A New Relativistic Quantum Mechanics

a reply to: delbertlarson

good thread. but can your equations make a cup of tea or perform any other useful purpose?

a reply to: hubrisinxs

The number of dimensions...

WHAT OP, if Planck's constant isn't? In the 2D, they have proven that it can be half (and multiples of)?

Oh, and S+F for asking!

Made my brain hurt for a bit!

a reply to: TEOTWAWKIAIFF

Agreed, you can even generalize to the Nth Dimension vector space. Planck's constant (h), 6.62607004 × 10-34 m2 kg / s, and was originally thought of as merely the proportionality constant need to measure the energy (E) of a wave with frequency (f). Which comes from the simple equation E = hf.

Now the h, after years of testing, has been corrected to h/2*pi. This was due to an attempt to measure the energy state of a photon with angular frequency w = 2*pi*h.

In a classical view, h is truly constant and can only take on multiples that are members of the reals, whereas in a quantum state h may be subject to some uncertainty. This has to do more with the fact that physical actions can not take on fully arbitrary values, it must occur in relation to some movements of h.

So, while you can have a physical action of less than h, it will still be some multiple of h.

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?

My view on my work above, and high energy physics in general, is that practical advances typically follow from basic understanding. Skyscrapers weren't built immediately after Newton's laws; radios weren't built immediately after Maxwell developed his equations; particle accelerators were not built by Lorentz; the microchip was not built by Schrödinger. Yet none of those practical devices could have functioned without the understanding that those great physicists provided.

There are practical goals that we have today that we don't have the knowledge to provide. Eliminating disease and pestilence, a cure for old age, abundant production of clean energy and water, and travel to the stars are all big goals for mankind to strive for. What we are missing is the underlying knowledge on how to achieve them.

I do not know if fundamental physics will get us to the grandiose goals mentioned in the paragraph above, or if it will get us to smaller goals, or if it will get us to goals we don't even yet foresee. However I do believe that unearthing nature's secrets is important, and that it does have the potential for later practical breakthroughs.

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.

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.

I am glad you took the time to comment!

Xi is the wave function. Correct. It is similar to the Xi in Schrodinger's Equation. It should be square-integrable, obey the Born rule, and the domain of Xi is (x, y, z and t). Of course you can convert between Cartesian, cylindrical and spherical coordinates for the spatial arguments.

Actually (1) and (2) apply to matter as well. They relate to the "matter wave equations" first credited to de Broglie.
(see here: en.wikipedia.org... )

Shrodinger used the de Broglie equations, along with the non-relativistic energy expression, to develop his equations for non-relativistic quantum mechanics. (see here: en.wikipedia.org... ) The Shrodinger equation is used very successfully to calculate the hydrogen atom energy states.

For my ABC Preon model, I postulate two preons that make up the massive leptons. (A third preon contributes to hadronic matter.) Each of the preons has a mass far greater than the mass of the known massive leptons, and hence the internals of the bound states (the preons within the massive leptons) are highly relativistic. In that realm, Schrodinger's equation will not apply. So I set out to derive a completely relativistic equation for stationary states. That is what you see in the OP.

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 know that there is already an approach to get the Lamb shift, but it comes about as a result of perturbation theory, and my approach is to instead develop an exact equation for relativistic quantum mechanics.

I had multiple purposes for this thread. One was to seek guidance concerning a solution to that rather nasty Equation (28). A second purpose was to get comments (such as yours) that will assist me in strengthening the eventual paper I submit for publication. Thank you for your comment, and please let me know if there are any other points that are not clear.

a reply to: hubrisinxs

Thanks again for the suggested post on solving the equation. I had thought about how to write a computer program to solve it numerically, and some of what I was looking at doing is similar to what you link to. But what is linked to is further along than I was, and as such it is quite helpful. One issue though is that I need to better understand my boundary conditions. At large r, say six sigma, we can probably safely use psi=0. The other three boundaries are not as clear, however. Also, I know that the solution will only exist for certain values of En, but in the arbitrary case I don't know what the values of En are. In fact, one purpose of the equation is to find the values of En. That is of course a basic ingredient of quantum mechanics - there are quantized energy states, and one task is to find them.

What I had been thinking, for the hydrogen case, was to put in the known solution to the non-relativistic, non-hyperfine case as a starting point. I would also use the experimentally determined value for En. Then let a computer relax that solution to the true solution. But that is only a high level thought - it is not clear to me yet how to implement it. And since there is no known solution for preonic leptons, even that approach doesn't quite get me to where I want to be.

But in any event, thanks again for the link. It has been helpful.

The OP was written shortly after a Letter on this was rejected by Physical Review Letters. I extracted the equations and put in a few words and posted. Then I explained things a bit in the OP.

The Letter was rejected three times. The first rejection, which was laughable really, said that they assumed it was correct, but it was not important enough for publication. I suspect this is a standard rejection given to all papers in order to reduce the editorial and reviewing load. Once I pointed out that this work went to the heart of physics, and was clearly important, it was rejected on the basis that the problem of relativistic quantum mechanics is considered solved. They pointed out that "deriving a relativistic generalization of the Schroedinger equation resulted in Dirac equation for electrons (and other spinor particles), Klein-Gordon equation (scalar particles), Proca equation (vector particles) etc.". 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.) I pointed out that the Klein-Gordon approach is similar to mine, although we start with different expressions and are led to different results. My result takes us to an exact relativistic treatment for stationary states and allows solutions without resort to perturbation theory, which can, in principle, offer solutions where perturbation theory has failed. PRL replied that since I had not included field quantization, and since I had not offered proof, my effort was to be rejected. I admitted that I had not actually calculated the meson mass spectrum, but that publication would help by getting others to perhaps do so, and that is why I wanted to publish. But I accepted their decision at that point and withdrew the paper.

When publishing truly path-breaking works in the past (An Absolute Theory for the Electrodynamics of Moving Bodies, the ABC Preon Model, Derivation of Maxwell's Equations From a Two Component Aether, and ECOFusion) I have followed a consistent path. First, an attempt to publish in the Physical Review. Then looking at their reasons for rejection and addressing them. Finally publishing in Physics Essays. The reviews I get along the way can always be used to strengthen the eventual publication. Once, a Physical Review reviewer even found an error and suggested how to correct it.

In the present case I have also benefited from some of your comments here. If anyone has any more comments, either constructive or critical, please let me know. I plan to edit my work and submit to Physics Essays in the not too distant future.

a reply to: delbertlarson

Sorry if I'm late to the party.

Looks great Del! I'm glad to see you made it into a thread!

S+F

a reply to: delbertlarson

Glad I was helpful, and this kinda reminds me of an anecdote about my favorite Math professor.

One afternoon I was sitting in the office of my professor, who was also my advisor, when a grad student walked in and asked if he taught the analysis classes then frantically began to scribble equations on the board. Afterwards he turned and started to ramble about molecular chemistry and topological spaces... anyway, the professor looked at the equations for a few mins and said, "yep, those are some serious equations and their looks like their should be some numerical solutions, but you can't always let the fact there is a math answer lead you to the logical conclusion that it is physically happening."

Or like I tell my students, sometimes Functions give you answers, but you have to reject them because they do not make sense in the context of the problem.

Anyway, you seem to grasp the context of these equations way more than I do, so good luck and hopefully you find those boundary conditions. I would love to see that the next Einstien used a little math help from me

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.

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.

a reply to: delbertlarson

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.)

I agree.

It makes poor sense (to my mind, at least), to model it as a matrice - the only possible logic for doing that is integration in a formula. However the observed universe is physical in nature.

originally posted by: Arbitrageur

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.

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.

Thanks for your comment, Arbitrageur. When undertaking this new approach to high-velocity QM, one hope was that we could get a non-perturbative solution that would incorporate all spectroscopic results of the Hydrogen atom, and these would include high-velocity corrections, hyperfine splitting, and the Lamb shift, all of which are now treated with perturbative methods. A tall order, no doubt, but that was one goal. The high-velocity corrections and hyperfine splitting should be in the formalism already. A possibility for the origin of the Lamb shift, in my thinking at the moment, is that it comes from the postulated hard core - but that is pure speculation on my part at this time.

Note that I should not have used the word "relativistic" in this thread. I was using "relativistic" as a synonym for "high velocity", but that was an error. A non-local theory such as described above cannot be "relativistic".

A paper based on the OP has now been published in the reviewed journal Physics Essays. Here is a link to the paper, although it may be behind a paywall. The reference is ``An empirical and classical approach for nonperturbative, high velocity, quantum mechanics'', D.J. Larson, Physics Essays, Volume 30: Pages 264-268, 2017.

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...

A reviewer also raised the point about a plane wave not being able to serve as the foundation for the more general case. In remarks in the paper I noted that there is an implicit assumption in the derivation. It is implicitly assumed that the relations derived from the plane wave analysis hold in the general case. Then, using that assumption, I show how Schrödinger's equation can likewise be derived in the case of the low velocity energy formula. Since the objection relates to a generalization based on the plane wave, and not on the form of the energy equation used, derivation of Schrödinger's equation in this way adds some credence to my approach. Essentially, I assert that the plane wave tells us something fundamental about the quantum nature of physics, which we can then extend to other situations.

originally posted by: mbkennel
Too many equations, not enough words.

The publication has many more words. So did the version of this sent to Physical Review Letters. After PRL rejected this I was a bit ticked off and posted the OP. The Physics Essays paper does a better job of presentation than the OP.

originally posted by: hubrisinxs
Here is a Link to a pdf on how to solve partial differential equations It is from Cornell university

Thanks again for the link. I studied it and thought for a couple of months about the problem. I came up with an algorithm that solves n by m equations in three passes through the matrix and comes up with an exact (to within computational rounding error) solution. This is an alternative to the fast convergence way of solving things. In my solution you will always get an answer also. I suspect my way might use more memory though. (I am not expert on this so I don't know.)

Once six months pass I hope to post an article on InfoGalactic. (The editor at Physics Essays has kindly given me special permission to do this after six months passes.) If so, I'll let everyone know.

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?

delbertlarson:

A New Relativistic Quantum Mechanics

Yes, yes, yes, this all very good. Not discounting or disrespecting your talent for mathematics, ultimately, it is all down to knowing 'variables', and which ones to measure and quantify, which ones to use, and which ones it is 'safe' to ignore or discard.

You then have to take into account each variable's inter-relationship with other variables, and uncover the 'laws' that predicate them. In mathematics, it is easy to abstractedly break natural laws (and lead oneself down the wrong rabbit hole), after all, mathematics is nothing more than an imposed rationale upon nature by the human mind. Truths found without breaking natural law are the only 'real' truths, because they are 'universal' and remain constant, no matter what natural circumstance arises.

Of course, once you have completed your mathematical abstraction, you then have to interpret it correctly and present it to the world so that everyone can comprehend and understand it. I envy you your mathematical comprehension, I wish I had it so that I could model my own mathematical papers on specific aspects of nature that I am interested in.

Stay real and good luck

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?

You can use matrices to model things mathematically and get correct answers for experiments. I am not arguing that. The Pauli spin matrices advanced understanding of quantum mechanics, and the Dirac matrices clearly work to do experimental predictions. Spin 1/2 entities are either "up" or "down" when measurement collapses their wave-function, so a small finite number of labels can express that. If we want to just express that fact, the matrix does the job.

However, a matrix takes us away from a classical view. It doesn't well describe what is happening in a spinning top or a gyroscope. Once we get to macroscopic objects where there is a continuum of possible angular momenta possible, it is better to model things with a vector perpendicular to the spin, and envision each small region in the spinning entity as undergoing circular motion. (Or nearly circular motion if it undergoes precession.) In this classical view, each small volume region has a velocity vector that circulates during spinning as well.

I believe that the central problem haunting physics is the view that particles are point-like. That is where all the infinities come from. The attempt in the OP is to arrive at a non-local QM so that we can again view the wave-function as a real thing with flows of finite (non-zero volume) "stuff". In such a view we should be able to look at all things, including spin, more from a classical standpoint. We do have to admit that the wave-function only exists in quantized states, and that interactions cause collapse from one state to another, but this view frees us to think about things within those states as classical. And I always think the classical view is clearer to model physically.

a reply to: elysiumfire

Thanks for the support.