Relativity is often presented as something abscond, ridden with strange paradoxes challenging the common sense. And the mathematics allowing to handle it is really for a small elite. However, what this mathematics predicts is not so difficult to comprehend. The only real difficulty is of accepting a change of paradigm: what we see, our familiar flat space and time, is not the reality, but a perspective effect, a local vision of a more complicated space and time, called the Minkowski space. Unfortunately, our mind cannot make a mental image of the Minkowski space. We can however handle it with Minkowski diagrams, as we shall see further into this chapter.
Our familiar perspective makes far building look smaller than closer buildings. But these buildings are not altered! When we move closer, we see them normally again, while the previous buildings now look small. In a very similar way, Relativity makes perceive differently relativistic objects. However, the Relativistic perspective does not affect far objects (the farther the stronger) but moving objects (the faster, the stronger). So, a passenger of a Relativistic spaceship, looking at another spaceship, will see it crushed (in its length) and heavier. But a passenger of the second spaceship will see it normally. From his own Relativistic perspective, it is now the first spaceship which will look crushed and heavier to him.
The rôle of the speed of light was not understood before the Michelson and Morley experiment in 1887. In this time, the movement of the light (electromagnetic waves) was understood as something moving at their own speed, into an existing absolute space, like waves on the surface of the water. After this view, as Earth moves very quickly in space (30km/s around the sun), then it would be possible to somewhat catch up the light at a certain time, and not six months later, when Earth moves in an opposite direction from the previous.
However, the experiment showed no difference!
It is in 1905 than Einstein solved the problem: the speed of light is not a speed by itself, but the maximum speed that the Relativistic perspective allows to see, for any moving object. If we launch a rocket with enough fuel to go at ten times the speed of light, we shall see it approaching the speed of light, more and more closely, but without ever reaching it. Only light goes at the speed of light, but it is only because there is no possible to see any faster speed.
The notion of a curved space around a mass is also hard to comprehend, as long as we grasp to notions such as straight lines. A common comparison is with the curved surface of water into a whirlpool (or a rubber membrane with a weight on it). If somebody could live into the two dimensions of the water surface, he would see a normal two dimensional space close to him, and strange distortions of objects further into the whirlpool. In our three dimensions space, similar distortions appear, making a black hole look like these bubbles which occurred in the glass of ancient windows.
For us living on Earth, the distortion of space caused by the gravitational field of Earth is too weak to be visible with the naked eye. It is however visible to precision instruments, and we have to account with it while designing technologies like the GPS.
However, a good way to think is that the free path into space of, for instance, an apple, is curved by Earth, instead of being parallel to Earth's path. This makes that this apple will look to us as falling toward the ground. This is what we call gravitation, but it is in facts a direct and visible consequence of the curvature of space-time around Earth.
One of the first, and more important consequences of Relativity, was to force to abandon the view of an absolute space, which would be «something» containing the objects, like a sheet of paper contains drawings. This goes well in favour of space appearing only as a consequence of the behaviour of the particles, a way for our minds to understand the movement of these particles, while not existing by itself.
This makes the theory of the logical self-generation process directly compatible with Relativity, without any need to adapt it, without any need to add any ad-hoc entity, created mysteriously, or self-existing: «matter», «continuum», «brane», etc.
Although the theory of the logical self-generation process does not directly predicts Relativity, we shall see that Relativity is, after all, a simpler way to work, for such a process.
The following diagrams are Feynman diagrams, showing quantum interactions, and their cause to effect relations. However, contrarily to the usual practice, space is from left to right, while time is from the bottom to the top).
Normally, space has three dimensions. However, for understanding, we represent only one. The whole theory of course needs the three, but the reasoning made with these diagrams are still valid.
For now, we suppose that things happen in a classical way, that is, in a non-relativistic way. This is the case with very low speeds, as in our usual life experience.
Let us assume that these particles are electrons. Electrons have a mass and an electric charge.
Each red ¤ symbol is a quantum interaction (a nib). Purple arrows are electromagnetic interactions between these particles: photons, which transport energy, and move at the speed of light. Into this drawing, the speed of light is represented by an angle of 45 degrees. The green waves show the transportation of the charge and mass of the electrons, between two quantum interactions. I call this the «mechanical wave», as it is what most resembles our concept of a particle moving at a given speed. However the «material» electrons appears to our observation only as chains of quantum interactions, linked by these waves. Each chain of quantum interactions forms the observable trajectory of one electron, into space and time.
Although this is usually not shown in Feynmann diagrams, I drew green «waves», which represent the quantum wave of the electrons (Remember, that thing which does jokes like passing through two slots at a time). They disperse between two interactions, until the electron collapses into only one point (the new ¤ symbol).
So that we now have the «shape» of each nib. Of course an abstract object has no form, but we can see, on this diagram, the angles where the different influences happen, into the space time: photons, arrival and departure of the mechanical wave:
Each nib (quantum interaction) can receive photon influence coming from any other nib situated in the «light cone» of the past (in the drawing, the two purple arrows in the bottom). And this light cone spreads toward the past at the speed of light. So, the further in the past, the farthest the distance where this light was emitted.
Conversely, the nib will emit electromagnetic influence (under the form of a photon quantum wave) on the «light cone» of the future (the two upper purple arrows): this wave will flee it at the speed of light.
Any other event, situated either inside or outside of the two cones, will be completely ignored! They cannot interact with our nib, as they do not see its photon wave, or their own wave is not received.
These properties are summarized into the symbol of the nib ¤ by the four cross-like antennas, which represent the past and future light cones of the nib.
We also see, on the picture, the green waves, which move at the mechanical speed of the electron, as previously. It is its own quantum wave, which transports its charge, mass, etc. However, the electron was going at some speed before the interaction, and at a different speed after. This is summarized by the two angles e and s.
The big flaw of classical physics is to place all these features into a pre-existing space and time. This of course makes impossible to explain how these space and time exist, and of what they are made of. But this especially makes impossible to understand how physical phenomenon bend this space and time. This is however required, as, after General Relativity, mass is bended space. So if a mass appears somewhere, we must be able to explain how it bends space... which is perfectly impossible, if we place these objects into a pre-existing flat space!
For this reason, we must revert our usual reasoning. We must think at nibs as existing independently of space and time, like the elements of a mathematical series (save that the series is more complicated).
This simple fact is enough to demonstrate that it is matter which creates space, and not space which contains matter.
From this simple reason, we need to know how they will organize relative to each other.
In a classical mathematical iteration series, for instance a series of numbers, we can classify the results in terms of proximity of their values. This creates a one dimension space. We also noted in chapter III-4 that the chaining of these elements is a cause and effect relationship. And this chaining of causes and effects is the exact equivalent of the time we experiment into our physical universe. So any iteration series of numbers can be described as events passing at a regular pace, and situated into a one dimension space. This is how space and time are generated, how they are the structure of the set of numbers (In the language of the Sets Theory).
We can imagine more complex iteration series, for instance series of binomials, or trinomials. These will create a two dimensions space, or a three dimensions space. Their cause and effect chaining will create a time. So that these trinomials series will behave just like our space and time! (non-relativistic, however)
So, we can postulate that our nibs are nothing more than this series of trinomials (And only the fact that we are also part of it, make them appear as «concrete» and «observable», as seen in chapter III-5). Each nib has ultimately no place, it even has no sense to speak of the place of a purely logical event. However, they are linked by their «light cone». So they will organize into a set structure (in the meaning of the Set Theory) equivalent to our familiar space-time, with chaining of nibs (quantum interactions) describing mechanical trajectories, while exchanges (photons) move at the speed of light.
So, this very structure of our nibs is at the origin of space and time, but also of some «obvious» properties of our universe:
-That our universe has three dimensions of space and one of time (the chaining of the nibs)
-That the particles remain confined into our usual three dimensions, instead of disappearing into other dimensions.
-That two particles which lose contact, make the round trip around a full galaxy, and come again in the same place, can still interact together. This property is not obvious, from the point of view of the self-generation process. However it can be deduced from the way the nibs are linked together.
These properties are usually understood as the particles being bound into the space-time continuum, like drawings are bound on the surface of a sheet of paper. But now, we can explain these properties without supposing such a mysterious continuum: all the physics is a huge scaffolding of events, where elements are connected with an absolute precision, up to the infinite, in such an extend that particles always stay into our three dimensions, and always meet together when they happen to move close of each other. If there was not this absolute precision, particles moving apart, and reassembling again, may just not meet, passing apart of each other in some fourth dimension. There is nothing such ever observed in physics.
These are obvious properties, you may say. So obvious and so familiar, that we never noticed that they need an explanation too. The metaphysical theory of the logical self-generation brings such an explanation.
Still a problem remains, thought: the bending of space-time. The nibs seen above generate an Euclidian (flat) space-time, when we know that our universe is relativistic, with curved space. So let us see about this.
Let us simply draw the graphics of two nibs interacting in a relativistic way. Left, from the point of view of the red nib, right from the point of view of the blue nib.
These diagrams, while still being Feynmann diagrams, are also a slightly different representation of the Minkowski diagrams, which allow to demonstrate, from simple geometry considerations, all the oddities of Restrained Relativity: lengthened time of an object moving at a different speed, flattening of a fast moving object, Lorentz factor, absolute limit of the speed of light.
What strikes me first before anything else, is that these nibs are simpler than the previous non-relativistic nibs. Indeed, non-relativistic nibs had to receive the light from several different directions, depending on their speed. Problem, how a nib can know that it is moving? For this, it needs to be in constant contact with a continuum of space... A certainly very familiar notion, but which does not make sense in the theory of the logical self-generation. The relativist nib, on the contrary, always sees the light coming on it from the same direction, and always sends it in the same direction, regardless of its orientation (speed) in the Minkowski space. Into the Minkowski diagram with one dimension, this thus makes four directions, which are symbolized by the four branches of the nib symbol. Thus these four branches are into the Minkowski space, and nowhere else.
But we remember that the non-relativistic nib requires two angles, e and s, for the incoming and exiting mechanical wave. These angles reflect the fact that the particle's velocity has changed, during the interaction. However, the incoming mechanical wave and the corresponding light cone are now perfectly aligned, and this makes that we need only the exit angle e (in light green on the previous image). This makes less cases to manage than with two independent directions in a non-relativistic nib. Such a need for simplicity may be an important factor in the selection of the laws of physics. Thus, a non-relativistic space, despite it looks simpler to our intuition, would have an actually more complicated operation. In both cases, anyway, the space must be generated, and from this point of view an Euclidean space has no advantage, compared to a relativistic universe.
This other drawing shows this time a collection of nibs into a gravitational field.
For nibs obeying Special Relativity, there is no preferred orientation for the way the succession of nibs knit space-time. In some places, it is a direction, on other, it is a different direction, just like in a knitting, where a linear growth generates a curved surface. In the image above, we have a gravitation field around an object (the large vertical dotted line). The plain allows are «universe lines» (trajectory of a local observer) while the dotted lines are «simultaneity lines» (same time).
Thus our nibs can very well form a space with a complex geometry, such as a gravitational field (image above) without the need for a «rubber membrane» which would be distorted by gravity (a common image, and tempting, but which induces the misconception as what space would be «something» similar to a membrane.)
What is interesting with the nibs and the theory of logical self-generation process, is that space is not pre-existing, but it appears as the structure of the set of all the nibs (structure in the meaning of the Sets Theory) (We can also say that this space is an emergent property). Thus, there is no mystery to the nibs generating this bizarre Minkowski space, or the strange curvature of space around a mass. They could easily generate much more complicated space structures. Thus, there is no need to ask how an Euclidean space can be folded. Quite simply, this Euclidean space does not exist as such, it is only a projection of the Minkowski space, in our usual references frame (coordinates of the local observer), the only thing that our mind is able of perceiving or conceiving.
So, this is how is explained, in a very simple way, one of the most puzzling mysteries of modern physics.
The energy of a particle, relative to another, would simply be a function of the angle they do in the Minkowski space, angle which tells their relative speed. This angle cannot change spontaneously, as the logical self-generation process is forced to keep it. However, it can change with an interaction. When this happens, the arrival of the mechanical wave and its re-emission form an angle, as seen on the previous images.
If we have a gravitational field, it is the whole local self-generation process which makes an angle, with respect to others around. This is enough to explain the space distorted by gravity. Especially, the deformed space around a body therefore contains energy, which is simply the mass of this body, according to the formula E = mc2.
In order to ensure the transfer of information from an influencing mass to an influenced mass, scientists generally admit the existence of a gravitational field. This field is a mathematical wave propagating, just like the photon wave is doing too.
So we can propose a model similar to the photons for the gravitational field: gravitons move from any massive object to any other, in order to change their movement, just as we saw for the electromagnetic field.
An alternative hypothesis, however, is that the very process of knitting the fabric of space time, would allow for the propagation of information from the attracting mass to the attracted mass, and in a general way to maintain the exact shape of the space deformation around the attracting mass. This may work, but in order to have gravitational waves, we need to have two opposites forces, usually an inertial term and a spring-like term. We do have these two in the case of light (electric and magnetic field) and Relativity similarly predicts a «magnetogravitational field» beside the gravitational field we know. To transmit both with only the nibs network is more complicated however. But if this work, we do not need the gravitational field at all, and especially not the graviton. (Or rather, we could explain the gravitational field as information, see waves, propagating along the lattice or nibs, real or virtual. The graviton would be similar to the phonon, which is not a particle by itself, but the quantum of energy exchange from an atom to the crystal lattice) This would be very nice, as, in this way, we would 100% explain all the aspects of gravitation and General Relativity (gravitons, gravitational field, gravitational waves, deformation of space, etc.) with only the nibs seen above, without any need for something else, and even not adding ad-hoc properties to them (like a «gravitational field» similar to the electromagnetic field), just the properties required for Special Relativity. For this reason, this hypothesis looks sympathetic, but to assess its likelihood require deeper examination, beyond my possibilities.
It is to be noted that a popular hypothesis in physics predicts a space filled with Higgs Bosons, impeding the movement of the particles in a way to give them mass. These Higgs bosons are good candidates for a lattice of «nibs of space», as seen in chapter III-4. If so, this lattice may also transmit the gravitation field, under the form of a phonon-like graviton. Further, it would also be responsible of the shape of space, which is linked to the mass. If we interpret this in the way of chapter III-4, then we could say that the neutral state of our nib would be the Higgs boson, playing the role of the nib of space. But if its gets a charge, then it would form the ordinary particles. Just as I am writing (January 2012), the Higgs boson is probably in the process of being discovered...
We shall see in the next chapter how this need of simplicity for the basic elements of physics may pose severe constrains on the possible laws of physics themselves, even to the point of making impossible a more complicated physics than ours. And if our relativistic nib seems more complicated than an Euclidian nib, it is actually simpler. And, in more, it is able of explaining in a simple way all the properties of space and gravitation, without any further element. Euclidian nibs mandatorily require an addition of a gravitational field to do the same job, while remaining unable to explain Relativity.
We note that, in a general way, any particle will oscillate in a gravitational wave (as predicted by Relativity, although not yet proven). Equally, any electrical particle bearing a charge (electric charge, «colour» charge) will too move according to the corresponding electromagnetic field or wave. This movement is a movement of the mechanical wave of the particle, not a quantum interaction. However, this movement actually influences where the next quantum interaction will take place. This strongly suggests a common base for these various waves. For instance a particle bearing an electric charge would see the Minkowsky space in a different way than an uncharged one. In the language of Relativity, it would be a different local observer than a neutral particle, although with the same place and speed.
If so, there is nothing astonishing if a neutral particle and a charged particle behave differently, as their «universe lines» are totally different.
Ideas, texts, drawings and realization: Richard Trigaux.
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