Mordred

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

Lol sorry I find what you described above even more restrictive on likelyhood. No of course you think restrictive likelyhood isn't an issue. I however feel it does apply and should always be considered. That's one of the reasons I rarely ever join threads involving aliens and UFOs the defenders of UFOs and Aliens always tend to ignore the odds against any likelihood. They also tend to come up with highly imaginative means of justification. I provided a few ideas on plausible means of travel and applied a bit of realistic physics. Take that as you will they are factors regardless of conjecture or opinion.

Absolutely agree on that lol

Yeah good luck with that. The point being simply achieving such a technological advanced state wouldn't be common place event. Hence it's restrictive on likelihood..... The other point being is that in order for one to justify alien visitation has huge restrictions on likelyhood. Yeah great possible sure.. what's the likelyhood of any system near enough to potentially matter ? Doesn't really work to justify that as actually occurring to justify our UFO sitings...

Sure but have you ever noticed is that those requirements are incredibly restrictive on any likelihood of existing in the first place ? Particularly when you start factoring in let's say age of stellar solar systems vs likelihood of achieving sufficient technological development for the scenario you just described. One of many

How about simple practicality ? It makes absolutely no sense to have to wait a century or more get information returned. You are well aware of time dilation for a craft in regards to the at home time frame compared to flight time. You cannot randomly ignore involved factors. Great you can send signals back at c. Yeeha so what ? You still have to get to Earth and factor in the time differentials for time dilation. It would be more practical to build a solar system scale telescope and get data faster.

Really and is that particularly practical unless the aliens live on some nearby star system where it's close enough we could detect chemical and biological signatures via spectography or recieve their signals ? Not very practical in my opinion. Your still looking at years for signals. Yeah that would certainly require some new physics lol. However unlikely still has some plausibility.

Do you want any information resulting from any studies to return to home planet ? It doesn't matter if the occupants are biological or not in that regard. What would be the point of any visitation if you cannot return with any data or resources

If you want turnaround to home planet in any reasonable time frame it's unavoidable even then its too slow for cosmological distances

Muc Much like that. It's a feasible possibility one could gather resources as they go but it would have to be of sufficient size for any manufacturing of those resources. As well as population growth. One could use the Oort cloud to hide in as their are lots of objects in the Oort cloud that escapes detection.

If we're sticking to known physics a feasible possibility being the Alcubierre drive it's feasible if one can solve the solutions for reduced energy requirements and eliminate any need for negative mass. Theoretically this would address the collision scenario as the spacetime bubble would cause deflection. However it also in turn generates a greater problem that the bubble may also cause gamma ray production. One study I'm familiar with showed that even at 50 percent c. That gamma ray production could wipe out life on the planet it's leaving and arriving at. However I've only ever come across the one paper on it. Other than that I can't think of any viable means that isn't a 1 way trip. Which really negates curious visitations. Colonization would be far more likely than visitation in a 1 way trip scenario. Though one other possibility is some species that lives strictly in space however that would require am extremely large craft with a huge infrastructure for resource production

That understanding is correct. The elephant your missing is that their are two categories (primarily) for cosmic rays. Primary and secondary. Primary cosmic rays are those sent from stellar objects like the Sun Secondary cosmic rays are those particles produced by the Primary rays interactions with our atmosphere. Neutrons are part of the secondary group. Part of that process includes mesons decays to that further allows leptons to form. Here is an examination of some of the different processes at different atmospheric levels https://pdg.lbl.gov/2019/reviews/rpp2019-rev-cosmic-rays.pdf

Cyclic universe models is one possible cause for our universe coming into existence. It does nothing to address how the first universe developed but for this thread your not concerned about that. This however doesn't really follow. The conditions of the BB according to mainstream physics was in a thermal equilibrium state. The extreme high temperature wouldn't even allow atoms to form. The four forces were in a state of thermal equilibrium. Once electroweak symmetry breaking occurs the 4 fources could separate. Gravity Em, weak and strong force. Particles could then drop out of thermal equilibrium. That's simply one process where it would be impossible for past information ideas etc would be literally obliterated even assuming such things could even survive the initial collapse of the previous universe.