Mordred

Here is food for thought. If the period between each waveform crest is uniform in distance. Taking the probability function [math]|\psi|^2[/math] that would mean your particles have the highest probability of being uniformly distributed as well as travelling in precisely the same direction and momentum. Does that in any way sound realistic ? Then you have the detail of the Debroglie or Compton wavelengths. Seems to be missing in your analysis.

Show me a parity wavefunction. I will wait to see your reply then tonight I will post you a parity waveform image. Multiparticle systems have constructive and destructive interference patterns with bosons having the least self interference. Ok let's try this you recognize that electrons have magnetic dipole moments. So let's a classical analogy take two magnets and mount them on two spinning axis. Measure the interference patterns between them. With two electrons you will always get interferences this is due to their antisymmetric parts so your multiparticle waveform should look extremely noisy with various spikes and different amplitudes and spikes. Ie via constructive and destructive interference. Not to mention further interference from the quantum harmonic oscillator. To make matters worse your particles will be traveling in different directions as they cross paths they often interfere. Trust me your waveforms are far too uniform to describe a multi particle system.

Sigh no you would not get a uniform sinusoidal wave if you measure a multiparticle system. You would get numerous crests that look like that animation but with further interference and different crest patterns . Multiparticle systems have interference patterns. In particular fermions have far greater self interference.

From what I have seen from your images you have the wrong waveforms to describe particles. They are too sinusoidal. I'm sorry if you don't get what I mean but you should compare the wavefunction on this link. https://en.m.wikipedia.org/wiki/Schrödinger_equation Now looking at that animation I can tell you there is no charge on that particle. Take one of your sinusoidal waves now calculate the probability of locating a particle. If all your sinusoidal waves have equal amplitude you will have equal probability of locating a particle at each amplitude

Now if your looking for the Dirac spin dispersion well your going to need considerable work. https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.ks.uiuc.edu/Services/Class/PHYS480/qm_PDF/chp10.pdf&ved=2ahUKEwiHgNXIx5HpAhVMsZ4KHY3pB3cQFjAIegQIBxAB&usg=AOvVaw0nBTTYsivo9b0CH5G7igbS The steps to follow are in this Relativistic quantum mechanics article and you will note I mentioned a few of these issues when I first described the Klien Gordon equation.

The problems I have with your equations is how do you localize the probability of the particle position ? How does it work with the Pauli exclusion principle when from the sounds of your descriptive the spin 1/2 particle waveform will be symmetric instead of antisymmetric ? At what point do you incorporate the Probability nature inherent in the Schrodinger equations ? Ie the uncertainty principle ? How do you even maintain units of a quanta ? Everything you have presented amounts to classical waveforms. They don't have any probabilities. They have a range of amplitudes that are not discrete as per units of quanta. So how can you claim to match the results of the Schrodinger equation ? Let's examine the first part of the time dependent Schrodinger equation. Try this thought experiment. I'm going to borrow this from Griffiths intruductory to Quantum mechanics. Take a rope 50 feet long. Keep swinging it up and down so you get a uniform standing wave throughout the length of the rope. What is the wavefunctions position ? About the only accurate thing you can tell me is the waveforms length and it's amplitude. How do you localize a particle when the waveform has no determinant position ? Ie you are uncertain as to its position. Now take the rope and shake it once. So that you get a single amplitude. Now you can give a certainty of the wavefunctions position but now your uncertain of it wavelength. Now on particles that only comes in units of quanta energy levels [/math] What would a waveform with energy as the amplitude look like when the only valid energy levels are units of quanta ? in essence simply posting the equations you have does not show how you factor in the above Ie discrete units of quanta etc. In essence supply a proof of how you derived the equation you posted so one cam check it's compatibility with the mathematical proof of the Schrodinger equation. Ok so take the Schrodinger equation for example that equation DOES NOT DESCRIBE A PARTICLE. It describes the wavefunction which you the probability of locating the particle via [math]|\psi|^2[/math] it is not a description of the particle itself. It gives you the possible position and momentum of the particle. Within the bounds of the uncertainty principle. In other words if you solve the Schrodinger equation for [math]\psi (x,t)[/math] you will get the probability of finding the particle in some region in space that varies as a function of time. With the highest probability density being the square of the probability amplitude. It does not and never did identify particle spin etc. Valid energy levels [math]E=\hbar\omega [/math] Here read this concerning Schrodinger equation it's detailed enough to start. https://www.google.com/url?sa=t&source=web&rct=j&url=https://users.physics.ox.ac.uk/~smithb/website/coursenotes/qi/QILectureNotes3.pdf&ved=2ahUKEwjM9pC5vZHpAhW1On0KHS8_DGsQFjABegQIBBAB&usg=AOvVaw0iTLlnjR4K8hbXeR-TaVhs

I fully agree there are numerous methods to compactify a group. I would well imagine there are methods I am not familiar with. It's nice to see a good discussion on the topic. It is a very commonly misunderstood term in physics particularly on forums. Some other methods is Aleksandrov compactification, Wilson Compactification, Hausdorff compactification and Stone Cech compactification.

https://en.m.wikipedia.org/wiki/Compactification_(physics) See here the keep in mind I'm discussing dimensional compactification as opposed to flux compactification in the above link. Though in both cases given above in the link you are contacting a group or set to its finite portions to avoid infinities.

Let's give a simplified example. Let's take a metric space and assign 4d dimensions {x,y,z,t} now at each coordinate I wish to map how temperature varies over time. Now for extreme accuracy I want to measure at each infinitesimal coordinate so I can apply partial derivatives. (Calculus of variations) So we can assign a set to temperature at each infinitesimal coordinate. Now ordinarily that set (dimension recall this value can vary without changing any other value) would be infinite in possible range. However I can place a boundary at Planck temperature and 0 Kelvin. I have now a infinitisimal topological metric space. Whose region is defined by the boundary of infinitisimals (point like) and it's dimension has been compactified by the upper and lower temperature bounds. However as I am using infinitisimal regions I have another infinity problem in the number of spaces. So I must set some boundary to that. So as we can never measure below the Planck length I can now limit the number of infinitsimal spaces which limits the number of seperate temperature sets.

No it is still the same in physics. It isn't based on sizes but on the sets of differentials. In the Brian Greene example he isn't even referring to the sets of reals but the complex differential sets. The meaning of dimensional compactification doesn't change from mathematics to physics. Physics employs all mathematical rules and this is part of how many of the physics terminology is defined. Many charts used in parameter space are not volumes per se but can use the same coordinates on graph. Phase space is a good example where your graphing amplitude of a signal. A topological space doesn't require a metric space see the link above for examples involving sets. If you want to properly understand physics regardless of theory you must understand it's mathematics. Not the verbal explanations physicists use to describe those mathematics to make it understandable to the average reader.

Let's put this into perspective. You want someone to do the math for you. Ok so would you understand the statement. The first property in the definition of a Calabi-Yau manifold. X is compact if every collection of sets [math]V_j\in\tau[/math] which covers X ie [math] X=U_jV_j[/math] which has a finite subcover. If the index j runs over finitely many sets then this condition is met. If j runs over infinitely many sets. This would require that there exists a finite subcollection of sets... This is an example of compactification for the topological spaces used in Calabi-Yau manifolds. Source being String Theory on Calabi-Yau manifolds by Brian R Green. Can possibly understand that statement without understanding differential geometry and holonomies of topological spaces ? https://en.m.wikipedia.org/wiki/Topological_space https://en.m.wikipedia.org/wiki/Hausdorff_space https://en.m.wikipedia.org/wiki/Holonomy https://en.m.wikipedia.org/wiki/Parameter_space https://en.m.wikipedia.org/wiki/Configuration_space_(mathematics) https://en.m.wikipedia.org/wiki/Phase_space The following links above all involved in the example I gave.

Ok to to OP. As a professional physicist I can tell you that no descriptive only approach will ever be accepted as a theory. Lets take the term "compactify a dimension ". What does a physicist mean or even a mathematician mean by that term. To answer that question you must first define the word dimension. Any independent variable or other mathematical object such as a function, matrix, tensor or group. So space has three independent variables to define position. {x,y,z} each of these values can change without changing the other value. So let's take the dimension x described by the set of Real numbers. Uh oh we have a problem. This set is infinite. We don't like infinite groups or sets in physics. So let's compactify (make this set finite) All infinite groups contain a finite set. So we can compactify this dimension by restricting the set to the applicable finite portions. Now apply the definition I gave of dimension under mathematics and subsequently physics to String theory when one states String theory uses day 14 compact dimensions. What he is really saying I have 14 effective degrees of freedom Ie 14 independent variables that are all compactified into finite sets. Strings are compactified by the Direchlet and Neumann boundary conditions Ie open strings by the former and the latter for closed strings. All strings describe waveforms. They are not little objects or matter constituents they describe particle wavefunctions. Each particle has a set number of degrees of freedom. Ie charge, spin, etc etc. String theory follows all the rules of GR with regards to spacetime and uses precisely the same transformation rules. One of the best lessons I learned to understand invariance under SR came from a string theory textbook. How to compactify the set [math]\mathbb{R}^4[/math] into the light cone gauge. Properly studied one will learn that a String corresponds to the action of a point particle. Ie you will need to understand Langrangian action in order to understand Polowskii action or Nambu Goto action. https://en.m.wikipedia.org/wiki/Nambu–Goto_action Note the part describing Parameter space.... We describe a string using functions which map a position in the parameter space. This is your extra dimensions

Here this may help it's a basic level however it illustrates the problems with trying to apply the classical view to a particles intrinsic spin. https://www.google.com/url?sa=t&source=web&rct=j&url=http://physics.mq.edu.au/~jcresser/Phys301/Chapters/Chapter6.pdf&ved=2ahUKEwjg3evY347pAhUXJDQIHQQvCkoQFjAMegQICBAB&usg=AOvVaw0yaFzZDTtdlZy9E9oaeWYe Particularly treating a point particle which on scatterring experiments if it has a radius it would be less than [math]10^{-18} [/math] it will then explain why the classical view doesn't work with this.

Ask yourself the following questions. 1) do you need a wavefunction to describe two spin states ie spin 1/2 up or 1/2 spin down ? 2) what is the probability nature of wavefunctions in QM ? This is where you must look into. Many of QM's wavefunctions are probability functions that is described as a wavefunction. This is different from physical waveforms. https://en.m.wikipedia.org/wiki/Wave_function Note the part of QM stating it is a complex variable probability function

Nature. We detect and can measure the magnetic moment of all standard particles including the neutron. Even though it is charge neutral. You must be able to account for it in order to properly describe spin. Ok let's take this further if you rotate a spin 1/2 particle by 360 degrees that particle will not return to its original state. You require a 720 degree rotation. Yet a spin 1 particle only requires a 360 degree rotation https://en.m.wikipedia.org/wiki/Spin_(physics) See here for reference. Now earlier I stated three different 1/2 spin particles that will have three different gyroscopic magnetic moments.

We cross posted see above

You cannot treat particle spin strictly by its angular momentum term. You also have it's magnetic moment. That is what you are missing and why you believe you can treat particle spin in classical terms which is wrong.

How does that equate to deflection from a magnet ? Ie Stern Gerlach apparatus ? If spin is determined by the classical terms your using how does that make sense ? These questions come back to the magnetic moments involved in spin. Specifically the possible orientations of the magnetic moment due to spin. (I seriously hope you do not have the image of a spinning particle like a spinning top) when you look at the magnetic moments and the angular momentum terms for a point like particle you will find that would not make sense.

Consider this challenge you have only two discrete values for the spin of an electron. How do you produce two discrete values from a sinusoidal wave ? How do you determine the precise points on that sinusoidal wave that denotes spin 1/2 up or down ? You will need to answer this with the Stern Gerlach experiment in mind. https://en.m.wikipedia.org/wiki/Stern–Gerlach_experiment

Having looked over your article in more detail. I hate to point this out but if you studied nucleon Spectrography which led to the discovery of quarks. You would recognize you have energy levels not covered by 0, 1/2,1 particles see electric charge of the quark family and learn the isospin correspondence. This will correspond to the cross sections which is extremely important in particle physics and cannot be ignored. You will also discover a symbol conflict (one of many) [math]\Gamma [/math] width of excited state/decay rate. This statement in section 8 conflicts with GR. Your theory is not Lorentz invariant interaction rates will vary depending on observer under relativity. Common example muon decay rates. Now even though no elementary particle has spins other than those mentioned you can have other spin values such as spin 3/2, spin 2, spin 5/2 etc. I would strongly suggest you look into spin in greater detail and what spin entails in the intrinsic magnetic moment Ie [math]\mu_s=g_e\frac {-e}{2m_e}S [/math] where g_e is the gyro magnetic factor of the electron. You will find that for example the gyro magnetic factor of the proton will be different. Yet both particles are spin 1/2. Then to confuse matters further the neutron will also have a different gyroscope magnetic moment. Can you identify why this is the case? Secondly can your theory explain why this is the case ?

I often tend to get that wrong lol I will strive to watch for it in the future good catch Well in QFT all particles are field excitations. So how one defines a particle varies a bit in the the operators between QM ( position and momentum) to what is described above which is the first part above. Scalar fields can also often use the symbol [math]\phi [/math] a good example is the Freidman equations of state for scalar fields in cosmology. https://en.m.wikipedia.org/wiki/Equation_of_state_(cosmology) If you look at the scalar field example you will note it also employs the potential and kinetic energy of a field. This is often employed to model the HIGGS field, the cosmological constant and inflation with variations on that equation in the link. If the OP likes I can offer to work up an example of a photon field to get a better feel of how the creation and annihilation operators will give rise to photon particle number density. (It's one of the simpler examples as bosons are symmetric) ie Pauli exclusion principle. As well as the photon being its own antiparticle which adds further simplifications. Just for information on the [math]\psi[/math] this is commonly the Four component Dirac field where [math]\psi_L,\psi_R[/math] are two component left and handed spinor fields in particle physics.

For the OP this is just a primer to help understand the basics of QFT and how force is applied. Keep in mind this is a workup I did on this forum a few years back but it saves a lot of latex. You should be able to get the gist of how QFT differentiates from QM. One difference to recognize and I didn't cover is that the Schrodinger equation is first order while the Klien Gordon is second order. (This is a conflict of QFT to QM that requires a seperate fix). The repair comes into play when you factor in particle number density... Just in case your not familiar with time derivatives (the overdots) https://en.m.wikipedia.org/wiki/Time_derivative This paper is rather advance but it will give you a good idea of how the Langrangian is used to describe the standard model. https://www-d0.fnal.gov/results/publications_talks/thesis/nguyen/thesis.pdf It should give you a good idea of what you are up against...

Thanks I will look at these after work but at a glance I concur with Studiot. Force is fundamental in both both QM and QFT. I will post how QFT handles force after work. The main difference between QM and QFT is that QFT is Lorentz invariant through the application of the Klien Gordon equation (though that isn't the only issue.) I haven't checked your equations yet for Lorentz invariance though that will be essential. Another essential aspect of QM and QFT is the positive norm basis of a particle. For example the probability of locating a particle is the amplitude squared.

I hate to say it but from a glance you should really look into a tensor format for [math]\Omega[/math] and [math]\Gamma[/math]. Though I still need time to go through this. Though I would prefer the paper you show in your video. It should be easy to post the pdf of that paper so I don't need the video. The thing is the Langrangian of each force already incorporates the energy momentum of each particle. With the probabilities of the Feymann path integrals. So I would like to see what advantage your alternative has compared to the methodology of QFT which other than gravity can already unify the strong, weak and electromagnetic force.

Either way the only way to calculate the amount of gamma ray burst would be to specifically model the thermodynamic procresses of each specific body. The amount and type of each element involved in fusion processes can greatly vary with stellar bodies. I don't see how a generic formula that can apply to numerous bodies of even the same type is feasible.