlinger concerning a new theory of foundational quantum physics, where it is asked: what does your model predict, and how is it different to, or how does it add to what we already know? Am I just exploiting what has already been achieved to save my phenomena, save my model, like the many mystics surrounding quantum mechanics — ‘What the Bleep Do We Know’, etc.? On the surface that may appear so; but I’m confident I am not. Firstly, as stated in my preface, I came across these ‘quantum like’ problems while thinking about the fractal long before I had ever researched quantum mechanics in any depth. Secondly, in some elementary form, I am offering a model that should replicate not only the quantum, but also cosmological observations, that can explain them through a model. Essentially, my model predicts the observations and conjectures made about reality by a geometry that is already claimed to explain reality. My fractal model does not address gravity — though it does the distribution of the so-called dark matter in the universe — and the specific behaviour of light and the atom, such as spontaneous emission and ‘quantum leap’ of the electron in the atomic shell. Coupled with this, I also suggest the model explains reality through what has been developed as economic principles. There is also a room for a theory of knowledge to come from this fractal model, and then this I do believe I can explain the real from the surreal; the real from the illusion. Unfortunately for me — or not — the mystics also enjoy the fractal, and they see it quantum in support of their view of reality: I do not see it at all by their view. I see the fractal as a geometry that has not been fully explored and that it may be an insight into the 'big questions’, that’s all.

4.3.3 Where is the Particle? Where is the Wave? – in Reality? I argue ‘the particle’ of the fractal is all the objects in our reality: for example, the tree I see out my window, and the computer I work with. ‘The wave’ is found in that they are all part of an evolution that forms the fractal: as the fractal evolves; they are particles

30 Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald forming — by wave — a fractal. The particles — the objects — all have a history and together they make up — in my examples — a forest, and an economy or network for the computer.

4.3.4 Pi (p) More poignant to this claim is that these items have variance in the population, they share — when studied as a group in the field of statistical mathematics — the property of Pi. Pi implies rotation and cycles and that rotation has been demonstrated in this paper to be part of a wave evolution. I believe this Pi evidence of the wave-like properties of a particle in reality. The emergence and evolution of the (Koch snowflake) fractal invoke Pi (p). The bit’s rotate — spiral — in cycles as they propagate akin to how quantum mechanics is described. Through the fractal, we have a direct window into electromagnetism and the quantum world: where bits (particles) and waves of different frequency are in an (unobserved) superposition, with non-location until ‘observed’. This sinusoidal wave emergence is best described by the same equation, the Euler Formula, (equation 1), as used to describe wave behaviour in quantum mechanics:

℮�� = �� + �� (1)

The Euler equation, in the context of quantum mechanics, was argued by leading quantum scientist Richard Feynman to be ‘the most remarkable formula in mathematics’[30].

From quantum theory; as point positions scribed during the emergence of the fractal spiral are discrete, complex numbers i are invoked to describe positions between these discrete points.

4.3.4.1 Unifying Exponentials with Cycles The progressive perspective of the fractal — showing quantum osculation behaviour and rotation (Pi) complements the previous retrospective perspective of the fractal — demonstrating exponential behaviour. With them seen together, we may now have an explanation as to why paradoxically go together. It appears that they are different aspects, different perspectives, of the same geometry.

31 Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald

4.3.4.2 Experiment to Test of Pi in the Fractal This Pi claim is a prediction and needs to be tested. I would like to propose and test or experiment to show Pi is in the fractal. Simply — it is not simple — clip all the parts, all the branches, of a tree and weigh them and test their distribution for normal distribution where Pi is found in its equation.

4.3.4.3 The Economics Demand Function the Wave Function of Our Reality. It was in my economics teaching that I first explored the fractal nature of reality and I found that the economics demand curve evolved and behaved as a fractal evolution, and this evolution invoked Pi — it has a vector component[31]. The demand curve is a superposition curve showing all the possibilities of prices concerning the quantity of goods (particles) and is all-encompassing — used from ‘micro’ to ‘macro’ economics. It is also a very strange curve in that — interestingly to quantum mechanics — it does not exist: prices are point (observation) like, and not broad ‘smeared- out’ waves as the curve shows. I also found that the demand function is bound to the supply (production) function of the fractal. To investigate the ‘quantum’ properties of fractal attractor, the fractal Koch Snowflake was chosen for its unrealistic quantitative property compared to the Mandelbrot set fractal of being regular regularity (same but same) at all scales.

4.3.4.4 The Fractal Derived Demand Curve the de Broglie Wave Function? By the de Broglie wave function (and quantum mechanics) all things are said to (‘weirdly’) have a wave function — be described as both a wave and a particle. Here in this investigation, by the fractal, the quantum world and ‘economic’ reality act as the same. From this, I claim the answer to this ‘weird’ quantum conundrum is that they are both aspects of the fractal geometry.

The de Broglie wave function of quantum mechanics is directly akin to — if not by definition, that same as — the MU curve. It is described by the equation

ℎ (2) � = � where � is the wavelength, ℎ is Planck’s constant, and p the momentum of a photon particle (a bit). Drawn on a diagram, � against p, the downward sloping ‘demand curve’ like the curve is revealed. The resemblance is given credence when the � is compared to the price or utility, and the p (momentum) the velocity or frequency related to the

32 Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald quantity demanded. It is a stretch, but through the fractal, both are revealed and to be the relationship the crux of this investigation: it should at least open a further investigation.

4.3.5 Duality — Complementarity Not only can the fractal demonstrate wave/particle duality, but duality is also an inherent property of a fractal. One can get an idea of us just by observing the fractal, and its many examples; they all share the same shape, but are simultaneously different from one another in shape. Same but different. This duality can be expanded to the ability to demonstrate that they are predictable and that they are equally unpredictable; they regular-irregular; there is ‘order and chaos’... and so on. This duality property is within — quite literally — is scale-invariant; it is held at all scales upon which it can be observed.

I will address what this insight means for an understanding of determinism and free will in the next section (4.3.11) once I have explained more; however, it is safe to say that here too there is duality.

4.3.6 Insights into Time The iterating fractal — by its very nature — offers direct insight into the foundation question, what is time? From the fractal having an ‘iteration beat’ — that leads to growth and development of a fractal structure; to its emergent formation working all in one — ‘arrow’ — of direction. While the following discussion on time and the fractal directly pertain to my investigation, they also open an invitation for further discussions.

4.3.6.1 Time and Measurement of Reference Points Returning to the fractal landscape section, a landscape with no reference points no measurement to depicting scale may equally be a landscape with no reference to time. A fractal in isolated superposition demonstrates no time. It is not until a reference point provided, an observation made that time emerges

When a reference point is added to the, or a change made to a current reference point, a sense of time -since of change – has taken place. Further to this, even the clock reference point — in Figure 6 — gives a reference to time; without the clock, the image is timeless – or time-invariant. The fractal with observation demonstrates the passing of time, but not absolute time, it is relative time. The numbered time gives a reference

33 Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald relative to some marker —another reference point — in time. Today daily time is set by atomic clocks and our annual calendar to an event that took place some 2000 revolutions of the sun ago.

These two properties of the fractal are ever prevalent to our reality; one can easily find themselves in a timeless environment by taking away the clock, or any measure of time, and any distinguishing references reference points.

4.3.6.2 Iteration Beats The key mechanism to the fractal emergence is the iteration beat. This beat may demonstrate an internal clock. This regular ‘beat’ or iteration of discrete ‘bits’ forms a fractal object by propagating bits as a wave. The production of ‘particles’ — is how light is explained where photons are explained to propagate — like a wave — at light speed. With this, it may be reasonable to assume that if one could stay with the frontier bit, right on the edge of the fractal, all concept of time would cess.

4.3.6.3 Absolute vs Relative Time: There is still the question about time concerning the emergence of the fractal and its iteration-time, but it is a difficult one. Is there any notion of absolute time here: time outside the emergence of the fractal? Or is time relative, in that it is all about the model: no iteration, no time. If it were just the model on its own — not iterating; there is no time. With iteration there is time. On this, my thoughts: time is on one hand — as by the fractal properties light and the universe revealed in my work — absolute; on the other hand, without any light, maybe it is not.

4.3.6.4 Iteration-Time and the Genetic Clock One application of this fractal beat may be the genetic clock in the evolution of species. The fractal directly demonstrates evolution (section 4.3.9) and this evolution only takes place with iteration- time. The regularity of gene mutations in the genome (the genetic clock) allowing us to date by genetic mutations may be evidence of this property.

4.3.6.5 Time and Uniformity In earlier work on the fractal I demonstrated the fractal demonstrates the geological principle: the key to the past is in the present. I argued that this property is inextricable to an evolving fractal.

34 Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald

4.3.6.6 The Fractality of Time 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 there details in between.

4.3.6.7 The Paradox of Our Perception of Time The way time is perceived may have its origin to the fractal. The following was something I identified in my early paper and think it corresponds to how some psychologists think of time[32]. As the fractal iterates through time, early iterations changes to the shape are noticeably the greatest; as the shape forms, changes are difficult to discern. This may explain why we perceive time to slow early in one’s life, and fast as we get older. This builds on the claim that time is perceived to run slow when events are happening, in accidents etc — changes are noticeable early on, but as the shape is set and reference point become familiar or perception of time increases.

4.3.7 Addressing the Emptiness and Symmetry of the Atom In keeping with the discoveries from my investigations relating the presence of (Pareto) power laws with a fractal structure, as evidenced at least in the universe and an economy; is this structure relevant and evident at the atomic level. Can the fractal explain why the atom is the way it is? I think it can and that the atom is a fractal. The size of the atom, of the fractal, is limited by —what I have termed — the fractal (paradigm) distance: the iteration-time from iteration-time 0 to fractal equilibrium, an iteration-time of 7 ± 2 iteration-times. This insight explains the atoms nucleus centred structure and empty large outer shell. This insight comes directly from the fractal- Hubble diagram (Figure 8) that I presented in my fractal cosmology paper. With the ‘fractal paradigm’ and the distribution of sized triangle bites per distance strongly positioned at the position of the observer, the origin of the diagram.

35 Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald

Figure 8 Insight into Atom Structure from Fractal. Hubble Diagram. The full observable fractal ranges from a strongly clustered to the distant.

This distribution is akin to how Lord Ernest Rutherford’s empty atom[17] — which is described to be 99.999999999% empty between the outer electrons and the inter nucleus — is described. Concerning an observation at the smallest bit size (7 iterations), the largest bit size is extremely large: the smallest bit size is some 99% of the largest bit size; and conversely, to the largest, the smallest is extremely small. This large ‘field’ size scale can be calculated now be shown — from this investigation — to also share quantum-like behaviour.

A sceptic to this must keep in mind — as I have iterated — a fractal shares these simple properties; however, come in an infinity of forms, and they do iterate.

4.3.7.1 Atomic Symmetry Concerning the symmetry; this has to do with the duality property of the fractal; that there seems to be an anti or contrary rotation, bit, or other property to the fractal. This claim is in response to Professor Frank Closes question he has posed many times [33] as to why there is such symmetry in the atom and cosmos. I hope that my findings inspire more investigation.

4.3.8 Fractal Decay and a Wave Package If the emergence of the (Koch snowflake) fractal is ‘played’ in reverse then decay is demonstrated. With the fractal, I can demonstrate decay from a complex object — the snowflake — to a simple object with respect to (iteration) time. As time passes the

36 Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald detail of the snowflake diminishes and leaves the original core triangle bit. Fractal decay is the reverse of fractal development and is also logarithmic. The significance of this is that if we put the two together; the development and the decay of the fractal, and we know that they behave as a wave, we have something akin to the when package of a quantum entity — a wave package.

4.3.8.1 Atomic Half-life The decaying fractal demonstrates (Lord Rutherford’s) radioactive half-life[34]: the decay of detail is an exponential function. And oddly similar to Rutherford’s atomic discoveries, the fractal snowflake is transmuted — decayed — to a singles triangle bit.

4.3.9 Demonstrating Evolution If the bits are assumed to change with iteration this is a direct demonstrate evolution. As the fractal is made-up of bits or particles any change to the particles will change the shape of the fractal and this change — or information — will be transferred as a wave.

4.3.10 Insights into Knowledge The findings of this work have a direct significance to how we know and this work opens the door to a fractal theory of knowledge. This will be covered in a separate work.

4.3.11 Determinism and Freewill Here too we can address the problem of whether reality is determined or not. The fractal suggests there is — again — a duality evident here; things — phenomena — are determined and these are studied and categorised in the field we term science, while and at the same time these same things phenomenon are chaotic and unpredictable. The classic example was the weather, we can understand it, but prediction outside a finite period of time, this hopeless. So, in one sense we have lines of fractality, of pattern — something we can form an equation from or an algorithm; while on the other hand, we have indeterminacy, of chaos, of unpredictability and all within an independent isolated system.

Freewill in a fractal system, I argue, comes from a different application of the measurement problem — the addition reference points. A system or fractal is chaotic until a reference or measurement of some kind is made, thus bounding or controlling the system. In an example, a steering device to any machine, to an aircraft or

37 Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald automobile, is to me like ‘the observation’ to a chaotic system. The steering column controls the chaos, it bounds it. Without it, we have chaos and no control; but a nut — for example — holding the steering column allows for control.

4.3.12 On Quantum Interpretations At this point I hope that my work has shown that the quantum can be explained by understanding the fractal geometry. I also trust that I have addressed some of the quantum interpretations even if not going into them specifically. I do believe by side on Einstein’s perspective quantum: the quantum is — thought strange — real and natural and can be now be explained.

4.3.12.1 Many worlds I’ve thought long and hard on Everett’s Many Worlds interpretation: it does appear to be an outlier, at least for a fractal interpretation. While the fractal demonstrates what is posited by the Many Worlds interpretation — it too ‘branches’ and shows a set of ‘all possibilities’ — I am reluctant to accept that this (it) is the reality and that — in reality — ‘the universe splits’ as described. I think it is an illusion. Early in my thinking on the fractal I wrote a blog on a theory of imagination and posited that imagination is the ability of — at least — humans to think about all the possibilities without anything enacting something for real and that this is demonstrated with the fractal showing all these possibilities. The human mind can do this imagining very quickly, but the reality is the action of doing and making choices and this is the domain of economic theory — not to mention chaos theory. While I agree that in a quantum state — the fractal landscape — all possibilities are given; in the real and measured world of our own, all these possibilities are a place of imagination. On saying this, I have often thought that there is one property of the fractal that shows that each of us is each other’s potential: the entire population — in our case all humans — has all the possibilities, all the branches, one could take, and that is, in a sense, a many-worlds perspective.

Demonstrating a ‘many worlds’ by the fractal is an economic problem; the cost of production is exponential and the fractal demonstrates that there is a limit of how much can be processed — and it is not infinite. The fractal is produced at the fractal processing speed — the fractal speed: the maximum speed of being able to create a discernible or knowable shape — and this speed determines the speed of zoom or magnification into the fractal. It is also the speed of the fractal-wave. The slowest speed

38 Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald can be demonstrated by one drawing the Koch snowflake by hand; a faster demonstration is with a modern computer. The production speed is thus limited by the processing power of production. The average modern computer (in 2020) cannot produce many more than 8 iterations in one position (without zooming) before the computer crashes with overload.

More than this I am concerned that this topic too large and rather outside the scope of this paper: I hope to address it in a more direct and focused setting.

5 Conclusions This investigation has shown that the development of the emergent fractal through iteration-time correspondences with the many issues associated with the special quantum nature of light. As discrete bits are added at regular time interval — forming fractal structure — they propagate information in the form of an oscillating sinusoidal wave with exponential wavelength and frequency dimensions — and arguably — at a constant speed to an observer within the fractal. The fractal model was able to address the quantum ‘measurement problem’; showing it is a property all fractals where position and scale are unknown until another ‘bit of information’ — an observation — is added to the landscape. Before observation, the iterating fractal is oscillating — ‘spinning’ — in a superposition of all directions and all symmetries and as a result can address questions surrounding the problem of quantum spin and quantum entanglement: these were shown to be properties of an isolated fractal, before any observation was made to or within the fractal set. A key finding was that the fractal demonstrates duality as a fundamental property: one consequence of this property is that quantum-like — oscillating — perspective of the fractal marries in duality with an exponential (cosmological like) retrospective perspective. The two are different perspectives of the same geometry and as a result, may be the (missing) link to a unifying theory: the quantum and the cosmological problems are two sides or perspectives of the same geometry — fractal geometry. Other outlying properties of the fractal were discussed, such as its corresponding to issues of knowledge, the shape and size of the atom, and it was acknowledged that this investigation used somewhat elementary assumptions, but as a result offers — in the ‘light’ of the importance of other historical applications by geometries, ellipses etc. — an important insight into

39 Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald reality none the less. It is as if we are agents to the fractal as the planet are agents to Newton’s Laws and the ellipse.

6 Acknowledgments Firstly, I would like to thank my wife and children for their patience and support. Thank you to my student’s and colleague’s in the International Baccalaureate programmes in Stockholm Sweden area — Åva, Sodertalje, and Young Business Creatives — for their help and support. Without the guiding words, support and supervision of Homayoun Tabeshnia, this work may never have come to being. For their direct belief and moral support, I would also like to thank Maria Waern, Dr Ingegerd Rosborg and Dr Marie. Mathematicians Rolf Oberg, Peter Morris and Tosun Ertan helped and guided me no end.

40 Making Sense of Light and the Quantum by an Experiment on an Isolated Emergent Fractal Blair D. Macdonald

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