John Henke

And then you also have to use linear algebra. I mean isnt it the linear algebra that gets those shapes? Again it goes back to the equality of the two equations. If one can do it why cant the other?

Yes those are all equations of free particles. To get waves like those in the link you add to the lowercase gamma component its complex conjugate.

You can get either symmetric or anti-symmetric particles by making it definitively the case that whenever two particles coexist in a wavefunction, one of the particles must have its omega underbar t values increased by 2. Since particles with spin 1 will complete one rotation every time omega underbar t grows by 2, these particles will instantly complete one full rotation due to this added value of 2 and be symmetric, allowing for any arbitrary number of them to coexist. Since particles with ½ spin will complete one rotation every time omega underbar t grows by 4, these will be antisymmetric and a third particle would be excluded thus adhering to the Pauli exclusion principle. Furthermore, this may be used in conjunction with the theory that the magnetic dipole moment is determined by the natural positive or negative curvatures in the position eigenvalues. This curvature can be removed using depletion operators from all but one axis, the axis with the magnetic dipole moment (see article for details on depletion operators, but long story short, they use s to get rid of charge). Furthermore, one of the many oddities of curvature, is that it only decreases by the inverse square of the distance when the particle is moving at C. The argument then is that the axis containing the magnetic dipole moment is the axis in which the particle’s axes have been rotated through Minkowski spacetime sucht that it is traveling through time at the speed of light. This theory has led me to a new model for the Lorentz transformation. I haven’t yet written this on the forum, but my definition of time has two parts: evolving time and initial time. One interpretation of this is that at the beginning of time, gamma components spread out across the universe as functions of initial time to the ends of the universe in the positive and negative directions. From there they grew through evolving time which can also be positive or negative. This means that if, for example, initial time is negative, then all the inputs with negative initial time values will become more negative while all the positive inputs will decrease. This is by definition the particle’s location (which is x=0) moving further from all particles on its negative axis and closer to all particles on its positive. Now this position can’t actually be determined when it’s a wavefunction possibly due to the equality and therefore interchangeability of outputs. But it could give a well defined position and axis when in particle form (a waveparticle without spin or angular momentum). Also, omega components are functions of evolving time only. This essentially spreads out the wave as described. So when I say position, I don’t mean the position of the particle but of the relative position of the input. The wavefunction is a function of x. So obviously every input has an x value based on its input. But as my wavefunction is only a function of t, it gets its relative position not from its input but from the output of its waveparticle, its x eigenvalue. And so to get a y axis and a z axis as well, you would need to multiply in other versions of my wavefunction that each have wave particles within them whose eigenvalues represent the position of y or z. I always thought these had spin and angular momentum, but I’m starting to realize they might not (either way the equations allow for it). Then one can normalize it basically using the same equation used in Griffiths’. As to Lorentz invariance, as mentioned, I’ve got a new model. In this model the wavefunctions always have their axes rotated through Minkowski space time such that they are traveling through yhe fourth dimension at the speed of light. Now as mentioned there are other axes that can be multiplied in. The rule, then, is that any axes that does not have values of omega overbar and k overbar that equate, cannot be used as the axis of the magnetic dipole moment but must instead have a k value that is so much larger than the omega value that there is no or almost no growth in them. Moreover, such an axis will include no or almost no energy the omega overbar value being very small. Only the single axis, and the rotation of them through Minkowski space time, that results in omega overbar and k overbar values that equate can be used as the axis of the magnetic dipole moment and spin. This model also updates my model of the energy eigenvalue with the same condition on the rotation of its axes. As to a proof, I would argue that the graphs, when adhering to the concepts I’ve described, of e^i(kx-wt) and my wavefunction both equate and thus can both describe the same phenomena equally well. This requires that when the angular momentum is ½ and the spin is ½, that the units of t in my theory are multiplied by a factor of 4/tau, when at an angular momentum (or spin) of 1/2, because these complete a rotation every time t grows by 4 rather than tau. However, since k overbar and w overbar are unchanged for particles without angular momentum or spin (which are just particles), it’s still useful to differentiate them with the bar. And since eigenfunctions scale these same equations by amounts proportional to k and w (which now equate to k overbar and omega overbar), those equate as well. If you look at the graphs in the video, in the article or in the mathematica notebook, and if you keep in mind that the output of the waveparticle equates to the position relative to the source of the particle (the source being its x=0), the two simply equate. The only differences are that this wavefunction has naturally occurring curvatures, and it can theoretically be used to describe a particle but these are added functionalities. No functionality is subtracted. And I want to be clear. My wavefunction and its eigenfunctions are meant to replace e^i(kx-wt) and its eigenfunctions and to be fit into Schrodinger's, Dirac's, Klein Gordon in the same way that e^i(kx-wt) and its eigenfunctions are. And if it's been shown to be the same at a fundamental level, I don't know how there could be problems at any higher levels because all the same operations and alterations can be applied to both equations.

I'm sorry studiot. I misinterpreted that. What I've been describing are apparently wave equations. The wavefunctions are still Dirac's, Schrodinger's, etc, if I've understood the terminology correctly.

By the way, when I say lowercase gamma component I mean the lowercase beta, lowercase zeta or lowercase eta. These all have angular momentum as opposed to their uppercase versions which dont. Perhaps thats been poorly defined.

Well, the value of n is the same for all particles. It basically determines a Planck-constant like value such that if k bar=1, then n is unchanged. And n could also be used to find the value of omega bar=1 using theta. So n would determines a Planck constant like point. But if there was an army of physicists and supercomputers working on this, and they found the value of n (using the varying curvatures each particular value of n will have), then actually the units would be totally fundamental. At a given value of w bar and k bar and at a given input, there would more or less be an inititely long number that describes that position. Now this is in contrast to the units currently in use. I assume the universe is purely mathematical in structure and if that is the case, then there is a very particular value that the universe assigns to what we call one meter. This value is almost definitely not one. So this theory would have more fundamental descriptions of time and space. I am very suspicious of your avoidance of answering a simple question. I'm not avoiding it. I plainly admit I don't know because it would take an army of physicists and super computers to find it. That said, for the most part things work the same at any given value of n as long as it's extremely high compared to t. The only thing that changes is the curvatures which are at relatively micro scales. Therefore, if you wanted to model an infinite square well 1 nm in length, at an arbitrary high value in n you could translate my numbers into SI and not much would change aside from the curvatures being wrong at a relatively micro level.

I still have not had an answer to that question. I did answer this. I said that gamma is not the wavefunction. I've defined it in more detail above, but an example of a wavefunction would be a lowercase gamma component multiplying an omega component with spin, both of these divided by an uppercase gamma component. You put this into a Hilbert space, normalize it, etc and use its solutions to Schrodinger's or Dirac's. The example I just gave was of a free particle, but if you want to put it into an infinite square well, then you can add to the existing lowercase gamma component its complex conjugate. This cancels out the imaginary part and leaves the real part. Then at the lowest possible energy level it resembles jump rope with beginning and end points at the boundaries but is still rotated through time because the omega component rotates it. And then k bar can be increased by integers or alternatively one could simply multiply the equation by additional lowercase gamma components divided by uppercase. At some level these two solutions might equate and if so, should be fit into the mathematics. Well, the value of n is the same for all particles. It basically determines a Planck-constant like value such that if k bar=1, then n is unchanged. And n could also be used to find the value of omega bar=1 using theta. So n would determines a Planck constant like point. But if there was an army of physicists and supercomputers working on this, and they found the value of n (using the varying curvatures each particular value of n will have), then actually the units would be totally fundamental. At a given value of w bar and k bar and at a given input, there would more or less be an inititely long number that describes that position. Now this is in contrast to the units currently in use. I assume the universe is purely mathematical in structure and if that is the case, then there is a very particular value that the universe assigns to what we call one meter. This value is almost definitely not one. So this theory would have more fundamental descriptions of time and space. So I'm starting to realize that my original approach to getting superposition was wrong. This was the approach above where I argue that k bar and omega bar vary over time. I'm starting to think that physicists use a different approach which involves, vaguely, using many different solutions all together, linear algebra and all that. And if this is the case, then the same thing should be done with my equation when substituted into Schrodinger's. Thoughts?

a constant that varies, that's a clever trick how does that one work? Yes, my mistake, I meant a constant that's very high. And to be clear, gamma components can have angular momentum, not spin.

Ignore that last chart. It's wrong and I can't edit it out for some reason. Also, I forgot to define s which is a constant that approaches infinity. And omega would equate to the inverse of theta at E=1 if you want to take the interpretation that time and space are both very small.

So this will be long, but I would like to clarify my mathematics, which with all of your input, have been developing. So there are six gamma components listed in the conditional equation. Each is achieved by substituting in one of the combinations of variables for delta, epsilon and iota. Gamma components are basically composed of two sides each resembling the definition of e: (1+1/n)^n. If they have spin one, one side is going to rotate the same way as the other even though the first side will have a t that is growing and the other shrinking such that this will grow. Now if you take an equation of e, and make it a function of n, then it will grow very quickly at first, and then more slowly. This is essentially why scaling n scales the rate of growth, and is also why multiplying by the square root of k bar is going to scale down the rate of growth proportional to k bar. However, because scaling down the rate of growth doesn’t affect the number of rotations per that length, the number of rotations per length will increase due to k bar (if it’s a gamma component with spin). A higher omega bar, on the other hand, will make time be more effectual than it is for other particles and so the gamma component will grow faster. A gamma component looks like an x eigenfunction only it doesn’t spin over time and it will be incredibly small. Perhaps, it can have small eigenvalues and then omega would be very small as well such that the change in t equates to the rate of growth of the eigenvalues at the speed of light. Or you can scale up the eigenfunctions by theta (all symbols used in this theory are not meant to equate to any others outside it): The short explanation of rate of growth is that it is how fast these will grow relative to each other and has to cancel with the scale of omega components. Here’s a chart: Now to Omega Components There are nine omega components. I won’t go into as much detail with these because they are essentially the same as gamma components, except they are more or less on the scale of one (because they don’t subtract with another e-like equation) and when they multiply gamma components will cause them to rotate through time (if they have spin). Like gamma components, each particular component has its own attributes varying in scale, which can be e, 1 or 1/e—and spin which can be 1, ½ or 0. Now To Waveparticles In order to form a waveparticle, omega components multiply no more and no less than one gamma component, for example a lowercase beta multiplied by an uppercase omicron. The angular momentum can be increased by multiplying a waveparticle by a lowercase gamma component divided by an uppercase, and omega component can be multiplied in to increase the spin by ½ or 1. Unless otherwise indicated, all these components have the same n, omega overbar and k overbar. All the other equations have this equation for a waveparticle in them although they also multiply and/or divide other omega and/or gamma components. Importantly, in all cases an input in the function has a position value that is determined by the eigenvalue of this waveparticle within the equation. So, for example, if you divide this waveparticle with spin by a lowercase gamma component, then it is what I argue to be a replacement for the wavefunction, and it still has a position determined by the eigenvalue of the waveparticle without the uppercase gamma component dividing it. Now this new wavefunction has k overbar and w overbar values that may continuously vary arbitrarily over time such that it can take on any arbitrary shape, and it may have probability scalars such that it can be normalized. I would like to argue, in other words, that all the techniques applied to the wavefunction are also applied to this new wavefunction. Hilbert space, for example, still applies, probability, etc. See the article for more detail. I’ve omitted all but the fundamentals. Now all three of your challenges and questions I’ve found enriching and thought provoking, and so in that spirit, I will return the challenge. It involves a thought experiment: imagine there’s another planet that has a species that has reached approximately the same point in physics as on this planet. They have discovered the equations I've used and use them, albeit more adeptly than I, as solutions to their mathematical equivalents of Schrodinger’s, Dirac’s, etc. They haven’t discovered the wavefunction used on Earth. Someone discovers the wavefunction used on Earth and perhaps he doesn’t understand the more complicated equations in physics, and so the professors consider this wavefunction to be too far off the beaten path. Can you mathematically prove this thought experiment is an impossibility by showing that my equation for the wavefunction and my eigenfunctions are incompatible substitutes for the wavefunction and its eigenfunctions in Schrodinger’s, Dirac’s, etc?

So does this mean that the wavefunction is not a viable option either? I'm not sure how it differs such that it can express this rather abstract idea. But this is really interesting. Anyway, I will look into this further. Very interesting. Okay, so one option, and this is admittedly improvised conjecture, is there are two wavefunctions, one for the positive x axis and one for the negative. Then you can use different forms of the wavefunction one with the positive and one with the negative curvatures I've discussed and that might serve as the dipole moments. And actually this reminds me of another way the theory can be tested which is that almost everything is approximate. This is not so true with the wavefunction because it uses a perfect n that approaches infinity. However, with my numbers you'll find that everything is approximate, aside from certain things like Planck's constant or the speed of light. And that model of dipole moments might fit nicely with matrices because there are four potential forms that particles with spin can take and that might help define four rows in a matrix. And again, two of the four have positive curvature and two of the four negative.

So the wavefunction has omega and k and my equations have omega overbar and k overbar which are basically the same except that they continue to apply when there is no spin or angular momentum. So I don't see what the wavefunction has that my equation doesn't that's allowing it to have a magnetic moment if mine doesn't. Again, my new stance is that you're simply substituting my equation and its eigenfunctions into Schrodinger's replacing the wavefunction or its eigenfunctions, and as far as I can tell, my equations are capable of all behaviors seen in the wavefunction. But if you believe it's not I would be very curious as to why.

Moreover multiple V overbars can multiply to get this into multiple spacial dimensions and time. I will continue working on my article to make this all clearer.

Correction: multiplying by omega components (not gamma components) increases spin by increments of 1 or 1/2 or 0 each depending on the component. No of course not. Look at the equations. Each point in space time is given a phase. Perhaps youve misread the graphs. The blue part is the real part and the gold the imaginary. The only thing about the graphs that has changed is the definition that the x eigenvalue of a waveparticle (this equation occuring in all of my equations) determines the position--and this is always by definition the case even when the waveparticle (denoted lambda in the article) is divided by other components such that it doesn't look like the x eigenvalue is growing over space. Given this definition of position, the graphs of the quantum wavefunction and my wavefunction should look the same provided they are both used as solutions to Schrodinger's, Dirac's, etc. Furthermore, although this gets more into my argument for the equation for a particle--these x eigenfunctions, these waveparticles, are best thought of as x axis over time (when in a single dimension). That's what I argue an x eigenfunction represents, and that's what I argue a particle essentially is, a spin zero x eigenfunction.

So are you saying angular momentum is quantized? Because multiplying by a lowercase gamma component divided by its corresponding uppercase version could quantize angular momentum as it incrementally increases the rate of rotation analagous to how multiplying by multiple gamma components with spin will increase the spin. To be clear your multiplying a V bar, a wavefunction, by that. It is going to increase the angular momentum by increments of 1/2 with each multiplication of a lowercase gamma component divided by its uppercase version where all the components in the wavefunction have the same values for omega overbar and k overbar.

Ah I did not realize that was the case Mordred, thank you. There is a solution. You multiply by a lowercase gamma component divided by its corresponding uppercase version. And Swansont, I am currently away from my computer but I will do some more illustrative work on Mathematica later

You've got perhaps a dozen variables (which you have not described in any detail). "Streamlined" is not the word that comes to mind. I would argue starting out with something simpler leads to less opportunity at higher levels, for instance the lack of curvature. How so? What are "fundamental" measurements of time and length? In this model, n established a length would have a non arbitrary value assigned to it, that it would be given by nature and by no human choice or decision. For example, let's say n is a 1x1^1000, then that's going to determine a very particular value after t grows by 1. It will be completely non arbitrary and fundamental. You are getting waaaay ahead of yourself. How about passing the introductory tests first. Of course I'm getting ahead of myself. That's what a test is. If I had the answer already then it wouldn't be a test. There are many tests, as I've mentioned, I already have the answer to, for instance, all the tests you've given me: you substitute my wavefunction or my eigenfunctions in for the wavefunctions or eigenfunctions used in the text studiot posted, and that gets the equation for the energy orbitals of hydrogen. If you take a V bar and add to its lowercase gamma component the complex conjugate of itself, then that's a 1D particle in a well as long as its a solution to Schrodinger's.

Oh, I'm well aware that's already been calculated. What I'm essentially arguing is that you would just replace my wavefunction or its eigenfunctions into the appropriate locations, and then I too would have calculated the orbitals.

As to the letters currently in use, none of them equate to any others currently in use with the exceptions of C and h bar. I hope that clarifies things. I will work on using more subscripts (I ran out of letters). As to increasing spin, an oversight on my part: you can just multiply in any arbitrary number of omega components to increase it. As to Lorentz invariant--upon further reflection--yes, you're right, it's not. I’ll admit this is an aspect of the theory that has posed a considerable challenge as getting definitions of w overbar and k overbar to agree with energy, momentum, velocity, relativity, time etc—this is difficult. However, I believe it is doable and I’m going to continue working on it. Now to a more general issue that should address most of the other concerns. It’s never been my goal to rewrite all of physics, which is absurd. My goal is to replace a part of them that I argue is problematic, but you guys have clarified that I need to fit the theory more explicitly into the existing framework. A simple solution seems to be, generally, to just argue that V overbar (my version of the wavefunction) or one of its eigenfunctions replaces every wavefunction or eigenfunction you would see in any equation in physics. I’m not sure, but I don’t think V overbar would still have w overbar and k overbar values that vary over t, but rather this work would be done by linear algebra. Thoughts? And similar is true of the V with an overbar and underbar which is a particle with boundary conditions and involves adding a matching complex conjugate of a lowercase gamma component to the existing one. At any rate, this replacement should work because the graphs of the two sets of equations, I believe, are identical. Then I’m not arguing anything has changed beyond the substitution. For instance, this substitution should have no impact on the energy states of hydrogen, isospin or a gyroscope magnetic moment at least not after n is calculated so that the units can be converted into SI. And I will continue to argue for an equation of a particle, but that’s more or less a separable theory that is not glued to the first. The obvious question then is why this new wavefunction is preferable. First and foremost, it is far more streamlined. Now gamma components and omega components form the wavefunction, the x eigenfunction, the momentum and energy eigenfunctions (and perhaps even a particle). This is arguably more “natural” and philosophically viable. Also, this model is less arbitrary. This gives a more specific description of spin and chirality, as it’s naturally occurring, this in contrast to the more arbitrary equations in use. Furthermore, measurements of time and length would be fundamental as opposed to the arbitrary units currently used. And also gravity might be explained, possibly dark matter and energy as well, probably as curvatures in the x eigenfunction. These would serve as the preeminent tests of the theory—tests, mind you, that physics as a whole has not yet passed. And Mordred that’s an impressive balance between brevity and clarity you gave in that overview. And thank you so much studiot and Mordred for taking the time to read the article and for your keen insights. They’ve inspired a lot of thought.

And, Swansont, there is already an equation for a 1D particle in a well in the paper.

Fair enough. Perhaps I misread the tone. Don't get me wrong, I sincerely appreciate every constructive criticism, and I've gotten a lot out of this forum already, and for that, I'm honestly very appreciative. Please criticize away, only lets be constructive. I'm getting pretty tired (it's 3:04 am where I live), but I will define my symbols tomorrow and update you with a new draft, but now I think I will go to bed. Thank you again.

Okay, so you still haven't read the article you're criticizing. That's okay. I suggested it's tested with force. It has a well defined definition of gravity. That's why I said I might be able to find the value of n based on the value of gravity. And there are other tests that could be given that have already been passed, for example, whether or not spins of 0, 1/2 and 1 are naturally occuring. No, I define all the letters in the article, which I really wish you guys would read. And actually whether or not spins of 0, 1/2 and 1 are naturally occurring is a test that the current math would fail because arbitrary scalars are used that force the math to have those spins. I don't use arbitrary scalars.

That's why you asked. This theory is not at those higher stages yet. Again, n is an unknown. To answer your question, the gamma components are similar in structure to the definition of e: (1+1/n)^n, but n doesn't approach infinity. It's better explained in the article, but long story short, the higher n is, the more slowly these grow. So if I don't know n, then I don't know the rate of growth. Therefore, I don't know the values where k bar and omega bar equate to one, which determines the locations where E=1 and p=1. This is all in the article.

In order to calculate that, I would first need to know the value of n in the equation for gamma components. This is part of the more general problem that the equation currently has, which is that, until n is known, Planck-constant-like floor in energy isn't either. If one were to assume that the curvature in, say, gamma were gravity, n might be calculable. I'll try to run that soon. Is there a particular reason you asked that question?

No, that's not right. Maybe substitute in the eigenfunctions instead.