Archive for March, 2019

435(6): Rules for Quantization in m Space

435(6): Rules for Quantization in m Space

I arrived at Note 435(6) using the same transformation rules throughout. In all occurrences r is replaced by r / m(r) power half and t is replaced by m(r) power half t. It follows that psi (r, t) of Eq. (4) is replaced by psi(r, t) of Eq. (5). The quantization rules remain the same, because the frame (r, phi) is the same. The state of the particle is completely described by its wavefunction, so I decided to start the analysis with the wavefunction, and to replace r by r / m(r) power half and t by m(r) power half t inside the wavefunction. This gives Eq. (5), in which psi is a function of r and t. So the quantization rules are Eq. (2) and (3) because they are defined in frame (r, t) and psi is defined in terms of r and t. This procedure leads to the modified Planck quantization (10), which uses the expectation value of m power half computed self consistently with the wavefunction (5). This leads self consistently to Eq. (15), which is an equation for the quantized m(r) power half. This philosophy is based on the fundamental role of the wavefunction. The Born normalization remains the same. Since all this is completely new to physics, there is no precedent, so any self consistent procedure can be used. As usual, experiments must decide whether the results are acceptable or not.

comment-435(6).pdf

435(6): Rules for Quantization in m Space

435(6): Rules for Quantization in m Space

After experimenting with the notes for UFT435, I decided to adopt the rules (1) and (2) for quantization. They are applied for the free particle in this note, but can be applied to any wavefunction. They result in shifts and splittings given by Eq. (14). These shifts and splittings are due to m space, which can be thought of as the vacuum. So this gives an explanation of the radiative corrections in terms of m(r) functions, getting rid of all the obscurities of quantum electrodynamics. Eq. (14) shows that the Planck quantization is modified by the expectation values of m(r) power half. So the latter is quantized, meaning that the m space is quantized. The problem being considered defines the quantization. The free particle problem is the simplest case. This theory shows that general relativity and quantum mechanics have been unified, because m(r) of general relativity has been quantized. So I intend to base Sections 1 and 2 of UFT435 on this note.

a435thpapernotes6.pdf

435(5): Brief Review of Fundamentals Planck Quantization in m Space

435(5): Brief Review of Fundamentals Planck Quantization in m Space

This not checks fundamentals and demonstrates that the m theory is based on the Minkowski metric (13) in m space. This discovery was made in UFT416 and led to a number of important advances. In quantum mechanics the m theory leads to shifts and splittings due to m space itself, notably the Lamb shifts. The Planck quantization E = h bar omega is generalized in m space to Eq. (35), valid for any wavefunction psi and illustrated here by the free particle wave function. The general replacement rule is r goes to r / m(r) half and t goes to m(r) half t.

a435thpapernotes5.pdf

435(4): Free Particle Time Dependent Schroedinger Equation

a435thpapernotes4.pdf

435(4): Free Particle Time Dependent Schroedinger Equation

a435thpapernotes4.pdf

435(3): Splits and Shifts due to Frame Transformation

435(3) OK thanks, here it is. The complete interpretation of the Lamb shift must be based on these equations. The left hand side has the advantage of giving the number of energy levels without having to compute the expectation value of the hamiltonian (right hand side).

On Tue, Mar 26, 2019 at 6:52 PM Horst Eckardt <mail> wrote:

There was no document attached.
Horst

Am 26.03.2019 um 13:10 schrieb Myron Evans:

a435thpapernotes3.pdf

435(3): Splits and Shifts due to Frame Transformation