Mordred

\.begin{array}{rcl} a&b&c\\a&b&c\\a&b&c\end{array} \begin{array}{rcl} a&b&c\\a&b&c\\a&b&c\end{array} interesting the \begin{array} self activates f(z) = \left\{ \.begin{array}{rcl} a&b&c\\a&b&c\\a&b&c\end{array} \right . \[f(z) = \left\{ \begin{array}{rcl} a&b&c\\a&b&c\\a&b&c\end{array} \right .\]

\[\vec{v}_e+p\longrightarrow n+e^+\] \[\array{ n_e \searrow&&\nearrow n \\&\leadsto &\\p \nearrow && \searrow e^2}\]

your welcome glad to help

Correct now your getting it +1 on seeing that connection

It's a workable descriptive not completely accurate but sufficient for a layman understanding. Getting into the renormalization aspects would be a bit too advanced it's sufficient to accept that it's a renormalized value.

Well at least Chatgp got that part correct as that's precisely what it's used for. The VeV is used in a similar manner just an fyi

Here is the association of VeV to Fermi-constant Fermi's interaction - Wikipedia

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 \[|M|^2=E\acute{E}|M_0^2|=E\acute{E}(M_Pc^2)^2G^2_F\] \[\frac{d\sigma}{d\Omega}=(\frac{h}{8\pi}^2)\frac{M_pc^4(\acute{E})^2G^3_F}{[(E+M_p^2)-Ecos\theta]}\] \[\frac{d\sigma}{d\Omega}=(\frac{h}{8\pi}^2)\frac{M_pc^4(\acute{E})^2G^3_F}{M_pc^2}(1+\mathcal{O}(\frac{E}{M_oc^2})\] \[\sigma=(\frac{\hbar cG_F\acute{E}^2}{8\pi})^2\simeq 10^{-45} cm^2\] \

you won't find that equation in a textbook, textbooks only show the basic equations in math speak in this case you would usually see the first order equation this delves into the second order. just as most textbooks won't show the equation \[H_z=H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}}\] this shows the expansion rate H varies over time (it will also help to better understand the first equation as well as the Hogg paper I posted. now as you mentioned DM and DE one line of research is Higgs being responsible. Sterile neutrinos (right hand are heavier than left hand neutrinos ) antimatter and matter neutrinos. so the calculated abundance could fall into range \[\Omega_pdmh^2=\frac{G^{3/2}T_0^3h^2}{H_0\sigma v}=\frac{3*10-{27} cm^3s^{-1}}{\sigma v}\] research is still on going. Just as the equation of state for the Higgs field may explain inflation as well as the cosmological constant. That should sufficiently show that what really goes on in the professional circles isn't something one can simply google at best that just gives hints

no coordinate choice affects the mass distribution. I could describe the universe in numerous different coordinate choices example Euclidean, spherical cylindrical etc without causing any difference. It is precisely why we use invariance. The mathematics is set up that way so that we do not have any coordinate choice dependency. you know full well GR fully describes time dilation the FLRW metric is a GR solution. We don't arbitrarily choose DM and DE as the full explanation those two terms are simply placeholders until we can determine the cause of each. We still can measure their effects through indirect evidence. I rarely give downvotes so its someone else. As far as sampling range is concerned, redshift is only one of many pieces of evidence of an expanding universe. In point of detail its not even close to the strongest evidence. Its the one most ppl are familiar with but the real evidence comes from our thermodynamic laws in regards to temperature and how it influences the SM model of particles via processes such as BB nucleosynthesis in regards to the CMB. One danger of trying to understand cosmology by rote instead of learning the math is that too often you get incorrect information. I will give an example if I looked up hydrogen and its temperature it could form with stability a google search will state 3000 kelvin. However if one knows how to use the Saha equations that would reveal that value equates to 75 % of the potential hydrogen. Hydrogen can start to form as low as 6000 kelvin=25% 4000 kelvin for 50 %. That is just one example. however knowing this one can study the metallicity of our universe evolution via hydrogen, lithium, deuterium etc. So I just described another piece of evidence for expansion. In other words were not restricted to redshift to determine if our universe is expanding . In point of detail we do not rely on redshift in cosmology it is too full of other influences such as gravitational redshift, transverse redshift, Integrated Sache-Wolfe effect, Doppler redshift. etc etc. We examine all pieces of possible evidence to confirm the accuracy of cosmological redshift. Nor do we use the generic formula everyone sees on google. https://en.wikipedia.org/wiki/Redshift this formula only works for nearby objects it loses accuracy as near as one MPC. The full formula includes the influence of the evolution history of matter, radiation and Lambda. details can be found here "Distance measures in cosmology" David W. Hogg https://arxiv.org/abs/astro-ph/9905116 side note the paper also applies to luminosity distance we also have a different formula for Luminosity distance than what one would google. \[H_O dl=(1+z)|\Omega_k|^{-1/2}sinn[\Omega_k^{1/2} \int^z_o\frac{d\acute{z}}{\sqrt{(1+\acute{z})^2\Omega_R+(1+\acute{z}\Omega_m-\acute{z})(2+\acute{z})\Omega_\Lambda}}]\] What this equation shows is that matter, radiation and Lambda density not only influences expansion rates it also influences redshift and luminosity as well as any curvature term k

No there is no assumptions due to coordinate choice. You already know time dilation is a consequence of spacetime curvature or Relativistic inertia. The math and observational evidence shows us that there is no curvature term k=0. So where would you get time dilation ? This has already previously been mentioned. As massless particles travel at c we can ignore the inertial gamma factor. A higher density past the answer either. To go into greater detail if you take 3 time slices say time now, time at the CMB say z=1100. And a slice at say universe age 7 billion years old. If you describe the geometry of each slice. Each slice has a uniform mass distribution so no slice has a non uniform mass distribution to have a curvature term. Hint this is the real advantage of the scale factor a. No time slice has any change in geometry or curvature it's simply volume change between slices and density changes as a result of the ideal gas laws

Without looking at that link as the material needs to be posted here. The math done in that paper was done by your colleague correct ? By your statement above he refused to describe the mathematics in regards to quantum Strangeness so that paper wouldn't contain that detail with the needed math. Using toroids is nothing new in physics a cyclotron can be described using a toriod geometry. Yes you can mathematically describe any geometry in regards to an earlier comment of yours. Regardless if the person who did the math refused your conjecture then that wouldn't have the math beyond what the two of you were working on.

Add kinematics as it's used in every physics theory including the entirety of the SM model f=ma always applies for example.

Ok let's make it easier for when your looking at Higgs related papers E is energy , \(\rho\) is energy density, v is used for VeV. Think of VeV as a coupling constant for Higgs interactions a lot of the equations apply it in that manner. Energy is the ability to perform work. Energy density is the mean average over some field volume. Three distinct properties with distinctions in the mathematics Hope that helps

Correct the only direct confirmation is via LHC and Atlas etc. Studies are continually improving at each CERN LHC etc upgrade. We barely hit the required energy levels in 2012 so yes research is continually improving.

Usually first and second year QM. However I should mention those boring lessons your getting now will apply at every level of physics. In particular any physics involving kinematics. However this prevent you from learning QM early on.

inflationary gravity waves Weak field limit transverse , traceless components with \(R_{\mu\nu}=0\) \[h^\mu_\mu=0\] \[\partial_\mu h^{\mu\nu}=\partial_\mu h^{\nu\mu}=0\] \[R_{\mu\nu}=8\pi G_N(T_{\mu\nu}-\frac{1}{2}T^\rho_\rho g_{\mu\nu})\] vacuum T=0 so \(\square h_{\mu\nu}=0\) transverse traceless wave equation \[\nabla^2h-\frac{\partial^2h}{c^2\partial t^2}=\frac{16\pi G_N}{c^4}T\] inhomogeneous perturbations of the RW metric \[ds^2=(1+2A)dt^2-2RB_idtdx^i-R^2[(1+2C)\delta_{ij}+\partial_i\partial_j E+h_{ij}]dx^idx^j\] where A,B,E and C are scalar perturbations while \(h_{ij}\) are the transverse traceless tensor metric perturbations each tensor mode with wave vector k has two transverse traceless polarizations. \[h_{ij}(\vec{k})=h_\vec{k} \bar{q}_{ij}+h_\vec{k} \bar{q}_{ij}\] *+x* polarizations The linearized Einstein equations then yield the same evolution equation for the amplitude as that for a massless field in RW spacetime. \[\ddot{h}_\vec{k}+3H\dot{h}_\vec{k}+\frac{k^2}{R^2}h_\vec{k}=0\] https://pdg.lbl.gov/2018/reviews/rpp2018-rev-inflation.pdf

Just to add for acceleration involving change in direction will involve transverse redshift. Just to add some useful relations more for the benefit of any readers not familiar with the types of redshift. \[\frac{\Delta_f}{f} = \frac{\lambda}{\lambda_o} = \frac{v}{c}=\frac{E_o}{E}=1+\frac{hc}{\lambda_o} \frac{\lambda}{hc}\] Doppler shift \[z=\frac{v}{c}\] Relativistic Doppler redshift \[1+z=(1+\frac{v}{c})\gamma\] Transverse redshift \[1+z=\frac{1+v Cos\theta/c}{\sqrt{1-v^2/c^2}}\] If \(\theta=0 \) degrees this reduces to \[1+z=\sqrt\frac{1+v/c}{1-v/c}\] At right angles this gives a redshift even though the emitter is not moving away from the observer \[1+z=\frac{1}{\sqrt{1-v^2/c^2}}\] From this we can see the constant velocity twin will have a transverse Doppler even though the velocity is constant. The acceleration as per change in velocity is straight forward with the above equations as the redshift/blueshift will continously change with the change in velocity term. The equations in this link will help better understand the equivalence principle in regards to gravity wells such as a planet https://en.m.wikipedia.org/wiki/Pound–Rebka_experiment The non relativistic form being \[\acute{f}=f(1+\frac{gh}{c^2})\]

In essence that's correct without going too indepth on the differences between operators and propogators of QFT. You can accurately treat it as a fundamental constant of the Higgs field with regards to how the field couples to other particles for the mass term I really wouldn't trust Chatgp your far better off in this regard studying the standard model via the Lanqrangian equations. For the W boson it's the SU(2) group and U(1) groups for the relevant details with Higgs. It's also why I recommended starting with Quantum field theory Demystified as it's reasonably well explained for the laymen to grasp.

The VeV isn't an issue it's something you observe only during scatterrings via say a particle accelerator it's a local property at each particle such as the W boson simply put a coupling term. The probabilities are much the same as the probabilities associated with Feymann path integrals. It isn't the vacuum energy density itself so it's not anywhere near Like the vacuum catastrophe from QM.

We cross posted Migl but I included a primary missing detail in terms of VEV being a probability value much like a weighted sum in statistics.

Might be easier to understand that in statistical mechanics, QM and QFT the expectation value is the probabilistic expected value of the result (measurement) of an experiment. It can be thought of as an average of all the possible outcomes of a measurement as weighted by their likelihood, and as such it is not the most probable value of a measurement. What that statement tells us is that it includes all possible outcomes. It is a probability function. Expectational values is used regularly in statistical mechanics, QM and QFT. Path integrals also have probability weighted sums

If your certain of your equations and it's validity I'm sure your going to want to test them. If you think about it I provided the essential equations to do just that with a given dataset such as Planck. I certainly do when I model build or simply test and cross check any new relations/interactions. Those equations apply LCDM. to the cosmological redshift. As far as a new value of G well all I can say to that is good freaking luck on that score with what you have shown so far. this is a listing of the various types of studies and results form them for variations of G tests for spatial dependence is page 200 onward http://www2.fisica.unlp.edu.ar/materias/FisGral2semestre2/Gillies.pdf

fair enough, something to keep in mind if your looking at cosmological redshift is that the expansion rates are not linear. The equation above shows this as the resultant is to determine the Hubble value at a given Z compared to the value today. The relations under the square root is the evolution of the energy density for matter, radiation and Lambda. You can learn these here. https://en.wikipedia.org/wiki/Equation_of_state_(cosmology) this related to the FLRW acecleration equations. described here https://en.wikipedia.org/wiki/Friedmann_equations that link supplies some very useful integrals with regards to the scale factor the evolution of the scale factor "a" using the above relations gives \[\frac{\ddot{a}}{a}=-\frac{4G}{3}(\rho+3P)+\frac{\Lambda}{3}\] however to get the FLRW metric cosmological redshift equation you will also need the Newton weak field limit treatments as per GR. Particularly for curvature K=0 if your interested in that let me know and I'll provide more details

ok First off you have vacuum energy and vacuum energy density confused. The first case though not a useful form for energy density. The VeV is the vacuum expectation value VeV this isn't the density. This is a term describing the effective action https://en.wikipedia.org/wiki/Effective_action for Higgs the effective action is defined by the equation \[v-\frac{1}{\sqrt{\sqrt{2}G^0_W}}=\frac{2M_W}{g}\] here \(M_W\) is the mass of the W boson and \( G^0_W\) is the reduced Fermi constant. These are used primarily when dealing with Feymann path integrals in scatterings or other particle to particle interactions involving Higgs in particular dealing with the CKMS mass mixing matrix. So its not your energy density more specifically they describe CKMS mixing angles or Weinberg mixing angles. for the above without going into too much detail the mixing angles are \[M_W=\frac{1}{2}gv\] \[M_Z=\frac{1}{COS\Theta_W}\frac{1}{2}gv=\frac{1}{Cos\theta_W}M_W\] more details can be found here. Page three I'm starting to compile the previous pages now if you want the vacuum energy density the FLRW has a useful equation. \[\rho_{crit} = \frac{3c^2H^2}{8\pi G}\] if you take the value of the Hubble constant today and plug it into that formula you will get approximately \(5.5\times 10^{-10} joules/m^3\) if you convert that over you will find your fairly close to 3.4 GeV/m^3 which matches depending on the dataset used for the Hubble constant. The confusion you had was simply not realizing the VeV isn't the energy density. hope that helps. I won't get into too many details of the quantum harmonic oscillator via zero point energy but if you take the zero point energy formula and integrate over momentum space d^3x you will end up with infinite energy. So you must renormalize by applying constraints on momentum space. However even following the renormalization procedure you still end up 120 orders of magnitude too high. There has been resolutions presented to this problem however nothing conclusive enough. Quantum field theory demystified by David Mcmahon has a decent coverage of the vacuum catastrophe edit forgot to add calculating the energy density for the cosmological constant uses the same procedure as per the critical density formula.