Mordred

Just keep in mind simply linking the paper isn't sufficient where possible copy paste the relevant details here so no one is required to go offsite to look over your paper. Other than that having mathematical detail is excellent we don't mind alternative theories provided they are testable (ie mathematics). We do get some pretty wacky Speculations here if you have mathematics then it's a huge help. For latex here use \[\frac{1}{2}\.] I placed a period on last command to keep from activating. Good luck

You would be surprised how many ppl we see that don't know how that term is applied. It's simply become habit to define it. Understanding clear logic doesn't allow one to ignore physics however. As I mentioned numerous times you still haven't addressed your faster than c signals. Anyways you seem to refuse to acknowledge that a physics model requires far more than verbal logic. It's pointless for me to continue trying to provide direction for improvement from you. Good luck with your idea as you seem to feel your idea is complete and requires no improvement I see no point in continuing. Good luck Just an FYI toroid based models at the quantum level already exist and have been tested for and are still being examined. So it will take far more than verbal logic to be convincing. Although they wouldn't be useful to you from your descriptives of your model idea. They don't make the same claims you do.

Try thinking of sound due to vibration for starters then consider which materials tend to vibrate more or less than other materials. Some materials such as a tuning fork has a resonant vibration to match a specific frequency.

For example very little here really makes sense. I can only assume the first part discusses intrinsic curvature rather than extrinsic. The term dimension in physics refers to effective degrees of freedom it's not strictly a geometric axis. Though x, y,z are effective degrees of freedom so is spin color charge etc etc etc. Some dimensions can even describe a strictly mathematical effective degree of freedom. You still haven't explained how you get signals from a wave faster than c as a result of your toroids

Unfortunately spacetime doesn't curve on its own. One could argue how to describe R=0 till they are blue in the face. Occams nothing is as good as any other way to describe it lol.

It's really has little to do with how to verbally describe something. Anyone can claim this or that. The wording really doesn't matter. In order to confirm viability of those claims you need something beyond verbal or pictures etc. That tool is mathematics using known physics. A theory has no use whatsoever if it cannot be tested for viability. It's a simple truth I realize it's disappointing to hear that from me but I would lying to state otherwise. It's easy to describe a toriod under geometry. The mathematics exist for Bohmian guiding wave action so at least a large part of the legwork is available. That would be a good start.

Funstrating isn't it. You know somethings there but you can't define it. Any infinite quantity has a finite portion but the finite portion is outside R=0

An important detail as Markus just mentioned R=0, cannot be defined The mathematics breaks down is the short hand descriptive. Its also not part of any finite group. We can't define anything particle related there as well. For the same reasons...if you can't define the spacetime the particles would reside in. Its impossible to define any particle presence

That's ok anyone can easily confirm the first equation is the photon propogator its in dozens of textbooks. It a standard form for the Feymann rules. Including the one I provided lmao however thanks for the support. Takes time but it can be accomplished. If you really want to learn I would start with vectors and spinors learn their components and addition rules. Then do so under field treatments. Once you do that GR becomes rather easy. To get a handle on QM and QFT statistical mechanics is the next route as it also uses the vectors/ spinors. Path integrals uses momentum space hence you need the above as its momentum space/phase space includes probability wavefunctions for all possible paths (path taken is the least action). The amplitude of that wavefunction giving the highest probability ( the weighted sum). Those probabilities are determined using Fourier transformations. QFT uses the Klein Gordon equation which is Lorentz invariant. However QM uses the Schrodinger equation which is not Lorentz invariant. This also means the photon propagator can come in different forms depending on the gauge its being applied in. There is also a couple of different forms for Feymann. So you can easily see a solid understanding of vectors/ spinors as standalone and as fields is essential and applies at all levels of physics and in every physics theory. Start there the rest will come far easier by default. should also mention calculus of variations is also applicable for integrals

That is why I don't waste my time trying if they can't take the time to show the error. I don't mind being corrected but I won't change what I've been professionally taught on someone's word without collaborative proof. Certainly not from some bland statement of being wrong without any further detail

whatever you wish to believe I seriously doubt you know how to use any of the equations I mentioned nor have any real understanding of particle physics to begin with. I won't waste any of my time with you either considering I actually hold a degree in particle physics I don't need to . Go ahead mathematically show me being incorrect with the formulas I provided. Impress me beyond your bland statements of me making errors Prove your case instead of simply declaring errors. If you wish to accuse me of errors you had best back it up.

There is 195 Countries in the World. Plenty of those countries also have UFO sightings. They all have their own policies on classified information. So how can secrecy through classification have any real meaning on UFO's ? They also have their own research programs

of course if you want to avoid all that math a simpler way would be to use the Langrangian representation for the photon as opposed to the antiphoton. the relativistic Langrangian of a free photon is \[\mathcal{L}_0-\frac{\epsilon\hbar}{c}v\cdot \omega\] where \(\epsilon\) in this case is the helicity + for photon - for antiphoton. The conjugate momentum is the linear momentum \[p-\partial\mathcal{L}_0\partial v=\frac{e\hbar\omega}{c}\] the energy of the photon and antiphoton is \[H-\pm\hbar\omega-\hbar v\] + for photon - for antiphoton. \[H=p\cdot v+s\cdot \omega-L_0-s\cdot \omega\cdot v\] so now I've shown two methods that describe the same thing....if you like I can skip to the creation annihilation operator method... just let me know or you can pick up quantum field theory Demystified it has an excellent section on it. for all the previous its the QM methodology and applies their operators (position and momentum) if you have further doubts then please start a new thread so we don't hijack this one. PS probably the easiest example of how photons interact and how cross sections are applied study Thompson scatterings. Though they likely won't show the anti-photon it will demonstrate the importance of cross sections

You can easily confirm what I state by simply googling Shall I do it for you "Some particles, such as the photon, are their own antiparticle. Otherwise, for each pair of antiparticle partners, one is designated as the normal particle " https://en.m.wikipedia.org/wiki/Antiparticle There that wasn't too hard was it ? Took me less than 10 seconds.... As far as Breit Wigner and Fermann integrals https://pdg.lbl.gov/2011/reviews/rpp2011-rev-cross-section-formulae.pdf For Breit Wigner. Feymanns golden rule https://en.m.wikipedia.org/wiki/Fermi's_golden_rule#:~:text=In quantum physics%2C Fermi's golden,result of a weak perturbation. Anything else I can do for you? how about providing you the Feymann integral itself for the photon. photon \[i\Delta_{\mu\nu}(k)=\frac{i}{-k^2-i\epsilon}[g_{\mu\nu}-\frac{k_\mu k_\nu}{k^2}(1=\alpha)\] antiphoton \[i\Delta_{\mu\nu}(k)=-\frac{i}{-k^2-i\epsilon}[g_{\mu\nu}-\frac{k_\mu k_\nu}{k^2}(1=\alpha)\] notice the only difference is the sign so if the two encounter each other they annihilate. However that is true for every particle antiparticle pair regardless if it is its own antiparticle or has a difference in charge...μ is the polarization index rule 4 of the Feymann rules is you symmetrice between identical bosons as the anti-photon is antisymmetric to begin with you follow the Dirac rules for asymmetric particles in essence fermionic rules. you Multiply \(\mu\) with \(\epsilon^*_\mu\) for incoming particles and \(\epsilon_\mu \)for outgoing particles. \(\epsilon\) is the dimensional regularization parameter. (renormalization ).The rest of the Feymann rules I suggest you get a decent textbook on the topic. There is 10 primary rules. However their are also special rules for different theories such as \(\phi^3\) or \(\phi^4\) here is Fermi's golden rule ( prefer the format) Fermi's Golden Rule \[\Gamma=\frac{2\pi}{\hbar}|V_{fi}|^2\frac{dN}{DE_f}\] density of states \[\langle x|\psi\rangle\propto exp(ik\cdot x)\] with periodic boundary condition as "a"\[k_x=2\pi n/a\] number of momentum states \[dN=\frac{d^3p}{(2\pi)^2}V\] decay rate \[\Gamma\] Hamilton coupling matrix element between initial and final state \[V_{fi}\] density of final state \[\frac{dN}{dE_f}\] number of particles remaining at time t (decay law) \[\frac{dN}{dt}=-\Gamma N\] average proper lifetime probability \[p(t)\delta t=-\frac{1}{N}\frac{dN}{dt}\delta t=\Gamma\exp-(\Gamma t)\delta t\] mean lifetime \[\tau=<t>=\frac{\int_0^\infty tp (t) dt}{\int_0^\infty p (t) dt}=\frac{1}{\Gamma}\] relativistic decay rate set \[L_o=\beta\gamma c\tau\] average number after some distance x \[N=N_0\exp(-x/l_0)\] as opposed to here but they are equivalent. https://en.wikipedia.org/wiki/Fermi's_golden_rule here is some relevant details on Breit Wigner cross sections. Breit Wigner cross section \[\sigma(E)=\frac{2J+1}{2s_1+1)(2S_2+1)}\frac{4\pi}{k^2}[\frac{\Gamma^2/4}{(E-E_0)^2+\Gamma/4)}]B_{in}B_{out}\] E=c.m energy, J is spin of resonance, (2S_1+1)(2s_2+1) is the #of polarization states of the two incident particles, the c.m., initial momentum k E_0 is the energy c.m. at resonance, \Gamma is full width at half max amplitude, B_[in} B_{out] are the initial and final state for narrow resonance the [] can be replaced by \[\pi\Gamma\delta(E-E_0)^2/2\] The production of point-like, spin-1/2 fermions in e+e− annihilation through a virtual photon at c.m. \[e^+,e^-\longrightarrow\gamma^\ast\longrightarrow f\bar{f}\] \[\frac{d\sigma}{d\Omega}=N_c{\alpha^2}{4S}\beta[1+\cos^2\theta+(1-\beta^2)\sin^2\theta]Q^2_f\] where \[\beta=v/c\] c/m frame scattering angle \[\theta\] fermion charge \[Q_f\] if factor [N_c=1=charged leptons if N_c=3 for quarks. if v=c then (ultrarelativistic particles) \[\sigma=N_cQ^2_f\frac{4\pi\alpha^2}{3s}=N_cQ^2_f\frac{86.8 nb}{s (GeV^2)}\] 2 pair quark to 2 pair quark \[\frac{d\sigma}{d\Omega}(q\bar{q}\rightarrow \acute{q}\acute{\bar{q}})=\frac{\alpha^2_s}{9s}\frac{t^2+u^2}{s^2}\] cross pair symmetry gives \[\frac{d\sigma}{d\Omega}(q\bar{q}\rightarrow \acute{q}\acute{\bar{q}})=\frac{\alpha^2_s}{9s}\frac{t^2+u^2}{t^2}\] The last details I copied from my own research of with regards to Early universe processes including electroweak symmetry breaking. You can find plenty of examples of how to use them here https://www.scienceforums.net/topic/128332-early-universe-nucleosynthesis/ if you really want to learn Feymannintegrals I suggest Feynman Integrals Stefan Weinzierl https://arxiv.org/abs/2201.03593 providing precise step by step on a forum is quite frankly impossible. For example it would take literal pages to explain the Casimer trick for sum of amplitudes for the path integrals. Let alone using Feymann's trick for the integrals. thankfully tools such as Mathematica with the Feycalc package can handle those steps. PS anyone familiar with Breit Wigner may notice that the Fermi golden rule is integrated into the Breit Wigner formula

Well the problem with the dark matter spectrum is that indirect evidence gives all the characteristics of either a weakly interactive particle likely candidate being right hand neutrinos ( this is the main focus of my research at the Professional level) or axioms. Being weakly interactive you don't get clumping as you would with matter. So it's rather tricky to get stars made up of dark matter. As evidence points toward " does not interact with EM force." Clumping is highly unlikely. The same goes with the strong force. A weakly interactive particle may interact with other weakly interactive particles such as other neutrinos . The Higgs field for mass terms and gravity. For detection using EM any viable detection so far involves x rays due to specific interactions so we can only get indirect evidence using the EM spectrum. Other indirect evidence being the mass terms with gravity. I don't find anything beyond the above too likely but who knows I could be wrong on that. However from my research I strongly consider right hand neutrinos as the most likely candidate.

Agreed on that, there are cases where the witness really didn't want the attention. One would tend to give those witnesses greater credibility. Doesn't mean a mistaken identity wasn't involved etc etc. I tend to have more respect for the cases where it's clear the motivation has nothing to do than generate monetary gain or attention seeking.

I personally don't base my opinion of any physicist by how popular they are in the media etc. Yes they tend to excel at taking complex topics and simplifying for the public which is very useful and beneficial. It generates interest to help generate new students as well as enhances interest for research etc. So that's never a bad thing. However I tend to focus on their research papers etc. Neil DeGrasse papers aren't bad but someone like Sean Carroll has a wider range of recommended literature. However that's just me

One thing I learned over the years is monetary gain isn't the only reason for hoaxes or seeking fame. Many cases is simply a means to get attention. It's not just restricted to UFO sightings either but literally every aspect of science when you include all the alternate and wildly exotic articles you find on the internet.

It's best to regard spacetime as simply the arena where the SM model of particles/fields reside. It really is simply a volume that uses the Interval (ct) to give time dimensionality of a length. Spacetime curvature under this describes the particle paths and the easiest way to understand this is to use parallel transport. (The equations of the EFE also uses parallel transport) If spacetime is flat two parallel beams of light will remain parallel. If you have positve curvature those beams will converge. If you have negative curvature they will diverge. For gravity use the same manner. Draw two lines at some distance apart and connect them to the CoM. You will notice those lines converge as you approach the centre of mass. Another useful tool to understand why particles follow different paths is to realize that all particle motion obeys the principle of least action. (This includes Feymann integrals as well as spacetime geodesics). Terms such as fabric etc gives false impressions of spacetime being some material or substance. It really is simply a metric that describes a volume and spacetime paths (null geodesics for massless particles such as photons). What affects the paths is all matter and force fields of the SM model. The coupling constants collectively give rise to the mass terms (mass is resistance to inertia change). They also have strange stars that suggest with certain neutron stars all quarks become strange quarks. Some models really stretch the imagination but surprisingly enough do have enough viability to warrant research. As for myself I study some of these as they often include unique ways to mathematically describe fields and states that I find useful for model developments. They also have papers suggesting a dark sector of a wide range of particles such as dark photons etc. Yeah I don't agree with the theory myself I ran across it a few years back.

All All good Found a decent article for the OP though older describes the proton-neutron ratios of exchange in our atmosphere due to cosmic ray interaction. " At sea level, neutrons contribute about 10 percent of the total radiation exposure to man from cosmic rays (ref. 1). Neutrons reaching the Earth's surface are principally created in the Earth's atmosphere by the interaction of the primary cosmic rays with oxygen and nitrogen nuclei at high altitudes and in the subsequent development of a hadronic cascade down through the atmosphere. (Relatively few neutrons are present in the primary galactic cosmic radiation or solar radiation reaching the Earth because their radioactive half-life is approximately 12 min.) Two nuclear reactions are important in the production of cosmic-ray neutrons: direct inelastic reactions producing "knock-on" neutrons, with energies from about 1 MeV to well in excess of 1 GeV, and evaporation " https://ntrs.nasa.gov/api/citations/19760008919/downloads/19760008919.pdf

Who claims we don't research the possibility? However one shouldn't ignore other research simply because it doesn't match what they wish to prove.

Lack of any confirmations from other sources is one factor. Let's try this tact I have recognized expertise in physics. Does that automatically mean everything I state is the factual ? Simply having some qualification doesn't mean the person isn't fallible or necessarily even telling the truth. Without going into names their are numerous accredited experts with PH.Ds in physics that write articles where I really wish to know what glue they were sniffing. A good example was an arxiv article describing using nukes to peek beyond the EH...yes it was written by PH.D

Oh I read the article I simply don't find it convincing. That's my conclusion after reading it. Simple as that

What of it, it's little different of any number of other impressive looking articles on sightings. It's certainly nothing that equates to an accepted and confirmed sighting. You may choose to believe that article and it's claims doesn't mean I'm about to.

Doubtful he mentioned chargeless as well as the correct mean lifetime for an unbound neutron