Are laws or physics entirely arbitrarian, or in which extent can we deduce them from the theory of the logical self-generation process? Said otherwise, does this theory pose constrains on the possible laws of physics? And if yes, until when does this allow to deduce the laws of physics?
The main laws of physics are absolute conservation laws: of energy, mass, charge, motion, etc. But also, the constants of physics and the laws of physics never change. This would be a direct logical consequence of the rule 5 seen in chapter III-3: in a system of logical implication, once solved the founding paradoxes, then each logical implication is strictly determined. Clearly, once created into a first implication, the laws of physics reproduce identically at each of the following implication, up to the infinite. And this obviously implies that the constants of physics do not change. This is obviously also true for the quantities they handle. For instance, the electric charge of a system remains constant, and the creation or destruction of charge is automatically accompanied with the creation or destruction of an opposite charge. These constraints have an infinite force, as any logical constraint, to the extent that charge and anticharge can be created or anihilate only in the same quantum event.
We could wonder, after chapter IV-5, why the nib has this «form»?
It is because, if it had no such relativistic properties, there would be no gravity. Gravitation is not a «field» like the electric field, but deformation of space. Deformation too small to be visible to our eyes, but enough to attract our bodies toward the ground. Relativity and Gravitation are linked. Without relativity, there would be no gravity.
We can wonders what would happen in a world without gravity. If our universe had no gravity, but all things otherwise equal, it would be now filled uniformly with a gas of hydrogen and helium at very low pressure and cold temperatures. No sun and no star to light up this dizzying vacuum, or to create the other elements required for forming planets and allow for the emergence of life. Instead, an eternal billiards of neutral atoms, colliding indefinitely without ever organizing together. Such worlds are logically possible, so they probably exist, at least as logical objects. But it is clear that no body allows to incarnate into them.
So we can say that the law of gravitation is anthropic (chapter IV-6). Gravity being a consequence of Relativity (especially of the Minkowski space), thus the later is also essential for the emergence of life. Relativity is also anthropic. Non-relativistic universes, such as series in sets of trinomials, really have three dimensions much looking like our own. However they are not Minkowski space, so they are not relativistic. And so, without gravitation, they do not allow for the emergence of life.
We can still assume that there are other solutions than gravitation to bring matter to clump together, interact and evolve enough to give life. But the relativistic universe, with its gravity, seems the easiest way to achieve this. The case should not be so easy, because even in our universe, only a tiny proportion of the total matter is effectively under the right conditions to give life. So, more complex solutions are even more unlikely.
We said repeatedly here, in previous chapters, that the particles always remain in the three-dimensional space, with a perfect precision. Actually no, because at small scale, space is rough, bumpy. The Heisenberg uncertainty also allow particles to exist for a short time, when they should not. They also allow for fluctuations of space to exist. Thus, in this bumpy space, the particles are not ideally into the three dimensions. The difference is certainly small, but it is observable.
Why is it this way?
Let us compare with a gas: although this gas is formed of a large number of molecules moving in every directions, the gas has an uniform average temperature, uniform pressure, uniform density, etc. The comparison is of course with our vacuum formed of virtual particles which in average stay very close to our three-dimensional space. However, the gas behaves in this way because the particles exchange energy with each other, which leads to an averaging effect. But there is nothing similar with the nibs.
This suggests that gathering into a three-dimensional space is an intrinsic property of nibs... like for the trinomials, which cannot exist out of their three dimensional set structure. Or it would be a consequence of their «form». However, we can also assume the existence of a «shepherd process» bringing back the particles in our three-dimensional space, as soon as they move at a short distance. Such a mechanism could be a logical feedback, as discussed in chapter IV-6: from an immeasurable number of evolution opportunities of our universe, only one is consistent (with three dimensions), so that this one would be selected. Temporary differences (Heisenberg uncertainty, rough space) would not be an issue, but larger discrepencies would lead to inconsistencies, such as the disappearance of matter and charges into other dimensions. Thus, any departure from the norm would be quickly corrected. In this case, it is remarkable that something so abstract as a logical feedback could have such a force, and act tirelessly for countless times, as to be one of the most powerful actors of physics. But it is not a wonder, if our universe is formed of logical elements. In its field, logic has an infinite force, and it never wears out.
The physicists use to say that vacuum has properties, such as the speed of light, the constants of physics, etc. This implies that vacuum would be «something», a «rubber membrane», or even an «aether», which this time was cautiously given relativistic properties, not to be caught again by Michelson and Morley. And regardless of how this aether would be squashed by the equations of Einstein.
In fact, we really saw in chapter IV-4 that the nibs generate space, and even the relativistic space-time. In doing so, they necessarily do in a specified way, always the same. We saw for instance that the limit of the speed of light, and this speed itself, is generated by the angle (in the Minkowski space) where each nib «sees» the previous. We can rely on the same principle to explain all the other constants, gravitation, electric field, etc.
Thus, not only space is the structure (in the meaning of the Sets Theory) of the whole sets of nibs, but in more, these nibs confer it properties, such as being relativistic, to be traversed by electric fields, magnetic fields, weak or strong fields etc. in proportions determined by physical constants such as the permittivity of vacuum.
So, all the complexity of our world goes to the nibs, and how they connect, instead of an hypothetical «aether». But after all, it is much more simple in this way, to have only nibs, rather than assuming nibs more a continuum.
And when we try to measure the properties of vacuum, our measuring instrument shows in facts the properties of the nibs of which this instrument is itself made. It is remarkable that we actually always find the same result, even if we build another device.
And space is really an «abstract» property, which exists only as a convenient way to describe the interactions between nibs.
Nuclear reactions are in principle symmetrical, for instance always giving the same amount of matter and antimatter. There are however a few violations of symmetry, such as with the decay of kaons (unstable particles formed of two quarks), which gives a little more often a particle than an anti-particle. Today, such phenomena occur only in the laboratory, but shortly after the Big Bang, at a time where all kinds of particle existed in equilibrium, this deviation could favour matter over antimatter matter, explaining that only it exists today.
Such a violation of symmetry is still a mystery for physics. Even for the theory of the logical self-generation, it requires that the founder nib was created with this arbitrary property, by the simple play of the creative absurdity, without external cause. This problem can also be discussed into the frame of the anthropic principle (chapter IV-6). There is however an experimental evidence toward the creative absurdity producing an arbitrary deviation: observation in the laboratory of violations of varying amplitudes, into a quark-gluon plasma. Here appear «domains» with each a different physics! Thus, the same causes resulting into the same effects, physicists managed to get close enough of the Big Bang to observe the creation of a law of physics! However this law has little influence in practice, and anyway these domains disappear when the quark-gluon plasma cools off to ordinary matter.
However there is an hypothesis where this violation of symmetry would be explained in a simple and logical way, that we saw in chapter IV-5, under the title «an elegant explanation of the gravitational field». In this hypothesis, the gravitational field, and the associated deformation of space, is not transmitted like the other fields, but as waves in the front of reification of the logical self-generation system. (at need, this front of reification would be the work of virtual particles, such as for instance the famous Higgs bosons). Thus, mass would be explained by deformation of this front, which is also the relativistic curvature of the space around this mass. Other types of charges could also be explained by other kinds of deformations of this front.
These waves of deformation of the front of reification have symmetrical properties, whether they are ahead or behind the general average. Different types of waves would then correspond to different types of charges. For instance, an advance would correspond to a particle, and a lateness to an anti-particle. However, it is well known that when a wave takes a certain magnitude, its form is no more symmetrical (between the top and the bottom) (in physics, it is said that it appears nonlinear phenomena). Then a similar phenomenon on a front of reification may favor the particle over the anti-particule, or more generally the violations of symmetries in the weak interaction.
An evidence toward the interpretation of the properties of particles as geometric position of the nib into the Minkowski space, is that the kaons, while violating the matter-antimatter symmetry, also violate in the same proportions the left-right symmetry.
The previous reasoning allowed to find back some of the most bizarre properties of photons and vacuum.
My intuition commands me to look forward into this direction. It may only miss only one item, to end connecting this part to known physics. We shall already see, in the next chapter IV-8, some encouraging results, such as to predict two types of particles which actually exist: bosons and fermions, and some of their more bizarre properties, such as to be unobservable on their path.
Could we predict other entities, such as the electric field, the weak interaction, the strong interaction?
Could we, from simple geometric considerations on the shape of the nibs, predict the exact values of constants of physics, such as the coupling constants of the various fundamental forces? (Any prediction of this kind would win a well-deserved Nobel to its author, and validate the theory of the logical self-generation process to the eyes of official science).
I'm not sure of this. Indeed, we saw that the nibs can have «ad hoc» non-demonstrable properties, set randomly (an anthropic random, chapter IV-6,) in the time of the the Big Bang (or creative absurdity, see chapter III-3, rule 3). These nibs are then logically constrained to produce other identical nibs, transmitting their properties, without changing them. It is this logical constraint which forbids ordinary physics to change its own laws.
We even have a recent experimental demonstration of this, with the RHIC experiment (chapitre IV-9) where we precisely witnessed the arbitrary attribution, at random, of a value to a parameter of a law of physics. This validates the idea as what the numerous parameters of the laws of physics cannot be predicted, but that they were determined in the Big Bang. And that another universe would have different values for these parameters.
However, Quantum Mechanics predicts the formation of «domains», areas of space having different laws of physics (Ancient publications rather say «textures», and it is the word I used in version 1). It is what was actually observed into quark-glons plasma. What says the theory of the logical self-generation process, is that appeared a logical indeterminism, or a paradox, which resolution would result in the emergence of a new arbitrary law, as explained in Chapter III-3, Rule 6. This new law is then constrained to spread without being changed.
So, after the theory of the Big Bang, the four fundamental forces would have appeared only a few tiny fractions of a second after the Big Bang, during a special event, called «symmetry breaking», a time where, as says the logical self-generation theory, the previous laws were taken in default, forcing the apparition of new different laws. Since, these new laws are forced to propagate without being changed.
It is therefore not sure at all that we can demonstrate all the physics, if it includes such arbitrary elements, see local and accidental elements.
However we might try, for example by posing that a nib with an electric charge is the same than a nib with a neutral charge, but with a different orientation in the Minkowski space (for instance in another dimension). Thus, a neutral particle and a charged particle would have a different local space and universe lines, which then easily explains their very different behaviour, without invoking anything else than Special Relativity. It would be fascinating to find the electric field, see the weak and strong interactions, out of such simple geometry considerations into the Minkowski space!
So this leads us to the current (2012) state of my thinking on this topic. Of course I continue to think, and if I find, I shall add chapters to this part.
(Added January 2017)
For those who know the Set Theory only by its bad reputation of abstruse and useless theory, they will wonder how it can be a major determinant of physics. It is, nevertheless, a perfect demonstration of one of the main theses of this book: that our physical world is logical by itself (logical self-generation process), and not made of objects which would mysteriously behave according to logical laws.
To understand this, consider that some sets have structures (not all). Let us see how.
A simple set is the one of the real numbers (floating point numbers), called R. Let us consider more precisely R3, which is the set of the triplets of number x, y and z. These triplets can be combined according to certain laws of internal composition: addition and multiplication. What is interesting is that a group of triplets is identical, but displaced, if it is subjected to an addition operation. Rotations, scale changes, etc. are also possible, which do not destroy the original group. These apparently abstract notions exactly match what we observe in the physical world: moving or rotating objects does not modify them. Physicists say that these properties are invariant, or invariances, or symmetries, which occur in this case with R3, or more precisely the set structure R3, which corresponds to our three-dimensional space.
Hardly more complicated laws of internal composition (addition of velocities with a maximum c, the speed of light) give Relativity, which makes possible energy, gravitation, black holes, etc. in the Minkowski space (similar to ours on a small scale, but which can be distorted by Relativity).
Thus, our space would not be a homologue of a mathematical space, it would be directly a mathematical space.
At this point, any student learning Sets Theory wondered if there were no other structures than the simple R3. Yes there are. They are not taught at school because they are more complicated. But there are some, corresponding to other invariances or symmetries of the elements of the sets.
The thing is, there are not many.
And that mathematicians most probably discovered all of them, as for the Platonic solids.
Indeed, there are not many laws of internal compositions giving coherent results with the elements of their sets, this meaning keeping some invariances.
The idea here is that each of these structures would generate a law of physics!
Thus their list matches the one of all possible laws of physics, including the ones which occur at levels of energy impossible to attain today.
We find this list on wikipedia (except for Relativity, which I have added in italics):
translation in time
linear momentum (inertia)
angular momentum (rotation inertia)
spatial parity (left-right symmetry)
charge parity (electric charge symmetry)
time parity (time symmetry)
CPT (charge, left-right and time symmetry)
U(1) gauge transformation
isospin (charmed and strange quarks)
SU(2)L gauge transformation
baryon number (number of protons and neutrons)
quark flavor (type of quark)
Standard Model (The whole physics)
The additions in italics are from me, for more accessible explanations, when possible.
We find several important mathematical symmetries precisely associated with laws of physics: U, P, S, SU. I could not find confirmation in this article that all possible group structures correspond to physical laws. But from other articles I have read, this would be the case. This assumes that there would also be no other mathematical set structures leading to coherent results.
This has various consequences:
-All physical universes would have roughly the same laws of physics
-However, the preceding mathematical considerations do not specify the values of the different parameters of these laws. Thus each physical universe would have different parameters, and thus a different physics (chapter IV-9), although based on Relativity and the same Standard Model as us (provided that both are complete).
-The universes of consciousness, which do not contain particles, but elements of consciousness experience (sensations, ideas, etc.), could also have the equivalent of «laws of physics». Some may even resemble our physical world, for the same reasons, for example space and space invariances. However, the non-Aristotelian nature of the elements of the consciousness experience certainly leads to other laws, different from our physical world, where space does not exist as such, but is an image in a consciousness. This space will therefore not be defined as physical space is, but rather as in a dream. At this point it is difficult to speculate, given the little experimental information (NDE, RR4), but these worlds would function rather like dreams, about which we saw in chapter III-8 that they also have self-generation laws, and even more rigorous as one might think. See also in Chapter V-10, under «Dissolution of Consciousness».
-It is possible that consciousness and the universes of consciousness possess the equivalent of laws of physics, also resulting from mathematical structures. Thus many laws, obligations, or impossibilities in the domain of consciousness could result from analogues of the conservation laws, or analogues of thermodynamics. However, it is difficult to be more accurate: consciousness does not obey the classical mathematics, but non-Aristotelian logics, which have never been studied in details. We can therefore expect enormous differences. We shall see some of these laws throughout the fifth part on consciousness. One of the most precise analogues I found is with entropy, chapter V-7. However in the realm of consciousness, entropy seems constructive instead of destructive. This difference would result from the non-Aristotelian nature of consciousness. But if we use Aristotelian logic to create for example a system of laws, then we fall back on a precise analogue of the destructive physical entropy... which is therefore not just a joke.
(Added in January 2017)
A bit of fun physics, yes!
Take for example a balloon: useless and interesting object by excellence, which sometimes enters through our windows. When this happens, we can make something useful of it.
Well, it makes a kind of a «schtoung», and from that point on, people start screaming and losing their minds. So do the experiment alone.
If you are careful, you will notice another weaker sound, a kind of whistle, which immediately follows the main sound.
Any soccer player will explain you that this sound is due to the Helmholtz resonance of the air inside the balloon, exactly as in a guitar string or an organ pipe. However, unlike the latter, the different frequencies are not distributed in integer ratios but more randomly. This explains why the sound is somewhat unpleasant (except for the balafons, where the art is to harmonize the resonances of the calabashes).
Now, listen to the sound of the sun (recorded by space probes): it looks much like the balloon (if you take caution to shift it at a similar frequency). The reason for this is that the underlying mathematics is the same.
More precisely, there are several modes of vibration for a sphere. A first series of modes, called f, contains only one. A second series, called p, contains three. A third series, d, contains five, f, contains seven, and so on. This is explained in the same way as with the strings of the guitars, except that the division of the resonant space takes place at the same time according to the radius and also according to the circumference, whence the two numbers instead of one for the string.
Now we find exactly the same organization for the solutions of the Schrödinger equation, which defines the orbitals of the electrons around the atom, with the same parameters (there are four in all)! Organization which is in turn at the origin of all the chemistry and crystals!
Even stronger: do the same experiment with a rugby ball. Well, you will not hear any difference with the ear, but a spectrometer will show you: there are more frequencies. Any rugby player will kindly explain you why: in a soccer ball, the three dimensions x, y and z are the same, and therefore these three resonances are at the same frequency. While in a rugby ball, the length x is greater, and therefore its frequency is shifted with respect to y and z. We find exactly the same phenomenon with an atom subjected to a magnetic field: the spectral lines multiply, in pairs, hexuplets, etc. This is called the Zeeman effect.
So it is the Zeeman effect that harmonizes the sound of rugby balls.
And of balafons.
Bravo the Mandingoes, who discovered the Zeeman effect in the 13th century.
These are theories proposed by scientists, in order to explain the apparent contradictions between Relativity and Quantum Mechanics. They are still speculative today (2012).
The String theory assumes that the particles are not points, but small vibrating strings, each resonance producing one of the known particles. This theory in its current state is not compatible with the theory of the nibs, as it remains in the concept of objects arranged in a pre-existing space, of which we must then explain the nature, which is necessarily sub-particulate and extra-particulate. Moreover, this theory predicts a space with 11 dimensions, some of which being «wrapped» in an ad-hoc way, to be unobservable. Too many adjustments, in my opinion.
Supersymmetry, on its side invokes an additional parameter in the classification of the known particles, so that each one has a supersymmetric partner. The existence of such supersymmetric particles has been postulated mainly to explain dark matter in astronomy, because they do not interact with ordinary matter. This theory is fully compatible with everything written into this part, it just is not proven. The lightest supersymmetric particles are within reach of the CERN collider. So, we should soon find them... or if not, abandon the theory of supersymmetry.
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