Mordred

The intended purpose will be to eventually migrate this into a full article using current cosmological parameters. Its a project I've been building towards for several years now and has always been a primary focus of my studies. Now I'd like to formalize it however evidently there is issues going on with lengthy edits as I just lost all the latex work above yet again lmao

good plan will do as much as possible

This thread will take me a considerable amount of time as I will be examining various treatments of BB nucleosynthesis and development of an eventual article of processes involved. for the initial stages I will simply be gathering the relevant formulas. Prior to symmetry Break Relevant equations The FLRW metric of the LCDM universe is used by the LCDM model of the Big bang to describe the evolution history of our Observable universe. The model starts at 10^{-43} seconds forward from a low entropy, hot dense state. One plausible explanation of how our universe began prior to that include quantum fluctuations. The model only describes our Observable portion as we do not know what occurs beyond the Cosmological event horizon. The FLRW metric is given as follows \[d{s^2}=-{c^2}d{t^2}+a({t^2})[d{r^2}+{S,k}{(r)^2}d\Omega^2]\] \[S\kappa(r)= \begin{cases} R sin(r/R &(k=+1)\\ r &(k=0)\\ R sin(r/R) &(k=-1) \end {cases}\] where k is the curvature term, a is the scale factor both being dimensionless quantities. The contributions of each particle species via their corresponding equations of state is determines how our universe expands. The evolution history can be determines as a function of Cosmological redshift via the following equation \[H_z=H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}}\] where the standard model may be represented by the covariant derivative form of the Langrangian \[\mathcal{L}=\underbrace{\mathbb{R}}_{GR}-\overbrace{\underbrace{\frac{1}{4}F_{\mu\nu}F^{\mu\nu}}_{Yang-Mills}}^{Maxwell}+\underbrace{i\overline{\psi}\gamma^\mu D_\mu \psi}_{Dirac}+\underbrace{|D_\mu h|^2-V(|h|)}_{Higgs}+\underbrace{h\overline{\psi}\psi}_{Yukawa}\] \[V_{ckm}=V^\dagger_{\mu L} V_{dL}\] The gauge group of electroweak interactions is \[SU(2)_L\otimes U(1)_Y\] where left handed quarks are in doublets of \[ SU(2)_L\] while right handed quarks are in singlets the electroweak interaction is given by the Langrangian \[\mathcal{L}=-\frac{1}{4}W^a_{\mu\nu}W^{\mu\nu}_a-\frac{1}{4}B_{\mu\nu}B^{\mu\nu}+\overline{\Psi}i\gamma_\mu D^\mu \Psi\] where \[W^{1,2,3},B_\mu\] are the four spin 1 boson fields associated to the generators of the gauge transformation \[\Psi\] The 3 generators of the \[SU(2)_L\] transformation are the three isospin operator components \[t^a=\frac{1}{2} \tau^a \] with \[\tau^a \] being the Pauli matrix and the generator of \[U(1)_\gamma\] being the weak hypercharge operator. The weak isospin "I" and hyper charge \[\gamma\] are related to the electric charge Q and given as \[Q+I^3+\frac{\gamma}{2}\] with quarks and lepton fields organized in left-handed doublets and right-handed singlets: the covariant derivative is given as \[D^\mu=\partial_\mu+igW_\mu\frac{\tau}{2}-\frac{i\acute{g}}{2}B_\mu\] \[\begin{pmatrix}V_\ell\\\ell\end{pmatrix}_L,\ell_R,\begin{pmatrix}u\\d\end{pmatrix}_,u_R,d_R\] The mass eugenstates given by the Weinberg angles are \[W\pm_\mu=\sqrt{\frac{1}{2}}(W^1_\mu\mp i W_\mu^2)\] with the photon and Z boson given as \[A_\mu=B\mu cos\theta_W+W^3_\mu sin\theta_W\] \[Z_\mu=B\mu sin\theta_W+W^3_\mu cos\theta_W\] the mass mixings are given by the CKM matrix below \[\begin{pmatrix}\acute{d}\\\acute{s}\\\acute{b}\end{pmatrix}\begin{pmatrix}V_{ud}&V_{us}&V_{ub}\\V_{cd}&V_{cs}&V_{cb}\\V_{td}&V_{ts}&V_{tb}\end{pmatrix}\begin{pmatrix}d\\s\\b\end{pmatrix}\] Bose Einstein Statistics \[n_i = \frac {g_i} {e^{(\varepsilon_i-\mu)/kT} - 1}\] Fermi-Dirac statistics \[ n_i = \frac{g_i}{e^{(\epsilon_i-\mu) / k T} + 1}\] Maxwell Boltzmann \[\frac{N_i}{N} = \frac {g_i} {e^{(\epsilon_i-\mu)/kT}} = \frac{g_i e^{-\epsilon_i/kT}}{Z}\] Saha Boltzmann equation (calculate hydrogen decoupling \[\frac{n_i+n_e}{n_i}=\frac{2}{\omega^3}\frac{g_i+1}{g_i}exp[-\frac{(\epsilon_i+1-\epsilon_i)}{k_BT}\]

The ones I find frustrating are the posters that resort to insult tactics after you spend considerable time trying to correct misconceptions, explain why they are wrong, or describe something that you support with material written by professionals in a particular field. It truly does make one feel that they are literally wasting their time. In those circumstances it never seems to matter how much supportive documentations such as professional peer review material, the relevant mathematics etc you present to support your statements. In those cases I have to constantly remind myself that even when you cannot help said individual you invariably help other readers. Eventually though one has to report the individual which the moderation staff does an excellent job of cooling the situation down.

Well that's a first I never heard of Vaidya spacetime any recommended literature on it ? I spotted this article which seems to have a half decent coverage but if you are familiar with better I would appreciate it "Geometry of the Vaidya spacetime" by Armand COUDRAY & Jean-Philippe NICOLAS https://arxiv.org/pdf/2101.06544

Be well

Thread reported I'm tired of your attitude

No it can involve rapidity but is not the only methodology. I do recall that discussion lol I actually enjoyed that discussion.

Sigh (hopefully you don't get insulted again) lets show you how this works. start with the Lorentz transformation. \[\acute{t}=\gamma(\frac{vx}{c^2})\] \[\acute{x}=\gamma(x-vt)\] \[\acute{y}=y\] \[\acute{z}=z\] the two equations most relevant are the first two note the velocity term velocity is the vector rate of change in position and direction. As you doubt everything I state and argue everything I state here https://www.physicsclassroom.com/class/1DKin/Lesson-1/Speed-and-Velocity Oh my it specifies inertia frames https://en.wikipedia.org/wiki/Lorentz_transformation you can read it for yourself and don't take my word for it if you choose acceleration is handled via rapidity the equations are also in that link. https://en.wikipedia.org/wiki/Free_fall Newtons laws of inertia https://en.wikipedia.org/wiki/Newton's_laws_of_motion note that the freefall link specifies no force acting upon the body it is in freefall no net force however Newtons laws of inertia still apply. The body is in motion, one can arbitrarily choose any event as the rest frame under SR it could be the twin leaving the planet or the stay at home twin both twins are in inertial frames (not accelerating, constant velocity). the same applies to freefall Alice is the observer on Earth. Bob is the Observer in freefall. The choice of who is the rest frame is arbitrary with the above transformation. Hopefully in the freefall state your know \[m_g=m_i\] equivalence principle gravitational mass is equivalent to inertial mass. if not google Principle of equivalence. we wont get into tidal forces just yet but succinctly if you have two bodies in freefall the vector direction is towards the CoM. the tidal force between the two bodies is \[\frac{d^2x}{dt^2}-\frac{MG}{r^3}x\] now I suggest you study again the above further applies to the addition of velocities \[U=v+\acute{U}\] where v is the velocity between observers U and \[\acute{U}\] is the two observers.

I Strongly suggest you study the terminology you will find those statements are 100% accurate under both SR and GR. You do not need to take my word for it pick up ant SR or GR textbook Seriously you post something for everyone to read where does reading thoughts enter the picture ? This is a forum anyone can respond at any time whether you like it or not. That's is part of the rules on a public forum that you agreed to when you signed up.

If your addressing a specific individual you should state that but when you leave a question on a physics forum. Anyone can answer said question. That is precisely the purpose of this forum

You asked what real waves I directly answered this question and answered it correctly

I don't particularly see describing it as a non causal wave to be an issue here. As long as it's understood to represent individual components of the train separately powered via the engine. I've still been considering the hyperbolic Lorentz transforms in regards to the different acceleration rates.

Will you please stop trying to insult me. I personally couldn't care what your opinion of me is but this is starting to get old real fast. Stick to the forum topic...

Well sorry if you took that as an insult it's a simple statement of fact nothing more. There are after all other readers

If I choose to reply I will do so.

Good analysis +1 Unfortunately no real wave travels faster than c. I will have time to respond further later on RL

Dissipates into the ground and effectively neutralizes.

Well the ground is conductive but conductivity will vary location to location. An easy way to see this is lightning strikes. This is a good example of the EM field in our atmosphere interacting with the Earths surface. (The term grounding) in electrical circuits dissipates unwanted electrical charge via Earth surface the grounded conductor is bonded to.

We still don't know the fate of the universe. Collapse is one possibility however we could eventually get heat death instead due to expansion. Other scenarios is the big rip however that one isn't too likely. If the cosmological constant aka dark energy stays constant then we're likely heading to heat death. However if at some point the cosmological constant does reduce then a collapse can occur. I should note expansion isn't directly due to expansion per se but via the thermodynamic relations of the various particles residing in our universe. Photons and neutrinos as well as other relativistic particles (radiation) gas a different equation of state to matter. https://en.m.wikipedia.org/wiki/Equation_of_state_(cosmology) How those relations in the link above evolve over time is given by [math]H_z=H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}}[/math] This equation is used to calculate the value of Hubbles parameter \[H_z\] at a given cosmological redshift compared to the value today \[H_0\]

That's the impression I have as well hence trying to keep my answers applicable to how it's taught in high school aka flow of charge.

Good coverage Studiot +1

I wouldn't say stubbornly we hope to find it but I don't believe we achieved the necessary energy levels yet. The reason isn't because we need the graviton to explain spacetime curvature aka gravity. The graviton if ever found would be a tremendous help to renormalize gravity.

Yeah I've read proposals on different parts of the rigid body requiring different accelerations at each part so I do understand where your coming from on that aspect. One of the distinctions between Newton rigid bodies and relativistic rigid bodies is literally in how one defines the criteria of a rigid body. The relativistic rigid body allows for length contraction, while the criteria for the Newtonian version must maintain its length. If I recall the articles I've come across though there is still causation issues in signals propagating greater than c in particular with acceleration/rapidity which relates to the hyperbolic rotation of the Minkowskii metric. The different accelerations will result in differing Hyperbolic rotations throughout the rigid body. If I recall but would have to double check the Born rigidity article under SR article I linked also refers to that. to be honest though as far as the OP is concerned I'm still trying to fathom what he means by neutral simultaneity. Might just be a translation error Would those involved in this discussion prefer I stick to SR treatment as opposed to GR treatment as things can get immensely complex under GR for rigid bodies ?

I have yet to see a treatment where Born rigidity holds true. Care to provide one ? Lol course we can also examine Ehrenfests treatment https://en.m.wikipedia.org/wiki/Ehrenfest_paradox Though that will be a bit off topic though still involving a rigid body. Edit if you have a good example of Born rigidity that doesn't violate spacetime causality feel free to post it.