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originally posted by: Nochzwei
a reply to: delbertlarson
good thread. but can your equations make a cup of tea or perform any other useful purpose?
originally posted by: mbkennel
a reply to: delbertlarson
I don't understand the physical assumptions and setup. (1) and (2) are about a photon. (3) is about a particle with nontrivial mass. What is the purpose of performing substitutions using them both? Doesn't make sense to me. What does the 'm' in (3) refer to? Mass, I presume, but of what? Are you trying to model a hypothetical photon with mass? (in which case (1) and (2) are incorrect).
Too many equations, not enough words.
What is the physical situation you are trying to model? What assumptions? What is the meaning of xi? Is it a wavefunction?
Is it square integrable? Adheres to Born rule? What is its domain?
Photon mass searches have turned up null experimentally as have observations for photon dispersion (different propagation speed for varying frequency) in astrophysical/cosmological events.
Any theory needs to be tested to have value (to me, at least) so of course it would add value to your theory if you could demonstrate an alternate calculation method for the Lamb shift. I suppose one of the things you're asking for in this thread is help in making calculations from your model, such as for example demonstrating it predicts the Lamb shift. Unfortunately I don't know how to get the Lamb shift out of your model, but I wish you luck in figuring out how to do that because that or other verifiable predictions would make it more interesting and perhaps useful.
originally posted by: delbertlarson
Although my aim was for my preonic theory, it is also true that if my approach is correct, then it should be applicable to the Hydrogen atom as well. It would be a great test of my theory if the Lamb shift would come out of it.
I replied to that objection stating that it never made physical sense to me that the Dirac treatment would just plop matrices down for something that was a spin in order to linearize an inherently non-linear equation, and that it moved us from physics to pure mathematics. (A spin should be modeled as a vector circulation, not a matrix, in my opinion.)
originally posted by: Arbitrageur
Any theory needs to be tested to have value (to me, at least) so of course it would add value to your theory if you could demonstrate an alternate calculation method for the Lamb shift. I suppose one of the things you're asking for in this thread is help in making calculations from your model, such as for example demonstrating it predicts the Lamb shift. Unfortunately I don't know how to get the Lamb shift out of your model, but I wish you luck in figuring out how to do that because that or other verifiable predictions would make it more interesting and perhaps useful.
originally posted by: delbertlarson
Although my aim was for my preonic theory, it is also true that if my approach is correct, then it should be applicable to the Hydrogen atom as well. It would be a great test of my theory if the Lamb shift would come out of it.
originally posted by: micpsi
The mathematics is totally wrong. One cannot assume the relativistic wave function is a plane wave (equ. 6), work out what equation it satisfies and then claim that the equation is the general relativistic wave equation of a spinless particle! The general solution of a scalar wave equation with Lorentz invariance that describes a spinless particle moving in a potential field V is NOT a plane wave. That's the form of a FREE relativistic particle moving in the ABSENCE of an interaction potential V. It is mathematically wrong to work back from a particular solution in which V = 0 to an equation that is supposed to hold in the general case where V ≠ 0. The mathematical howlers in the analysis would not get past any physical journal editor. What has been misinderstood is that you can use equ. 1 with E^2 = p^2c^2 + (mc^2)^2 and equ. 6 only when the particle is free (V = 0). The relativistic wave equation in a potential V is well-known and can be found here:
en.wikipedia.org...
originally posted by: mbkennel
Too many equations, not enough words.
originally posted by: hubrisinxs
Here is a Link to a pdf on how to solve partial differential equations It is from Cornell university
A spin should be modeled as a vector circulation, not a matrix, in my opinion.
A New Relativistic Quantum Mechanics
originally posted by: Zelun
A spin should be modeled as a vector circulation, not a matrix, in my opinion.
Amateur here. It seems to me that a spin can be perfectly modeled with a matrix. Or a quaternion, sans Heaviside. Not trying to be cheeky - how does the notation used change the outcome?