Richard Oldani

We reformulate matrix mechanics by incrementally heating a single hydrogen atom in order to derive the complete, diagonalized Hamiltonian matrix. The spectral lines and transition probabilities cannot be generated by reversing time thereby demonstrating asymmetry. Experimental evidence in support of the theoretical model is obtained from experiments performed with the simplest quantum system, an electron cyclotron. Wave mechanics is also reformulated by altering the original Schrödinger equation describing a time symmetric, conservative system to a system of two independent equations describing a time asymmetric, non-conservative system.

Matrix mechanics describes the spectral emissions of hydrogen gas, but quantum mechanics concerns the emission and absorption of radiation by a single atom. To obtain the spectral emissions of a single hydrogen atom we reformulate matrix mechanics by introducing thermal energy in infinitesimal increments and registering the spectral lines one by one until a complete spectrum is obtained. Wave mechanics is reformulated from a conservative to a non-conservative system by linking the output of matrix mechanics to the input of wave mechanics. To describe the gradual increase and decrease of energy by a quantum system we integrate between two specific endpoints, the atomic orbitals, and two specific times, the period τ, which are the conditions necessary for Hamilton’s principle. The Lagrangian method is shown to be superior for analyzing quantum theory because it describes quantum systems relativistically as evolutions in time.

We hypothesize that quantum mechanics is incomplete because it does not take into consideration the absorption of energy by quantum systems as described by matrix mechanics. To be complete quantum mechanics must include both matrix and wave mechanics, and due to the conservation of energy the first (absorption) must be carried out to completion before the second one (emission) can begin. The combined model of matrix and wave mechanics integrates naturally with Einstein’s use of independent coordinate systems K and K’ to describe the absorption and emission of radiation. All subsequent mathematical models are versions of this physical model.

The author poses an interesting question about gravitational potential energy. The reviewers have voiced opposition for various reasons but do not offer an improved interpretation of potential energy. In the article, the Hamiltonian of the system i...

Einstein published four papers in 1905 that revolutionized our understanding of the fundamental concepts of space, time, mass, and energy. We draw attention here to an idea in one of the 1905 papers that revolutionizes our understanding of quantum mechanics, but its significance was never understood. We use it to derive classical interpretations of matrix and wave mechanics, resolve the “collapse” problem, and demonstrate that the standard model is deficient in its physical interpretation of Nature.

In view of the title, I was hoping for a clarification of the minimal knowledge I have of the subject matter. Instead, my understanding became still more obscure. You use “isomers of elementary particles,” but it is not clear what is meant by that. W...

Differences between the quantum mechanical and relativistic concepts of time observed in GPS satellites are accounted for by applying the equivalence principle to the transitioning electron of an atomic clock. This allows a differential equation of motion to be derived for the electron in the Minkowski space between electron shells. By applying Hamilton’s principle we transform the differential equation into a relativistically correct integral equation of motion, the time integral of a Lagrangian. This newly derived equation accounts for the abstract mathematics of the more familiar non-relativistic model by means of a physical interpretation. Abstract rotations in Hilbert space are replaced by real rotations of particle field geometries in Minkowki space that describe the electron transition and emission of a photon. Because the properties of energy are universal the same integral equations are able to be used to describe the time evolution of galaxies despite vast differences in lifetime. The comparison of gravitational and electromagnetic energy exchanges by means of radial and transverse fields leads to an alternative to the standard model that is based on a field model. It explains the observed properties of galaxies as a superposition of neutrinos localized within the horizon of a black hole with spins aligne d . The particle properties of free neutrinos are accounted by means of a classical field geometry ; specifically, a spin that is orient ed in space with rotational inertia due to energy. A test of the standard model is proposed based on differing views for flavor oscillation.

In our investigation of the time evolution of energy states Einstein’s interpretation from more than a century ago is found to have greater internal consistency than that of non-relativistic quantum mechanics. We choose to align more closely with his methods by abandoning the non-relativistic Hamiltonian method, which has been the standard for nearly a century, in favor of a relativistically correct Lagrangian method. Integral equations of motion for the absorption and emission of radiation are derived that underlie and anticipate the differentially motivated Schrödinger equation. This new interpretation applies to a large volume of experimental evidence of both classical and quantum mechanical origin. Among the examples discussed in support are Planck’s law describing black body radiation, matrix mechanics, the function of the simplest quantum mechanical system an electron cyclotron, chaos theory, and evolutionary biology.

The title has changed because the objective has also changed. The purpose of earlier versions was to clarify Einstein’s intent when he formulated his quantum theory of radiation: why choose statistical methods to derive Planck’s law, why emphasize momentum, and why are both important to a “final theory”. We find that Einstein’s methods have the common property that they are formulated statistically in continuous space and time. It means that the problem of the quantum-classical divide does not exist in any of his theories, and that his results are fully consistent in the presence of non-linear gravitational fields. To see if his unconventional methods can provide the insights necessary to resolve the long-standing problem of wave function collapse we will compare how the two versions interpret causality. We show that Gödel’s incompleteness theorem is key to resolving wave function collapse.

The author introduces many new terms, arguments, and mathematical derivations making this paper difficult to understand. The references which usually serve as a starting point in discussing a new theory are almost entirely unfamiliar to me. As his th...