## Fwd: 432(5) Pion and Quark Mass Spectrum

I am glad that we have reached agreement. The discussion of the notes always strengthens the concepts and ideas. This is like Amundsen and Scott exploring the Antarctic. Amundsen used four navigators to make sure the South Pole was mapped accurately, and to mark the positions of the depots of food. The dogs were well trained and the progress was fast, using Olympic standard skiers. Amundsen left one navigational instrument for Scott, together with a letter for the King of Norway. This must have been found by the rescue party from Cape Evans and McMurdo Sound. So checking and good planning makes all the difference. Amundsen had plenty of trouble, falling into crevasses and so on, but he could move quickly.

432(5) Pion and Quark Mass Spectrum

Thanks for the explanantion, fully agreed.

Horst

Am 04.03.2019 um 07:45 schrieb Myron Evans:

432(5) Pion and Quark Mass Spectrum

Many thanks, the q1 and q2 are charges, and it should be r and not r squared. The wave equation development of pion mass is a good idea, and can be developed from Eq. (28) onwards. This development took place in UFT431, in your Section 3 and led to a satisfactory theory of elementary particle masses. This semi classical theory is the quantum relativistic interaction of a proton or neutron with the classical strong field, and proceeds in exactly the same way as the Dirac theory of the quantum relativistic interaction of an electron with the classical electromagnetic field, through the minimal prescription E goes to E – U, p goes to p – q. So this theory should give all the features that Dirac gives. The difference is that the quantized strong field (the pion) has mass, and in the standard model the quantized electromagnetic field (the photon) does not have mass. In Eq. (31), the m(r) power half function causes a shift in energy in exactly the same way as the Lamb shift, as you showed in previous work. There are three pions, so m(r) must be chosen in Eq. (31) to give three energy levels. The pions are in fact energy levels, the old physics had a bad habit of converting them into mass using m = E / c squared. This procedure can be rejected. So the wave function in Eq. (1) is not the free particle Schroedinger wave function because of the presence of m(r). Eq. (31) also contains the expectation values of m(r) power half. I agree about the importance of the wave equation approach to determining the pion masses,as developed in UFT431. Equation (28) onwards is the same development and Eq. (31) should give the three pion energy levels. This determines the wave function to be used. Eq. (31) for the energy levels of the strong field contains a mass, and this can be interpreted as the classical mass of the strong field. The three pion energy levels are three energy levels of the total relativistic energy of the strong field and by wave particle duality can be identified with three angular frequencies via E = h bar omega. So a choice of wavefunction and of m(r) can be made for equation (31) to give three energy levels. This is a development of your incisive method in UFT431 Section 3. The energy levels must be discrete and not continuous because there are three discrete pions. So the wavefunction and the m(r) must be chosen to give these experimental results. Similarly the energy levels in Eq. (32) could be interpreted as the three quarks inside a proton, but quarks are unobservables, so I think that we must proceed in our own way. Similarly teh wave function and m(r) can be chosen to give any number of particles. The overall method is to start with Eq. (28) for any field, quantize it into a wave equation and proceed as in UFT431 Section 3, or by applying the Dirac method to Eq. (28). This is in fact second quantization, and a quantum field theory emerges. Photons and pions are real particles in m theory, not virtual particles. There can be no virtual particles in ECE theory because virtual particles are based on the Heisenberg principle of indeterminacy, refuted in UFT175, and rejected by the Einstein / de Broglie School.

432(5) Pion and Quark Mass Spectrum

First a question of understanding: What ar q_1 and q_2 in eq.(15)? And is there really a squared r value in the denominator?

Concerning the determination of pion masses, I have mixed feelings about this. May I formulate some objections? A mass parameter already enters the basic equation (4). Therefore determining additional mass variations via m=E/c^2 seems to be not very consequent. Looking at eq.(4), it is more an equation for a massive particle like a proton to determine additional "excitation spectra" of the proton. On can interpret these as the sought interaction field masses but it is not clear if these are discrete or continuous. The results depend essentially on the potential. Eq. (31) only determines the kinetic energy of a free particle in m space. The wave function then is more or less a free-particle wave function without boundaries. This cannot be what we are looking for. The minimum requirement would be a "particle in a box". I would find it much more consistent to determine masses from a quantized wave equation. Can we make some thoughts in this direction in future work?

Nevertheless the considerations in this note are important to describe quantummechanical interaction of elemtary particles with fields.Horst

Am 01.03.2019 um 12:12 schrieb Myron Evans:

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