Mordred

This particular article seems most appropriate to this thread The Double Slit Experiment and Quantum Mechanics https://www.hendrix.edu/uploadedFiles/Departments_and_Programs/Physics/Faculty/The Double Slit Experiment and Quantum Mechanics.pdf " Let me say this again to emphasize it. Your eyeball is covered with a large number of photon detectors. When you see something, each detector counts the number of photons it received and transmits that number to the brain. Some of the detectors (the cones) can detect the energy of the photons, and they transmit that value to the brain also (thus providing color vision). Your eyeball works much like the detector portion of a digital camera. You have never observed a light wave in your life, but you have added up the numbers of photons striking different places on your retina to create a diffraction pattern. To me, the most convincing evidence that all particles, including photons, are always detected as individual and whole particles was observing the output of a particle detector on an oscilloscope. The output is a series of pulses. Each pulse represents the passage of one particle (a photon, an electron, or whatever) through the detector. You get the same effect with an old fashioned geiger counter: each click represents the passage of a particle through the detector. If you have never had the opportunity to observe this, you should at least read Wikipedia’s article on particle detectors. "

So what ? any time a photon has a scattering event (interaction) the original photon is absorbed in inelastic scatterings such as a camera detecting the photon or the screen used in the detector. Elastic scatterings such as a mirror is a distinctively different process.

also doesn't help that I often have to edit latex etc so my posts tend to take a considerable time to complete and tend to get cross posted by numerous others as a result So I will readily take the blame or part of the blame in this case lmao This is some studies I've been working on in my spare time in my Nucleosynthesis thread in Speculations. For right hand neutrinos using Majaronna mass terms the related mass terms via CKMS and PMNS mass mixing matrices are as follows as nearly as I've been able to gather from research. I recognize that most won't understand below but its here to indicate that my earlier statement has validity. \[m\overline{\Psi}\Psi=(m\overline{\Psi_l}\Psi_r+\overline{\Psi_r}\Psi)\] \[\mathcal{L}=(D_\mu\Phi^\dagger)(D_\mu\Phi)-V(\Phi^\dagger\Phi)\] 4 effective degrees of freedom doublet complex scalar field. with \[D_\mu\Phi=(\partial_\mu+igW_\mu-\frac{i}{2}\acute{g}B_\mu)\Phi\]\ \[V(\Phi^\dagger\Phi)=-\mu^2\Phi^\dagger\Phi+\frac{1}{2}\lambda(\Phi^\dagger\Phi)^2,\mu^2>0\] in Unitary gauge \[\mathcal{L}=\frac{\lambda}{4}v^4\] \[+\frac{1}{2}\partial_\mu H \partial^\mu H-\lambda v^2H^2+\frac{\lambda}{\sqrt{2}}vH^3+\frac{\lambda}{8}H^4\] \[+\frac{1}{4}(v+(\frac{1}{2}H)^2(W_mu^1W_\mu^2W_\mu^3B_\mu)\begin{pmatrix}g^2&0&0&0\\0&g^2&0&0\\0&0&g^2&g\acute{g}\\0&0&\acute{g}g&\acute{g}^2 \end{pmatrix}\begin{pmatrix}W^{1\mu}\\W^{2\mu}\\W^{3\mu}\\B^\mu\end{pmatrix}\] Right hand neutrino singlet needs charge conjugate for Majorana mass term (singlet requirement) \[\Psi^c=C\overline{\Psi}^T\] charge conjugate spinor \[C=i\gamma^2\gamma^0\] Chirality \[P_L\Psi_R^C=\Psi_R\] mass term requires \[\overline\Psi^C\Psi\] grants gauge invariance for singlets only. \[\mathcal{L}_{v.mass}=hv_{ij}\overline{I}_{Li}V_{Rj}\Phi+\frac{1}{2}M_{ij}\overline{V_{ri}}V_{rj}+h.c\] Higgs expectation value turns the Higgs coupling matrix into the Dirac mass matrix. Majorana mass matrix eugenvalues can be much higher than the Dirac mass. diagonal of \[\Psi^L,\Psi_R\] leads to three light modes v_i with mass matrix \[m_v=-MD^{-1}M_D^T\] MajorN mass in typical GUT \[M\propto10^{15},,GeV\] further details on Majorana mass matrix https://arxiv.org/pdf/1307.0988.pdf https://arxiv.org/pdf/hep-ph/9702253.pdf The other detail is if the above has accuracy then the cross sections for anti neutrinos would be similar to below A possible antineutrino cross section calculation massless case \[\vec{v}_e+p\longrightarrow n+e^+\] Fermi constant=\(1.1663787(6)*10^{-4} GeV^{-2}\) \[\frac{d\sigma}{d\Omega}=\frac{S|M|^2\acute{p}^2}{M_2|\vec{p_1}|2|\vec{p_1}|(E_1+m_2c^2)-|\vec{p_1}|\prime{E_1}cos\theta}\] Fermi theory \[|M|^2=E\acute{E}|M_0^2|=E\acute{E}(M_Pc^2)^2G^2_F\] \[\frac{d\sigma}{d\Omega}=(\frac{h}{8\pi}^2)\frac{M_pc^4(\acute{E})^2G^3_F}{[(E+M_p^2)-Ecos\theta]}\] \[\frac{d\sigma}{d\Omega}=(\frac{h}{8\pi}^2)\frac{M_pc^4(\acute{E})^2G^3_F}{M_pc^2}(1+\mathcal{O}(\frac{E}{M_oc^2})\] \[\sigma=(\frac{\hbar cG_F\acute{E}^2}{8\pi})^2\simeq 10^{-45} cm^2\] prior to electroweak symmetry breaking A possible antineutrino cross section calculation massless case \[\vec{v}_e+p\longrightarrow n+e^+\] Fermi constant=\(1.1663787(6)*10^{-4} GeV^{-2}\) \[\frac{d\sigma}{d\Omega}=\frac{S|M|^2\acute{p}^2}{M_2|\vec{p_1}|2|\vec{p_1}|(E_1+m_2c^2)-|\vec{p_1}|\prime{E_1}cos\theta}\] Fermi theory \[|M|^2=E\acute{E}|M_0^2|=E\acute{E}(M_Pc^2)^2G^2_F\] \[\frac{d\sigma}{d\Omega}=(\frac{h}{8\pi}^2)\frac{M_pc^4(\acute{E})^2G^3_F}{[(E+M_p^2)-Ecos\theta]}\] \[\frac{d\sigma}{d\Omega}=(\frac{h}{8\pi}^2)\frac{M_pc^4(\acute{E})^2G^3_F}{M_pc^2}(1+\mathcal{O}(\frac{E}{M_oc^2})\] \[\sigma=(\frac{\hbar cG_F\acute{E}^2}{8\pi})^2\simeq 10^{-45} cm^2\] as stated this is simply to be informative that there is standard model methods to help make accurate predictions for something such as anti neutrinos prior to discovery and with this be able to look for signatures and evidence. This is an overview of the types of signatures were looking for this particular set of slides gives an example of the DM cross section under DM decay. https://www.hip.fi/cosmoseminars/wp-content/uploads/sites/15/2020/10/Drewes-2020.pdf related papers DARK MATTER AS STERILE NEUTRINOS http://arxiv.org/abs/1402.4119 http://arxiv.org/abs/1402.2301 http://arxiv.org/abs/1306.4954 in direct answer to the excellent question by the sterile neutrinos must have a mean lifetime longer than the age of the universe to match the cross section provided by https://www.hip.fi/cosmoseminars/wp-content/uploads/sites/15/2020/10/Drewes-2020.pdf further details on the reason for the mean lifetime provided by the article further articles Next decade of sterile neutrino studies by Alexey Boyarsky, Dmytro Iakubovskyi, Oleg Ruchayskiy https://arxiv.org/pdf/1306.4954.pdf Detection of An Unidentified Emission Line in the Stacked X-ray spectrum of Galaxy Clusters Esra Bulbul, Maxim Markevitch, Adam Foster, Randall K. Smith, Michael Loewenstein, Scott W. Randall https://arxiv.org/abs/1402.2301 Neutrino Masses, Mixing, and Oscillations Revised October 2021 by M.C. Gonzalez-Garcia (YITP, Stony Brook; ICREA, Barcelona; ICC, U. of Barcelona) and M. Yokoyama (UTokyo; Kavli IPMU (WPI), UTokyo). https://pdg.lbl.gov/2022/reviews/rpp2022-rev-neutrino-mixing.pdf this portion will help relate Fermi's Golden rules in terms of those cross sections provided including mean lifetime from the Breit Wigner distrbution cross sections. 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 \[N=N_0\exp(-x/l_0)\]

You raise some good points @Markus Hanke there so I'm going to detail the above interms of how N=Body codes such as Gadget use in Millenium and the Mare-Nordstrum simulation apply the above factors described by your sand dune analogy. There is several stages to consider Jeans instability which provide in-fall rates due to gravitational collapse https://en.wikipedia.org/wiki/Jeans_instability the expansion rates must also be considered as well as the momentum terms of the particles involved. At first the density perturbations are linear however as they deviate from linear to non linear there is an intermediate stage where one doesn't require a full non linear treatment. This is the Zel'Dovich approximation \[\vec{r}(t)=a(t)\vec{x}+b(t)\vec{f}(\vec{x})\] the first term is the expansion rates and the second term is the peculiar velocities of the vector field \(\vec{f}(t)\) The formula shows a production of voids separated by walls of dark matter https://en.wikipedia.org/wiki/Zeldovich_pancake now the problem with this is that it will break down when the density perturbations start crossing each other so we then have to employ a full non-linear treatment \[\frac{d^2 \vec{r}_i(t)}{dt^2}=\sum_{k\neq i}\frac{GM_k m_i}{|\vec{r}_k-\vec{r}_i|^2}(\vec{r}_k-\vec{r}_i)\] the above is incredibly difficult to compute for large N body simulations so one has to employ Fourier transformations to solve the Poisson equations this leads to PM (particle_Mesh) https://en.wikipedia.org/wiki/Particle_mesh and the improvement P3M (particle-particle-particle-mesh) https://en.wikipedia.org/wiki/P3M for DM halos itself one can employ the spherical symmetric approximation Press-Schechter mass function for halos https://en.wikipedia.org/wiki/Press–Schechter_formalism all the above naturally involve https://en.wikipedia.org/wiki/Virial_theorem so as one can see the situation is extremely complex for large N-Body simulations which is the fundamental point you raised in your post @joigus answered this In the same manner as GR though with the new applicable mass terms MOND is compatible with GR yes the above is correct and how you described DM does allow for halo formation but also as the filament to void separations of LSS filament structure. See above for the related formulas edit forgot to add an important detail Zel'dovich pancake development actually leads to the NFW profile use for galaxy rotation curves. https://en.wikipedia.org/wiki/Navarro–Frenk–White_profile

We aren't incapable but no single set of equations solve every problem. GR by itself isn't suitable to deal with infall rates v outfall rates as applicable to LSS and galaxy formation, nor formation of DM halos. Other hydrostatic formulas are required. I will be detailing those involved as I had planned on doing so in regards to Markus last post using his sand dune analogy. (though I will drop the analogy itself.)

Ever use light sensors you don't require a brain to detect light. Take an infrared camera for example you can see plants in the camera though it won't show as green lol not only does sunlight reach plants aka photosynthesis but they can also absorb and emit light. The main point however is that you can detect light by other means other than the human brain.

It's not that GR is inaccurate. The difficulty is that with a galaxy you have an axisymmetric spacetime with a disk that also has rotation. That only covers certain galaxy types. Each galaxy type would require its own set of EFE solutions. If you look at the links I included in response to Migl you will see a proposed set of solutions for spiral galaxies.

Zwicky did use the mass luminosity relations to make his velocity determination. Though Oort also did as well. Invariably the mass-luminosity relations is required though that often gets missed as most ppl typically focus on the redshift relations. Both are involved, in point of detail in this instance in order to determine redshift you need the mass luminosity relations to begin with however for some reason readers don't find the luminosity relations itself as relevant as the redshift... I will leave it in the hands of the historians as to who is considered the father of DM.

ditto this can easily get sidetracked.

Noted I didn't think you were arguing with me though. I however did want to add detail beyond the rough and tumble earlier post which I couldn't do at work. yes what you have is correct I suspect the notational differences is from the usage of spectral decomposition. I don't know how familiar you are with spectral decompositions but in essence \(\lambda\) is the eugenvalue with orthonormal vectors eugenvectors U. So your recasting a symmetric d x d matrix M \[u_i \cdot u_j=\epsilon _{ij}\] the lambda term are diagonal under matrix \(\Lambda\) values \(\lambda_1, \lambda_2....\lambda_d\) you also have matrix Q where U_d is on columns and matrix Q^T where the U_d are row vectors. \[M=\sum^d_{i=1}\lambda_iu_iu_i^T\] where any U is linearly independent. For any i \(Q\Lambda Q^Tu_i=Q\Lambda=Mu_i\) with U_I being orthonormal \(QTq=I\) thus Q is invertible so for any j \[(\sum_i\lambda u_iu_i^T)u_j=\lambda_ju_j=Mu_j\] so \[M=\sum_i\lambda_i u_iu_i^T\] https://www.stat.ucdavis.edu/~xdgli/Xiaodong_Li_Teaching_files/135Note1.pdf the notation of this article is a bit different but essentially the same relations I have in this post. Hopefully though this will help however as we don't want to get too sidetracked from your last post I am in agreement that's its more a notational mayhem likely through the use of spectral index notations. course it also doesn't help that even with spectral decompositions no two articles use the same nomenclature.

yes There are treatments using the EFE here is one example https://arxiv.org/pdf/2405.04933 another example using Gravitomagnetism https://arxiv.org/pdf/2303.06115 one article I particularly like that isn't model specific other than GR. TOWARDS A FULL GENERAL RELATIVISTIC APPROACH TO GALAXIES https://arxiv.org/pdf/2106.12818

not quite lol though still +1 \[e^{\lambda_j t}\] is the directional derivative taking the previous Hamilton statement under spectral decomposition. see here in regards to Hermitean directional derivatives https://en.wikipedia.org/wiki/Matrix_exponential look under Directional derivatives under \[G_{ij}\] though I will use my get out of jail card for forgetting to mention its a restricted directional example for simplification. Your likely more familiar with the form \[H|\psi(t)\rangle=i\hbar|\psi(t)\] \[\psi(t)=exp(-\frac{iH(t)}{\hbar})\] \[U=exp(-\frac{iH(t)}{\hbar})\]

Lets do a simple example (though unless you understand QM won't really be simple) Unitary space \[\langle u,v\rangle=\mathbb{C}^n\] you have the inner products of a complex unitary space (Hilbert space). In terms of the Schrodinger equation the continous evolution must take the form \[\rho\rightarrow U\rho U^\dagger\] where U is the unitary operator. the Hamilton governing this is \[H=\sum^d_{j=1}\lambda_j|j\rangle\langle j|\] which gives unitary form \[U=\sum^d_{j=1}e^{\lambda_j t}|j\rangle\langle j|\] in other words one requires a bit of preliminary mathematics and QM to understand the above. Example the d above the sum is not dimension it is an integer defined by a renormalization scheme. Seeing that above the sum automatically tells me its a normalized state

Key word Unitary operator. For example how is an operator defined under QM ? What makes that operator Unitary? 2 key operators in QM position and momentum. These however are not the Unitary operators Doesn't describe the Unitary operator itself given as \[U^\ast U=1\] The Unitary operator must preserve the inner product of the Hilbert space. Keep in mind I'm trying to avoid terminology such as bounded, isomorphism , adjoint etc. An easy example is the rotation matrices these are Unitary operators. A unitary operator can change to orientation, coordinates or state itself but cannot change the magnitude (norm of the state). Every Unitary operator is normal. Categories of Unitary operators being Unitary space, Unitary transformation, or Unitary matrix. A Unitary space is a complex vector field with a distinguished positive definate Hermitean form A Unitiary transform is a surjective transform between two Unitary spaces U,V. A Unitary matrix is a complex valued matrix whose inverse is equal to its conjugate transpose. See why I stated very rough and gritty in the above ?

Unitary is equivalent to normalized in essence. So take a unit vector that unit vector is normalized to value 1. So for example \(c=\hbar=K=1\) Now as you cannot have a negative probability by multiplying the square of the probability amplitude you get a positive value. The conserved portion requires a closed group or system where you have no forces involved for conservation of momentum example being the Schrodinger equation you normalize the group and that group is finite. Example 1 loop integral is a closed group. That's a rough and gritty explanation the details get more intense.

New paper regarding Hubble contention https://arxiv.org/abs/2408.06153 Edit forgot to add a few years back local cluster measurements by HOLICOW were not matching up to CMB measurements. The bulk of the research as to cause from what I've been able to gather have been in regards to local group calibrations similar to the above paper.

It's one of the possibilities though one that I find rather tricky particularly when you further consider a few details. Those details include the need for DM for early universe large scale structure formation. Gravitational lensing effects not fully accountable by nearby baryonic matter. Another detail is often missed is that when one goes to measure galaxy rotation curves it's necessary to use mass to luminosity relations. The Mass to luminosity relations show that only 10 to 20 percent the total luminosity can be accounted by baryonic matter content. Even though DM doesn't interact with the EM field it does affect gravity. It is this effect that further shows up in the mass luminosity relations. Part of my courses was using spectography to examine M31 and other local galaxies and examine the mass-luminosity to rotation curves. This is one detail Zwicky noted when he first examined rotation curves and pushed the examinations beyond mathematical error. One you rarely ever see discussed is the integrated early and late time Sache Wolfe effects due to overdensity and underdensity regions (this effect also includes localized expansion rates ). Other possibilities not mentioned yet being Machos and axioms. Though those possibilities I don't follow but they are still current approaches.

Ad block works for my laptop using chrome for my android I use ad Block with Samsung internet Explorer.

As far as opinions on DM I've always leaned toward sterile neutrinos even though I have examined treatments using Majaronna mass coupling RH neutrinos and 3 species I still haven't seen how to account for the total mass. The research is still ongoing in that regard.

Interesting product and yes a pocket size Geiger counter would be useful for a large number of industries provided they have accuracy. Thanks for pointing +1

Bye hopefully when you come back your attitude is improved.

For someone who claims to be correct you certainly missses applying Newtons three laws of inertia. Which is the reason Swansont gave you the correct reply. Think about your scenario and apply all three laws.

Been examining a newer way of looking at Feymann integrals that greatly helps simplify some of the mathematics. The method employs the charge conjugation relations to simplify allowable interactions on Feymann integrals. https://arxiv.org/pdf/hep-ph/9601359 Figured this would get a bit of interest for discussion.

I will have to read that book sometime could be enertaining

It's done in the FLRW metric for any time period prior to the dark ages prior to recombination and the detection availability is the CMB (indirect signature detection). However that requires math using known physics.