The determination of “Uncertainty Principle”

In 1927 Werner Heisenberg subjected a strange development of quantum theory to the careful examination of the most important members of Copenaghen School. From the experiments, this development seemed to limit the possibility of knowing at the same time the parameters of position, energy or momentum of any particle described in quantum way.

After due considerations, Bohr and others found that the reason for the impossibility of knowing simultaneously the position and the energy of a particle was that “the particle could not have any definite position and energy".

This statement, which turned the experimental impossibility into a philosophical principle, soon started to have a great importance in the description of microphysical properties, and became a physical principle that Sir Eddington named: "uncertainty principle". Eddington said:

“All scientific authorities agree with the fact that at the bases of all physical phenomena there is the misterious formula:

q p - p q = ih/2p

We do not understand it yet. Perhaps, if we could understand it, we would not find it so fundamental.

A skilled mathematician has the advantage of using it (...) Not only does it lead us to the phenomena described by the previous quantum theories, like the rule of h, but also to many other phenomena. Therefore, the old formulas are quite useless.”

In the second member of the formula, besides h (acting atom) and the purely numeric factor 2p, a misterious i (square root of –1 ) appears.

But it is nothing but a very famous subterfuge; in the past century many physicists and engineers knew very well that the square root of -1 in their formulas was a sort of signal warning from waves or oscillations.

The second member has nothing strange; on the contrary, it is the first one which astonishes us.

We call p e q some coordinates and momenta consulting our dictionary of space-time world and our rough experience. But all of that does not explain us either their real nature or the reason why p^.q differs from q^.p.

It is obvious that p and q cannot represent simple numerical measures because if it were possible, q^.p-p^.q would be = 0.

According to Schrodinger, p is an “operator”. Its “momentum” is not a quantity, but a signal which enables us to do a particular mathematical operation on some quantities following it.

It is obvious from Eddington’s considerations that, since the beginning the uncertainty principle has always been “indeterminate”. Afterwards, following a Condon’s idea, Robertson found at last an intuitive interpretation of the quantities q and p.

He got closer to the physical meaning of “the uncertainty principle”, finding that in order to establish with precision the position of a particle and to know simultaneously its momentum, there is a relation according to which the product of a probable mistake of positions and momentum is at least as great as Planck’s constant 
divided by 4p.  So, in general this relation should be valid:

Dp^.q ³ h/4p

Where Delta (D) associated with p and q establishes that we have to consider a range of values deriving from a probable error in a “mensuration”.

This is the only relationship with reality to be conceived for the uncertainty principle. It had however a great influence in asserting its supremacy in the philosophical relationship of quantum mechanics with the realist theories contesting its completeness.

Unlike quantum mechanics, no realist theory has ever given a theoretical justification to the uncertainty principle.

Now not only is the Wave Field Theory able to provide a theoretical justification, but also a plausible model, entirely consistent with the wave model of particle as the “spherical involute”.

By observing a plane involute we realize that the wave structure is not a central symmetrical structure. Infact, in order to consider it this way, we must go away from the resonance orbit. Moreover, the more we go away from it, the more we can consider it as a spherical, symmetrical structure. While, in the vicinity of the resonance orbit, the involute has a precise eccentricity.

The static figure shows a specific point in the vicinity of the orbit in which the eccentricity, which lies near the resonant wavefront developing the involute, is highlighted. But in the real wave source, this eccentricy, or “non-simmetry”, moves at the velocity of light in the resonance orbit, with the resonant wavefront in the orbit.

As a result, no mensuration can ever identify the real position of eccentricy, and therefore, nobody will ever be able to indicate or to place in space-time the center of the resonance orbit of a particle.

This forced ignorance prevents us from knowing the exact effects of interaction between photons and particles.

As a consequence, we cannot establish exactly the effect of the relative symmetry principle but with a sort of uncertainty that is a conseguence of the wave nature and of the structure of the physical-geometric model of particle.

All of that does not change the central position of the resonance orbit.

This uncertainty, out of ignorance, does not give any philosophical evidence for the existence of real parameters concerning the central position of the resonance orbit of the particle.

Through the wave model of the spherical involute we can interpretate the elementary particles’ properties, and know the most misterious mathematical theories of Dirac and Schrodinger, to which a consistent and causal physical interpretation has always been difficult associate.

Scrodinger interpreted the Dirac equation in order to establish the correct value of Spin and of the electron’s gyromagnetic ratio.

The solution of Dirac equation for a free electron, for which there was already a mathematical justification of its spin, implies the existence of a special motion for particle which Schrodinger called: Zitterbewegung, a sort of trembling which seems moving the particle by vibration at the velocity of light about the position it occupied in any point of its trajectory.

In quantum electrodynamics this motion is not considered in a realistic way, and it is misteriously linked to the existence of the Heisemberg uncertainty principle, seeing that it is hypothetically justified, in a non-causal way by the uncertainty of the position of an electron in a region having the same dimensions as Compton length.

On the contrary, now with an understandable and rational model, we can verify that the apparent motion is not real, but in a perfect casual and deterministic way it depends on the variation in eccentricity of the wave field travelling at the velocity of light together with the resonant wavefront on the resonance orbit of the spherical involute.