(Permalink) Let us see again Figure 1 of chapter IV-5: material particles appear as trajectories formed by series of nibs, connected by a «mechanical» wave. However, photons do not appear like this. They are a single arrow linking two observable quantum interactions, without any observable effect on their trajectory. In a more general way, they do not have the dotted arrow which marks the transfer of mass (and other charges) at a mechanical speed.

But there is worse: according to Special Relativity, an observer riding a photon would see no time elapsing between his departure and arrival. In addition, he would see the world completely crushed, so that the distance between the start and end would be zero... Even if for us it is billions of light years!

So it is not necessary to suppose that photons are particles existing on their own (unlike protons, neutrons, etc.). It is enough to note that they combine two quantum interactions in a single event, in a pure Feynman diagram. And indeed, according to Relativity, the departure and the arrival of a photon are two perfectly superimposable events, and therefore indistinguishable. So we can legitimately pose that they are the same and single quantum event. And indeed, this unique event involves only two particles, and only two.

This explains very well
several very intriguing fundamental properties of the photons: that
they can be superimposed in an infinite number in one place. Or that
they can be unobservable (we see only their departure and arrival).
Or, similarly, that they have no influence on matter, along their
trajectory. These properties can be perfectly explained, and very
simply, if they are *not here.*

*This paragraph added on August 18, 2020:* This nature of the photons also explains the temporal weirdness
observed in the Aspect experiment
(chapter IV-2) and in the Wheeler experiment
(chapter IV-11).
Indeed, in the relativistic referential of the photon, the emitter, the receiver and the observation
device all are *in the same place.*
And thus in *the same moment,* in an unique quantum interaction involving the three.

So long as we are here, we can do the same reasoning for all the fields known by physics: each field has its own way of transmitting energy, and possibly other charges between the «material» particles such as the electron or the neutron. And thus, each field will have one (or more) mediator particle, having the same «immaterial» properties as the photon.

The two preceding paragraphs accurately describe a set of properties, that the physicists summarize in this way, in the language of physics: each field has one (or more) mediator particle, called a boson, which obeys the Bose-Einstein statistics.

Metaphysics which allows you to write stuff like that, it goes a little beyond the astrology rubric of the TV, doesn't it?

We can even go further: if, for the photon, the start and arrival are superimposed in the Minkowski space, on the other hand an ordinary observer like us will really see a separate starting point and ending point. Thus a trajectory between the two. The relativistic perspective unfolds a single point into a trajectory! It is this infinite unfolding (from zero to a given dimension) which makes appear, to our eye, all the stuff like photons and electromagnetic waves moving at exactly the speed of light. All these things which can be seen only when this unfolding occurs. From here these properties of photons and other bosons, to move precisely at the speed of light, or to be undetectable on their trajectory. And all this stuff of electromagnetic field, equations of Maxwell and the like, are just the description of the relationship between the photon emitter and the receiver, without any need to assume anything which would move or deploy into space. Even not «something» which would be a field. Only pure logic. Never we felt so surely that there is no «matter» or space, only logical relationship, and that the laws of physics are only logical laws.

I had the intuition of this long ago, from something studied at school: when light goes through matter, it undergoes refraction, from the smaller speed of light in matter. And the refraction angle is such that the angled trajectory is still the fastest speed for the photons! This can happen only if the photon «know» in which direction to start. But this is in contradiction with Relativity. The unfolding explained above is an elegant explanation of this apparent transfer of information backward in time.

Let us add in passing that some laws of classical physics are therefore a direct and mandatory consequence of Relativity. Let us think at this, before trying to unify them!

Of course the vision of electromagnetic waves propagating in space remains relevant, for instance for a radio technician. But it is only a way for our mind to grasp at a purely logical reality, which ultimately has no form and no place. An epicycle (note 79), in a way, but which simplifies the calculations, rather than complicating them.

At last, even the «material» particles such as the proton or the electron (physics says that they obey the Fermi-Dirac statistics) also exist in an abstract form, of quantum waves, between two quantum interactions (their mechanical wave). They can therefore also behave according to the statistics of Bose-Einstein... provided, however, that they do not undergo quantum interactions with each other, or from other particles they may encounter. This condition is fulfilled at very low temperatures. And we actually observe, since recently, «Bose-Einstein condensates» at very low temperatures, where matter moves in a strange way, like only one giant atom.

(Permalink) One of the basic concepts of physics is the «field», such as the electrical field. These fields explain everything, because it is them which govern the movement of particles, their changes of state, etc.

However, these fields
are new elements, and inherently different of others, that classical
physics does not explain, just being happy to observe them, measure
them, etc. For the theory of the logical self-generation process,
they pose a problem, as they would require to add *ad-hoc*
elements.

It is enough, however, to note that what transmits the interaction is the abstract wave sent by the the nib. Each nib transmitting its own wave, particles at a distance will be influenced by all these nibs, in a way to change their movement. Thus, it is no required to invoke the influence of «something» which would be a field. Everything comes down to the nibs, and to their abstract waves. Their properties are certainly not very simple, but at least they have the advantage of assuming all the work, without offshoring it to countries inaccessible to science.

Fields, like photons (bosons) are therefore only convenient concepts for our minds, without any proper existence, but which however describe very well how the nibs interact two by two.

And we have a practical evidence of this (fields being only consequences of photons or bosons): it is impossible to directly measure, or even detect a field, without taking some energy of it, that is without exchanging some real photons (or other bosons).

On the contrary we can perfectly well detect matter without modifying it (without giving it information), for instance with an experiment of interference: we can infer that one of the slots is open or closed by the observation of interference, without that theses slots «see» the light which passes through them.

(Permalink) We could have very well imagined, in chapter III-4, instead of nibs, a continuum of space, a «membrane», which state in a given point and time would be a function of previous states (A modification dx, dy, and dz would be a function of values x, y, and z at a time -dt, which implies differential equations and a differentiable space). At first glance, it is quite conceivable. We can therefore assume that universes exist, which would work in this way. Of course these worlds are not quantum, they even not have atoms, but fields of different kinds of matter, where each is more or less present in each point. It is like this that the world was imagined, before the discovery of atoms. Just like in a simulation of chemistry, where the concentrations of different reagents vary by location. At first glance, it looks much like our own universe, except that there are no atoms.

Would such an universe allow for the evolution to life? I doubt it, because there are several serious arguments against this.

-How could «fields» of matter react chemically to give new molecules? The incredible variety of our chemistry is based on the availability of a large number of different atoms, which can combine in millions of possible molecules. However, atoms are quanta of matter. Without Quantum Mechanics, therefore, there is no chemistry, and, therefore, no life. By contrast, we can imagine particles sets entirely different of ours, up to infinity, as long as they are quantum: there must be at least some which are conducive of a chemistry of life, see to even more extraordinary things.

-Worse, with no molecules, no DNA, and therefore no way to store information in a small scale! No more neurons, therefore no reasoning, no information! Well, maybe an eternal beatitude, perhaps...

-If we look again at the image 1 of chapter IV-3, showing two relativistic continua which do not join, we have a view of another problem: non-quantum continua of space must be able to join again together in all circumstances. Otherwise, simply moving our hand would be enough to send it in a parallel universe, and we would be unable to recover it! It could even happen situations where space would be irremediably crumpled and torn, as a vulgar car sheet (everyone knows that a damaged sheet of a car cannot be flattened again). To avoid this, our continuum should have the same property than the surface of water: when two drops of water meet, they form a single surface, instead of mingling together like the Olympic rings. Whatever strain we inflict to the surface of water, storm, tsunami, cataclysm, it always reform a perfectly smooth and flat surface. As our hypothetical continua... But if the water has this property, it is because it is quantum! Made up of molecules, able to move and reorganize, and reform a new smooth surface an infinite number of times, without never wearing. Eh yes, the superb mirror of a mountain lake is a quantum effect...

Another difficulty of the Continua, is that if structures appear, they do not have intrinsic dimensions: a microbe could have the size of a car, or on the contrary a whole planet would have the size of a microbe, with all its civilizations! Our world of atoms with fixed sizes (imposed by quantum mechanics) does not suffer from this problem, and each level has its own structures, which allow the larger structures to organize in turn in a stable and predictable manner.

Worse, there is nothing for these structures to remain stable! While a structure such as the atom represents a minimum energy, which thus cannot degrade in something still simpler.

-Finally, numerical
simulations of Continua and differential equations (functions of
time) do not exist as such on computers. We even not know to do it,
in facts. This branch of mathematics, called analysis, can solve only
some very specific problems. On the opposite, simulations all use the **finite
elements** method: space is divided into a grid, and time in turns,
like in the chess game. It therefore falls again into something
quantum!

Mathematics know to make sets of numbers, and we can easily imagine series creating trinomials, therefore existing in a space indistinguishable of our physical space. Quantum Mechanics would just be such a series. But to self-generate a true continuum (in the mathematical sense of a function of x, y, z, t, continuous, differentiable, without finite elements) seems infinitely more complicated. The only way is to solve the differential equations of these different fields. But, precisely, we do not know to solve these equations!

The only case where we have derivable continua, with differential equations that we known to solve exactly, without finite elements, are the linear differential equations. These equations have solutions which can be calculated exactly, for any date. In this case we find the «waves» of the particles, which description is actually not quantum. For example the Maxwell equations, which describe the radio waves. However these waves cross each other in space, while ignoring each other. If only them were existing, our universe would be a freezing vacuum, populated only with the whooshing of the original radiation. For these waves to interact in interesting ways, we need non-linear differential equations... that we do not know to solve.

**But the most serious is
that a universe formed only of continuous fields, contains a logical
indeterminism:** for a law of cause and effect to play, where the cause
should be, in relation to the effect? One second before? One
microsecond before? Mathematicians elude this problem in differential
equations, by naming this time «dt» (delta t), which can
be made arbitrarily small. Into formulas... For the actual
calculation, we need to determine a value! For instance, we take a
basic time, small enough, with the calculation by finite elements.
But in a real system, nothing allows to lift the logical
indeterminism, when dt connects a cause and its effect, since nothing
allows to assign a value to dt.

It is therefore
needed that each present moment in a peculiar spot is influenced by
really past elements, excluding the present
(otherwise it influences itself, thus becoming still more paradoxical).
The cause must also be
within a certain distance (in space) of the effect, otherwise we
would have a universe composed of «threads» evolving each
for itself. Rule 5 of Chapter
III-3 requires that this relation is constant. The simplest
solution is that **an action at a given instant and precise spot has
its cause in another unique instant and spot in the past.** So that
we have a continuous series of paradoxes resolutions, in an universe
which, at large scale, looks like a continuum.

This is exactly what happens in a... quantum interaction. When two nibs exchange a boson. Here is the origin of the quantum organization of our universe! (Solutions with quantum events with several causes, or spread in an area, are also possible in theory, but much more complex.) However, if the distance (in time or space) between the cause and the effect was constant, to comply with rule 5, we would have a «soup» universe, where changes would remain local, without influence at a great distance. A much richer solution was that the time and distance ratio remains constant. The ratio between a distance and a time is a speed. From there comes the speed of light, the absolute maximum, at the origin of Relativity, which also allows for gravitation. This relativistic world is far more interesting (anthropic) than a soup universe, because there is no maximum distance for the quantum interactions to occur. So, electromagnetic waves can bring us the heat of the Sun, Internet, images of distant galaxies, etc. Thus Quantum Mechanics and Relativity would simply be logically required for the operation of a universe filled with fields and fit with a history (chapter IV-3), instead of a simple mathematical time. Of course we could resolve the above paradox in other ways, but the way they do in our universe is probably the one which offers the greatest ratio of possibilities over simplicity.

Therefore, we have a solution to the paradox, probably the easiest we can find (connecting only two nibs, with a constant «angle», and thus relativistic). And this is precisely how things are in our universe! After the theory of the logical self-generation, the appearance of this solution solved the indeterminacy, with a creative absurdity (Chapter III-3, rule 3), while generating the founding nibs of our universe. To say the same thing in the language of the physics of the Big Bang, this phase transition would be the first which occurred in our universe, in the Plank time, and which would have seen the emergence in a single operation of Quantum Mechanics (probably an unified force), Relativity, space and time (from a previous state, that physicists call the «quantum vacuum», where none of these things are defined).

So, it appears that the quantification of matter, quantum mechanics (and Relativity), is forced by the greatest mathematical difficulty of continuous systems, or even perhaps by the logical impossibility of a non-quantum physics able of producing an History and stable micro-structures. Probably, non-quantum universes are not favourable to life, such as a universe containing only radio waves... or only spiritual auras. On the other hand, an infinite number of different quantum laws seems possible, of which many may be favourable to life. These universes are even not necessarily physical, as psychical universes are also quantum, in their own way. We can even imagine more complex relationships between two nibs, or more, which would give spaces equipped with more complex Relativity and a Quantum Mechanics.

We can also imagine non-relativistic quantum universes, but then they do not have a gravitation. Therefore, Relativity is also anthropic, at least partially.

What is properly astounding, is that nature was finally unable to do better than human mathematicians. My respects to the white coats! Probably an exact analytical solution of a random differential equation does not exist, explaining very well that our universe does not work in this way... and that the mathematicians have not found it.

This impossibility is a
strong argument, if not a demonstration, **that any field is
necessarily quantified.**

And this is precisely one of the basic axioms of Quantum Mechanics...

I would even suppose that computer simulations which would mimic the quantum laws would be more effective than the finite elements method. A case where these simulation are at pain is when there are very different scales involved: one must provide with several grids, and switch from one to another, depending on the progress of the calculation. A quantum simulation would just have to use quanta of different wavelengths, and perform all the calculations with the same scale. For example a weather simulation would use «aerons» with a long wavelength for overall phenomena, and other small with a short wavelength for storms, an element on which weather simulations are awkward. These «quanta» would resemble the «wavelets» of some analytical methods... and we can too think at photons being only this.

A last, we note that even the «universes» of pure consciousness, such as the dream, are also, in a way, «quantum», that is, consisting of individual elements arranged in a chain of cause and effect, to give a time and an History. We shall see in the fifth part, that consciousness itself is also «quantum» (note 91), that is, composed of a succession of instant scenes, even though we are usually not aware of this.

(Permalink) What is above seems to be in contradiction with physics, which essentially considers continuous fields, such as the electric field of the radio lessons. When the theory of the logical self-generation considers instead individual interactions, of which these fields are only a consequence.

However this contradiction is only apparent. There is in fact a non-duality between the two visions (Chapitre I-3).

Indeed, mathematically, we can consider the fields as the global result of individual quantum interactions (the electric field formed of photons), as predicted by the theory of the logical self-generation. But we can also consider mathematically the quantum interactions (photons) as a consequence of the fields. In this case, the non-duality between the two interpretations is a simple «change of referential»... or two equivalent different conceptual systems, (chapitre I-9), describing the same reality.

Indeed, physicists reason as follows: If we consider continuous fields, interacting with matter, then there is no analytical solution for the manner in which these fields behave. Mathematicians then use another tool: the perturbation theory, where the field is modified by jumps, by small individual disturbances. The appearance of a continuous field that we experience with our sense, would result only of the great number of such small jumps.

If we consider that each of these individual disturbances is, for instance, a photon, then we find again the apparently absurd statement in the beginning of this chapter: photons do not exist as individual objects, they are only an artifice of calculation. Which, again, explains their strangest properties, such as to be undetectable on their journey!

The physicists therefore stumbled on their side on the same «absurd» conclusion than we found in the beginning of this chapter.

But what is astounding is that this artifice of calculation can be visible to the naked eye, for example with the scintillations emitted by a radioactive body (which excites a fluorescent screen, as in a spinthariscope), or directly with the experience described in chapter IV-2. That a mathematical artefact appears as a physical object to our senses (chapter III-5), really shows the ultimate logical nature of our universe, without any need of a mysterious «material reality» to explain it.

(Permalink)
The hardest problem
that physicists have to solve today for obtaining an unified theory
of all the forces, is the incompatibility between the Theory of
Relativity (gravitation/geometry of space) and Quantum Mechanics
(electrical, weak and strong forces). The vision presented in this
chapter and in chapter
IV-6, leads to a possible solution to this problem: gravitation
and the geometry of space are an **emerging property** of the
behaviour of a large number of individual nibs, and not forces
existing by themselves like the electrical force. This situation
would be similar to the one of the global behaviour of liquids and
gases, as in thermodynamics, from the statistics of the behaviour of
the individual molecules.

Unfortunately, the solution to this problem is very difficult, and for example we cannot easily infer such a simple thing as the boiling point of water, from the properties of its molecule, yet the most studied one.

Thus, if the content of these chapters is correct, then we can obtain an overall knowledge of physics, if we however accept that Relativity and Quantum Mechanics remain two incompatible conceptual systems (chapter I-9), both valid in different situations.

A common domain would
perhaps be possible, at a high energy, in the case of an unified
force. But in this case, this force, not only moves the hypothetical
particles that obey to it, but in more it governs the shape of space.
In these conditions, this **quantum gravitation** is likely not
obeying the rule of having three dimensions.

(Modified in January 2017. Former version on the wayback machine)

(Permalink) In this whole book, I deliberately avoided discussing Wave Mechanics, its concepts and descriptions, in order to avoid confusion or overloading the text. But I could not totally ignore it, hence this subchapter.

Indeed, the view of the world after Wave Mechanics seems totally different from the one of Quantum Mechanics. In Wave Mechanics, an electron is a system of waves, which can, for example, revolve around an atom, as we would see a wave rotating around a whirlpool in the water. This wave is not in one point, it extends in space around it, and even theoretically to infinity, occupying the whole cosmos (allowing quantum non-locality, for example tunnel effect). Then, when certain conditions are present, this wave begins to oscillate around the atom, for example from right to left. The oscillation increases, until a part of the wave breaks off, and forms a photon which separates away like an independent wave. The remainder of the wave continues to rotate around the atom, and to represent the electron here, just in a lower orbit.

This vision seems totally opposite to the one of the quantum world, with its instantaneous interactions at a precise point, which we call here a nib (chapter III-4), with its symbol ¤. On the contrary, in Wave Mechanics, we have continuous fields everywhere, and emission is a process which takes time, involving a gradual transformation of fields and waves. However, if we reflect in depth, we observe that all these waves are the superposition of elementary waves, just as a sound can be decomposed into harmonics. And, guess what, each of these harmonics matches exactly a particle or a state of Quantum Mechanics. Even their appearance and their disappearance matches exactly the quantum appearance or disappearance of the particles.

This means that Quantum Mechanics and Wave Mechanics are just two different conceptual systems (Chapter I-9), which describe exactly the same reality. Despite their apparent incompatibility, there is no contradiction between the two. I could have used wave mechanics for my theory, it would be just as exact, but more complicated. The nibs were much more intuitive and accessible than the wave symphony. Perhaps somebody will rewrite my book using the second.

Physicists have long sought to reconcile the two theories, which seemed to give totally contradictory results according to the experiments, for example, light which sometimes behaves as a particle, sometimes as a wave. The debate on the nature of light lasted for a century! They finally succeeded: the equations of one theory can be derived from the other. The picture above of the sound harmonics gives a good idea of the method they used, but it is of course mathematically more complicated.

I shall conclude this chapter with saying that **the non-duality between
Wave Mechanics and Quantum Mechanics is the solution to the above
problem of the self-generation of a system of continuous fields instead of nibs.**

(Added in January 2020)

(Permalink) Science is evolving so fast that it made substantial progress while I was writing this book.

Thus, around 2000, when I was writing version 1, science popularisation journals were talking about the wave-particle «duality» between Quantum Mechanics and Wave Mechanics. The two were incompatible, and sometimes one or the other was relevant to describe the world, without we knew why. Therefore, I presented this as a mystery, and an example of non-duality (chapter I-3) between two Aristotelian theories which were incompatible according to this logic.

So, it was not a problem if I used only one of the two theories, Quantum Mechanics, in chapter III-4 and following, to build the theory of logical self-generation: considering our world as a series, in the mathematical sense of the word, of «nibs».These nibs being, in the physical world, the quantum interactions. This was all the less a problem when, in a fit of Popperian zeal, some scientists went so far as to consider the quantum interaction as the only defined reality, saying that waves would not be observable independently of these quantum interactions.

However, the discovery of a common mathematical formalism, allowing to switch from one theory to the other, put them on an equal footing. What if the «nibs» were not enough to describe reality? The theory of logical self-generation would be flawed.

In this month of January 2020 I learned about the new official theory which unites the two: the Quantum Field Theory, from a young 21 year old expert, invited to present it at the Nalanda Buddhist Monastery, near Toulouse. And this time the turn is clearly complete: Quantum Field Theory speaks mainly of fields (and therefore of waves, since these fields propagate). Should we abandon quantum interaction, the basis of my own theory of self-generation?

Fortunately not, because quantum interaction remains, as a time and place where a multitude of possibilities reify themselves into a single reality. I think that we can still consider the fields as simply the equation which will determine the place and time of reification of the nibs, each reification modifying in return the fields (reducing the number of possible values to one). But then, which of the two, fields or interactions, is the one which allows the other to exist? In fact from the point of view of logical self-generation, this is not important, and the question doesn't even make sense. What is important is that the different elements of the world create each other, through the law of cause and effect (the laws of physics), without assuming that any absolute «material reality» produces them, or even is necessary.

It is therefore not necessary to rewrite my theory of logical self-generation to adapt it to the Quantum Field Theory. But it was still needed to answer the objection it arises. If one is not convinced, one can still replace the punctual nib by an extended field in space, a nib-field. This extension in no way prevents us from considering this nib-field as an element of a series. Just that it is less obvious than with the point nib.

* *

*(Added on June 28, 2020)* There is something bothering
me about quantum field theory, and I finally figured out why: the
concept of field requires a space in which the field exists. This
goes against the theory of logical self-generation, where space and
time are only appearances: the structure (in the Bourbaki sense) of the set of the
quantum interactions. Example: two particles exchanging a photon. If we could
get on board the photon, we would find that its life time is null. Why is that? Because
in the Minkovski's space (the relativistic
space-time), the path between these two particles is zero. Which is
counter-intuitive, when we see one of the two particles in a galaxy
billions of light years away, and the other in our eye. Where does
this difference come from? It comes from our own relativistic point
of view, different from that of the photon, which «unfolds»
its trajectory, and gives it a length, a path, etc. which
does not exist in reality. Hence all the weird quantum properties of
photons, which are curious but which logically follow from Relativity:

- That we cannot observe the photon on its path. Of course, there is nothing there which is the photon.

- That, in the case of a trajectory with refraction, the photon «knows» in which direction to start, in order to give the shortest path. It does not need to violate Relativity to do this, since it is at the same time at the starting point and at the end point.

- The results of the delayed choice experiments (Wheeler experiment, chapitre IV-11), Young's slits (Chapitre IV-2), or Aspect experiment (Chapitre IV-2): the photon «seeing» simultaneously the transmitter, the device and the detector, has the same behaviour all along the path that we see.

Where fields come into play is when classical physics says that the propagation of the photon is due to the propagation of an electromagnetic field. In view of the above, we can say the opposite: the electromagnetic field is, like space and time, an appearance, which describes the behaviour of the photon, once its trajectory is unfolded. An epicycle. A convenient epicycle, which we shall not abandon, because it allows to build a lot of useful devices. But fundamentally, it is an illusion, with no reality of its own. This is how the theory of logical self-generation explains how this illusion appears, without assuming ad-hoc metaphysical entities, nor seeing unfathomable mysteries.

**
Ideas, texts, drawings and realization: Richard Trigaux (Unless indicated otherwise).
**

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