Dubbelosix

Then ask for references. I will look into it. I thought it was an undergraduate knowledge that a system is not given a process to produce an eigenstate... I will look. hold your horses. https://arxiv.org/pdf/1607.06438v4.pdf https://www.physicsforums.com/threads/is-the-collapse-of-a-wave-function-deterministic-or-random.847032/ http://www.thphys.uni-heidelberg.de/~stamatescu/Studies/PDF/collapse_wave_fct.pdf try some of these, there are references to the random collapse. A good one https://physics.stackexchange.com/questions/130007/is-the-mechanics-of-the-wave-function-in-the-quantum-mechanics-deterministic

The experiment is evidence if you can provide a better interpretation, please do. Because I think it would reserve the next Nobel Prize. No quantum mechanics is not wrong. Incomplete, that is what I have been talking about, especially when we consider how a system collapses into an Eigenstate. You said quantum mechanics can provide an answer to how otherwise uncorrelated photons know which path to take to ensure an interference pattern emerges... please explain your knowledge. Because it has baffled the greatest minds and yet is one of the rarely talked about subjects in physics. If you conform to science as I understand it (and I don't leave myself often many degree's of freedom for error) you are very welcome to speak with me. I have attempted to heal what has happened before, so let's just try and keep it that way.

Yes it indeed is only an interpretation, but one that has guided the way of many physicists thinking over the years including a superfluous amount of literature that will pertain to random occurrences in nature. Yes, the evolution of a wave function can be deterministic. I have been trying to explain since post 1) this is not the case in the Copenhagen interpretation, please read me carefully since the collapse is often considered random..

No hidden variables... but hey, nonlocal one's have not been ruled out yet, so let's remain scientific about this. My opinion has nothing to do with this, unless you reason my opinion with logic, in which case, read what I said again and come back. Let's not confuse the audience, the experimental evidence is compelling.

Or the fact an evolution of a wave function, is otherwise, deterministic.

''The Copenhagen theory makes no predictions'' IS A very infamous statement. Personally, I find it a cop-out. An interpretation has to be incomplete if the previous I have explained is to be understood properly. The collapse of a wave function, must not be a fundamental process. I cannot stress it enough based on the single interference paradox. Sorry for my terminology.

You cannot predict the energy level, or eigenstate a system will choose in the theory of Copenhagen. Well... not that I actually believe ''you cannot do it'' only that it seems strange that when a model is unable to do something, many take it seriously... like randomness, as an explanation to otherwise, dynamic processes we are yet to fathom. The universe is not borne from randomness if and only if, classical theory is not emergent.

The wave function is often taken as a random process. There are strong reasons to object this conclusion. 1) The wave function evolution is actually entirely deterministic - it is only the collapse of the wave function which is often considered random, especially within the Copenhagen frame of mind. 2) The wave function can fundamentally show, that there could be an intrinsic over-reaching statistical field that could be governing everything. For claim 2), since claim 1) I don't expect there to be any objections to, can be supported with evidence in the following way: 'The strangest thing about the double slit experiment that I have never forgotten and I am still puzzled today, that even when you reduce the experiment to one particle at a time being shot through the slits, the interference pattern on the screen still emerges. The photons are totally unrelated, but somehow the particles know which region of the interference pattern is the most likely to land on. Note, those particles have no knowledge about where the other particles landed or where even future particles will land. Though somehow, each photon reaches the screen ''knowing'' which regions which are the most likely landing and most unlikely landing spots. To me quantum theory has to be incomplete, because our physics does not explain how these particles know where to land.'' It is an experimental (fact) that this happens above, but quantum mechanics is insofar incomplete to adjust an explanation of how this can happen, without some obvious explanation, like perhaps things are deterministic at the fundamental level. Even though this seems like a very rational view in the experimental case above, it seems like it is almost never talked about because it contradicts any simplification in the theory as (they) would like us to believe in. There is simply not enough physics to describe the situation above and yet still prescribe to a scaled down version of ''what will happen, simply will.''

No problem, of course there is resemblance. The zitter motion comes from the angular momentum interpretation of [math]\omega[/math] which has dimensions of an inverse time. It is encountered many times in physics. In the early theory, it was believed the electron could have been a photon traversing a zig zag motion through space, hence, why we called it zitter motion. This interpretation was Dirac's. But like many of Dirac's idea's... and even objections, they never caught on. This was because he was a revolutionary mind of his day - when I hear people of talking about ''we need the next Einstein,'' conditions where much different than what you will count today for many reasons: 1) That is, peer reviewers may not do the best job 2) More papers are created today and as a result, finding the nail in the haystack could be a true saying when comparing the find for the next Einstein 3) Radical idea's today are often met with negative criticism, often guised as ''honest criticism.'' This may be based on either a lack of understanding, education or even just hostility which let's admit it, is encountered in every stretch of life. 4) Maybe the idea is too bizarre: ie. the physics may pertain to remodelling the theory or relativity. These kind of claims should be taken with a pinch of salt. However, if there ever does exist a claim, which there very well could be, that extensions to relativity is required, then yes, we will need to consider the evidence. It is considered by some physicists, that dark matter may be an indication that relativity breaks down on global scales. 5) Take into consideration also, that our physics is incomplete and no one can come to agree on everything. There are loads of examples of 5). A recent discussion of the wave function and more specifically the double slit experiment (involving the Afshar experiment) provided a friend of mine (with excellent education) enough reason to believe it contradicts the Copenhagen interpretation. It seems, that great names have also taken it to mean this, including Doctor John Cramer, but maybe for bias reasons, since he thinks it supports his own Transactional interpretation. I cannot uphold or confirm with any integrity that this is why John has done this, but I will state it for the audience since obviously some people will be thinking this way, but I have no doubt personally of Cramers own integrity concerning the matter. Personally I am not educated enough yet to understand why the experiment may be flawed, only that I know of one example in which I have often taken as an '''incompleteness'' to quantum mechanics concerning the wave function. As I wrote on a forum: ''The strangest thing about the double slit experiment that I have never forgotten and I am still puzzled today, that even when you reduce the experiment to one particle at a time being shot through the slits, the interference pattern on the screen still emerges. The photons are totally unrelated, but somehow the particles know which region of the interference pattern is the most likely to land on. Note, those particles have no knowledge about where the other particles landed or where even future particles will land. Though somehow, each photon reaches the screen ''knowing'' which regions which are the most likely landing and most unlikely landing spots. To me quantum theory has to be incomplete, because our physics does not explain how these particles know where to land.'' The only conclusions from an early age, and even now, that I think could even explain the 'single interference anomaly'' is some notion of determinism within the theory. The pilot wave was considered shortly, but really, I only mentioned it as an example, since when later my physicist friend commented that it is experimentally out of date. Once again, a statement I cannot uphold myself, maybe due to my own education. Nevertheless, these are great examples of how broad of understanding, and how broad the difference of thinking can be. In my case, its just lack of reading enough material. But rest assured, I do not believe I am far from it. A few more years of home education, and I think I'll be able to understand more cases of the Lie algebra, not just the confined knowledge I have of it, but something more akin to Mordred, who has expressed the importance of it within the sets or subspaces. It's a subject I am still learning, along with set theory, which is why, you will rarely encounter me talking about them.

Almost! But you need some other formulae to argue it. I have taken the liberty of finding a relevant paper by an author I highly regard as a theorist. It's been some time since I read it, but if my memory is correct, is not actually a bad introductory into those ideas. http://fqxi.org/data/essay-contest-files/Hestenes_Electron_time_essa.pdf?phpMyAdmin=0c371ccdae9b5ff3071bae814fb4f9e9

So it seems like I have used the Wigner function correctly. I have been primarily using it on a Hamiltonian which can otherwise be described by the curvature tensor. Here is another example of how you use it - you calculate the lowest ground state energy in such a way - [math]<H> = \int \int W(q,p)(\frac{p^2}{2m} + \frac{m \omega^2 q^2}{2})\ dqdp = \frac{\hbar \omega}{2}[/math] We have defined mean values for the function and inequalities which has given a much richer physics. Some of the inequalities are weaker than others. Or more generally [math]<H> = \int \int W(q,p)H(q,p)\ dqdp [/math] paper on curvature and Hilbert space. https://sci-hub.bz/https://doi.org/10.1142/S0217732393001148

I wanted to check to see whether the Wigner function was defined correctly in the work. It shows, there are things possibly missing from the description ~ here is an excerpt from some material I am reading ''The Wigner function is defined as the transform of the density operator, multiplied by the normalization factor [math]\frac{1}{2 \pi \hbar}[/math].'' Early work I read, considered inequalities of the form [math]|W(q,p)| \geq \frac{1}{\pi \hbar}[/math] but the factor of 2 in the denominator should not be forgotten about. So yeah! I've been oversimplifying the physics accidently. The function is related to the Weyl transform. [math]\bar{A}(x,p) = \int\ e^{\frac{-ipy}{\hbar}}\ <\frac{x + y}{2}|A|\frac{x - y}{2}>\ dy[/math] This is the Weyl transform [math]\bar{A}[/math] of some operator [math]A[/math] and has been expressed in the x-basis [math]<x|A|x>[/math]. The Weyl transform itself turns an operator into a function of x and p. One property of the Weyl transfrom is that the trace of the product of two operators is given by the integral over the phase space of their Weyl transforms, [math]Tr[AB] = \frac{1}{\hbar} \int \int \bar{A}(x,p)\bar{B}(x,p)\ dxdp[/math] Of course, densities are given, in this case in the position basis [math]<x|\rho|x>\ = \psi(x)\psi*(x)[/math] The Wigner function can be generalized into mixed, in much the same way as the density operator. Even though there is more physics to consider from the Wigner function than I previously took into account, it looks like I have most of relationships correct concerning the probability distributions of the form [math]\int W(q,p)\ dp = <q|\rho|q>[/math] [math]\int W(q,p)\ dq = <p|\rho|p>[/math] http://www.stat.physik.uni-potsdam.de/~pikovsky/teaching/stud_seminar/Wigner_function.pdf In that link though, it does state an identity for the Wigner function and the Planck action as [math]W(q,p)^2\ dq dp = \frac{1}{\pi \hbar}[/math] In such a case, we can see that [math]W(q,p)^2\ dq dp =\ <q|\rho|q><p|\rho|p> = \frac{1}{\pi \hbar}[/math] Though if this: [math]W(q,p)^2\ dq dp =\ <q|\rho|q><p|\rho|p> = \frac{1}{\pi \hbar}[/math] Is a true relationship, like the linked worked seems to suggest http://www.stat.physik.uni-potsdam.de/~pikovsky/teaching/stud_seminar/Wigner_function.pdf then I have applied it correctly, save notation differences. The Weyl transform concerning two probability distributions: [math]Tr[\rho_A\rho_B] =\ <\psi_A|\psi_B>[/math] is [math]W_{AB}(q,p)^2\ dqdp = \frac{1}{\pi \hbar}<\psi_A|\psi_B>[/math] This has strong correlations to previous identities we looked at recently as well. As you can see, the Wigner function is a probability measure itself.

You can also write the inequality in terms of the Wigner function, [math]|<\psi(0)|\psi(t)>|^2 \geq \cos^2(|W(q,p)| <R_{ij}> - <\psi|R_{ij}|\psi> )\Delta t \geq \cos^2(\frac{[<H> - <\psi|H|\psi> ]\Delta t}{\hbar})[/math] (I missed the greater than or equal to sign before at the beginning when I featured the inequality, but if the Wigner function gives rise to an inequality below, then the above may be a true inequality. remember that [math]|W(q,p)| \geq \frac{1}{\pi \hbar}[/math] [math]\dot{s} = |W(q,p)|\sqrt{<\psi|R_{ij}^2|\psi>}[/math] [math]\dot{s} = \sqrt{<\dot{\psi}|\dot{\psi}>}[/math] (I think I done this right?)

''In quantum mechanics, the Fubini–Study metric is also known as the Bures metric.[2] However, the Bures metric is typically defined in the notation of mixed states, whereas the exposition below is written in terms of a pure state. The real part of the metric is (four times) the Fisher information metric.[2]'' ''In the context of quantum mechanics, CP1 is called the Bloch sphere; the Fubini–Study metric is the natural metric for the geometrization of quantum mechanics. Much of the peculiar behaviour of quantum mechanics, including quantum entanglement and the Berry phase effect, can be attributed to the peculiarities of the Fubini–Study metric.'' Added because it is educational and, it gives us a new terminology for the Bure's metric, something we looked at much earlier. https://en.wikipedia.org/wiki/Fubini–Study_metric

In certain conditions, they can become deconfined, that is, they can behave like independent particles ''Spinons are one of three quasiparticles, along with holons and orbitons, that electrons in solids are able to split into during the process of spin–charge separation, when extremely tightly confined at temperatures close to absolute zero.[1] The electron can always be theoretically considered as a bound state of the three, with the spinon carrying the spin of the electron, the orbiton carrying the orbital location and the holon carrying the charge, but in certain conditions they can become deconfined and behave as independent particles.''

http://sci-hub.bz/10.1007/BF02819419 http://aapt.scitation.org/doi/10.1119/1.16940 The Mandelstam-Tamm inequality can be written in the following way, with [math]c = 8 \pi G = 1[/math] (as usual), we can construct the relationship: (changing notation only slightly) [math]|<\psi(0)|\psi(t)>|^2 > \cos^2(\frac{[<R_{ij}> - <\psi|R_{ij}|\psi> ]\Delta t}{\hbar}) = \cos^2(\frac{[<H> - <\psi|H|\psi> ]\Delta t}{\hbar})[/math] [math] = \cos^2(\frac{\Delta H \Delta t}{\hbar})[/math] for [math]0 < t < \frac{\pi \hbar}{2 \Delta H}[/math] where [math]|\psi(0)>[/math] is the state at [math]t=0[/math]. So how long does it take for a particle probability to reach the half life? In the zeno effect models, when a particle reaches its half life, it is likely to decay and any measurements made on it after its half life could very well result in the anti-zeno effect. In the decay probability model, we say the system has reached it's half life when the decay probability [math]|<\psi(0)|\psi(t)>|^2[/math] is [math]\frac{1}{2}[/math]. The inequality tells us that the half life is greater than [math]\frac{\hbar}{4 \Delta H}[/math] Another implication is that for short times the non-decay probability will fall off more slowly than the parabola [math]1 - (\frac{\Delta H t}{\hbar})^2[/math]. Mandelstam and Tamm derived this type of inequality from a better known relation of theirs [math]\Delta H \Delta A \geq \frac{\hbar}{2}|\frac{d<A>}{dt}|[/math] Here [math]A[/math] is taken to be the projector on the state [math]|\psi(0)>[/math] so that [math]A = |\psi(0)><\psi(0)|[/math] It is possible to obtain the identity [math]\Delta<A^2>\ =\ <A>(1 - <A>)[/math] In which [math]<A>\ = |<\psi(0)|\psi(t)>|^2[/math]

The inequalities recently, as I noted, where objects we encountered before, in the previous studies, they were related to ''survival probabilities.'' The inequalities a few posts back, turns out has a name, they are called Mandelstam-Tamm inequalities. They are it turns out (something more I have learned) related to decay models, just as the zeno effect depended on the survival probabilities. The physics is converging. http://iopscience.iop.org/article/10.1088/0305-4470/16/13/021/pdf http://streaming.ictp.trieste.it/preprints/P/83/041.pdf http://sci-hub.bz/10.1088/0305-4470/16/13/021

Using the geometry featured in a reference we have has, the geodesic length is [math]|\psi_0 - \psi_1| = \sqrt{2 - 2\cos \alpha} = 2 sin\frac{\alpha}{2}[/math] The [math]\cos \alpha[/math] is calculated the following way: [math]\cos \alpha = \frac{<\psi_0|\psi_1> + <\psi_1|\psi_0>}{2}[/math] And from this, it states in literature that the inequality holds [math]\cos \alpha \leq |<\psi_0|\psi_1>|[/math] And so the length of a curve on the unit sphere connecting [math]\arccos |<\psi_0|\psi_1>|[/math] With it, you can actually set up an inequality of the form [math](t_1 - t_0)\sqrt{<\psi|H^2|\psi> - <\psi|H|\psi>^2} \geq \hbar \arccos |<\psi|\psi>|[/math] Notice, we have encountered this before and so is additional physics to a previous look at the object - we looked at it in two forms, we could write it in terms of the curvature tensor with some additional constants and/or we could write it as the difference of the Hamiltonian energies. They are known as binding energies when you take the difference like this, just as we saw in the Penrose model and in this model (early on). The statistical equivalent of taking the difference of these Hamiltonians was [math]\sqrt{|\psi|^2\ln[|\psi|^2] - |\hat{\psi}(i)|^2\ln[|\hat{\psi}(i)|^2]}[/math] and so for a two particle system we would have [math]\sqrt{|\psi|^2\ln[|\psi|^2] - |\hat{\psi}(i)|^2\ln[|\hat{\psi}(i)|^2]} - \sqrt{|\psi|^2\ln[|\psi|^2] - |\hat{\psi}(j)|^2\ln[|\hat{\psi}(j)|^2]}[/math] Since for two particles [math](i,j)[/math].Since we already established this relationship with geometry, it must also stand true for the curvature tensor that the inequality also holds ~ with [math]c = 8 \pi G = 1[/math] [math](t_1 - t_0)\sqrt{<\psi|R_{ij}^2|\psi> - <\psi|R_{ij}|\psi>^2} \geq \hbar \arccos |<\psi|\psi>|[/math] http://www.physik.uni-leipzig.de/~uhlmann/PDF/UC07.pdf

If we identify [math]\frac{1}{2}<\dot{\psi}|\mathbf{M}|\dot{\psi}>[/math] (1) with wave functions [math]|\psi> = e^{iHt}|q>[/math] [math]<\psi| = <q| e^{-iHt}[/math] In these last two equations, though the wave function will give rise to a probability of the wave function with dimensions of either [math]1/L[/math]. [math]1/L^2[/math] or cubed density (volume) [math]1/L^3[/math] we will not renormalize it in this approach, we'll leave that to the reader to assume there is some differential attached in there to remove the density. ie. [math]<\psi|\psi>\ dV[/math] for a wave function in three dimensions. In the two equations, we will also assume for the largest part there is encoded a generalized position [math]q[/math]. You'll see why when we reach equations 5 and 6. and identify it as ''being akin'' to the following equation [math]k_BT = \frac{1}{2}mc^2 =\frac{1}{2} \frac{dq}{dt} \cdot \mathbf{M} \cdot \frac{dq}{dt}[/math] (2) where [math]q[/math] is the generalised position and so [math]\dot{q}[/math] is the generalized velocity and knowing that [math]k_BT\ dt^2 = \frac{1}{2}mc^2\ dt^2 = \frac{1}{2}dq \cdot \mathbf{M} \cdot dq[/math] (3) When considering the Hertz principle of least curvature, the mass is often set equal to 1 without loss of generality in the theory - you may do such a thing if all the masses are equal, or if you wish to continue with a ''massless theory'' - whatever the motive, keep in mind that a massless theory would not have the mass tensor. This is why you will come to encounter some authors write it in the form: [math]ds^2 \equiv c^2\ dt^2 = \frac{1}{2}dq \cdot \mathbf{M} \cdot dq[/math] (4) According to the almost similar nature of the first expressions relationship with equation 2, we can theorize some relationships, one related to the kinetic energy and another related to the metric [math]k_BT = \frac{1}{2}<\dot{\psi}|\mathbf{M}|\dot{\psi}>[/math] (5) featuring the mass tensor on the RHS but not the mass term on the LHS, it would also hold that [math]ds^2 = \frac{1}{2}<\psi|\mathbf{M}|\psi>[/math] (6) The mass tensor in this model, appears to be a metric tensor. I'll even propose the possible quantization: [math]\hbar = \frac{1}{2}t^{-1} <\psi|\mathbf{M}|\psi>[/math] The temperature was once again, related to the curve, [math]k_BT = \frac{1}{2}m(\frac{ds}{dt} \cdot \frac{ds}{dt})[/math] and the curve in our Hilbert space was identified using the Wigner function, here as the square of the metric [math]ds^2[/math], [math]<\dot{\psi}|\dot{\psi}>\ = |W(q,p)^2|\ <\psi|R^2_{ij}|\psi>\ \geq \frac{1}{\hbar^2}\ <\psi|H^2|\psi>[/math] and as noted, will satisfy a Schrodinger equation [math]\frac{1}{ i \hbar}H|\psi> = |\dot{\psi}>[/math] remember, [math]ds = cdt[/math]. From this under the Jacobi formulation there exists an action related to the temperature: [math]k_BT = \frac{p \cdot \dot{q}}{2}[/math] In which [math]\frac{1}{2}p \cdot \dot{q}[/math] is the minimized action. Further under the Jacobi formulation, the action is related to the following relationships for the temperature [math]k_BT\ dt = \int p \cdot dq[/math] So the interesting thing now which is different to my last thoughts, I thought the mass tensor could be just a mass term acting on a matrix, but it is actually identified as a more complicated object which appears to be a [metric tensor]. I need more literature on this to understand it.

Ok, I am not sure about yours either, if it was just to say the phenomenon also exhibit pair phenomenon, then ok. I just thought that maybe you where implying something.

Composite does not mean not fundamental. Quarks also experience a similar phenomenon - ie. you can never find a lone quark. They are composite as well.

No. I would have remembered because you asked me if I have posted about this and I don't recall posting this anywhere except on facebook in my own subforum. Yes, well there has been attempts to measure the ''shape of electron.'' In phase space, it seems meaningless to talk about points since points themselves are smeared like a ''Planck cell.'' Plus, points does not really make sense in any of the physical theories we chose, self energies for classical electrons encounter singularities - relativity also encounters singularities when the radius goes to zero. So there are existing problems with our models when thinking about the electron without a structure. https://www.livescience.com/14322-electron-shape-standard-model-particle-physics.html Electrons also experience a secondary phenomenon. Electrons can be split up into what some scientists consider, the elementary fundamental constituents - such as a spinon, orbitons and holons. The real tricky question is to explain this phenomenon - because they do behave in circumstances as independent particles. This is achieved through low temperatures in solid mediums.

Me too!

It's not my theory, its one that has existed for a while so no, it wouldn't be me. Here is the paper I was referring to. http://www.cybsoc.org/electron.pdf These scientists actually have a much more complicated second paper they published later, but for the life of me cannot remember the name of it. It extends everything more compactly. Oh ok, some one here has found that second paper! Big moon-faced children, full of energy ready to go supernova.

It's not that its a mistranslation per se though there are many cases you can show what you said --- it actually has a number of different interpretations... oh dear... I should stay away from this Theology was a perverse interest for me for many years without any... religious roots. Did you lot know, the number 666 appears four times in the Bible? However, my own numerical calculations to the Greek text shows that the numerical calculation of the name ''Jesus Christ'' comes to 888. The chances of this are very slim.I could calculate those chances but I am very tired at the moment, may do it later. It seems likely 666 was the actual number they intended. The Bible neither had one author. At the very least, it had about 44 authors maybe more. It consists of 66 books but that is not the true collections - many ... heretical gospels which talked about the early years of Christ when he was a child, among many other books that the later church, where inexorably carte blanche.