The fundamental hypothesis of the theory of repositioning is defined as follows:

Each particle is in constant repositioning, based on data it receives from
its environment.

By particle is meant proton, neutron or electron, the latter being the perfect
item for this demonstration; the nature of the first two will be clarified at a later stage. The above statement
is a very new starting point. Let’s confirm it by specifying the nature of data in question and the way it’s actually
propagating.

2- The waves system Every day observation leads us to know what we mean by waves; all the waves we know of are delayed waves,
divergent, like waves on the water surface of a pond where you have just thrown a pebble. We are not aware,
in our environment, of any convergent, advanced waves although mathematically speaking they are perfectly licit.
As part of this hypothesis, we take a space which is filled up with an ideal
medium into which would simultaneously travel, for symmetry purposes, these two types of waves:
Going from the centre which will be here the particle, a wave train drifts out towards the outside, while another
set converges in, from the outside. If they are of same speed c (that of the light) and are in phase at the same
frequency ν, they will both coincide to make a wave system which is stationary and centred on the particle.

The particle is the central part of this system, but it is not restricted to it.
In theory, the wave system has no boundaries, but one may be led to think that, once it has travelled a certain
distance from the particle it becomes disrupted in the overall oscillation of the environment usually referred to
as emptiness, which do not however prevent data from propagating. For a better understanding, this drawing is in one
dimension. Indeed, one ought to imagine a three-dimension structure, with spherical waves.

Byrepositioning I mean that the centre goes to a new position every time
a vibration occurs, based on the change in shape of the wave system. We will come across and study several examples.
Generally speaking, the advanced wave which conveys data in from the entire universe dictates the particle’s position,
and the retarded wave conveys out, towards the exterior, data on the position or motion related to it.

3- Definitions Besides the beat, or phase wave or positioning wave we have just seen, it is important to define the other two basic
components of the system we introduced. Namely, two waves that vibrate at the same frequency ν, with a celerity c and
that travel opposite directions. We will refer to them as received waves, convergent waves or advanced waves
to qualify waves originating from the outside and travelling in a decreasing radius. Likewise we will refer to them as emitted,
divergent or retarded waves when talking about waves travelling from the centre in an increasing radius. We can also
talk about informant and informed waves. Such set of three waves actually compiles this complex system which is the
particle.

4- Inertia principle A particle may reposition itself in all directions throughout space. The new position is given by this dual wave system,
namely concentric, divergent and retarded on the one hand, convergent, and advanced on the other hand that both ensure
that data circulates both ways. If the former travel along with this particle in motion and convey in an increasing
radius data relating to this particle’s position and motion, the latter may come from all over space and inform the
particle on a position imposed by the Universe structure – chiefly its distribution of masses. The particle constantly
tends to return to this very position, and appears as though suspended to all space directions. If we make an attempt
at shifting it, for example by pushing it in a given direction, it will tend to go back to the position initially
assigned by the universe, it will resist to the shifting process by repositioning itself to the initial position,
hence the principle of inertia. But as we know, this principle only occurs in the first phase of the shifting process.
Indeed, the newly acquired factor, be that a new position or a new speed, is taken into account with each positioning,
is then maintained and objects to any new modification.
It then leads to the fact that the inertia is that all the more important, everything being equal besides, that the
particle tends on more frequent occasions to come back to its assigned position, by resorting to more frequent
repositioning. That is to say that it will reposition itself at shorter intervals. We suspect that there is
relationship between the inertia I and the frequency at which repositioning occurs ν_{0}; and we may write :

KI_{0} = k ν_{0} (1)

K and k being constants to the dimensions of the waves system and the universe.
This takes us back to Louis de Broglie’s remarkable intuition (Thesis 1925, p 33), namely : “we can therefore accept
that, following a great principle applying to Nature, to each portion of energy with its own mass m_{0}
is related a periodical phenomenon occurring at a frequency ν_{0} such as we have :

Thus obtained, this formula (2), where the inertia is indicated with the letter
I so as to avoid any confusion with mass, usually indicated with M :

I_{0}.c^{2} = I_{0}.Vv = hν_{0} (2)

implies that the position or motion of a particle, both sizeable by inertia
opposed to change in position, are reset with each repositioning occurring with the frequency ν_{0}
by the combination between the acquired data (the motion) and data received from its environment. This is a good explanation of the Mach'principle.
Furthermore we have to see there the origin of all energies; we will have the opportunity to come back on this subject.

5- The uncertainty principle The undulatory nature of particles and the way they interact by interferences allows us to explain the uncertainty principle formulated by Werner Heisenberg in 1925 under the general form of two relations.
According to the Repositioning theory, every measure is made by the mean of two interfering wave systems. So, the precision of the measure is limited by the characteristics of waves.
In general, if we want to know well the frequency of a wave, we have to make a measure large enough in space or in time in order the two wave systems interfere on a sufficient distance. During this time, the particle moves. Let's see that for each of the two relations :

1- ΔE. Δt ≥ ћ
According to the fundamental relation E = hν, if we want to know the energy of a particle, or to lessen uncertainty upon ΔE, we have to measure precisely its frequency ; thus to carry a measure that will last an important part of a period. Δt must be large.

2- Δx. Δp ≥ ћ
The particle moving, if we want to know its position with precision, to reduce Δx, we must make a short measure, so we know only a tiny fraction of the wave, and only roughly its frequency or its energy.

The reduced Planck Constant ћ, being the indivisible quantum of action brought into play at every repositioning, it is naturally it that becomes the referee.

6- Conclusions

This particle model comes as new in physics, but once brought to light it stands out due to its evident simplicity and its great power. It is able to take again and to explain, in a same theoretical set, the greater part of phenomenons we observe in physics and which, up to now, seem very ill-matched.

Furethemore, we will see the universal character of the repositionig theory; here are two examples :

The Planck constant is at the heart of our model and it applies to all formulas related to motion of particles. Elsewere on this site I show how the planck constant measures the information of Universe. Thus the motion of the tiniest particle depends on this information. That gives us a strong and universal base for the theory of repositioning.

It is also this set of two waves, on the scale of the universe, which is at
the origin of the distribution of the masses, as well of the
components of the living matter as those of the objects which fill the cosmos.
It is an important step in direction of the unification of
sciences in a universal theory which, on the basis of a clear, well understood physics,
would go, always inside the same system, until the explanation of the universe, the living and the evolution.